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
[ 52, 49, 69, 3 ]
69
[ "52-49=3", "69+3=72", "72-3=69" ]
Current State: 69:[52, 49, 69, 3], Operations: [] Exploring Operation: 52-49=3, Resulting Numbers: [69, 3, 3] Generated Node #2: [69, 3, 3] from Operation: 52-49=3 Current State: 69:[69, 3, 3], Operations: ['52-49=3'] Exploring Operation: 69+3=72, Resulting Numbers: [72] 72,69 equal: Goal Reached Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[52, 49, 69, 3], Operations: [] Exploring Operation: 52-49=3, Resulting Numbers: [69, 3, 3] Generated Node #0,0: 69:[69, 3, 3] Operation: 52-49=3 Exploring Operation: 69-52=17, Resulting Numbers: [49, 3, 17] Generated Node #0,1: 69:[49, 3, 17] Operation: 69-52=17 Exploring Operation: 52+49=101, Resulting Numbers: [69, 3, 101] Generated Node #0,2: 69:[69, 3, 101] Operation: 52+49=101 Exploring Operation: 69-49=20, Resulting Numbers: [52, 3, 20] Generated Node #0,3: 69:[52, 3, 20] Operation: 69-49=20 Moving to Node #0,0 Current State: 69:[69, 3, 3], Operations: ['52-49=3'] Exploring Operation: 69/3=23, Resulting Numbers: [3, 23] Generated Node #0,0,0: 69:[3, 23] Operation: 69/3=23 Exploring Operation: 69/3=23, Resulting Numbers: [3, 23] Generated Node #0,0,1: 69:[3, 23] Operation: 69/3=23 Exploring Operation: 69+3=72, Resulting Numbers: [3, 72] Generated Node #0,0,2: 69:[3, 72] Operation: 69+3=72 Exploring Operation: 3/3=1, Resulting Numbers: [69, 1] Generated Node #0,0,3: 69:[69, 1] Operation: 3/3=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[3, 23], Operations: ['52-49=3', '69/3=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[52, 49, 69, 3], Operations: [] Exploring Operation: 52-49=3, Resulting Numbers: [69, 3, 3] Generated Node #0,0: 69:[69, 3, 3] Operation: 52-49=3 Moving to Node #0,0 Current State: 69:[69, 3, 3], Operations: ['52-49=3'] Exploring Operation: 69/3=23, Resulting Numbers: [3, 23] Generated Node #0,0,0: 69:[3, 23] Operation: 69/3=23 Moving to Node #0,0,0 Current State: 69:[3, 23], Operations: ['52-49=3', '69/3=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 78, 71, 73, 46 ]
14
[ "73-71=2", "46*2=92", "92-78=14" ]
Current State: 14:[78, 71, 73, 46], Operations: [] Exploring Operation: 73-71=2, Resulting Numbers: [78, 46, 2] Generated Node #2: [78, 46, 2] from Operation: 73-71=2 Current State: 14:[78, 46, 2], Operations: ['73-71=2'] Exploring Operation: 46*2=92, Resulting Numbers: [78, 92] Generated Node #3: [78, 92] from Operation: 46*2=92 Current State: 14:[78, 92], Operations: ['73-71=2', '46*2=92'] Exploring Operation: 92-78=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[78, 71, 73, 46], Operations: [] Exploring Operation: 78-71=7, Resulting Numbers: [73, 46, 7] Generated Node #0,0: 14:[73, 46, 7] Operation: 78-71=7 Exploring Operation: 78-73=5, Resulting Numbers: [71, 46, 5] Generated Node #0,1: 14:[71, 46, 5] Operation: 78-73=5 Exploring Operation: 73-71=2, Resulting Numbers: [78, 46, 2] Generated Node #0,2: 14:[78, 46, 2] Operation: 73-71=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[73, 46, 7], Operations: ['78-71=7'] Exploring Operation: 73-46=27, Resulting Numbers: [7, 27] Generated Node #0,0,0: 14:[7, 27] Operation: 73-46=27 Exploring Operation: 73-7=66, Resulting Numbers: [46, 66] Generated Node #0,0,1: 14:[46, 66] Operation: 73-7=66 Exploring Operation: 46-7=39, Resulting Numbers: [73, 39] Generated Node #0,0,2: 14:[73, 39] Operation: 46-7=39 Moving to Node #0,0,0 Current State: 14:[7, 27], Operations: ['78-71=7', '73-46=27'] Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,14 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,14 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[46, 66], Operations: ['78-71=7', '73-7=66'] Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,14 unequal: No Solution Exploring Operation: 46+66=112, Resulting Numbers: [112] 112,14 unequal: No Solution Exploring Operation: 46*66=3036, Resulting Numbers: [3036] 3036,14 unequal: No Solution Moving to Node #0,0,2 Current State: 14:[73, 39], Operations: ['78-71=7', '46-7=39'] Exploring Operation: 73+39=112, Resulting Numbers: [112] 112,14 unequal: No Solution Exploring Operation: 73-39=34, Resulting Numbers: [34] 34,14 unequal: No Solution Exploring Operation: 73*39=2847, Resulting Numbers: [2847] 2847,14 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:[71, 46, 5], Operations: ['78-73=5'] Exploring Operation: 71-5=66, Resulting Numbers: [46, 66] Generated Node #0,1,0: 14:[46, 66] Operation: 71-5=66 Exploring Operation: 46-5=41, Resulting Numbers: [71, 41] Generated Node #0,1,1: 14:[71, 41] Operation: 46-5=41 Exploring Operation: 71-46=25, Resulting Numbers: [5, 25] Generated Node #0,1,2: 14:[5, 25] Operation: 71-46=25 Moving to Node #0,1,2 Current State: 14:[5, 25], Operations: ['78-73=5', '71-46=25'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,14 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[46, 66], Operations: ['78-73=5', '71-5=66'] Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,14 unequal: No Solution Exploring Operation: 46*66=3036, Resulting Numbers: [3036] 3036,14 unequal: No Solution Exploring Operation: 46+66=112, Resulting Numbers: [112] 112,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[71, 41], Operations: ['78-73=5', '46-5=41'] Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,14 unequal: No Solution Exploring Operation: 71*41=2911, Resulting Numbers: [2911] 2911,14 unequal: No Solution Exploring Operation: 71+41=112, Resulting Numbers: [112] 112,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[78, 46, 2], Operations: ['73-71=2'] Exploring Operation: 46/2=23, Resulting Numbers: [78, 23] Generated Node #0,2,0: 14:[78, 23] Operation: 46/2=23 Exploring Operation: 78/2=39, Resulting Numbers: [46, 39] Generated Node #0,2,1: 14:[46, 39] Operation: 78/2=39 Exploring Operation: 78-46=32, Resulting Numbers: [2, 32] Generated Node #0,2,2: 14:[2, 32] Operation: 78-46=32 Moving to Node #0,2,2 Current State: 14:[2, 32], Operations: ['73-71=2', '78-46=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,14 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,14 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[46, 39], Operations: ['73-71=2', '78/2=39'] Exploring Operation: 46-39=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 46*39=1794, Resulting Numbers: [1794] 1794,14 unequal: No Solution Exploring Operation: 46+39=85, Resulting Numbers: [85] 85,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[78, 23], Operations: ['73-71=2', '46/2=23'] Exploring Operation: 78*23=1794, Resulting Numbers: [1794] 1794,14 unequal: No Solution Exploring Operation: 78+23=101, Resulting Numbers: [101] 101,14 unequal: No Solution Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,14 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
[ 6, 14, 94, 92 ]
22
[ "6+14=20", "94-92=2", "20+2=22" ]
Current State: 22:[6, 14, 94, 92], Operations: [] Exploring Operation: 6+14=20, Resulting Numbers: [94, 92, 20] Generated Node #2: [94, 92, 20] from Operation: 6+14=20 Current State: 22:[94, 92, 20], Operations: ['6+14=20'] Exploring Operation: 94-92=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 94-92=2 Current State: 22:[20, 2], Operations: ['6+14=20', '94-92=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[6, 14, 94, 92], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [6, 14, 2] Generated Node #0,0: 22:[6, 14, 2] Operation: 94-92=2 Exploring Operation: 94-14=80, Resulting Numbers: [6, 92, 80] Generated Node #0,1: 22:[6, 92, 80] Operation: 94-14=80 Moving to Node #0,0 Current State: 22:[6, 14, 2], Operations: ['94-92=2'] Exploring Operation: 6+14=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 22:[2, 20] Operation: 6+14=20 Exploring Operation: 14-6=8, Resulting Numbers: [2, 8] Generated Node #0,0,1: 22:[2, 8] Operation: 14-6=8 Moving to Node #0,1 Current State: 22:[6, 92, 80], Operations: ['94-14=80'] Exploring Operation: 92-80=12, Resulting Numbers: [6, 12] Generated Node #0,1,0: 22:[6, 12] Operation: 92-80=12 Exploring Operation: 92-6=86, Resulting Numbers: [80, 86] Generated Node #0,1,1: 22:[80, 86] Operation: 92-6=86 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[6, 12], Operations: ['94-14=80', '92-80=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[80, 86], Operations: ['94-14=80', '92-6=86'] Exploring Operation: 86-80=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 80+86=166, Resulting Numbers: [166] 166,22 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: 22:[2, 20], Operations: ['94-92=2', '6+14=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[6, 14, 94, 92], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [6, 14, 2] Generated Node #0,0: 22:[6, 14, 2] Operation: 94-92=2 Moving to Node #0,0 Current State: 22:[6, 14, 2], Operations: ['94-92=2'] Exploring Operation: 6+14=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 22:[2, 20] Operation: 6+14=20 Moving to Node #0,0,0 Current State: 22:[2, 20], Operations: ['94-92=2', '6+14=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 27, 6, 77, 89 ]
54
[ "89-77=12", "27*12=324", "324/6=54" ]
Current State: 54:[27, 6, 77, 89], Operations: [] Exploring Operation: 89-77=12, Resulting Numbers: [27, 6, 12] Generated Node #2: [27, 6, 12] from Operation: 89-77=12 Current State: 54:[27, 6, 12], Operations: ['89-77=12'] Exploring Operation: 27*12=324, Resulting Numbers: [6, 324] Generated Node #3: [6, 324] from Operation: 27*12=324 Current State: 54:[6, 324], Operations: ['89-77=12', '27*12=324'] Exploring Operation: 324/6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[27, 6, 77, 89], Operations: [] Exploring Operation: 77-6=71, Resulting Numbers: [27, 89, 71] Generated Node #0,0: 54:[27, 89, 71] Operation: 77-6=71 Exploring Operation: 89-77=12, Resulting Numbers: [27, 6, 12] Generated Node #0,1: 54:[27, 6, 12] Operation: 89-77=12 Exploring Operation: 89-27=62, Resulting Numbers: [6, 77, 62] Generated Node #0,2: 54:[6, 77, 62] Operation: 89-27=62 Exploring Operation: 77-27=50, Resulting Numbers: [6, 89, 50] Generated Node #0,3: 54:[6, 89, 50] Operation: 77-27=50 Moving to Node #0,1 Current State: 54:[27, 6, 12], Operations: ['89-77=12'] Exploring Operation: 12-6=6, Resulting Numbers: [27, 6] Generated Node #0,1,0: 54:[27, 6] Operation: 12-6=6 Exploring Operation: 27-12=15, Resulting Numbers: [6, 15] Generated Node #0,1,1: 54:[6, 15] Operation: 27-12=15 Exploring Operation: 6+12=18, Resulting Numbers: [27, 18] Generated Node #0,1,2: 54:[27, 18] Operation: 6+12=18 Exploring Operation: 12/6=2, Resulting Numbers: [27, 2] Generated Node #0,1,3: 54:[27, 2] Operation: 12/6=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[27, 6], Operations: ['89-77=12', '12-6=6'] Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,54 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 54:[27, 18], Operations: ['89-77=12', '6+12=18'] Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,54 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 54:[27, 2], Operations: ['89-77=12', '12/6=2'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,54 unequal: No Solution Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[27, 6, 77, 89], Operations: [] Exploring Operation: 89-77=12, Resulting Numbers: [27, 6, 12] Generated Node #0,1: 54:[27, 6, 12] Operation: 89-77=12 Moving to Node #0,1 Current State: 54:[27, 6, 12], Operations: ['89-77=12'] Exploring Operation: 12/6=2, Resulting Numbers: [27, 2] Generated Node #0,1,3: 54:[27, 2] Operation: 12/6=2 Moving to Node #0,1,3 Current State: 54:[27, 2], Operations: ['89-77=12', '12/6=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 10, 15, 15, 3 ]
23
[ "15-10=5", "15+3=18", "5+18=23" ]
Current State: 23:[10, 15, 15, 3], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [3, 5] Generated Node #2: [3, 5] from Operation: 15-10=5 Current State: 23:[3, 5], Operations: ['15-10=5'] Exploring Operation: 15+3=18, Resulting Numbers: [5, 18] Generated Node #3: [5, 18] from Operation: 15+3=18 Current State: 23:[5, 18], Operations: ['15-10=5', '15+3=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[10, 15, 15, 3], Operations: [] Exploring Operation: 10+15=25, Resulting Numbers: [15, 3, 25] Generated Node #0,0: 23:[15, 3, 25] Operation: 10+15=25 Exploring Operation: 15+3=18, Resulting Numbers: [10, 15, 18] Generated Node #0,1: 23:[10, 15, 18] Operation: 15+3=18 Exploring Operation: 10*3=30, Resulting Numbers: [15, 15, 30] Generated Node #0,2: 23:[15, 15, 30] Operation: 10*3=30 Exploring Operation: 10+3=13, Resulting Numbers: [15, 15, 13] Generated Node #0,3: 23:[15, 15, 13] Operation: 10+3=13 Exploring Operation: 15+3=18, Resulting Numbers: [10, 15, 18] Generated Node #0,4: 23:[10, 15, 18] Operation: 15+3=18 Moving to Node #0,2 Current State: 23:[15, 15, 30], Operations: ['10*3=30'] Exploring Operation: 15/15=1, Resulting Numbers: [30, 1] Generated Node #0,2,0: 23:[30, 1] Operation: 15/15=1 Exploring Operation: 30/15=2, Resulting Numbers: [15, 2] Generated Node #0,2,1: 23:[15, 2] Operation: 30/15=2 Exploring Operation: 30-15=15, Resulting Numbers: [15, 15] Generated Node #0,2,2: 23:[15, 15] Operation: 30-15=15 Exploring Operation: 15+15=30, Resulting Numbers: [30, 30] Generated Node #0,2,3: 23:[30, 30] Operation: 15+15=30 Exploring Operation: 30-15=15, Resulting Numbers: [15, 15] Generated Node #0,2,4: 23:[15, 15] Operation: 30-15=15 Moving to Node #0,3 Current State: 23:[15, 15, 13], Operations: ['10+3=13'] Exploring Operation: 15-13=2, Resulting Numbers: [15, 2] Generated Node #0,3,0: 23:[15, 2] Operation: 15-13=2 Exploring Operation: 15-13=2, Resulting Numbers: [15, 2] Generated Node #0,3,1: 23:[15, 2] Operation: 15-13=2 Exploring Operation: 15+15=30, Resulting Numbers: [13, 30] Generated Node #0,3,2: 23:[13, 30] Operation: 15+15=30 Exploring Operation: 15+13=28, Resulting Numbers: [15, 28] Generated Node #0,3,3: 23:[15, 28] Operation: 15+13=28 Exploring Operation: 15+13=28, Resulting Numbers: [15, 28] Generated Node #0,3,4: 23:[15, 28] Operation: 15+13=28 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 23:[15, 28], Operations: ['10+3=13', '15+13=28'] Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,23 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,23 unequal: No Solution No 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: 23:[15, 28], Operations: ['10+3=13', '15+13=28'] Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,23 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,23 unequal: No Solution No 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: 23:[13, 30], Operations: ['10+3=13', '15+15=30'] Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,23 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,23 unequal: No Solution No 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: 23:[15, 2], Operations: ['10+3=13', '15-13=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,23 unequal: No Solution No 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: 23:[15, 2], Operations: ['10+3=13', '15-13=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,23 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: 23:[10, 15, 18], Operations: ['15+3=18'] Exploring Operation: 10+18=28, Resulting Numbers: [15, 28] Generated Node #0,1,0: 23:[15, 28] Operation: 10+18=28 Exploring Operation: 18-10=8, Resulting Numbers: [15, 8] Generated Node #0,1,1: 23:[15, 8] Operation: 18-10=8 Exploring Operation: 15+18=33, Resulting Numbers: [10, 33] Generated Node #0,1,2: 23:[10, 33] Operation: 15+18=33 Exploring Operation: 15-10=5, Resulting Numbers: [18, 5] Generated Node #0,1,3: 23:[18, 5] Operation: 15-10=5 Exploring Operation: 10+15=25, Resulting Numbers: [18, 25] Generated Node #0,1,4: 23:[18, 25] Operation: 10+15=25 Moving to Node #0,4 Current State: 23:[10, 15, 18], Operations: ['15+3=18'] Exploring Operation: 18-10=8, Resulting Numbers: [15, 8] Generated Node #0,4,0: 23:[15, 8] Operation: 18-10=8 Exploring Operation: 10+18=28, Resulting Numbers: [15, 28] Generated Node #0,4,1: 23:[15, 28] Operation: 10+18=28 Exploring Operation: 10+15=25, Resulting Numbers: [18, 25] Generated Node #0,4,2: 23:[18, 25] Operation: 10+15=25 Exploring Operation: 15+18=33, Resulting Numbers: [10, 33] Generated Node #0,4,3: 23:[10, 33] Operation: 15+18=33 Exploring Operation: 15-10=5, Resulting Numbers: [18, 5] Generated Node #0,4,4: 23:[18, 5] Operation: 15-10=5 Moving to Node #0,0 Current State: 23:[15, 3, 25], Operations: ['10+15=25'] Exploring Operation: 15-3=12, Resulting Numbers: [25, 12] Generated Node #0,0,0: 23:[25, 12] Operation: 15-3=12 Exploring Operation: 25-3=22, Resulting Numbers: [15, 22] Generated Node #0,0,1: 23:[15, 22] Operation: 25-3=22 Exploring Operation: 3+25=28, Resulting Numbers: [15, 28] Generated Node #0,0,2: 23:[15, 28] Operation: 3+25=28 Exploring Operation: 15/3=5, Resulting Numbers: [25, 5] Generated Node #0,0,3: 23:[25, 5] Operation: 15/3=5 Exploring Operation: 15+3=18, Resulting Numbers: [25, 18] Generated Node #0,0,4: 23:[25, 18] Operation: 15+3=18 Moving to Node #0,1,4 Current State: 23:[18, 25], Operations: ['15+3=18', '10+15=25'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[18, 25], Operations: ['15+3=18', '10+15=25'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,23 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,23 unequal: No Solution Moving to Node #0,0,4 Current State: 23:[25, 18], Operations: ['10+15=25', '15+3=18'] Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 25*18=450, Resulting Numbers: [450] 450,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[15, 22], Operations: ['10+15=25', '25-3=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,23 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[15, 28], Operations: ['15+3=18', '10+18=28'] Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,23 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[15, 28], Operations: ['15+3=18', '10+18=28'] Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,23 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[25, 12], Operations: ['10+15=25', '15-3=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,23 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[15, 28], Operations: ['10+15=25', '3+25=28'] Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,23 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[30, 30], Operations: ['10*3=30', '15+15=30'] Exploring Operation: 30*30=900, Resulting Numbers: [900] 900,23 unequal: No Solution Exploring Operation: 30/30=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 30+30=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 30-30=0, Resulting Numbers: [0] 0,23 unequal: No Solution Moving to Node #0,2,4 Current State: 23:[15, 15], Operations: ['10*3=30', '30-15=15'] Exploring Operation: 15*15=225, Resulting Numbers: [225] 225,23 unequal: No Solution Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[15, 15], Operations: ['10*3=30', '30-15=15'] Exploring Operation: 15*15=225, Resulting Numbers: [225] 225,23 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,23 unequal: No Solution Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[25, 5], Operations: ['10+15=25', '15/3=5'] Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,23 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,23 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[18, 5], Operations: ['15+3=18', '15-10=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[10, 15, 15, 3], Operations: [] Exploring Operation: 15+3=18, Resulting Numbers: [10, 15, 18] Generated Node #0,4: 23:[10, 15, 18] Operation: 15+3=18 Moving to Node #0,4 Current State: 23:[10, 15, 18], Operations: ['15+3=18'] Exploring Operation: 15-10=5, Resulting Numbers: [18, 5] Generated Node #0,4,4: 23:[18, 5] Operation: 15-10=5 Moving to Node #0,4,4 Current State: 23:[18, 5], Operations: ['15+3=18', '15-10=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.921875
hs_5
mult_heuristic
[ 65, 60, 80, 12 ]
48
[ "80-65=15", "60*12=720", "720/15=48" ]
Current State: 48:[65, 60, 80, 12], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [60, 12, 15] Generated Node #2: [60, 12, 15] from Operation: 80-65=15 Current State: 48:[60, 12, 15], Operations: ['80-65=15'] Exploring Operation: 60*12=720, Resulting Numbers: [15, 720] Generated Node #3: [15, 720] from Operation: 60*12=720 Current State: 48:[15, 720], Operations: ['80-65=15', '60*12=720'] Exploring Operation: 720/15=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[65, 60, 80, 12], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [60, 12, 15] Generated Node #0,0: 48:[60, 12, 15] Operation: 80-65=15 Exploring Operation: 65-60=5, Resulting Numbers: [80, 12, 5] Generated Node #0,1: 48:[80, 12, 5] Operation: 65-60=5 Exploring Operation: 80-60=20, Resulting Numbers: [65, 12, 20] Generated Node #0,2: 48:[65, 12, 20] Operation: 80-60=20 Moving to Node #0,0 Current State: 48:[60, 12, 15], Operations: ['80-65=15'] Exploring Operation: 60-12=48, Resulting Numbers: [15, 48] Generated Node #0,0,0: 48:[15, 48] Operation: 60-12=48 Exploring Operation: 60/15=4, Resulting Numbers: [12, 4] Generated Node #0,0,1: 48:[12, 4] Operation: 60/15=4 Exploring Operation: 60/12=5, Resulting Numbers: [15, 5] Generated Node #0,0,2: 48:[15, 5] Operation: 60/12=5 Moving to Node #0,2 Current State: 48:[65, 12, 20], Operations: ['80-60=20'] Exploring Operation: 20-12=8, Resulting Numbers: [65, 8] Generated Node #0,2,0: 48:[65, 8] Operation: 20-12=8 Exploring Operation: 65-20=45, Resulting Numbers: [12, 45] Generated Node #0,2,1: 48:[12, 45] Operation: 65-20=45 Exploring Operation: 65-12=53, Resulting Numbers: [20, 53] Generated Node #0,2,2: 48:[20, 53] Operation: 65-12=53 Moving to Node #0,1 Current State: 48:[80, 12, 5], Operations: ['65-60=5'] Exploring Operation: 80-12=68, Resulting Numbers: [5, 68] Generated Node #0,1,0: 48:[5, 68] Operation: 80-12=68 Exploring Operation: 80-5=75, Resulting Numbers: [12, 75] Generated Node #0,1,1: 48:[12, 75] Operation: 80-5=75 Exploring Operation: 80/5=16, Resulting Numbers: [12, 16] Generated Node #0,1,2: 48:[12, 16] Operation: 80/5=16 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 48:[12, 16], Operations: ['65-60=5', '80/5=16'] Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,48 unequal: No Solution Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[5, 68], Operations: ['65-60=5', '80-12=68'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,48 unequal: No Solution Exploring Operation: 5*68=340, Resulting Numbers: [340] 340,48 unequal: No Solution Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,48 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 #0,1,1 Current State: 48:[12, 75], Operations: ['65-60=5', '80-5=75'] Exploring Operation: 12+75=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 12*75=900, Resulting Numbers: [900] 900,48 unequal: No Solution Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,48 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: 48:[12, 4], Operations: ['80-65=15', '60/15=4'] Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[65, 60, 80, 12], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [60, 12, 15] Generated Node #0,0: 48:[60, 12, 15] Operation: 80-65=15 Moving to Node #0,0 Current State: 48:[60, 12, 15], Operations: ['80-65=15'] Exploring Operation: 60/15=4, Resulting Numbers: [12, 4] Generated Node #0,0,1: 48:[12, 4] Operation: 60/15=4 Moving to Node #0,0,1 Current State: 48:[12, 4], Operations: ['80-65=15', '60/15=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 5, 19, 35, 33 ]
92
[ "5+19=24", "35+33=68", "24+68=92" ]
Current State: 92:[5, 19, 35, 33], Operations: [] Exploring Operation: 5+19=24, Resulting Numbers: [35, 33, 24] Generated Node #2: [35, 33, 24] from Operation: 5+19=24 Current State: 92:[35, 33, 24], Operations: ['5+19=24'] Exploring Operation: 35+33=68, Resulting Numbers: [24, 68] Generated Node #3: [24, 68] from Operation: 35+33=68 Current State: 92:[24, 68], Operations: ['5+19=24', '35+33=68'] Exploring Operation: 24+68=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[5, 19, 35, 33], Operations: [] Exploring Operation: 35-19=16, Resulting Numbers: [5, 33, 16] Generated Node #0,0: 92:[5, 33, 16] Operation: 35-19=16 Exploring Operation: 35-33=2, Resulting Numbers: [5, 19, 2] Generated Node #0,1: 92:[5, 19, 2] Operation: 35-33=2 Exploring Operation: 19+33=52, Resulting Numbers: [5, 35, 52] Generated Node #0,2: 92:[5, 35, 52] Operation: 19+33=52 Exploring Operation: 19+35=54, Resulting Numbers: [5, 33, 54] Generated Node #0,3: 92:[5, 33, 54] Operation: 19+35=54 Exploring Operation: 35/5=7, Resulting Numbers: [19, 33, 7] Generated Node #0,4: 92:[19, 33, 7] Operation: 35/5=7 Moving to Node #0,1 Current State: 92:[5, 19, 2], Operations: ['35-33=2'] Exploring Operation: 5+19=24, Resulting Numbers: [2, 24] Generated Node #0,1,0: 92:[2, 24] Operation: 5+19=24 Exploring Operation: 19+2=21, Resulting Numbers: [5, 21] Generated Node #0,1,1: 92:[5, 21] Operation: 19+2=21 Exploring Operation: 5*19=95, Resulting Numbers: [2, 95] Generated Node #0,1,2: 92:[2, 95] Operation: 5*19=95 Exploring Operation: 5-2=3, Resulting Numbers: [19, 3] Generated Node #0,1,3: 92:[19, 3] Operation: 5-2=3 Exploring Operation: 5+2=7, Resulting Numbers: [19, 7] Generated Node #0,1,4: 92:[19, 7] Operation: 5+2=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[2, 24], Operations: ['35-33=2', '5+19=24'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,92 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[5, 21], Operations: ['35-33=2', '19+2=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,92 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,92 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 92:[2, 95], Operations: ['35-33=2', '5*19=95'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,92 unequal: No Solution Exploring Operation: 2+95=97, Resulting Numbers: [97] 97,92 unequal: No Solution Exploring Operation: 2*95=190, Resulting Numbers: [190] 190,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 92:[19, 3], Operations: ['35-33=2', '5-2=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,92 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 92:[19, 7], Operations: ['35-33=2', '5+2=7'] Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,92 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 92:[19, 33, 7], Operations: ['35/5=7'] Exploring Operation: 19+7=26, Resulting Numbers: [33, 26] Generated Node #0,4,0: 92:[33, 26] Operation: 19+7=26 Exploring Operation: 19+33=52, Resulting Numbers: [7, 52] Generated Node #0,4,1: 92:[7, 52] Operation: 19+33=52 Exploring Operation: 33-19=14, Resulting Numbers: [7, 14] Generated Node #0,4,2: 92:[7, 14] Operation: 33-19=14 Exploring Operation: 33-7=26, Resulting Numbers: [19, 26] Generated Node #0,4,3: 92:[19, 26] Operation: 33-7=26 Exploring Operation: 33+7=40, Resulting Numbers: [19, 40] Generated Node #0,4,4: 92:[19, 40] Operation: 33+7=40 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 92:[19, 26], Operations: ['35/5=7', '33-7=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,92 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 92:[7, 52], Operations: ['35/5=7', '19+33=52'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 7+52=59, Resulting Numbers: [59] 59,92 unequal: No Solution Exploring Operation: 7*52=364, Resulting Numbers: [364] 364,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 92:[19, 40], Operations: ['35/5=7', '33+7=40'] Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 19*40=760, Resulting Numbers: [760] 760,92 unequal: No Solution Exploring Operation: 19+40=59, Resulting Numbers: [59] 59,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 92:[7, 14], Operations: ['35/5=7', '33-19=14'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,92 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 92:[33, 26], Operations: ['35/5=7', '19+7=26'] Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 33+26=59, Resulting Numbers: [59] 59,92 unequal: No Solution Exploring Operation: 33*26=858, Resulting Numbers: [858] 858,92 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: 92:[5, 33, 16], Operations: ['35-19=16'] Exploring Operation: 33+16=49, Resulting Numbers: [5, 49] Generated Node #0,0,0: 92:[5, 49] Operation: 33+16=49 Exploring Operation: 5+33=38, Resulting Numbers: [16, 38] Generated Node #0,0,1: 92:[16, 38] Operation: 5+33=38 Exploring Operation: 5+16=21, Resulting Numbers: [33, 21] Generated Node #0,0,2: 92:[33, 21] Operation: 5+16=21 Exploring Operation: 33-5=28, Resulting Numbers: [16, 28] Generated Node #0,0,3: 92:[16, 28] Operation: 33-5=28 Exploring Operation: 33-16=17, Resulting Numbers: [5, 17] Generated Node #0,0,4: 92:[5, 17] Operation: 33-16=17 Moving to Node #0,2 Current State: 92:[5, 35, 52], Operations: ['19+33=52'] Exploring Operation: 52-5=47, Resulting Numbers: [35, 47] Generated Node #0,2,0: 92:[35, 47] Operation: 52-5=47 Exploring Operation: 52-35=17, Resulting Numbers: [5, 17] Generated Node #0,2,1: 92:[5, 17] Operation: 52-35=17 Exploring Operation: 35+52=87, Resulting Numbers: [5, 87] Generated Node #0,2,2: 92:[5, 87] Operation: 35+52=87 Exploring Operation: 5+35=40, Resulting Numbers: [52, 40] Generated Node #0,2,3: 92:[52, 40] Operation: 5+35=40 Exploring Operation: 35/5=7, Resulting Numbers: [52, 7] Generated Node #0,2,4: 92:[52, 7] Operation: 35/5=7 Moving to Node #0,3 Current State: 92:[5, 33, 54], Operations: ['19+35=54'] Exploring Operation: 33-5=28, Resulting Numbers: [54, 28] Generated Node #0,3,0: 92:[54, 28] Operation: 33-5=28 Exploring Operation: 33+54=87, Resulting Numbers: [5, 87] Generated Node #0,3,1: 92:[5, 87] Operation: 33+54=87 Exploring Operation: 54-5=49, Resulting Numbers: [33, 49] Generated Node #0,3,2: 92:[33, 49] Operation: 54-5=49 Exploring Operation: 54-33=21, Resulting Numbers: [5, 21] Generated Node #0,3,3: 92:[5, 21] Operation: 54-33=21 Exploring Operation: 5+33=38, Resulting Numbers: [54, 38] Generated Node #0,3,4: 92:[54, 38] Operation: 5+33=38 Moving to Node #0,3,3 Current State: 92:[5, 21], Operations: ['19+35=54', '54-33=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,92 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,92 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[5, 49], Operations: ['35-19=16', '33+16=49'] Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,92 unequal: No Solution Exploring Operation: 5*49=245, Resulting Numbers: [245] 245,92 unequal: No Solution Exploring Operation: 5+49=54, Resulting Numbers: [54] 54,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[5, 87], Operations: ['19+33=52', '35+52=87'] Exploring Operation: 5*87=435, Resulting Numbers: [435] 435,92 unequal: No Solution Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 5+87=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[5, 19, 35, 33], Operations: [] Exploring Operation: 19+33=52, Resulting Numbers: [5, 35, 52] Generated Node #0,2: 92:[5, 35, 52] Operation: 19+33=52 Moving to Node #0,2 Current State: 92:[5, 35, 52], Operations: ['19+33=52'] Exploring Operation: 35+52=87, Resulting Numbers: [5, 87] Generated Node #0,2,2: 92:[5, 87] Operation: 35+52=87 Moving to Node #0,2,2 Current State: 92:[5, 87], Operations: ['19+33=52', '35+52=87'] Exploring Operation: 5+87=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.934896
hs_5
mult_heuristic
[ 7, 13, 43, 40 ]
89
[ "13-7=6", "43+40=83", "6+83=89" ]
Current State: 89:[7, 13, 43, 40], Operations: [] Exploring Operation: 13-7=6, Resulting Numbers: [43, 40, 6] Generated Node #2: [43, 40, 6] from Operation: 13-7=6 Current State: 89:[43, 40, 6], Operations: ['13-7=6'] Exploring Operation: 43+40=83, Resulting Numbers: [6, 83] Generated Node #3: [6, 83] from Operation: 43+40=83 Current State: 89:[6, 83], Operations: ['13-7=6', '43+40=83'] Exploring Operation: 6+83=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[7, 13, 43, 40], Operations: [] Exploring Operation: 7*13=91, Resulting Numbers: [43, 40, 91] Generated Node #0,0: 89:[43, 40, 91] Operation: 7*13=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[43, 40, 91], Operations: ['7*13=91'] Exploring Operation: 43+40=83, Resulting Numbers: [91, 83] Generated Node #0,0,0: 89:[91, 83] Operation: 43+40=83 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[91, 83], Operations: ['7*13=91', '43+40=83'] Exploring Operation: 91-83=8, Resulting Numbers: [8] 8,89 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_1
mult_heuristic
[ 1, 39, 56, 57 ]
40
[ "1+39=40", "57-56=1", "40*1=40" ]
Current State: 40:[1, 39, 56, 57], Operations: [] Exploring Operation: 1+39=40, Resulting Numbers: [56, 57, 40] Generated Node #2: [56, 57, 40] from Operation: 1+39=40 Current State: 40:[56, 57, 40], Operations: ['1+39=40'] Exploring Operation: 57-56=1, Resulting Numbers: [40, 1] Generated Node #3: [40, 1] from Operation: 57-56=1 Current State: 40:[40, 1], Operations: ['1+39=40', '57-56=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[1, 39, 56, 57], Operations: [] Exploring Operation: 56-39=17, Resulting Numbers: [1, 57, 17] Generated Node #0,0: 40:[1, 57, 17] Operation: 56-39=17 Exploring Operation: 57-39=18, Resulting Numbers: [1, 56, 18] Generated Node #0,1: 40:[1, 56, 18] Operation: 57-39=18 Exploring Operation: 57-56=1, Resulting Numbers: [1, 39, 1] Generated Node #0,2: 40:[1, 39, 1] Operation: 57-56=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[1, 39, 1], Operations: ['57-56=1'] Exploring Operation: 1+39=40, Resulting Numbers: [1, 40] Generated Node #0,2,0: 40:[1, 40] Operation: 1+39=40 Exploring Operation: 39+1=40, Resulting Numbers: [1, 40] Generated Node #0,2,1: 40:[1, 40] Operation: 39+1=40 Exploring Operation: 1+1=2, Resulting Numbers: [39, 2] Generated Node #0,2,2: 40:[39, 2] Operation: 1+1=2 Moving to Node #0,2,0 Current State: 40:[1, 40], Operations: ['57-56=1', '1+39=40'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[1, 39, 56, 57], Operations: [] Exploring Operation: 57-56=1, Resulting Numbers: [1, 39, 1] Generated Node #0,2: 40:[1, 39, 1] Operation: 57-56=1 Moving to Node #0,2 Current State: 40:[1, 39, 1], Operations: ['57-56=1'] Exploring Operation: 1+39=40, Resulting Numbers: [1, 40] Generated Node #0,2,0: 40:[1, 40] Operation: 1+39=40 Moving to Node #0,2,0 Current State: 40:[1, 40], Operations: ['57-56=1', '1+39=40'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 34, 86, 37, 30 ]
96
[ "37-34=3", "30/3=10", "86+10=96" ]
Current State: 96:[34, 86, 37, 30], Operations: [] Exploring Operation: 37-34=3, Resulting Numbers: [86, 30, 3] Generated Node #2: [86, 30, 3] from Operation: 37-34=3 Current State: 96:[86, 30, 3], Operations: ['37-34=3'] Exploring Operation: 30/3=10, Resulting Numbers: [86, 10] Generated Node #3: [86, 10] from Operation: 30/3=10 Current State: 96:[86, 10], Operations: ['37-34=3', '30/3=10'] Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[34, 86, 37, 30], Operations: [] Exploring Operation: 37-34=3, Resulting Numbers: [86, 30, 3] Generated Node #0,0: 96:[86, 30, 3] Operation: 37-34=3 Exploring Operation: 86-37=49, Resulting Numbers: [34, 30, 49] Generated Node #0,1: 96:[34, 30, 49] Operation: 86-37=49 Exploring Operation: 37-30=7, Resulting Numbers: [34, 86, 7] Generated Node #0,2: 96:[34, 86, 7] Operation: 37-30=7 Exploring Operation: 34-30=4, Resulting Numbers: [86, 37, 4] Generated Node #0,3: 96:[86, 37, 4] Operation: 34-30=4 Exploring Operation: 86-34=52, Resulting Numbers: [37, 30, 52] Generated Node #0,4: 96:[37, 30, 52] Operation: 86-34=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[34, 30, 49], Operations: ['86-37=49'] Exploring Operation: 49-30=19, Resulting Numbers: [34, 19] Generated Node #0,1,0: 96:[34, 19] Operation: 49-30=19 Exploring Operation: 34+30=64, Resulting Numbers: [49, 64] Generated Node #0,1,1: 96:[49, 64] Operation: 34+30=64 Exploring Operation: 49-34=15, Resulting Numbers: [30, 15] Generated Node #0,1,2: 96:[30, 15] Operation: 49-34=15 Exploring Operation: 34-30=4, Resulting Numbers: [49, 4] Generated Node #0,1,3: 96:[49, 4] Operation: 34-30=4 Exploring Operation: 34+49=83, Resulting Numbers: [30, 83] Generated Node #0,1,4: 96:[30, 83] Operation: 34+49=83 Moving to Node #0,1,3 Current State: 96:[49, 4], Operations: ['86-37=49', '34-30=4'] Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 49*4=196, Resulting Numbers: [196] 196,96 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[30, 15], Operations: ['86-37=49', '49-34=15'] Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,96 unequal: No Solution Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[34, 19], Operations: ['86-37=49', '49-30=19'] Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,96 unequal: No Solution Exploring Operation: 34*19=646, Resulting Numbers: [646] 646,96 unequal: No Solution Exploring Operation: 34+19=53, Resulting Numbers: [53] 53,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[30, 83], Operations: ['86-37=49', '34+49=83'] Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 30*83=2490, Resulting Numbers: [2490] 2490,96 unequal: No Solution Exploring Operation: 30+83=113, Resulting Numbers: [113] 113,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[49, 64], Operations: ['86-37=49', '34+30=64'] Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,96 unequal: No Solution Exploring Operation: 49+64=113, Resulting Numbers: [113] 113,96 unequal: No Solution Exploring Operation: 49*64=3136, Resulting Numbers: [3136] 3136,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 96:[37, 30, 52], Operations: ['86-34=52'] Exploring Operation: 37-30=7, Resulting Numbers: [52, 7] Generated Node #0,4,0: 96:[52, 7] Operation: 37-30=7 Exploring Operation: 52-30=22, Resulting Numbers: [37, 22] Generated Node #0,4,1: 96:[37, 22] Operation: 52-30=22 Exploring Operation: 52-37=15, Resulting Numbers: [30, 15] Generated Node #0,4,2: 96:[30, 15] Operation: 52-37=15 Exploring Operation: 37+52=89, Resulting Numbers: [30, 89] Generated Node #0,4,3: 96:[30, 89] Operation: 37+52=89 Exploring Operation: 30+52=82, Resulting Numbers: [37, 82] Generated Node #0,4,4: 96:[37, 82] Operation: 30+52=82 Moving to Node #0,4,2 Current State: 96:[30, 15], Operations: ['86-34=52', '52-37=15'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,96 unequal: No Solution Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,96 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,96 unequal: No Solution Moving to Node #0,4,0 Current State: 96:[52, 7], Operations: ['86-34=52', '37-30=7'] Exploring Operation: 52*7=364, Resulting Numbers: [364] 364,96 unequal: No Solution Exploring Operation: 52+7=59, Resulting Numbers: [59] 59,96 unequal: No Solution Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,96 unequal: No Solution Moving to Node #0,4,1 Current State: 96:[37, 22], Operations: ['86-34=52', '52-30=22'] Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,96 unequal: No Solution Exploring Operation: 37*22=814, Resulting Numbers: [814] 814,96 unequal: No Solution Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,96 unequal: No Solution Moving to Node #0,4,3 Current State: 96:[30, 89], Operations: ['86-34=52', '37+52=89'] Exploring Operation: 30+89=119, Resulting Numbers: [119] 119,96 unequal: No Solution Exploring Operation: 30*89=2670, Resulting Numbers: [2670] 2670,96 unequal: No Solution Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,96 unequal: No Solution Moving to Node #0,4,4 Current State: 96:[37, 82], Operations: ['86-34=52', '30+52=82'] Exploring Operation: 37+82=119, Resulting Numbers: [119] 119,96 unequal: No Solution Exploring Operation: 37*82=3034, Resulting Numbers: [3034] 3034,96 unequal: No Solution Exploring Operation: 82-37=45, Resulting Numbers: [45] 45,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[86, 30, 3], Operations: ['37-34=3'] Exploring Operation: 30+3=33, Resulting Numbers: [86, 33] Generated Node #0,0,0: 96:[86, 33] Operation: 30+3=33 Exploring Operation: 30-3=27, Resulting Numbers: [86, 27] Generated Node #0,0,1: 96:[86, 27] Operation: 30-3=27 Exploring Operation: 86+3=89, Resulting Numbers: [30, 89] Generated Node #0,0,2: 96:[30, 89] Operation: 86+3=89 Exploring Operation: 30/3=10, Resulting Numbers: [86, 10] Generated Node #0,0,3: 96:[86, 10] Operation: 30/3=10 Exploring Operation: 86-30=56, Resulting Numbers: [3, 56] Generated Node #0,0,4: 96:[3, 56] Operation: 86-30=56 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 96:[3, 56], Operations: ['37-34=3', '86-30=56'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,96 unequal: No Solution Exploring Operation: 3*56=168, Resulting Numbers: [168] 168,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[30, 89], Operations: ['37-34=3', '86+3=89'] Exploring Operation: 30*89=2670, Resulting Numbers: [2670] 2670,96 unequal: No Solution Exploring Operation: 30+89=119, Resulting Numbers: [119] 119,96 unequal: No Solution Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[86, 33], Operations: ['37-34=3', '30+3=33'] Exploring Operation: 86*33=2838, Resulting Numbers: [2838] 2838,96 unequal: No Solution Exploring Operation: 86+33=119, Resulting Numbers: [119] 119,96 unequal: No Solution Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 96:[86, 10], Operations: ['37-34=3', '30/3=10'] Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[34, 86, 37, 30], Operations: [] Exploring Operation: 37-34=3, Resulting Numbers: [86, 30, 3] Generated Node #0,0: 96:[86, 30, 3] Operation: 37-34=3 Moving to Node #0,0 Current State: 96:[86, 30, 3], Operations: ['37-34=3'] Exploring Operation: 30/3=10, Resulting Numbers: [86, 10] Generated Node #0,0,3: 96:[86, 10] Operation: 30/3=10 Moving to Node #0,0,3 Current State: 96:[86, 10], Operations: ['37-34=3', '30/3=10'] Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.94184
hs_5
mult_heuristic
[ 3, 61, 37, 31 ]
58
[ "3+61=64", "37-31=6", "64-6=58" ]
Current State: 58:[3, 61, 37, 31], Operations: [] Exploring Operation: 3+61=64, Resulting Numbers: [37, 31, 64] Generated Node #2: [37, 31, 64] from Operation: 3+61=64 Current State: 58:[37, 31, 64], Operations: ['3+61=64'] Exploring Operation: 37-31=6, Resulting Numbers: [64, 6] Generated Node #3: [64, 6] from Operation: 37-31=6 Current State: 58:[64, 6], Operations: ['3+61=64', '37-31=6'] Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[3, 61, 37, 31], Operations: [] Exploring Operation: 61-37=24, Resulting Numbers: [3, 31, 24] Generated Node #0,0: 58:[3, 31, 24] Operation: 61-37=24 Exploring Operation: 37-31=6, Resulting Numbers: [3, 61, 6] Generated Node #0,1: 58:[3, 61, 6] Operation: 37-31=6 Exploring Operation: 61-3=58, Resulting Numbers: [37, 31, 58] Generated Node #0,2: 58:[37, 31, 58] Operation: 61-3=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[3, 31, 24], Operations: ['61-37=24'] Exploring Operation: 3+24=27, Resulting Numbers: [31, 27] Generated Node #0,0,0: 58:[31, 27] Operation: 3+24=27 Exploring Operation: 31-3=28, Resulting Numbers: [24, 28] Generated Node #0,0,1: 58:[24, 28] Operation: 31-3=28 Exploring Operation: 31+24=55, Resulting Numbers: [3, 55] Generated Node #0,0,2: 58:[3, 55] Operation: 31+24=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[31, 27], Operations: ['61-37=24', '3+24=27'] Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,58 unequal: No Solution Exploring Operation: 31+27=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[3, 61, 37, 31], Operations: [] Exploring Operation: 61-37=24, Resulting Numbers: [3, 31, 24] Generated Node #0,0: 58:[3, 31, 24] Operation: 61-37=24 Moving to Node #0,0 Current State: 58:[3, 31, 24], Operations: ['61-37=24'] Exploring Operation: 3+24=27, Resulting Numbers: [31, 27] Generated Node #0,0,0: 58:[31, 27] Operation: 3+24=27 Moving to Node #0,0,0 Current State: 58:[31, 27], Operations: ['61-37=24', '3+24=27'] Exploring Operation: 31+27=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 59, 5, 32, 95 ]
63
[ "59+5=64", "32+95=127", "127-64=63" ]
Current State: 63:[59, 5, 32, 95], Operations: [] Exploring Operation: 59+5=64, Resulting Numbers: [32, 95, 64] Generated Node #2: [32, 95, 64] from Operation: 59+5=64 Current State: 63:[32, 95, 64], Operations: ['59+5=64'] Exploring Operation: 32+95=127, Resulting Numbers: [64, 127] Generated Node #3: [64, 127] from Operation: 32+95=127 Current State: 63:[64, 127], Operations: ['59+5=64', '32+95=127'] Exploring Operation: 127-64=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[59, 5, 32, 95], Operations: [] Exploring Operation: 95-59=36, Resulting Numbers: [5, 32, 36] Generated Node #0,0: 63:[5, 32, 36] Operation: 95-59=36 Exploring Operation: 95/5=19, Resulting Numbers: [59, 32, 19] Generated Node #0,1: 63:[59, 32, 19] Operation: 95/5=19 Exploring Operation: 32-5=27, Resulting Numbers: [59, 95, 27] Generated Node #0,2: 63:[59, 95, 27] Operation: 32-5=27 Exploring Operation: 59-32=27, Resulting Numbers: [5, 95, 27] Generated Node #0,3: 63:[5, 95, 27] Operation: 59-32=27 Exploring Operation: 95-32=63, Resulting Numbers: [59, 5, 63] Generated Node #0,4: 63:[59, 5, 63] Operation: 95-32=63 Start Sub Search at level 1: Moving to Node #0,4 Current State: 63:[59, 5, 63], Operations: ['95-32=63'] Exploring Operation: 5+63=68, Resulting Numbers: [59, 68] Generated Node #0,4,0: 63:[59, 68] Operation: 5+63=68 Exploring Operation: 63-5=58, Resulting Numbers: [59, 58] Generated Node #0,4,1: 63:[59, 58] Operation: 63-5=58 Exploring Operation: 59+5=64, Resulting Numbers: [63, 64] Generated Node #0,4,2: 63:[63, 64] Operation: 59+5=64 Exploring Operation: 63-59=4, Resulting Numbers: [5, 4] Generated Node #0,4,3: 63:[5, 4] Operation: 63-59=4 Exploring Operation: 59-5=54, Resulting Numbers: [63, 54] Generated Node #0,4,4: 63:[63, 54] Operation: 59-5=54 Moving to Node #0,4,2 Current State: 63:[63, 64], Operations: ['95-32=63', '59+5=64'] Exploring Operation: 64-63=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 63+64=127, Resulting Numbers: [127] 127,63 unequal: No Solution Exploring Operation: 63*64=4032, Resulting Numbers: [4032] 4032,63 unequal: No Solution Moving to Node #0,4,3 Current State: 63:[5, 4], Operations: ['95-32=63', '63-59=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,63 unequal: No Solution Moving to Node #0,4,0 Current State: 63:[59, 68], Operations: ['95-32=63', '5+63=68'] Exploring Operation: 68-59=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 59+68=127, Resulting Numbers: [127] 127,63 unequal: No Solution Exploring Operation: 59*68=4012, Resulting Numbers: [4012] 4012,63 unequal: No Solution Moving to Node #0,4,1 Current State: 63:[59, 58], Operations: ['95-32=63', '63-5=58'] Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 59*58=3422, Resulting Numbers: [3422] 3422,63 unequal: No Solution Exploring Operation: 59+58=117, Resulting Numbers: [117] 117,63 unequal: No Solution Moving to Node #0,4,4 Current State: 63:[63, 54], Operations: ['95-32=63', '59-5=54'] Exploring Operation: 63+54=117, Resulting Numbers: [117] 117,63 unequal: No Solution Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 63*54=3402, Resulting Numbers: [3402] 3402,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[59, 32, 19], Operations: ['95/5=19'] Exploring Operation: 59+19=78, Resulting Numbers: [32, 78] Generated Node #0,1,0: 63:[32, 78] Operation: 59+19=78 Exploring Operation: 59+32=91, Resulting Numbers: [19, 91] Generated Node #0,1,1: 63:[19, 91] Operation: 59+32=91 Exploring Operation: 32+19=51, Resulting Numbers: [59, 51] Generated Node #0,1,2: 63:[59, 51] Operation: 32+19=51 Exploring Operation: 59-32=27, Resulting Numbers: [19, 27] Generated Node #0,1,3: 63:[19, 27] Operation: 59-32=27 Exploring Operation: 32-19=13, Resulting Numbers: [59, 13] Generated Node #0,1,4: 63:[59, 13] Operation: 32-19=13 Moving to Node #0,1,3 Current State: 63:[19, 27], Operations: ['95/5=19', '59-32=27'] Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 19*27=513, Resulting Numbers: [513] 513,63 unequal: No Solution Exploring Operation: 19+27=46, Resulting Numbers: [46] 46,63 unequal: No Solution Moving to Node #0,1,4 Current State: 63:[59, 13], Operations: ['95/5=19', '32-19=13'] Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,63 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[59, 51], Operations: ['95/5=19', '32+19=51'] Exploring Operation: 59+51=110, Resulting Numbers: [110] 110,63 unequal: No Solution Exploring Operation: 59*51=3009, Resulting Numbers: [3009] 3009,63 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[32, 78], Operations: ['95/5=19', '59+19=78'] Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 32*78=2496, Resulting Numbers: [2496] 2496,63 unequal: No Solution Exploring Operation: 32+78=110, Resulting Numbers: [110] 110,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[19, 91], Operations: ['95/5=19', '59+32=91'] Exploring Operation: 19+91=110, Resulting Numbers: [110] 110,63 unequal: No Solution Exploring Operation: 19*91=1729, Resulting Numbers: [1729] 1729,63 unequal: No Solution Exploring Operation: 91-19=72, Resulting Numbers: [72] 72,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[5, 32, 36], Operations: ['95-59=36'] Exploring Operation: 32+36=68, Resulting Numbers: [5, 68] Generated Node #0,0,0: 63:[5, 68] Operation: 32+36=68 Exploring Operation: 32-5=27, Resulting Numbers: [36, 27] Generated Node #0,0,1: 63:[36, 27] Operation: 32-5=27 Exploring Operation: 36-32=4, Resulting Numbers: [5, 4] Generated Node #0,0,2: 63:[5, 4] Operation: 36-32=4 Exploring Operation: 36-5=31, Resulting Numbers: [32, 31] Generated Node #0,0,3: 63:[32, 31] Operation: 36-5=31 Exploring Operation: 5+32=37, Resulting Numbers: [36, 37] Generated Node #0,0,4: 63:[36, 37] Operation: 5+32=37 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 63:[5, 4], Operations: ['95-59=36', '36-32=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[5, 68], Operations: ['95-59=36', '32+36=68'] Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,63 unequal: No Solution Exploring Operation: 5*68=340, Resulting Numbers: [340] 340,63 unequal: No Solution Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[59, 5, 32, 95], Operations: [] Exploring Operation: 95-59=36, Resulting Numbers: [5, 32, 36] Generated Node #0,0: 63:[5, 32, 36] Operation: 95-59=36 Moving to Node #0,0 Current State: 63:[5, 32, 36], Operations: ['95-59=36'] Exploring Operation: 32+36=68, Resulting Numbers: [5, 68] Generated Node #0,0,0: 63:[5, 68] Operation: 32+36=68 Moving to Node #0,0,0 Current State: 63:[5, 68], Operations: ['95-59=36', '32+36=68'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.947917
hs_5
mult_heuristic
[ 86, 28, 2, 8 ]
21
[ "86-28=58", "58/2=29", "29-8=21" ]
Current State: 21:[86, 28, 2, 8], Operations: [] Exploring Operation: 86-28=58, Resulting Numbers: [2, 8, 58] Generated Node #2: [2, 8, 58] from Operation: 86-28=58 Current State: 21:[2, 8, 58], Operations: ['86-28=58'] Exploring Operation: 58/2=29, Resulting Numbers: [8, 29] Generated Node #3: [8, 29] from Operation: 58/2=29 Current State: 21:[8, 29], Operations: ['86-28=58', '58/2=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[86, 28, 2, 8], Operations: [] Exploring Operation: 86-28=58, Resulting Numbers: [2, 8, 58] Generated Node #0,0: 21:[2, 8, 58] Operation: 86-28=58 Exploring Operation: 86/2=43, Resulting Numbers: [28, 8, 43] Generated Node #0,1: 21:[28, 8, 43] Operation: 86/2=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[28, 8, 43], Operations: ['86/2=43'] Exploring Operation: 43-8=35, Resulting Numbers: [28, 35] Generated Node #0,1,0: 21:[28, 35] Operation: 43-8=35 Exploring Operation: 43-28=15, Resulting Numbers: [8, 15] Generated Node #0,1,1: 21:[8, 15] Operation: 43-28=15 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 21:[8, 15], Operations: ['86/2=43', '43-28=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[28, 35], Operations: ['86/2=43', '43-8=35'] Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,21 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[2, 8, 58], Operations: ['86-28=58'] Exploring Operation: 58/2=29, Resulting Numbers: [8, 29] Generated Node #0,0,0: 21:[8, 29] Operation: 58/2=29 Exploring Operation: 58-8=50, Resulting Numbers: [2, 50] Generated Node #0,0,1: 21:[2, 50] Operation: 58-8=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[8, 29], Operations: ['86-28=58', '58/2=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[86, 28, 2, 8], Operations: [] Exploring Operation: 86-28=58, Resulting Numbers: [2, 8, 58] Generated Node #0,0: 21:[2, 8, 58] Operation: 86-28=58 Moving to Node #0,0 Current State: 21:[2, 8, 58], Operations: ['86-28=58'] Exploring Operation: 58/2=29, Resulting Numbers: [8, 29] Generated Node #0,0,0: 21:[8, 29] Operation: 58/2=29 Moving to Node #0,0,0 Current State: 21:[8, 29], Operations: ['86-28=58', '58/2=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 59, 77, 14, 62 ]
94
[ "77-59=18", "14+62=76", "18+76=94" ]
Current State: 94:[59, 77, 14, 62], Operations: [] Exploring Operation: 77-59=18, Resulting Numbers: [14, 62, 18] Generated Node #2: [14, 62, 18] from Operation: 77-59=18 Current State: 94:[14, 62, 18], Operations: ['77-59=18'] Exploring Operation: 14+62=76, Resulting Numbers: [18, 76] Generated Node #3: [18, 76] from Operation: 14+62=76 Current State: 94:[18, 76], Operations: ['77-59=18', '14+62=76'] Exploring Operation: 18+76=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[59, 77, 14, 62], Operations: [] Exploring Operation: 62-59=3, Resulting Numbers: [77, 14, 3] Generated Node #0,0: 94:[77, 14, 3] Operation: 62-59=3 Exploring Operation: 62-14=48, Resulting Numbers: [59, 77, 48] Generated Node #0,1: 94:[59, 77, 48] Operation: 62-14=48 Exploring Operation: 77+14=91, Resulting Numbers: [59, 62, 91] Generated Node #0,2: 94:[59, 62, 91] Operation: 77+14=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[77, 14, 3], Operations: ['62-59=3'] Exploring Operation: 14*3=42, Resulting Numbers: [77, 42] Generated Node #0,0,0: 94:[77, 42] Operation: 14*3=42 Exploring Operation: 77+14=91, Resulting Numbers: [3, 91] Generated Node #0,0,1: 94:[3, 91] Operation: 77+14=91 Exploring Operation: 77-14=63, Resulting Numbers: [3, 63] Generated Node #0,0,2: 94:[3, 63] Operation: 77-14=63 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[3, 91], Operations: ['62-59=3', '77+14=91'] Exploring Operation: 3+91=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[59, 77, 14, 62], Operations: [] Exploring Operation: 62-59=3, Resulting Numbers: [77, 14, 3] Generated Node #0,0: 94:[77, 14, 3] Operation: 62-59=3 Moving to Node #0,0 Current State: 94:[77, 14, 3], Operations: ['62-59=3'] Exploring Operation: 77+14=91, Resulting Numbers: [3, 91] Generated Node #0,0,1: 94:[3, 91] Operation: 77+14=91 Moving to Node #0,0,1 Current State: 94:[3, 91], Operations: ['62-59=3', '77+14=91'] Exploring Operation: 3+91=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 51, 44, 61, 6 ]
61
[ "51-44=7", "7-6=1", "61*1=61" ]
Current State: 61:[51, 44, 61, 6], Operations: [] Exploring Operation: 51-44=7, Resulting Numbers: [61, 6, 7] Generated Node #2: [61, 6, 7] from Operation: 51-44=7 Current State: 61:[61, 6, 7], Operations: ['51-44=7'] Exploring Operation: 7-6=1, Resulting Numbers: [61, 1] Generated Node #3: [61, 1] from Operation: 7-6=1 Current State: 61:[61, 1], Operations: ['51-44=7', '7-6=1'] Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[51, 44, 61, 6], Operations: [] Exploring Operation: 51+6=57, Resulting Numbers: [44, 61, 57] Generated Node #0,0: 61:[44, 61, 57] Operation: 51+6=57 Exploring Operation: 44+6=50, Resulting Numbers: [51, 61, 50] Generated Node #0,1: 61:[51, 61, 50] Operation: 44+6=50 Moving to Node #0,0 Current State: 61:[44, 61, 57], Operations: ['51+6=57'] Exploring Operation: 44+61=105, Resulting Numbers: [57, 105] Generated Node #0,0,0: 61:[57, 105] Operation: 44+61=105 Exploring Operation: 44+57=101, Resulting Numbers: [61, 101] Generated Node #0,0,1: 61:[61, 101] Operation: 44+57=101 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[61, 101], Operations: ['51+6=57', '44+57=101'] Exploring Operation: 61+101=162, Resulting Numbers: [162] 162,61 unequal: No Solution Exploring Operation: 101-61=40, Resulting Numbers: [40] 40,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[57, 105], Operations: ['51+6=57', '44+61=105'] Exploring Operation: 57+105=162, Resulting Numbers: [162] 162,61 unequal: No Solution Exploring Operation: 105-57=48, Resulting Numbers: [48] 48,61 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: 61:[51, 61, 50], Operations: ['44+6=50'] Exploring Operation: 51-50=1, Resulting Numbers: [61, 1] Generated Node #0,1,0: 61:[61, 1] Operation: 51-50=1 Exploring Operation: 51+50=101, Resulting Numbers: [61, 101] Generated Node #0,1,1: 61:[61, 101] Operation: 51+50=101 Moving to Node #0,1,1 Current State: 61:[61, 101], Operations: ['44+6=50', '51+50=101'] Exploring Operation: 101-61=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 61+101=162, Resulting Numbers: [162] 162,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[61, 1], Operations: ['44+6=50', '51-50=1'] Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[51, 44, 61, 6], Operations: [] Exploring Operation: 44+6=50, Resulting Numbers: [51, 61, 50] Generated Node #0,1: 61:[51, 61, 50] Operation: 44+6=50 Moving to Node #0,1 Current State: 61:[51, 61, 50], Operations: ['44+6=50'] Exploring Operation: 51-50=1, Resulting Numbers: [61, 1] Generated Node #0,1,0: 61:[61, 1] Operation: 51-50=1 Moving to Node #0,1,0 Current State: 61:[61, 1], Operations: ['44+6=50', '51-50=1'] Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 98, 23, 4, 18 ]
30
[ "18-4=14", "98/14=7", "23+7=30" ]
Current State: 30:[98, 23, 4, 18], Operations: [] Exploring Operation: 18-4=14, Resulting Numbers: [98, 23, 14] Generated Node #2: [98, 23, 14] from Operation: 18-4=14 Current State: 30:[98, 23, 14], Operations: ['18-4=14'] Exploring Operation: 98/14=7, Resulting Numbers: [23, 7] Generated Node #3: [23, 7] from Operation: 98/14=7 Current State: 30:[23, 7], Operations: ['18-4=14', '98/14=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[98, 23, 4, 18], Operations: [] Exploring Operation: 98-18=80, Resulting Numbers: [23, 4, 80] Generated Node #0,0: 30:[23, 4, 80] Operation: 98-18=80 Exploring Operation: 23-18=5, Resulting Numbers: [98, 4, 5] Generated Node #0,1: 30:[98, 4, 5] Operation: 23-18=5 Exploring Operation: 98-23=75, Resulting Numbers: [4, 18, 75] Generated Node #0,2: 30:[4, 18, 75] Operation: 98-23=75 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[4, 18, 75], Operations: ['98-23=75'] Exploring Operation: 75-4=71, Resulting Numbers: [18, 71] Generated Node #0,2,0: 30:[18, 71] Operation: 75-4=71 Exploring Operation: 75-18=57, Resulting Numbers: [4, 57] Generated Node #0,2,1: 30:[4, 57] Operation: 75-18=57 Exploring Operation: 18-4=14, Resulting Numbers: [75, 14] Generated Node #0,2,2: 30:[75, 14] Operation: 18-4=14 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[4, 57], Operations: ['98-23=75', '75-18=57'] Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 4*57=228, Resulting Numbers: [228] 228,30 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 30:[18, 71], Operations: ['98-23=75', '75-4=71'] Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,30 unequal: No Solution Exploring Operation: 18*71=1278, Resulting Numbers: [1278] 1278,30 unequal: No Solution Exploring Operation: 18+71=89, Resulting Numbers: [89] 89,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[75, 14], Operations: ['98-23=75', '18-4=14'] Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 75*14=1050, Resulting Numbers: [1050] 1050,30 unequal: No Solution Exploring Operation: 75+14=89, Resulting Numbers: [89] 89,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[23, 4, 80], Operations: ['98-18=80'] Exploring Operation: 23+4=27, Resulting Numbers: [80, 27] Generated Node #0,0,0: 30:[80, 27] Operation: 23+4=27 Exploring Operation: 80/4=20, Resulting Numbers: [23, 20] Generated Node #0,0,1: 30:[23, 20] Operation: 80/4=20 Exploring Operation: 80-23=57, Resulting Numbers: [4, 57] Generated Node #0,0,2: 30:[4, 57] Operation: 80-23=57 Moving to Node #0,0,1 Current State: 30:[23, 20], Operations: ['98-18=80', '80/4=20'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 23*20=460, Resulting Numbers: [460] 460,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[4, 57], Operations: ['98-18=80', '80-23=57'] Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 4*57=228, Resulting Numbers: [228] 228,30 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[80, 27], Operations: ['98-18=80', '23+4=27'] Exploring Operation: 80*27=2160, Resulting Numbers: [2160] 2160,30 unequal: No Solution Exploring Operation: 80+27=107, Resulting Numbers: [107] 107,30 unequal: No Solution Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,30 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:[98, 4, 5], Operations: ['23-18=5'] Exploring Operation: 98-5=93, Resulting Numbers: [4, 93] Generated Node #0,1,0: 30:[4, 93] Operation: 98-5=93 Exploring Operation: 4+5=9, Resulting Numbers: [98, 9] Generated Node #0,1,1: 30:[98, 9] Operation: 4+5=9 Exploring Operation: 98-4=94, Resulting Numbers: [5, 94] Generated Node #0,1,2: 30:[5, 94] Operation: 98-4=94 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[4, 93], Operations: ['23-18=5', '98-5=93'] Exploring Operation: 4*93=372, Resulting Numbers: [372] 372,30 unequal: No Solution Exploring Operation: 4+93=97, Resulting Numbers: [97] 97,30 unequal: No Solution Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,30 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 #0,1,2 Current State: 30:[5, 94], Operations: ['23-18=5', '98-4=94'] Exploring Operation: 5*94=470, Resulting Numbers: [470] 470,30 unequal: No Solution Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,30 unequal: No Solution Exploring Operation: 5+94=99, Resulting Numbers: [99] 99,30 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:[98, 9], Operations: ['23-18=5', '4+5=9'] Exploring Operation: 98+9=107, Resulting Numbers: [107] 107,30 unequal: No Solution Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,30 unequal: No Solution Exploring Operation: 98*9=882, Resulting Numbers: [882] 882,30 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_3
sum_heuristic
[ 95, 93, 86, 9 ]
75
[ "95-93=2", "86-9=77", "77-2=75" ]
Current State: 75:[95, 93, 86, 9], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [86, 9, 2] Generated Node #2: [86, 9, 2] from Operation: 95-93=2 Current State: 75:[86, 9, 2], Operations: ['95-93=2'] Exploring Operation: 86-9=77, Resulting Numbers: [2, 77] Generated Node #3: [2, 77] from Operation: 86-9=77 Current State: 75:[2, 77], Operations: ['95-93=2', '86-9=77'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[95, 93, 86, 9], Operations: [] Exploring Operation: 95-86=9, Resulting Numbers: [93, 9, 9] Generated Node #0,0: 75:[93, 9, 9] Operation: 95-86=9 Exploring Operation: 95-93=2, Resulting Numbers: [86, 9, 2] Generated Node #0,1: 75:[86, 9, 2] Operation: 95-93=2 Moving to Node #0,1 Current State: 75:[86, 9, 2], Operations: ['95-93=2'] Exploring Operation: 86-2=84, Resulting Numbers: [9, 84] Generated Node #0,1,0: 75:[9, 84] Operation: 86-2=84 Exploring Operation: 86-9=77, Resulting Numbers: [2, 77] Generated Node #0,1,1: 75:[2, 77] Operation: 86-9=77 Moving to Node #0,0 Current State: 75:[93, 9, 9], Operations: ['95-86=9'] Exploring Operation: 93-9=84, Resulting Numbers: [9, 84] Generated Node #0,0,0: 75:[9, 84] Operation: 93-9=84 Exploring Operation: 93-9=84, Resulting Numbers: [9, 84] Generated Node #0,0,1: 75:[9, 84] Operation: 93-9=84 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[9, 84], Operations: ['95-86=9', '93-9=84'] Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[95, 93, 86, 9], Operations: [] Exploring Operation: 95-86=9, Resulting Numbers: [93, 9, 9] Generated Node #0,0: 75:[93, 9, 9] Operation: 95-86=9 Moving to Node #0,0 Current State: 75:[93, 9, 9], Operations: ['95-86=9'] Exploring Operation: 93-9=84, Resulting Numbers: [9, 84] Generated Node #0,0,0: 75:[9, 84] Operation: 93-9=84 Moving to Node #0,0,0 Current State: 75:[9, 84], Operations: ['95-86=9', '93-9=84'] Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 57, 78, 12, 80 ]
63
[ "80-78=2", "12/2=6", "57+6=63" ]
Current State: 63:[57, 78, 12, 80], Operations: [] Exploring Operation: 80-78=2, Resulting Numbers: [57, 12, 2] Generated Node #2: [57, 12, 2] from Operation: 80-78=2 Current State: 63:[57, 12, 2], Operations: ['80-78=2'] Exploring Operation: 12/2=6, Resulting Numbers: [57, 6] Generated Node #3: [57, 6] from Operation: 12/2=6 Current State: 63:[57, 6], Operations: ['80-78=2', '12/2=6'] Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[57, 78, 12, 80], Operations: [] Exploring Operation: 78-12=66, Resulting Numbers: [57, 80, 66] Generated Node #0,0: 63:[57, 80, 66] Operation: 78-12=66 Exploring Operation: 80-78=2, Resulting Numbers: [57, 12, 2] Generated Node #0,1: 63:[57, 12, 2] Operation: 80-78=2 Exploring Operation: 80-57=23, Resulting Numbers: [78, 12, 23] Generated Node #0,2: 63:[78, 12, 23] Operation: 80-57=23 Exploring Operation: 78-57=21, Resulting Numbers: [12, 80, 21] Generated Node #0,3: 63:[12, 80, 21] Operation: 78-57=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[57, 12, 2], Operations: ['80-78=2'] Exploring Operation: 57+12=69, Resulting Numbers: [2, 69] Generated Node #0,1,0: 63:[2, 69] Operation: 57+12=69 Exploring Operation: 12/2=6, Resulting Numbers: [57, 6] Generated Node #0,1,1: 63:[57, 6] Operation: 12/2=6 Exploring Operation: 57+2=59, Resulting Numbers: [12, 59] Generated Node #0,1,2: 63:[12, 59] Operation: 57+2=59 Exploring Operation: 12-2=10, Resulting Numbers: [57, 10] Generated Node #0,1,3: 63:[57, 10] Operation: 12-2=10 Moving to Node #0,1,0 Current State: 63:[2, 69], Operations: ['80-78=2', '57+12=69'] Exploring Operation: 69-2=67, Resulting Numbers: [67] 67,63 unequal: No Solution Exploring Operation: 2*69=138, Resulting Numbers: [138] 138,63 unequal: No Solution Exploring Operation: 2+69=71, Resulting Numbers: [71] 71,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[12, 59], Operations: ['80-78=2', '57+2=59'] Exploring Operation: 12+59=71, Resulting Numbers: [71] 71,63 unequal: No Solution Exploring Operation: 12*59=708, Resulting Numbers: [708] 708,63 unequal: No Solution Exploring Operation: 59-12=47, Resulting Numbers: [47] 47,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[57, 6], Operations: ['80-78=2', '12/2=6'] Exploring Operation: 57*6=342, Resulting Numbers: [342] 342,63 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,63 unequal: No Solution Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[57, 78, 12, 80], Operations: [] Exploring Operation: 80-78=2, Resulting Numbers: [57, 12, 2] Generated Node #0,1: 63:[57, 12, 2] Operation: 80-78=2 Moving to Node #0,1 Current State: 63:[57, 12, 2], Operations: ['80-78=2'] Exploring Operation: 12/2=6, Resulting Numbers: [57, 6] Generated Node #0,1,1: 63:[57, 6] Operation: 12/2=6 Moving to Node #0,1,1 Current State: 63:[57, 6], Operations: ['80-78=2', '12/2=6'] Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 40, 16, 64, 51 ]
43
[ "40+16=56", "64-51=13", "56-13=43" ]
Current State: 43:[40, 16, 64, 51], Operations: [] Exploring Operation: 40+16=56, Resulting Numbers: [64, 51, 56] Generated Node #2: [64, 51, 56] from Operation: 40+16=56 Current State: 43:[64, 51, 56], Operations: ['40+16=56'] Exploring Operation: 64-51=13, Resulting Numbers: [56, 13] Generated Node #3: [56, 13] from Operation: 64-51=13 Current State: 43:[56, 13], Operations: ['40+16=56', '64-51=13'] Exploring Operation: 56-13=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[40, 16, 64, 51], Operations: [] Exploring Operation: 64-16=48, Resulting Numbers: [40, 51, 48] Generated Node #0,0: 43:[40, 51, 48] Operation: 64-16=48 Exploring Operation: 51-16=35, Resulting Numbers: [40, 64, 35] Generated Node #0,1: 43:[40, 64, 35] Operation: 51-16=35 Moving to Node #0,0 Current State: 43:[40, 51, 48], Operations: ['64-16=48'] Exploring Operation: 51-40=11, Resulting Numbers: [48, 11] Generated Node #0,0,0: 43:[48, 11] Operation: 51-40=11 Exploring Operation: 48-40=8, Resulting Numbers: [51, 8] Generated Node #0,0,1: 43:[51, 8] Operation: 48-40=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[48, 11], Operations: ['64-16=48', '51-40=11'] Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,43 unequal: No Solution Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[51, 8], Operations: ['64-16=48', '48-40=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,43 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[40, 16, 64, 51], Operations: [] Exploring Operation: 64-16=48, Resulting Numbers: [40, 51, 48] Generated Node #0,0: 43:[40, 51, 48] Operation: 64-16=48 Moving to Node #0,0 Current State: 43:[40, 51, 48], Operations: ['64-16=48'] Exploring Operation: 48-40=8, Resulting Numbers: [51, 8] Generated Node #0,0,1: 43:[51, 8] Operation: 48-40=8 Moving to Node #0,0,1 Current State: 43:[51, 8], Operations: ['64-16=48', '48-40=8'] Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 3, 43, 75, 12 ]
49
[ "75-3=72", "72/12=6", "43+6=49" ]
Current State: 49:[3, 43, 75, 12], Operations: [] Exploring Operation: 75-3=72, Resulting Numbers: [43, 12, 72] Generated Node #2: [43, 12, 72] from Operation: 75-3=72 Current State: 49:[43, 12, 72], Operations: ['75-3=72'] Exploring Operation: 72/12=6, Resulting Numbers: [43, 6] Generated Node #3: [43, 6] from Operation: 72/12=6 Current State: 49:[43, 6], Operations: ['75-3=72', '72/12=6'] Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[3, 43, 75, 12], Operations: [] Exploring Operation: 75-12=63, Resulting Numbers: [3, 43, 63] Generated Node #0,0: 49:[3, 43, 63] Operation: 75-12=63 Exploring Operation: 75-43=32, Resulting Numbers: [3, 12, 32] Generated Node #0,1: 49:[3, 12, 32] Operation: 75-43=32 Moving to Node #0,0 Current State: 49:[3, 43, 63], Operations: ['75-12=63'] Exploring Operation: 3+43=46, Resulting Numbers: [63, 46] Generated Node #0,0,0: 49:[63, 46] Operation: 3+43=46 Exploring Operation: 63-3=60, Resulting Numbers: [43, 60] Generated Node #0,0,1: 49:[43, 60] Operation: 63-3=60 Moving to Node #0,1 Current State: 49:[3, 12, 32], Operations: ['75-43=32'] Exploring Operation: 12+32=44, Resulting Numbers: [3, 44] Generated Node #0,1,0: 49:[3, 44] Operation: 12+32=44 Exploring Operation: 32-12=20, Resulting Numbers: [3, 20] Generated Node #0,1,1: 49:[3, 20] Operation: 32-12=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[3, 44], Operations: ['75-43=32', '12+32=44'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 49:[3, 20], Operations: ['75-43=32', '32-12=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,49 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: 49:[63, 46], Operations: ['75-12=63', '3+43=46'] Exploring Operation: 63-46=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 63+46=109, Resulting Numbers: [109] 109,49 unequal: No Solution Moving to Node #0,0,1 Current State: 49:[43, 60], Operations: ['75-12=63', '63-3=60'] Exploring Operation: 60-43=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 43+60=103, Resulting Numbers: [103] 103,49 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 4, 89, 27, 61 ]
32
[ "89+27=116", "116/4=29", "61-29=32" ]
Current State: 32:[4, 89, 27, 61], Operations: [] Exploring Operation: 89+27=116, Resulting Numbers: [4, 61, 116] Generated Node #2: [4, 61, 116] from Operation: 89+27=116 Current State: 32:[4, 61, 116], Operations: ['89+27=116'] Exploring Operation: 116/4=29, Resulting Numbers: [61, 29] Generated Node #3: [61, 29] from Operation: 116/4=29 Current State: 32:[61, 29], Operations: ['89+27=116', '116/4=29'] Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[4, 89, 27, 61], Operations: [] Exploring Operation: 89-27=62, Resulting Numbers: [4, 61, 62] Generated Node #0,0: 32:[4, 61, 62] Operation: 89-27=62 Exploring Operation: 89-61=28, Resulting Numbers: [4, 27, 28] Generated Node #0,1: 32:[4, 27, 28] Operation: 89-61=28 Exploring Operation: 61-27=34, Resulting Numbers: [4, 89, 34] Generated Node #0,2: 32:[4, 89, 34] Operation: 61-27=34 Moving to Node #0,1 Current State: 32:[4, 27, 28], Operations: ['89-61=28'] Exploring Operation: 4+27=31, Resulting Numbers: [28, 31] Generated Node #0,1,0: 32:[28, 31] Operation: 4+27=31 Exploring Operation: 4+28=32, Resulting Numbers: [27, 32] Generated Node #0,1,1: 32:[27, 32] Operation: 4+28=32 Exploring Operation: 28-27=1, Resulting Numbers: [4, 1] Generated Node #0,1,2: 32:[4, 1] Operation: 28-27=1 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[4, 1], Operations: ['89-61=28', '28-27=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[28, 31], Operations: ['89-61=28', '4+27=31'] Exploring Operation: 28*31=868, Resulting Numbers: [868] 868,32 unequal: No Solution Exploring Operation: 28+31=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[27, 32], Operations: ['89-61=28', '4+28=32'] Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 27*32=864, Resulting Numbers: [864] 864,32 unequal: No Solution Exploring Operation: 27+32=59, Resulting Numbers: [59] 59,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 32:[4, 61, 62], Operations: ['89-27=62'] Exploring Operation: 62-4=58, Resulting Numbers: [61, 58] Generated Node #0,0,0: 32:[61, 58] Operation: 62-4=58 Exploring Operation: 62-61=1, Resulting Numbers: [4, 1] Generated Node #0,0,1: 32:[4, 1] Operation: 62-61=1 Exploring Operation: 61-4=57, Resulting Numbers: [62, 57] Generated Node #0,0,2: 32:[62, 57] Operation: 61-4=57 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[4, 1], Operations: ['89-27=62', '62-61=1'] Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[61, 58], Operations: ['89-27=62', '62-4=58'] Exploring Operation: 61*58=3538, Resulting Numbers: [3538] 3538,32 unequal: No Solution Exploring Operation: 61+58=119, Resulting Numbers: [119] 119,32 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[62, 57], Operations: ['89-27=62', '61-4=57'] Exploring Operation: 62*57=3534, Resulting Numbers: [3534] 3534,32 unequal: No Solution Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 62+57=119, Resulting Numbers: [119] 119,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 32:[4, 89, 34], Operations: ['61-27=34'] Exploring Operation: 89-4=85, Resulting Numbers: [34, 85] Generated Node #0,2,0: 32:[34, 85] Operation: 89-4=85 Exploring Operation: 34-4=30, Resulting Numbers: [89, 30] Generated Node #0,2,1: 32:[89, 30] Operation: 34-4=30 Exploring Operation: 89-34=55, Resulting Numbers: [4, 55] Generated Node #0,2,2: 32:[4, 55] Operation: 89-34=55 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 32:[4, 55], Operations: ['61-27=34', '89-34=55'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 4*55=220, Resulting Numbers: [220] 220,32 unequal: No Solution Exploring Operation: 4+55=59, Resulting Numbers: [59] 59,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[34, 85], Operations: ['61-27=34', '89-4=85'] Exploring Operation: 34*85=2890, Resulting Numbers: [2890] 2890,32 unequal: No Solution Exploring Operation: 34+85=119, Resulting Numbers: [119] 119,32 unequal: No Solution Exploring Operation: 85-34=51, Resulting Numbers: [51] 51,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 32:[89, 30], Operations: ['61-27=34', '34-4=30'] Exploring Operation: 89+30=119, Resulting Numbers: [119] 119,32 unequal: No Solution Exploring Operation: 89*30=2670, Resulting Numbers: [2670] 2670,32 unequal: No Solution Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,32 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
[ 77, 90, 74, 11 ]
82
[ "77+90=167", "74+11=85", "167-85=82" ]
Current State: 82:[77, 90, 74, 11], Operations: [] Exploring Operation: 77+90=167, Resulting Numbers: [74, 11, 167] Generated Node #2: [74, 11, 167] from Operation: 77+90=167 Current State: 82:[74, 11, 167], Operations: ['77+90=167'] Exploring Operation: 74+11=85, Resulting Numbers: [167, 85] Generated Node #3: [167, 85] from Operation: 74+11=85 Current State: 82:[167, 85], Operations: ['77+90=167', '74+11=85'] Exploring Operation: 167-85=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[77, 90, 74, 11], Operations: [] Exploring Operation: 90-11=79, Resulting Numbers: [77, 74, 79] Generated Node #0,0: 82:[77, 74, 79] Operation: 90-11=79 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[77, 74, 79], Operations: ['90-11=79'] Exploring Operation: 77-74=3, Resulting Numbers: [79, 3] Generated Node #0,0,0: 82:[79, 3] Operation: 77-74=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[79, 3], Operations: ['90-11=79', '77-74=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[77, 90, 74, 11], Operations: [] Exploring Operation: 90-11=79, Resulting Numbers: [77, 74, 79] Generated Node #0,0: 82:[77, 74, 79] Operation: 90-11=79 Moving to Node #0,0 Current State: 82:[77, 74, 79], Operations: ['90-11=79'] Exploring Operation: 77-74=3, Resulting Numbers: [79, 3] Generated Node #0,0,0: 82:[79, 3] Operation: 77-74=3 Moving to Node #0,0,0 Current State: 82:[79, 3], Operations: ['90-11=79', '77-74=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 10, 35, 69, 72 ]
65
[ "72-69=3", "10*3=30", "35+30=65" ]
Current State: 65:[10, 35, 69, 72], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [10, 35, 3] Generated Node #2: [10, 35, 3] from Operation: 72-69=3 Current State: 65:[10, 35, 3], Operations: ['72-69=3'] Exploring Operation: 10*3=30, Resulting Numbers: [35, 30] Generated Node #3: [35, 30] from Operation: 10*3=30 Current State: 65:[35, 30], Operations: ['72-69=3', '10*3=30'] Exploring Operation: 35+30=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[10, 35, 69, 72], Operations: [] Exploring Operation: 35-10=25, Resulting Numbers: [69, 72, 25] Generated Node #0,0: 65:[69, 72, 25] Operation: 35-10=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[69, 72, 25], Operations: ['35-10=25'] Exploring Operation: 72-69=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 65:[25, 3] Operation: 72-69=3 Moving to Node #0,0,0 Current State: 65:[25, 3], Operations: ['35-10=25', '72-69=3'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 6, 85, 84, 95 ]
80
[ "6+85=91", "95-84=11", "91-11=80" ]
Current State: 80:[6, 85, 84, 95], Operations: [] Exploring Operation: 6+85=91, Resulting Numbers: [84, 95, 91] Generated Node #2: [84, 95, 91] from Operation: 6+85=91 Current State: 80:[84, 95, 91], Operations: ['6+85=91'] Exploring Operation: 95-84=11, Resulting Numbers: [91, 11] Generated Node #3: [91, 11] from Operation: 95-84=11 Current State: 80:[91, 11], Operations: ['6+85=91', '95-84=11'] Exploring Operation: 91-11=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[6, 85, 84, 95], Operations: [] Exploring Operation: 95-85=10, Resulting Numbers: [6, 84, 10] Generated Node #0,0: 80:[6, 84, 10] Operation: 95-85=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[6, 84, 10], Operations: ['95-85=10'] Exploring Operation: 84-6=78, Resulting Numbers: [10, 78] Generated Node #0,0,0: 80:[10, 78] Operation: 84-6=78 Moving to Node #0,0,0 Current State: 80:[10, 78], Operations: ['95-85=10', '84-6=78'] Exploring Operation: 10+78=88, Resulting Numbers: [88] 88,80 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
[ 45, 32, 59, 94 ]
42
[ "45+32=77", "94-59=35", "77-35=42" ]
Current State: 42:[45, 32, 59, 94], Operations: [] Exploring Operation: 45+32=77, Resulting Numbers: [59, 94, 77] Generated Node #2: [59, 94, 77] from Operation: 45+32=77 Current State: 42:[59, 94, 77], Operations: ['45+32=77'] Exploring Operation: 94-59=35, Resulting Numbers: [77, 35] Generated Node #3: [77, 35] from Operation: 94-59=35 Current State: 42:[77, 35], Operations: ['45+32=77', '94-59=35'] Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[45, 32, 59, 94], Operations: [] Exploring Operation: 94-59=35, Resulting Numbers: [45, 32, 35] Generated Node #0,0: 42:[45, 32, 35] Operation: 94-59=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[45, 32, 35], Operations: ['94-59=35'] Exploring Operation: 35-32=3, Resulting Numbers: [45, 3] Generated Node #0,0,0: 42:[45, 3] Operation: 35-32=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[45, 3], Operations: ['94-59=35', '35-32=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[45, 32, 59, 94], Operations: [] Exploring Operation: 94-59=35, Resulting Numbers: [45, 32, 35] Generated Node #0,0: 42:[45, 32, 35] Operation: 94-59=35 Moving to Node #0,0 Current State: 42:[45, 32, 35], Operations: ['94-59=35'] Exploring Operation: 35-32=3, Resulting Numbers: [45, 3] Generated Node #0,0,0: 42:[45, 3] Operation: 35-32=3 Moving to Node #0,0,0 Current State: 42:[45, 3], Operations: ['94-59=35', '35-32=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 83, 85, 60, 94 ]
14
[ "83+85=168", "60+94=154", "168-154=14" ]
Current State: 14:[83, 85, 60, 94], Operations: [] Exploring Operation: 83+85=168, Resulting Numbers: [60, 94, 168] Generated Node #2: [60, 94, 168] from Operation: 83+85=168 Current State: 14:[60, 94, 168], Operations: ['83+85=168'] Exploring Operation: 60+94=154, Resulting Numbers: [168, 154] Generated Node #3: [168, 154] from Operation: 60+94=154 Current State: 14:[168, 154], Operations: ['83+85=168', '60+94=154'] Exploring Operation: 168-154=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[83, 85, 60, 94], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [60, 94, 2] Generated Node #0,0: 14:[60, 94, 2] Operation: 85-83=2 Exploring Operation: 94-85=9, Resulting Numbers: [83, 60, 9] Generated Node #0,1: 14:[83, 60, 9] Operation: 94-85=9 Exploring Operation: 83-60=23, Resulting Numbers: [85, 94, 23] Generated Node #0,2: 14:[85, 94, 23] Operation: 83-60=23 Exploring Operation: 94-83=11, Resulting Numbers: [85, 60, 11] Generated Node #0,3: 14:[85, 60, 11] Operation: 94-83=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[83, 60, 9], Operations: ['94-85=9'] Exploring Operation: 83-9=74, Resulting Numbers: [60, 74] Generated Node #0,1,0: 14:[60, 74] Operation: 83-9=74 Exploring Operation: 60-9=51, Resulting Numbers: [83, 51] Generated Node #0,1,1: 14:[83, 51] Operation: 60-9=51 Exploring Operation: 83+9=92, Resulting Numbers: [60, 92] Generated Node #0,1,2: 14:[60, 92] Operation: 83+9=92 Exploring Operation: 83-60=23, Resulting Numbers: [9, 23] Generated Node #0,1,3: 14:[9, 23] Operation: 83-60=23 Moving to Node #0,1,3 Current State: 14:[9, 23], Operations: ['94-85=9', '83-60=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[83, 85, 60, 94], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [83, 60, 9] Generated Node #0,1: 14:[83, 60, 9] Operation: 94-85=9 Moving to Node #0,1 Current State: 14:[83, 60, 9], Operations: ['94-85=9'] Exploring Operation: 83-60=23, Resulting Numbers: [9, 23] Generated Node #0,1,3: 14:[9, 23] Operation: 83-60=23 Moving to Node #0,1,3 Current State: 14:[9, 23], Operations: ['94-85=9', '83-60=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 58, 41, 76, 32 ]
55
[ "58+41=99", "76-32=44", "99-44=55" ]
Current State: 55:[58, 41, 76, 32], Operations: [] Exploring Operation: 58+41=99, Resulting Numbers: [76, 32, 99] Generated Node #2: [76, 32, 99] from Operation: 58+41=99 Current State: 55:[76, 32, 99], Operations: ['58+41=99'] Exploring Operation: 76-32=44, Resulting Numbers: [99, 44] Generated Node #3: [99, 44] from Operation: 76-32=44 Current State: 55:[99, 44], Operations: ['58+41=99', '76-32=44'] Exploring Operation: 99-44=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[58, 41, 76, 32], Operations: [] Exploring Operation: 76-58=18, Resulting Numbers: [41, 32, 18] Generated Node #0,0: 55:[41, 32, 18] Operation: 76-58=18 Exploring Operation: 41+32=73, Resulting Numbers: [58, 76, 73] Generated Node #0,1: 55:[58, 76, 73] Operation: 41+32=73 Exploring Operation: 76-41=35, Resulting Numbers: [58, 32, 35] Generated Node #0,2: 55:[58, 32, 35] Operation: 76-41=35 Exploring Operation: 76-32=44, Resulting Numbers: [58, 41, 44] Generated Node #0,3: 55:[58, 41, 44] Operation: 76-32=44 Exploring Operation: 41-32=9, Resulting Numbers: [58, 76, 9] Generated Node #0,4: 55:[58, 76, 9] Operation: 41-32=9 Moving to Node #0,4 Current State: 55:[58, 76, 9], Operations: ['41-32=9'] Exploring Operation: 58-9=49, Resulting Numbers: [76, 49] Generated Node #0,4,0: 55:[76, 49] Operation: 58-9=49 Exploring Operation: 76-58=18, Resulting Numbers: [9, 18] Generated Node #0,4,1: 55:[9, 18] Operation: 76-58=18 Exploring Operation: 76+9=85, Resulting Numbers: [58, 85] Generated Node #0,4,2: 55:[58, 85] Operation: 76+9=85 Exploring Operation: 58+9=67, Resulting Numbers: [76, 67] Generated Node #0,4,3: 55:[76, 67] Operation: 58+9=67 Exploring Operation: 76-9=67, Resulting Numbers: [58, 67] Generated Node #0,4,4: 55:[58, 67] Operation: 76-9=67 Moving to Node #0,3 Current State: 55:[58, 41, 44], Operations: ['76-32=44'] Exploring Operation: 58-44=14, Resulting Numbers: [41, 14] Generated Node #0,3,0: 55:[41, 14] Operation: 58-44=14 Exploring Operation: 41+44=85, Resulting Numbers: [58, 85] Generated Node #0,3,1: 55:[58, 85] Operation: 41+44=85 Exploring Operation: 44-41=3, Resulting Numbers: [58, 3] Generated Node #0,3,2: 55:[58, 3] Operation: 44-41=3 Exploring Operation: 58-41=17, Resulting Numbers: [44, 17] Generated Node #0,3,3: 55:[44, 17] Operation: 58-41=17 Exploring Operation: 58+41=99, Resulting Numbers: [44, 99] Generated Node #0,3,4: 55:[44, 99] Operation: 58+41=99 Moving to Node #0,0 Current State: 55:[41, 32, 18], Operations: ['76-58=18'] Exploring Operation: 32+18=50, Resulting Numbers: [41, 50] Generated Node #0,0,0: 55:[41, 50] Operation: 32+18=50 Exploring Operation: 41-32=9, Resulting Numbers: [18, 9] Generated Node #0,0,1: 55:[18, 9] Operation: 41-32=9 Exploring Operation: 41+18=59, Resulting Numbers: [32, 59] Generated Node #0,0,2: 55:[32, 59] Operation: 41+18=59 Exploring Operation: 41+32=73, Resulting Numbers: [18, 73] Generated Node #0,0,3: 55:[18, 73] Operation: 41+32=73 Exploring Operation: 32-18=14, Resulting Numbers: [41, 14] Generated Node #0,0,4: 55:[41, 14] Operation: 32-18=14 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 55:[18, 9], Operations: ['76-58=18', '41-32=9'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,55 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,55 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 #0,0,4 Current State: 55:[41, 14], Operations: ['76-58=18', '32-18=14'] Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,55 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[58, 41, 76, 32], Operations: [] Exploring Operation: 76-58=18, Resulting Numbers: [41, 32, 18] Generated Node #0,0: 55:[41, 32, 18] Operation: 76-58=18 Moving to Node #0,0 Current State: 55:[41, 32, 18], Operations: ['76-58=18'] Exploring Operation: 32-18=14, Resulting Numbers: [41, 14] Generated Node #0,0,4: 55:[41, 14] Operation: 32-18=14 Moving to Node #0,0,4 Current State: 55:[41, 14], Operations: ['76-58=18', '32-18=14'] Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_5
sum_heuristic
[ 6, 65, 86, 5 ]
10
[ "6+65=71", "86-5=81", "81-71=10" ]
Current State: 10:[6, 65, 86, 5], Operations: [] Exploring Operation: 6+65=71, Resulting Numbers: [86, 5, 71] Generated Node #2: [86, 5, 71] from Operation: 6+65=71 Current State: 10:[86, 5, 71], Operations: ['6+65=71'] Exploring Operation: 86-5=81, Resulting Numbers: [71, 81] Generated Node #3: [71, 81] from Operation: 86-5=81 Current State: 10:[71, 81], Operations: ['6+65=71', '86-5=81'] Exploring Operation: 81-71=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[6, 65, 86, 5], Operations: [] Exploring Operation: 86-65=21, Resulting Numbers: [6, 5, 21] Generated Node #0,0: 10:[6, 5, 21] Operation: 86-65=21 Exploring Operation: 65-6=59, Resulting Numbers: [86, 5, 59] Generated Node #0,1: 10:[86, 5, 59] Operation: 65-6=59 Exploring Operation: 65/5=13, Resulting Numbers: [6, 86, 13] Generated Node #0,2: 10:[6, 86, 13] Operation: 65/5=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[6, 5, 21], Operations: ['86-65=21'] Exploring Operation: 21-5=16, Resulting Numbers: [6, 16] Generated Node #0,0,0: 10:[6, 16] Operation: 21-5=16 Exploring Operation: 21-6=15, Resulting Numbers: [5, 15] Generated Node #0,0,1: 10:[5, 15] Operation: 21-6=15 Exploring Operation: 6+5=11, Resulting Numbers: [21, 11] Generated Node #0,0,2: 10:[21, 11] Operation: 6+5=11 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[5, 15], Operations: ['86-65=21', '21-6=15'] Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[6, 65, 86, 5], Operations: [] Exploring Operation: 86-65=21, Resulting Numbers: [6, 5, 21] Generated Node #0,0: 10:[6, 5, 21] Operation: 86-65=21 Moving to Node #0,0 Current State: 10:[6, 5, 21], Operations: ['86-65=21'] Exploring Operation: 21-6=15, Resulting Numbers: [5, 15] Generated Node #0,0,1: 10:[5, 15] Operation: 21-6=15 Moving to Node #0,0,1 Current State: 10:[5, 15], Operations: ['86-65=21', '21-6=15'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 25, 9, 61, 12 ]
83
[ "25+9=34", "61-12=49", "34+49=83" ]
Current State: 83:[25, 9, 61, 12], Operations: [] Exploring Operation: 25+9=34, Resulting Numbers: [61, 12, 34] Generated Node #2: [61, 12, 34] from Operation: 25+9=34 Current State: 83:[61, 12, 34], Operations: ['25+9=34'] Exploring Operation: 61-12=49, Resulting Numbers: [34, 49] Generated Node #3: [34, 49] from Operation: 61-12=49 Current State: 83:[34, 49], Operations: ['25+9=34', '61-12=49'] Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[25, 9, 61, 12], Operations: [] Exploring Operation: 25+9=34, Resulting Numbers: [61, 12, 34] Generated Node #0,0: 83:[61, 12, 34] Operation: 25+9=34 Exploring Operation: 9*12=108, Resulting Numbers: [25, 61, 108] Generated Node #0,1: 83:[25, 61, 108] Operation: 9*12=108 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[25, 61, 108], Operations: ['9*12=108'] Exploring Operation: 108-25=83, Resulting Numbers: [61, 83] Generated Node #0,1,0: 83:[61, 83] Operation: 108-25=83 Exploring Operation: 25+61=86, Resulting Numbers: [108, 86] Generated Node #0,1,1: 83:[108, 86] Operation: 25+61=86 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[61, 83], Operations: ['9*12=108', '108-25=83'] Exploring Operation: 83-61=22, Resulting Numbers: [22] 22,83 unequal: No Solution Exploring Operation: 61+83=144, Resulting Numbers: [144] 144,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[108, 86], Operations: ['9*12=108', '25+61=86'] Exploring Operation: 108+86=194, Resulting Numbers: [194] 194,83 unequal: No Solution Exploring Operation: 108-86=22, Resulting Numbers: [22] 22,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[61, 12, 34], Operations: ['25+9=34'] Exploring Operation: 61+12=73, Resulting Numbers: [34, 73] Generated Node #0,0,0: 83:[34, 73] Operation: 61+12=73 Exploring Operation: 12+34=46, Resulting Numbers: [61, 46] Generated Node #0,0,1: 83:[61, 46] Operation: 12+34=46 Moving to Node #0,0,0 Current State: 83:[34, 73], Operations: ['25+9=34', '61+12=73'] Exploring Operation: 34+73=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[61, 46], Operations: ['25+9=34', '12+34=46'] Exploring Operation: 61-46=15, Resulting Numbers: [15] 15,83 unequal: No Solution Exploring Operation: 61+46=107, Resulting Numbers: [107] 107,83 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
[ 90, 40, 46, 4 ]
80
[ "90+40=130", "46+4=50", "130-50=80" ]
Current State: 80:[90, 40, 46, 4], Operations: [] Exploring Operation: 90+40=130, Resulting Numbers: [46, 4, 130] Generated Node #2: [46, 4, 130] from Operation: 90+40=130 Current State: 80:[46, 4, 130], Operations: ['90+40=130'] Exploring Operation: 46+4=50, Resulting Numbers: [130, 50] Generated Node #3: [130, 50] from Operation: 46+4=50 Current State: 80:[130, 50], Operations: ['90+40=130', '46+4=50'] Exploring Operation: 130-50=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[90, 40, 46, 4], Operations: [] Exploring Operation: 90-46=44, Resulting Numbers: [40, 4, 44] Generated Node #0,0: 80:[40, 4, 44] Operation: 90-46=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[40, 4, 44], Operations: ['90-46=44'] Exploring Operation: 44-40=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 80:[4, 4] Operation: 44-40=4 Moving to Node #0,0,0 Current State: 80:[4, 4], Operations: ['90-46=44', '44-40=4'] Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,80 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
[ 36, 48, 76, 60 ]
72
[ "76-36=40", "48*60=2880", "2880/40=72" ]
Current State: 72:[36, 48, 76, 60], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [48, 60, 40] Generated Node #2: [48, 60, 40] from Operation: 76-36=40 Current State: 72:[48, 60, 40], Operations: ['76-36=40'] Exploring Operation: 48*60=2880, Resulting Numbers: [40, 2880] Generated Node #3: [40, 2880] from Operation: 48*60=2880 Current State: 72:[40, 2880], Operations: ['76-36=40', '48*60=2880'] Exploring Operation: 2880/40=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[36, 48, 76, 60], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [36, 60, 28] Generated Node #0,0: 72:[36, 60, 28] Operation: 76-48=28 Exploring Operation: 60-36=24, Resulting Numbers: [48, 76, 24] Generated Node #0,1: 72:[48, 76, 24] Operation: 60-36=24 Exploring Operation: 76-60=16, Resulting Numbers: [36, 48, 16] Generated Node #0,2: 72:[36, 48, 16] Operation: 76-60=16 Exploring Operation: 60-48=12, Resulting Numbers: [36, 76, 12] Generated Node #0,3: 72:[36, 76, 12] Operation: 60-48=12 Exploring Operation: 48-36=12, Resulting Numbers: [76, 60, 12] Generated Node #0,4: 72:[76, 60, 12] Operation: 48-36=12 Moving to Node #0,3 Current State: 72:[36, 76, 12], Operations: ['60-48=12'] Exploring Operation: 36+12=48, Resulting Numbers: [76, 48] Generated Node #0,3,0: 72:[76, 48] Operation: 36+12=48 Exploring Operation: 36-12=24, Resulting Numbers: [76, 24] Generated Node #0,3,1: 72:[76, 24] Operation: 36-12=24 Exploring Operation: 36/12=3, Resulting Numbers: [76, 3] Generated Node #0,3,2: 72:[76, 3] Operation: 36/12=3 Exploring Operation: 76-36=40, Resulting Numbers: [12, 40] Generated Node #0,3,3: 72:[12, 40] Operation: 76-36=40 Exploring Operation: 76-12=64, Resulting Numbers: [36, 64] Generated Node #0,3,4: 72:[36, 64] Operation: 76-12=64 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 72:[76, 24], Operations: ['60-48=12', '36-12=24'] Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,72 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,72 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 #0,3,2 Current State: 72:[76, 3], Operations: ['60-48=12', '36/12=3'] Exploring Operation: 76+3=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 76*3=228, Resulting Numbers: [228] 228,72 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 #0,3,3 Current State: 72:[12, 40], Operations: ['60-48=12', '76-36=40'] Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,72 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,72 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 #0,3,4 Current State: 72:[36, 64], Operations: ['60-48=12', '76-12=64'] Exploring Operation: 64-36=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 36*64=2304, Resulting Numbers: [2304] 2304,72 unequal: No Solution Exploring Operation: 36+64=100, Resulting Numbers: [100] 100,72 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 #0,3,0 Current State: 72:[76, 48], Operations: ['60-48=12', '36+12=48'] Exploring Operation: 76+48=124, Resulting Numbers: [124] 124,72 unequal: No Solution Exploring Operation: 76-48=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 76*48=3648, Resulting Numbers: [3648] 3648,72 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:[36, 48, 16], Operations: ['76-60=16'] Exploring Operation: 48/16=3, Resulting Numbers: [36, 3] Generated Node #0,2,0: 72:[36, 3] Operation: 48/16=3 Exploring Operation: 48-16=32, Resulting Numbers: [36, 32] Generated Node #0,2,1: 72:[36, 32] Operation: 48-16=32 Exploring Operation: 36+48=84, Resulting Numbers: [16, 84] Generated Node #0,2,2: 72:[16, 84] Operation: 36+48=84 Exploring Operation: 48-36=12, Resulting Numbers: [16, 12] Generated Node #0,2,3: 72:[16, 12] Operation: 48-36=12 Exploring Operation: 48+16=64, Resulting Numbers: [36, 64] Generated Node #0,2,4: 72:[36, 64] Operation: 48+16=64 Moving to Node #0,0 Current State: 72:[36, 60, 28], Operations: ['76-48=28'] Exploring Operation: 60+28=88, Resulting Numbers: [36, 88] Generated Node #0,0,0: 72:[36, 88] Operation: 60+28=88 Exploring Operation: 36+28=64, Resulting Numbers: [60, 64] Generated Node #0,0,1: 72:[60, 64] Operation: 36+28=64 Exploring Operation: 36-28=8, Resulting Numbers: [60, 8] Generated Node #0,0,2: 72:[60, 8] Operation: 36-28=8 Exploring Operation: 60-28=32, Resulting Numbers: [36, 32] Generated Node #0,0,3: 72:[36, 32] Operation: 60-28=32 Exploring Operation: 60-36=24, Resulting Numbers: [28, 24] Generated Node #0,0,4: 72:[28, 24] Operation: 60-36=24 Moving to Node #0,1 Current State: 72:[48, 76, 24], Operations: ['60-36=24'] Exploring Operation: 76-48=28, Resulting Numbers: [24, 28] Generated Node #0,1,0: 72:[24, 28] Operation: 76-48=28 Exploring Operation: 76-24=52, Resulting Numbers: [48, 52] Generated Node #0,1,1: 72:[48, 52] Operation: 76-24=52 Exploring Operation: 48-24=24, Resulting Numbers: [76, 24] Generated Node #0,1,2: 72:[76, 24] Operation: 48-24=24 Exploring Operation: 48+24=72, Resulting Numbers: [76, 72] Generated Node #0,1,3: 72:[76, 72] Operation: 48+24=72 Exploring Operation: 48/24=2, Resulting Numbers: [76, 2] Generated Node #0,1,4: 72:[76, 2] Operation: 48/24=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[24, 28], Operations: ['60-36=24', '76-48=28'] Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,72 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,72 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 #0,1,2 Current State: 72:[76, 24], Operations: ['60-36=24', '48-24=24'] Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,72 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,72 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 #0,1,3 Current State: 72:[76, 72], Operations: ['60-36=24', '48+24=72'] Exploring Operation: 76*72=5472, Resulting Numbers: [5472] 5472,72 unequal: No Solution Exploring Operation: 76-72=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 76+72=148, Resulting Numbers: [148] 148,72 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 #0,1,4 Current State: 72:[76, 2], Operations: ['60-36=24', '48/24=2'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 76*2=152, Resulting Numbers: [152] 152,72 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,72 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 #0,1,1 Current State: 72:[48, 52], Operations: ['60-36=24', '76-24=52'] Exploring Operation: 52-48=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 48*52=2496, Resulting Numbers: [2496] 2496,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 72:[76, 60, 12], Operations: ['48-36=12'] Exploring Operation: 76-12=64, Resulting Numbers: [60, 64] Generated Node #0,4,0: 72:[60, 64] Operation: 76-12=64 Exploring Operation: 60+12=72, Resulting Numbers: [76, 72] Generated Node #0,4,1: 72:[76, 72] Operation: 60+12=72 Exploring Operation: 76-60=16, Resulting Numbers: [12, 16] Generated Node #0,4,2: 72:[12, 16] Operation: 76-60=16 Exploring Operation: 60-12=48, Resulting Numbers: [76, 48] Generated Node #0,4,3: 72:[76, 48] Operation: 60-12=48 Exploring Operation: 60/12=5, Resulting Numbers: [76, 5] Generated Node #0,4,4: 72:[76, 5] Operation: 60/12=5 Moving to Node #0,2,0 Current State: 72:[36, 3], Operations: ['76-60=16', '48/16=3'] Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,72 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[16, 12], Operations: ['76-60=16', '48-36=12'] Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,72 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,72 unequal: No Solution Moving to Node #0,4,2 Current State: 72:[12, 16], Operations: ['48-36=12', '76-60=16'] Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[36, 32], Operations: ['76-60=16', '48-16=32'] Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 36*32=1152, Resulting Numbers: [1152] 1152,72 unequal: No Solution Exploring Operation: 36+32=68, Resulting Numbers: [68] 68,72 unequal: No Solution Moving to Node #0,0,4 Current State: 72:[28, 24], Operations: ['76-48=28', '60-36=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,72 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[36, 32], Operations: ['76-48=28', '60-28=32'] Exploring Operation: 36*32=1152, Resulting Numbers: [1152] 1152,72 unequal: No Solution Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 36+32=68, Resulting Numbers: [68] 68,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[76, 72], Operations: ['48-36=12', '60+12=72'] Exploring Operation: 76-72=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 76+72=148, Resulting Numbers: [148] 148,72 unequal: No Solution Exploring Operation: 76*72=5472, Resulting Numbers: [5472] 5472,72 unequal: No Solution Moving to Node #0,4,4 Current State: 72:[76, 5], Operations: ['48-36=12', '60/12=5'] Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,72 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 76*5=380, Resulting Numbers: [380] 380,72 unequal: No Solution Moving to Node #0,2,4 Current State: 72:[36, 64], Operations: ['76-60=16', '48+16=64'] Exploring Operation: 36+64=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 64-36=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 36*64=2304, Resulting Numbers: [2304] 2304,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[60, 8], Operations: ['76-48=28', '36-28=8'] Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,72 unequal: No Solution Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 60*8=480, Resulting Numbers: [480] 480,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[16, 84], Operations: ['76-60=16', '36+48=84'] Exploring Operation: 16*84=1344, Resulting Numbers: [1344] 1344,72 unequal: No Solution Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 16+84=100, Resulting Numbers: [100] 100,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[36, 88], Operations: ['76-48=28', '60+28=88'] Exploring Operation: 36+88=124, Resulting Numbers: [124] 124,72 unequal: No Solution Exploring Operation: 36*88=3168, Resulting Numbers: [3168] 3168,72 unequal: No Solution Exploring Operation: 88-36=52, Resulting Numbers: [52] 52,72 unequal: No Solution Moving to Node #0,4,3 Current State: 72:[76, 48], Operations: ['48-36=12', '60-12=48'] Exploring Operation: 76-48=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 76*48=3648, Resulting Numbers: [3648] 3648,72 unequal: No Solution Exploring Operation: 76+48=124, Resulting Numbers: [124] 124,72 unequal: No Solution Moving to Node #0,4,0 Current State: 72:[60, 64], Operations: ['48-36=12', '76-12=64'] Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 60+64=124, Resulting Numbers: [124] 124,72 unequal: No Solution Exploring Operation: 60*64=3840, Resulting Numbers: [3840] 3840,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[60, 64], Operations: ['76-48=28', '36+28=64'] Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 60*64=3840, Resulting Numbers: [3840] 3840,72 unequal: No Solution Exploring Operation: 60+64=124, Resulting Numbers: [124] 124,72 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 20, 20, 22, 15 ]
26
[ "20-15=5", "20/5=4", "22+4=26" ]
Current State: 26:[20, 20, 22, 15], Operations: [] Exploring Operation: 20-15=5, Resulting Numbers: [22, 5] Generated Node #2: [22, 5] from Operation: 20-15=5 Current State: 26:[22, 5], Operations: ['20-15=5'] Exploring Operation: 20/5=4, Resulting Numbers: [22, 4] Generated Node #3: [22, 4] from Operation: 20/5=4 Current State: 26:[22, 4], Operations: ['20-15=5', '20/5=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[20, 20, 22, 15], Operations: [] Exploring Operation: 20-20=0, Resulting Numbers: [22, 15, 0] Generated Node #0,0: 26:[22, 15, 0] Operation: 20-20=0 Exploring Operation: 20/20=1, Resulting Numbers: [22, 15, 1] Generated Node #0,1: 26:[22, 15, 1] Operation: 20/20=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[22, 15, 1], Operations: ['20/20=1'] Exploring Operation: 15-1=14, Resulting Numbers: [22, 14] Generated Node #0,1,0: 26:[22, 14] Operation: 15-1=14 Exploring Operation: 22+1=23, Resulting Numbers: [15, 23] Generated Node #0,1,1: 26:[15, 23] Operation: 22+1=23 Moving to Node #0,1,0 Current State: 26:[22, 14], Operations: ['20/20=1', '15-1=14'] Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[15, 23], Operations: ['20/20=1', '22+1=23'] Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,26 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[22, 15, 0], Operations: ['20-20=0'] Exploring Operation: 22*0=0, Resulting Numbers: [15, 0] Generated Node #0,0,0: 26:[15, 0] Operation: 22*0=0 Exploring Operation: 22+0=22, Resulting Numbers: [15, 22] Generated Node #0,0,1: 26:[15, 22] Operation: 22+0=22 Moving to Node #0,0,0 Current State: 26:[15, 0], Operations: ['20-20=0', '22*0=0'] Exploring Operation: 15+0=15, Resulting Numbers: [15] 15,26 unequal: No Solution Exploring Operation: 15*0=0, Resulting Numbers: [0] 0,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[15, 22], Operations: ['20-20=0', '22+0=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 32, 86, 21, 1 ]
75
[ "86-32=54", "21*1=21", "54+21=75" ]
Current State: 75:[32, 86, 21, 1], Operations: [] Exploring Operation: 86-32=54, Resulting Numbers: [21, 1, 54] Generated Node #2: [21, 1, 54] from Operation: 86-32=54 Current State: 75:[21, 1, 54], Operations: ['86-32=54'] Exploring Operation: 21*1=21, Resulting Numbers: [54, 21] Generated Node #3: [54, 21] from Operation: 21*1=21 Current State: 75:[54, 21], Operations: ['86-32=54', '21*1=21'] Exploring Operation: 54+21=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[32, 86, 21, 1], Operations: [] Exploring Operation: 86-21=65, Resulting Numbers: [32, 1, 65] Generated Node #0,0: 75:[32, 1, 65] Operation: 86-21=65 Exploring Operation: 32-21=11, Resulting Numbers: [86, 1, 11] Generated Node #0,1: 75:[86, 1, 11] Operation: 32-21=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[86, 1, 11], Operations: ['32-21=11'] Exploring Operation: 86-1=85, Resulting Numbers: [11, 85] Generated Node #0,1,0: 75:[11, 85] Operation: 86-1=85 Exploring Operation: 86-11=75, Resulting Numbers: [1, 75] Generated Node #0,1,1: 75:[1, 75] Operation: 86-11=75 Moving to Node #0,1,1 Current State: 75:[1, 75], Operations: ['32-21=11', '86-11=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[32, 86, 21, 1], Operations: [] Exploring Operation: 32-21=11, Resulting Numbers: [86, 1, 11] Generated Node #0,1: 75:[86, 1, 11] Operation: 32-21=11 Moving to Node #0,1 Current State: 75:[86, 1, 11], Operations: ['32-21=11'] Exploring Operation: 86-11=75, Resulting Numbers: [1, 75] Generated Node #0,1,1: 75:[1, 75] Operation: 86-11=75 Moving to Node #0,1,1 Current State: 75:[1, 75], Operations: ['32-21=11', '86-11=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 13, 45, 26, 15 ]
99
[ "13+45=58", "26+15=41", "58+41=99" ]
Current State: 99:[13, 45, 26, 15], Operations: [] Exploring Operation: 13+45=58, Resulting Numbers: [26, 15, 58] Generated Node #2: [26, 15, 58] from Operation: 13+45=58 Current State: 99:[26, 15, 58], Operations: ['13+45=58'] Exploring Operation: 26+15=41, Resulting Numbers: [58, 41] Generated Node #3: [58, 41] from Operation: 26+15=41 Current State: 99:[58, 41], Operations: ['13+45=58', '26+15=41'] Exploring Operation: 58+41=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[13, 45, 26, 15], Operations: [] Exploring Operation: 45/15=3, Resulting Numbers: [13, 26, 3] Generated Node #0,0: 99:[13, 26, 3] Operation: 45/15=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[13, 26, 3], Operations: ['45/15=3'] Exploring Operation: 26/13=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 99:[3, 2] Operation: 26/13=2 Moving to Node #0,0,0 Current State: 99:[3, 2], Operations: ['45/15=3', '26/13=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,99 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
[ 80, 19, 73, 4 ]
69
[ "80-73=7", "19*4=76", "76-7=69" ]
Current State: 69:[80, 19, 73, 4], Operations: [] Exploring Operation: 80-73=7, Resulting Numbers: [19, 4, 7] Generated Node #2: [19, 4, 7] from Operation: 80-73=7 Current State: 69:[19, 4, 7], Operations: ['80-73=7'] Exploring Operation: 19*4=76, Resulting Numbers: [7, 76] Generated Node #3: [7, 76] from Operation: 19*4=76 Current State: 69:[7, 76], Operations: ['80-73=7', '19*4=76'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[80, 19, 73, 4], Operations: [] Exploring Operation: 19+4=23, Resulting Numbers: [80, 73, 23] Generated Node #0,0: 69:[80, 73, 23] Operation: 19+4=23 Exploring Operation: 80-19=61, Resulting Numbers: [73, 4, 61] Generated Node #0,1: 69:[73, 4, 61] Operation: 80-19=61 Exploring Operation: 80/4=20, Resulting Numbers: [19, 73, 20] Generated Node #0,2: 69:[19, 73, 20] Operation: 80/4=20 Exploring Operation: 80-4=76, Resulting Numbers: [19, 73, 76] Generated Node #0,3: 69:[19, 73, 76] Operation: 80-4=76 Exploring Operation: 80-73=7, Resulting Numbers: [19, 4, 7] Generated Node #0,4: 69:[19, 4, 7] Operation: 80-73=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 69:[19, 4, 7], Operations: ['80-73=7'] Exploring Operation: 19+4=23, Resulting Numbers: [7, 23] Generated Node #0,4,0: 69:[7, 23] Operation: 19+4=23 Exploring Operation: 7-4=3, Resulting Numbers: [19, 3] Generated Node #0,4,1: 69:[19, 3] Operation: 7-4=3 Exploring Operation: 19-7=12, Resulting Numbers: [4, 12] Generated Node #0,4,2: 69:[4, 12] Operation: 19-7=12 Exploring Operation: 19+7=26, Resulting Numbers: [4, 26] Generated Node #0,4,3: 69:[4, 26] Operation: 19+7=26 Exploring Operation: 4*7=28, Resulting Numbers: [19, 28] Generated Node #0,4,4: 69:[19, 28] Operation: 4*7=28 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 69:[7, 23], Operations: ['80-73=7', '19+4=23'] Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,69 unequal: No Solution Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,69 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 #0,4,1 Current State: 69:[19, 3], Operations: ['80-73=7', '7-4=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,69 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 #0,4,3 Current State: 69:[4, 26], Operations: ['80-73=7', '19+7=26'] Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,69 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,69 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 #0,4,4 Current State: 69:[19, 28], Operations: ['80-73=7', '4*7=28'] Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,69 unequal: No Solution Exploring Operation: 19*28=532, Resulting Numbers: [532] 532,69 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,69 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 #0,4,2 Current State: 69:[4, 12], Operations: ['80-73=7', '19-7=12'] Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,69 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 #0,2 Current State: 69:[19, 73, 20], Operations: ['80/4=20'] Exploring Operation: 19+20=39, Resulting Numbers: [73, 39] Generated Node #0,2,0: 69:[73, 39] Operation: 19+20=39 Exploring Operation: 19+73=92, Resulting Numbers: [20, 92] Generated Node #0,2,1: 69:[20, 92] Operation: 19+73=92 Exploring Operation: 73-20=53, Resulting Numbers: [19, 53] Generated Node #0,2,2: 69:[19, 53] Operation: 73-20=53 Exploring Operation: 73-19=54, Resulting Numbers: [20, 54] Generated Node #0,2,3: 69:[20, 54] Operation: 73-19=54 Exploring Operation: 20-19=1, Resulting Numbers: [73, 1] Generated Node #0,2,4: 69:[73, 1] Operation: 20-19=1 Moving to Node #0,2,4 Current State: 69:[73, 1], Operations: ['80/4=20', '20-19=1'] Exploring Operation: 73+1=74, Resulting Numbers: [74] 74,69 unequal: No Solution Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,69 unequal: No Solution Exploring Operation: 73*1=73, Resulting Numbers: [73] 73,69 unequal: No Solution Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[20, 54], Operations: ['80/4=20', '73-19=54'] Exploring Operation: 20+54=74, Resulting Numbers: [74] 74,69 unequal: No Solution Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 20*54=1080, Resulting Numbers: [1080] 1080,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[73, 39], Operations: ['80/4=20', '19+20=39'] Exploring Operation: 73-39=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 73*39=2847, Resulting Numbers: [2847] 2847,69 unequal: No Solution Exploring Operation: 73+39=112, Resulting Numbers: [112] 112,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[19, 53], Operations: ['80/4=20', '73-20=53'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,69 unequal: No Solution Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[20, 92], Operations: ['80/4=20', '19+73=92'] Exploring Operation: 20*92=1840, Resulting Numbers: [1840] 1840,69 unequal: No Solution Exploring Operation: 20+92=112, Resulting Numbers: [112] 112,69 unequal: No Solution Exploring Operation: 92-20=72, Resulting Numbers: [72] 72,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[73, 4, 61], Operations: ['80-19=61'] Exploring Operation: 4+61=65, Resulting Numbers: [73, 65] Generated Node #0,1,0: 69:[73, 65] Operation: 4+61=65 Exploring Operation: 61-4=57, Resulting Numbers: [73, 57] Generated Node #0,1,1: 69:[73, 57] Operation: 61-4=57 Exploring Operation: 73+4=77, Resulting Numbers: [61, 77] Generated Node #0,1,2: 69:[61, 77] Operation: 73+4=77 Exploring Operation: 73-4=69, Resulting Numbers: [61, 69] Generated Node #0,1,3: 69:[61, 69] Operation: 73-4=69 Exploring Operation: 73-61=12, Resulting Numbers: [4, 12] Generated Node #0,1,4: 69:[4, 12] Operation: 73-61=12 Moving to Node #0,1,0 Current State: 69:[73, 65], Operations: ['80-19=61', '4+61=65'] Exploring Operation: 73*65=4745, Resulting Numbers: [4745] 4745,69 unequal: No Solution Exploring Operation: 73+65=138, Resulting Numbers: [138] 138,69 unequal: No Solution Exploring Operation: 73-65=8, Resulting Numbers: [8] 8,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[61, 69], Operations: ['80-19=61', '73-4=69'] Exploring Operation: 61+69=130, Resulting Numbers: [130] 130,69 unequal: No Solution Exploring Operation: 61*69=4209, Resulting Numbers: [4209] 4209,69 unequal: No Solution Exploring Operation: 69-61=8, Resulting Numbers: [8] 8,69 unequal: No Solution Moving to Node #0,1,4 Current State: 69:[4, 12], Operations: ['80-19=61', '73-61=12'] Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[73, 57], Operations: ['80-19=61', '61-4=57'] Exploring Operation: 73*57=4161, Resulting Numbers: [4161] 4161,69 unequal: No Solution Exploring Operation: 73+57=130, Resulting Numbers: [130] 130,69 unequal: No Solution Exploring Operation: 73-57=16, Resulting Numbers: [16] 16,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[61, 77], Operations: ['80-19=61', '73+4=77'] Exploring Operation: 61+77=138, Resulting Numbers: [138] 138,69 unequal: No Solution Exploring Operation: 77-61=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 61*77=4697, Resulting Numbers: [4697] 4697,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[80, 73, 23], Operations: ['19+4=23'] Exploring Operation: 80-23=57, Resulting Numbers: [73, 57] Generated Node #0,0,0: 69:[73, 57] Operation: 80-23=57 Exploring Operation: 80-73=7, Resulting Numbers: [23, 7] Generated Node #0,0,1: 69:[23, 7] Operation: 80-73=7 Exploring Operation: 80+23=103, Resulting Numbers: [73, 103] Generated Node #0,0,2: 69:[73, 103] Operation: 80+23=103 Exploring Operation: 73+23=96, Resulting Numbers: [80, 96] Generated Node #0,0,3: 69:[80, 96] Operation: 73+23=96 Exploring Operation: 73-23=50, Resulting Numbers: [80, 50] Generated Node #0,0,4: 69:[80, 50] Operation: 73-23=50 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[23, 7], Operations: ['19+4=23', '80-73=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,69 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[73, 57], Operations: ['19+4=23', '80-23=57'] Exploring Operation: 73-57=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 73+57=130, Resulting Numbers: [130] 130,69 unequal: No Solution Exploring Operation: 73*57=4161, Resulting Numbers: [4161] 4161,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 69:[80, 50], Operations: ['19+4=23', '73-23=50'] Exploring Operation: 80+50=130, Resulting Numbers: [130] 130,69 unequal: No Solution Exploring Operation: 80*50=4000, Resulting Numbers: [4000] 4000,69 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 69:[73, 103], Operations: ['19+4=23', '80+23=103'] Exploring Operation: 73+103=176, Resulting Numbers: [176] 176,69 unequal: No Solution Exploring Operation: 103-73=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 73*103=7519, Resulting Numbers: [7519] 7519,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 69:[80, 96], Operations: ['19+4=23', '73+23=96'] Exploring Operation: 80*96=7680, Resulting Numbers: [7680] 7680,69 unequal: No Solution Exploring Operation: 80+96=176, Resulting Numbers: [176] 176,69 unequal: No Solution Exploring Operation: 96-80=16, Resulting Numbers: [16] 16,69 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 #0,3 Current State: 69:[19, 73, 76], Operations: ['80-4=76'] Exploring Operation: 73-19=54, Resulting Numbers: [76, 54] Generated Node #0,3,0: 69:[76, 54] Operation: 73-19=54 Exploring Operation: 76-73=3, Resulting Numbers: [19, 3] Generated Node #0,3,1: 69:[19, 3] Operation: 76-73=3 Exploring Operation: 76-19=57, Resulting Numbers: [73, 57] Generated Node #0,3,2: 69:[73, 57] Operation: 76-19=57 Exploring Operation: 19+73=92, Resulting Numbers: [76, 92] Generated Node #0,3,3: 69:[76, 92] Operation: 19+73=92 Exploring Operation: 76/19=4, Resulting Numbers: [73, 4] Generated Node #0,3,4: 69:[73, 4] Operation: 76/19=4 Moving to Node #0,3,1 Current State: 69:[19, 3], Operations: ['80-4=76', '76-73=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[73, 4], Operations: ['80-4=76', '76/19=4'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[80, 19, 73, 4], Operations: [] Exploring Operation: 80-4=76, Resulting Numbers: [19, 73, 76] Generated Node #0,3: 69:[19, 73, 76] Operation: 80-4=76 Moving to Node #0,3 Current State: 69:[19, 73, 76], Operations: ['80-4=76'] Exploring Operation: 76/19=4, Resulting Numbers: [73, 4] Generated Node #0,3,4: 69:[73, 4] Operation: 76/19=4 Moving to Node #0,3,4 Current State: 69:[73, 4], Operations: ['80-4=76', '76/19=4'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.912326
hs_5
sum_heuristic
[ 49, 43, 44, 89 ]
52
[ "43+89=132", "132/44=3", "49+3=52" ]
Current State: 52:[49, 43, 44, 89], Operations: [] Exploring Operation: 43+89=132, Resulting Numbers: [49, 44, 132] Generated Node #2: [49, 44, 132] from Operation: 43+89=132 Current State: 52:[49, 44, 132], Operations: ['43+89=132'] Exploring Operation: 132/44=3, Resulting Numbers: [49, 3] Generated Node #3: [49, 3] from Operation: 132/44=3 Current State: 52:[49, 3], Operations: ['43+89=132', '132/44=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[49, 43, 44, 89], Operations: [] Exploring Operation: 89-43=46, Resulting Numbers: [49, 44, 46] Generated Node #0,0: 52:[49, 44, 46] Operation: 89-43=46 Exploring Operation: 89-49=40, Resulting Numbers: [43, 44, 40] Generated Node #0,1: 52:[43, 44, 40] Operation: 89-49=40 Exploring Operation: 44-43=1, Resulting Numbers: [49, 89, 1] Generated Node #0,2: 52:[49, 89, 1] Operation: 44-43=1 Exploring Operation: 89-44=45, Resulting Numbers: [49, 43, 45] Generated Node #0,3: 52:[49, 43, 45] Operation: 89-44=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[49, 44, 46], Operations: ['89-43=46'] Exploring Operation: 46-44=2, Resulting Numbers: [49, 2] Generated Node #0,0,0: 52:[49, 2] Operation: 46-44=2 Exploring Operation: 49-46=3, Resulting Numbers: [44, 3] Generated Node #0,0,1: 52:[44, 3] Operation: 49-46=3 Exploring Operation: 44+46=90, Resulting Numbers: [49, 90] Generated Node #0,0,2: 52:[49, 90] Operation: 44+46=90 Exploring Operation: 49-44=5, Resulting Numbers: [46, 5] Generated Node #0,0,3: 52:[46, 5] Operation: 49-44=5 Moving to Node #0,0,0 Current State: 52:[49, 2], Operations: ['89-43=46', '46-44=2'] Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,52 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[46, 5], Operations: ['89-43=46', '49-44=5'] Exploring Operation: 46+5=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 46*5=230, Resulting Numbers: [230] 230,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[44, 3], Operations: ['89-43=46', '49-46=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 44*3=132, Resulting Numbers: [132] 132,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[49, 90], Operations: ['89-43=46', '44+46=90'] Exploring Operation: 49+90=139, Resulting Numbers: [139] 139,52 unequal: No Solution Exploring Operation: 90-49=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 49*90=4410, Resulting Numbers: [4410] 4410,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[49, 43, 45], Operations: ['89-44=45'] Exploring Operation: 45-43=2, Resulting Numbers: [49, 2] Generated Node #0,3,0: 52:[49, 2] Operation: 45-43=2 Exploring Operation: 43+45=88, Resulting Numbers: [49, 88] Generated Node #0,3,1: 52:[49, 88] Operation: 43+45=88 Exploring Operation: 49-45=4, Resulting Numbers: [43, 4] Generated Node #0,3,2: 52:[43, 4] Operation: 49-45=4 Exploring Operation: 49-43=6, Resulting Numbers: [45, 6] Generated Node #0,3,3: 52:[45, 6] Operation: 49-43=6 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 52:[49, 2], Operations: ['89-44=45', '45-43=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 52:[43, 4], Operations: ['89-44=45', '49-45=4'] Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,52 unequal: No Solution Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 52:[45, 6], Operations: ['89-44=45', '49-43=6'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 52:[49, 88], Operations: ['89-44=45', '43+45=88'] Exploring Operation: 49+88=137, Resulting Numbers: [137] 137,52 unequal: No Solution Exploring Operation: 49*88=4312, Resulting Numbers: [4312] 4312,52 unequal: No Solution Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[43, 44, 40], Operations: ['89-49=40'] Exploring Operation: 43-40=3, Resulting Numbers: [44, 3] Generated Node #0,1,0: 52:[44, 3] Operation: 43-40=3 Exploring Operation: 43+40=83, Resulting Numbers: [44, 83] Generated Node #0,1,1: 52:[44, 83] Operation: 43+40=83 Exploring Operation: 44-43=1, Resulting Numbers: [40, 1] Generated Node #0,1,2: 52:[40, 1] Operation: 44-43=1 Exploring Operation: 44-40=4, Resulting Numbers: [43, 4] Generated Node #0,1,3: 52:[43, 4] Operation: 44-40=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[44, 3], Operations: ['89-49=40', '43-40=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 44*3=132, Resulting Numbers: [132] 132,52 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 52:[43, 4], Operations: ['89-49=40', '44-40=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,52 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[40, 1], Operations: ['89-49=40', '44-43=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[44, 83], Operations: ['89-49=40', '43+40=83'] Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 44+83=127, Resulting Numbers: [127] 127,52 unequal: No Solution Exploring Operation: 44*83=3652, Resulting Numbers: [3652] 3652,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[49, 89, 1], Operations: ['44-43=1'] Exploring Operation: 49*1=49, Resulting Numbers: [89, 49] Generated Node #0,2,0: 52:[89, 49] Operation: 49*1=49 Exploring Operation: 89-1=88, Resulting Numbers: [49, 88] Generated Node #0,2,1: 52:[49, 88] Operation: 89-1=88 Exploring Operation: 89-49=40, Resulting Numbers: [1, 40] Generated Node #0,2,2: 52:[1, 40] Operation: 89-49=40 Exploring Operation: 49+1=50, Resulting Numbers: [89, 50] Generated Node #0,2,3: 52:[89, 50] Operation: 49+1=50 Moving to Node #0,2,2 Current State: 52:[1, 40], Operations: ['44-43=1', '89-49=40'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 1+40=41, Resulting Numbers: [41] 41,52 unequal: No Solution Moving to Node #0,2,3 Current State: 52:[89, 50], Operations: ['44-43=1', '49+1=50'] Exploring Operation: 89*50=4450, Resulting Numbers: [4450] 4450,52 unequal: No Solution Exploring Operation: 89+50=139, Resulting Numbers: [139] 139,52 unequal: No Solution Exploring Operation: 89-50=39, Resulting Numbers: [39] 39,52 unequal: No Solution Moving to Node #0,2,1 Current State: 52:[49, 88], Operations: ['44-43=1', '89-1=88'] Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 49+88=137, Resulting Numbers: [137] 137,52 unequal: No Solution Exploring Operation: 49*88=4312, Resulting Numbers: [4312] 4312,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[89, 49], Operations: ['44-43=1', '49*1=49'] Exploring Operation: 89+49=138, Resulting Numbers: [138] 138,52 unequal: No Solution Exploring Operation: 89*49=4361, Resulting Numbers: [4361] 4361,52 unequal: No Solution Exploring Operation: 89-49=40, Resulting Numbers: [40] 40,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 46, 48, 37, 37 ]
99
[ "46-37=9", "48-37=11", "9*11=99" ]
Current State: 99:[46, 48, 37, 37], Operations: [] Exploring Operation: 46-37=9, Resulting Numbers: [48, 9] Generated Node #2: [48, 9] from Operation: 46-37=9 Current State: 99:[48, 9], Operations: ['46-37=9'] Exploring Operation: 48-37=11, Resulting Numbers: [9, 11] Generated Node #3: [9, 11] from Operation: 48-37=11 Current State: 99:[9, 11], Operations: ['46-37=9', '48-37=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[46, 48, 37, 37], Operations: [] Exploring Operation: 48-46=2, Resulting Numbers: [37, 37, 2] Generated Node #0,0: 99:[37, 37, 2] Operation: 48-46=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[37, 37, 2], Operations: ['48-46=2'] Exploring Operation: 37/37=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 99:[2, 1] Operation: 37/37=1 Moving to Node #0,0,0 Current State: 99:[2, 1], Operations: ['48-46=2', '37/37=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,99 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
[ 56, 20, 4, 94 ]
70
[ "56+94=150", "20*4=80", "150-80=70" ]
Current State: 70:[56, 20, 4, 94], Operations: [] Exploring Operation: 56+94=150, Resulting Numbers: [20, 4, 150] Generated Node #2: [20, 4, 150] from Operation: 56+94=150 Current State: 70:[20, 4, 150], Operations: ['56+94=150'] Exploring Operation: 20*4=80, Resulting Numbers: [150, 80] Generated Node #3: [150, 80] from Operation: 20*4=80 Current State: 70:[150, 80], Operations: ['56+94=150', '20*4=80'] Exploring Operation: 150-80=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[56, 20, 4, 94], Operations: [] Exploring Operation: 94-56=38, Resulting Numbers: [20, 4, 38] Generated Node #0,0: 70:[20, 4, 38] Operation: 94-56=38 Exploring Operation: 94-20=74, Resulting Numbers: [56, 4, 74] Generated Node #0,1: 70:[56, 4, 74] Operation: 94-20=74 Moving to Node #0,0 Current State: 70:[20, 4, 38], Operations: ['94-56=38'] Exploring Operation: 20/4=5, Resulting Numbers: [38, 5] Generated Node #0,0,0: 70:[38, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [38, 16] Generated Node #0,0,1: 70:[38, 16] Operation: 20-4=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[38, 5], Operations: ['94-56=38', '20/4=5'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,70 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[38, 16], Operations: ['94-56=38', '20-4=16'] Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,70 unequal: No Solution Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,70 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: 70:[56, 4, 74], Operations: ['94-20=74'] Exploring Operation: 56/4=14, Resulting Numbers: [74, 14] Generated Node #0,1,0: 70:[74, 14] Operation: 56/4=14 Exploring Operation: 74-56=18, Resulting Numbers: [4, 18] Generated Node #0,1,1: 70:[4, 18] Operation: 74-56=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 70:[74, 14], Operations: ['94-20=74', '56/4=14'] Exploring Operation: 74+14=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 70:[4, 18], Operations: ['94-20=74', '74-56=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,70 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
[ 98, 38, 40, 52 ]
78
[ "98-38=60", "52*60=3120", "3120/40=78" ]
Current State: 78:[98, 38, 40, 52], Operations: [] Exploring Operation: 98-38=60, Resulting Numbers: [40, 52, 60] Generated Node #2: [40, 52, 60] from Operation: 98-38=60 Current State: 78:[40, 52, 60], Operations: ['98-38=60'] Exploring Operation: 52*60=3120, Resulting Numbers: [40, 3120] Generated Node #3: [40, 3120] from Operation: 52*60=3120 Current State: 78:[40, 3120], Operations: ['98-38=60', '52*60=3120'] Exploring Operation: 3120/40=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[98, 38, 40, 52], Operations: [] Exploring Operation: 52-38=14, Resulting Numbers: [98, 40, 14] Generated Node #0,0: 78:[98, 40, 14] Operation: 52-38=14 Exploring Operation: 98-52=46, Resulting Numbers: [38, 40, 46] Generated Node #0,1: 78:[38, 40, 46] Operation: 98-52=46 Moving to Node #0,1 Current State: 78:[38, 40, 46], Operations: ['98-52=46'] Exploring Operation: 46-38=8, Resulting Numbers: [40, 8] Generated Node #0,1,0: 78:[40, 8] Operation: 46-38=8 Exploring Operation: 46-40=6, Resulting Numbers: [38, 6] Generated Node #0,1,1: 78:[38, 6] Operation: 46-40=6 Moving to Node #0,0 Current State: 78:[98, 40, 14], Operations: ['52-38=14'] Exploring Operation: 98-14=84, Resulting Numbers: [40, 84] Generated Node #0,0,0: 78:[40, 84] Operation: 98-14=84 Exploring Operation: 98/14=7, Resulting Numbers: [40, 7] Generated Node #0,0,1: 78:[40, 7] Operation: 98/14=7 Moving to Node #0,1,1 Current State: 78:[38, 6], Operations: ['98-52=46', '46-40=6'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[40, 7], Operations: ['52-38=14', '98/14=7'] Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[40, 8], Operations: ['98-52=46', '46-38=8'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[40, 84], Operations: ['52-38=14', '98-14=84'] Exploring Operation: 40+84=124, Resulting Numbers: [124] 124,78 unequal: No Solution Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,78 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 83, 68, 2, 26 ]
91
[ "83-26=57", "68/2=34", "57+34=91" ]
Current State: 91:[83, 68, 2, 26], Operations: [] Exploring Operation: 83-26=57, Resulting Numbers: [68, 2, 57] Generated Node #2: [68, 2, 57] from Operation: 83-26=57 Current State: 91:[68, 2, 57], Operations: ['83-26=57'] Exploring Operation: 68/2=34, Resulting Numbers: [57, 34] Generated Node #3: [57, 34] from Operation: 68/2=34 Current State: 91:[57, 34], Operations: ['83-26=57', '68/2=34'] Exploring Operation: 57+34=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[83, 68, 2, 26], Operations: [] Exploring Operation: 68+26=94, Resulting Numbers: [83, 2, 94] Generated Node #0,0: 91:[83, 2, 94] Operation: 68+26=94 Exploring Operation: 83-68=15, Resulting Numbers: [2, 26, 15] Generated Node #0,1: 91:[2, 26, 15] Operation: 83-68=15 Exploring Operation: 26/2=13, Resulting Numbers: [83, 68, 13] Generated Node #0,2: 91:[83, 68, 13] Operation: 26/2=13 Moving to Node #0,0 Current State: 91:[83, 2, 94], Operations: ['68+26=94'] Exploring Operation: 83+2=85, Resulting Numbers: [94, 85] Generated Node #0,0,0: 91:[94, 85] Operation: 83+2=85 Exploring Operation: 94-2=92, Resulting Numbers: [83, 92] Generated Node #0,0,1: 91:[83, 92] Operation: 94-2=92 Exploring Operation: 94-83=11, Resulting Numbers: [2, 11] Generated Node #0,0,2: 91:[2, 11] Operation: 94-83=11 Moving to Node #0,1 Current State: 91:[2, 26, 15], Operations: ['83-68=15'] Exploring Operation: 26/2=13, Resulting Numbers: [15, 13] Generated Node #0,1,0: 91:[15, 13] Operation: 26/2=13 Exploring Operation: 26-15=11, Resulting Numbers: [2, 11] Generated Node #0,1,1: 91:[2, 11] Operation: 26-15=11 Exploring Operation: 26-2=24, Resulting Numbers: [15, 24] Generated Node #0,1,2: 91:[15, 24] Operation: 26-2=24 Moving to Node #0,2 Current State: 91:[83, 68, 13], Operations: ['26/2=13'] Exploring Operation: 83+13=96, Resulting Numbers: [68, 96] Generated Node #0,2,0: 91:[68, 96] Operation: 83+13=96 Exploring Operation: 68+13=81, Resulting Numbers: [83, 81] Generated Node #0,2,1: 91:[83, 81] Operation: 68+13=81 Exploring Operation: 83-68=15, Resulting Numbers: [13, 15] Generated Node #0,2,2: 91:[13, 15] Operation: 83-68=15 Moving to Node #0,1,0 Current State: 91:[15, 13], Operations: ['83-68=15', '26/2=13'] Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,91 unequal: No Solution Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[13, 15], Operations: ['26/2=13', '83-68=15'] Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,91 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 13*15=195, Resulting Numbers: [195] 195,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[2, 11], Operations: ['68+26=94', '94-83=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,91 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[2, 11], Operations: ['83-68=15', '26-15=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,91 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[83, 92], Operations: ['68+26=94', '94-2=92'] Exploring Operation: 83+92=175, Resulting Numbers: [175] 175,91 unequal: No Solution Exploring Operation: 92-83=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 83*92=7636, Resulting Numbers: [7636] 7636,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[94, 85], Operations: ['68+26=94', '83+2=85'] Exploring Operation: 94+85=179, Resulting Numbers: [179] 179,91 unequal: No Solution Exploring Operation: 94*85=7990, Resulting Numbers: [7990] 7990,91 unequal: No Solution Exploring Operation: 94-85=9, Resulting Numbers: [9] 9,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[15, 24], Operations: ['83-68=15', '26-2=24'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,91 unequal: No Solution Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[83, 81], Operations: ['26/2=13', '68+13=81'] Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 83+81=164, Resulting Numbers: [164] 164,91 unequal: No Solution Exploring Operation: 83*81=6723, Resulting Numbers: [6723] 6723,91 unequal: No Solution Moving to Node #0,2,0 Current State: 91:[68, 96], Operations: ['26/2=13', '83+13=96'] Exploring Operation: 68*96=6528, Resulting Numbers: [6528] 6528,91 unequal: No Solution Exploring Operation: 96-68=28, Resulting Numbers: [28] 28,91 unequal: No Solution Exploring Operation: 68+96=164, Resulting Numbers: [164] 164,91 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 26, 4, 84, 12 ]
62
[ "26+84=110", "4*12=48", "110-48=62" ]
Current State: 62:[26, 4, 84, 12], Operations: [] Exploring Operation: 26+84=110, Resulting Numbers: [4, 12, 110] Generated Node #2: [4, 12, 110] from Operation: 26+84=110 Current State: 62:[4, 12, 110], Operations: ['26+84=110'] Exploring Operation: 4*12=48, Resulting Numbers: [110, 48] Generated Node #3: [110, 48] from Operation: 4*12=48 Current State: 62:[110, 48], Operations: ['26+84=110', '4*12=48'] Exploring Operation: 110-48=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[26, 4, 84, 12], Operations: [] Exploring Operation: 84/12=7, Resulting Numbers: [26, 4, 7] Generated Node #0,0: 62:[26, 4, 7] Operation: 84/12=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[26, 4, 7], Operations: ['84/12=7'] Exploring Operation: 26+7=33, Resulting Numbers: [4, 33] Generated Node #0,0,0: 62:[4, 33] Operation: 26+7=33 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[4, 33], Operations: ['84/12=7', '26+7=33'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,62 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
[ 1, 55, 27, 5 ]
77
[ "1*55=55", "27-5=22", "55+22=77" ]
Current State: 77:[1, 55, 27, 5], Operations: [] Exploring Operation: 1*55=55, Resulting Numbers: [27, 5, 55] Generated Node #2: [27, 5, 55] from Operation: 1*55=55 Current State: 77:[27, 5, 55], Operations: ['1*55=55'] Exploring Operation: 27-5=22, Resulting Numbers: [55, 22] Generated Node #3: [55, 22] from Operation: 27-5=22 Current State: 77:[55, 22], Operations: ['1*55=55', '27-5=22'] Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[1, 55, 27, 5], Operations: [] Exploring Operation: 55+27=82, Resulting Numbers: [1, 5, 82] Generated Node #0,0: 77:[1, 5, 82] Operation: 55+27=82 Moving to Node #0,0 Current State: 77:[1, 5, 82], Operations: ['55+27=82'] Exploring Operation: 1+5=6, Resulting Numbers: [82, 6] Generated Node #0,0,0: 77:[82, 6] Operation: 1+5=6 Moving to Node #0,0,0 Current State: 77:[82, 6], Operations: ['55+27=82', '1+5=6'] Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,77 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 98, 98, 93, 59 ]
93
[ "98-98=0", "59*0=0", "93+0=93" ]
Current State: 93:[98, 98, 93, 59], Operations: [] Exploring Operation: 98-98=0, Resulting Numbers: [93, 59, 0] Generated Node #2: [93, 59, 0] from Operation: 98-98=0 Current State: 93:[93, 59, 0], Operations: ['98-98=0'] Exploring Operation: 59*0=0, Resulting Numbers: [93, 0] Generated Node #3: [93, 0] from Operation: 59*0=0 Current State: 93:[93, 0], Operations: ['98-98=0', '59*0=0'] Exploring Operation: 93+0=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[98, 98, 93, 59], Operations: [] Exploring Operation: 98-59=39, Resulting Numbers: [98, 93, 39] Generated Node #0,0: 93:[98, 93, 39] Operation: 98-59=39 Exploring Operation: 98-98=0, Resulting Numbers: [93, 59, 0] Generated Node #0,1: 93:[93, 59, 0] Operation: 98-98=0 Exploring Operation: 93-59=34, Resulting Numbers: [98, 98, 34] Generated Node #0,2: 93:[98, 98, 34] Operation: 93-59=34 Exploring Operation: 98-59=39, Resulting Numbers: [98, 93, 39] Generated Node #0,3: 93:[98, 93, 39] Operation: 98-59=39 Exploring Operation: 98/98=1, Resulting Numbers: [93, 59, 1] Generated Node #0,4: 93:[93, 59, 1] Operation: 98/98=1 Moving to Node #0,0 Current State: 93:[98, 93, 39], Operations: ['98-59=39'] Exploring Operation: 98+39=137, Resulting Numbers: [93, 137] Generated Node #0,0,0: 93:[93, 137] Operation: 98+39=137 Exploring Operation: 98-93=5, Resulting Numbers: [39, 5] Generated Node #0,0,1: 93:[39, 5] Operation: 98-93=5 Exploring Operation: 93-39=54, Resulting Numbers: [98, 54] Generated Node #0,0,2: 93:[98, 54] Operation: 93-39=54 Exploring Operation: 98-39=59, Resulting Numbers: [93, 59] Generated Node #0,0,3: 93:[93, 59] Operation: 98-39=59 Exploring Operation: 93+39=132, Resulting Numbers: [98, 132] Generated Node #0,0,4: 93:[98, 132] Operation: 93+39=132 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[39, 5], Operations: ['98-59=39', '98-93=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,93 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 93:[98, 54], Operations: ['98-59=39', '93-39=54'] Exploring Operation: 98*54=5292, Resulting Numbers: [5292] 5292,93 unequal: No Solution Exploring Operation: 98+54=152, Resulting Numbers: [152] 152,93 unequal: No Solution Exploring Operation: 98-54=44, Resulting Numbers: [44] 44,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 93:[93, 59], Operations: ['98-59=39', '98-39=59'] Exploring Operation: 93*59=5487, Resulting Numbers: [5487] 5487,93 unequal: No Solution Exploring Operation: 93-59=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 93+59=152, Resulting Numbers: [152] 152,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[93, 137], Operations: ['98-59=39', '98+39=137'] Exploring Operation: 93+137=230, Resulting Numbers: [230] 230,93 unequal: No Solution Exploring Operation: 93*137=12741, Resulting Numbers: [12741] 12741,93 unequal: No Solution Exploring Operation: 137-93=44, Resulting Numbers: [44] 44,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 93:[98, 132], Operations: ['98-59=39', '93+39=132'] Exploring Operation: 98+132=230, Resulting Numbers: [230] 230,93 unequal: No Solution Exploring Operation: 132-98=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 98*132=12936, Resulting Numbers: [12936] 12936,93 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: 93:[98, 93, 39], Operations: ['98-59=39'] Exploring Operation: 98-39=59, Resulting Numbers: [93, 59] Generated Node #0,3,0: 93:[93, 59] Operation: 98-39=59 Exploring Operation: 93+39=132, Resulting Numbers: [98, 132] Generated Node #0,3,1: 93:[98, 132] Operation: 93+39=132 Exploring Operation: 93-39=54, Resulting Numbers: [98, 54] Generated Node #0,3,2: 93:[98, 54] Operation: 93-39=54 Exploring Operation: 98+39=137, Resulting Numbers: [93, 137] Generated Node #0,3,3: 93:[93, 137] Operation: 98+39=137 Exploring Operation: 98-93=5, Resulting Numbers: [39, 5] Generated Node #0,3,4: 93:[39, 5] Operation: 98-93=5 Moving to Node #0,2 Current State: 93:[98, 98, 34], Operations: ['93-59=34'] Exploring Operation: 98/98=1, Resulting Numbers: [34, 1] Generated Node #0,2,0: 93:[34, 1] Operation: 98/98=1 Exploring Operation: 98-34=64, Resulting Numbers: [98, 64] Generated Node #0,2,1: 93:[98, 64] Operation: 98-34=64 Exploring Operation: 98+34=132, Resulting Numbers: [98, 132] Generated Node #0,2,2: 93:[98, 132] Operation: 98+34=132 Exploring Operation: 98-34=64, Resulting Numbers: [98, 64] Generated Node #0,2,3: 93:[98, 64] Operation: 98-34=64 Exploring Operation: 98-98=0, Resulting Numbers: [34, 0] Generated Node #0,2,4: 93:[34, 0] Operation: 98-98=0 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 93:[34, 1], Operations: ['93-59=34', '98/98=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,93 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 93:[34, 0], Operations: ['93-59=34', '98-98=0'] Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 34-0=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 34*0=0, Resulting Numbers: [0] 0,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 93:[98, 64], Operations: ['93-59=34', '98-34=64'] Exploring Operation: 98*64=6272, Resulting Numbers: [6272] 6272,93 unequal: No Solution Exploring Operation: 98+64=162, Resulting Numbers: [162] 162,93 unequal: No Solution Exploring Operation: 98-64=34, Resulting Numbers: [34] 34,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 93:[98, 64], Operations: ['93-59=34', '98-34=64'] Exploring Operation: 98-64=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 98+64=162, Resulting Numbers: [162] 162,93 unequal: No Solution Exploring Operation: 98*64=6272, Resulting Numbers: [6272] 6272,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 93:[98, 132], Operations: ['93-59=34', '98+34=132'] Exploring Operation: 132-98=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 98*132=12936, Resulting Numbers: [12936] 12936,93 unequal: No Solution Exploring Operation: 98+132=230, Resulting Numbers: [230] 230,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 93:[93, 59, 1], Operations: ['98/98=1'] Exploring Operation: 93*1=93, Resulting Numbers: [59, 93] Generated Node #0,4,0: 93:[59, 93] Operation: 93*1=93 Exploring Operation: 59-1=58, Resulting Numbers: [93, 58] Generated Node #0,4,1: 93:[93, 58] Operation: 59-1=58 Exploring Operation: 93/1=93, Resulting Numbers: [59, 93] Generated Node #0,4,2: 93:[59, 93] Operation: 93/1=93 Exploring Operation: 93-59=34, Resulting Numbers: [1, 34] Generated Node #0,4,3: 93:[1, 34] Operation: 93-59=34 Exploring Operation: 59*1=59, Resulting Numbers: [93, 59] Generated Node #0,4,4: 93:[93, 59] Operation: 59*1=59 Moving to Node #0,1 Current State: 93:[93, 59, 0], Operations: ['98-98=0'] Exploring Operation: 93-0=93, Resulting Numbers: [59, 93] Generated Node #0,1,0: 93:[59, 93] Operation: 93-0=93 Exploring Operation: 93+0=93, Resulting Numbers: [59, 93] Generated Node #0,1,1: 93:[59, 93] Operation: 93+0=93 Exploring Operation: 59+0=59, Resulting Numbers: [93, 59] Generated Node #0,1,2: 93:[93, 59] Operation: 59+0=59 Exploring Operation: 93-59=34, Resulting Numbers: [0, 34] Generated Node #0,1,3: 93:[0, 34] Operation: 93-59=34 Exploring Operation: 59*0=0, Resulting Numbers: [93, 0] Generated Node #0,1,4: 93:[93, 0] Operation: 59*0=0 Moving to Node #0,1,4 Current State: 93:[93, 0], Operations: ['98-98=0', '59*0=0'] Exploring Operation: 93+0=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[98, 98, 93, 59], Operations: [] Exploring Operation: 98-98=0, Resulting Numbers: [93, 59, 0] Generated Node #0,1: 93:[93, 59, 0] Operation: 98-98=0 Moving to Node #0,1 Current State: 93:[93, 59, 0], Operations: ['98-98=0'] Exploring Operation: 59*0=0, Resulting Numbers: [93, 0] Generated Node #0,1,4: 93:[93, 0] Operation: 59*0=0 Moving to Node #0,1,4 Current State: 93:[93, 0], Operations: ['98-98=0', '59*0=0'] Exploring Operation: 93+0=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.942708
hs_5
mult_heuristic
[ 28, 77, 2, 46 ]
41
[ "46-28=18", "2*18=36", "77-36=41" ]
Current State: 41:[28, 77, 2, 46], Operations: [] Exploring Operation: 46-28=18, Resulting Numbers: [77, 2, 18] Generated Node #2: [77, 2, 18] from Operation: 46-28=18 Current State: 41:[77, 2, 18], Operations: ['46-28=18'] Exploring Operation: 2*18=36, Resulting Numbers: [77, 36] Generated Node #3: [77, 36] from Operation: 2*18=36 Current State: 41:[77, 36], Operations: ['46-28=18', '2*18=36'] Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[28, 77, 2, 46], Operations: [] Exploring Operation: 28+2=30, Resulting Numbers: [77, 46, 30] Generated Node #0,0: 41:[77, 46, 30] Operation: 28+2=30 Exploring Operation: 77-28=49, Resulting Numbers: [2, 46, 49] Generated Node #0,1: 41:[2, 46, 49] Operation: 77-28=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[77, 46, 30], Operations: ['28+2=30'] Exploring Operation: 77-46=31, Resulting Numbers: [30, 31] Generated Node #0,0,0: 41:[30, 31] Operation: 77-46=31 Exploring Operation: 77-30=47, Resulting Numbers: [46, 47] Generated Node #0,0,1: 41:[46, 47] Operation: 77-30=47 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[46, 47], Operations: ['28+2=30', '77-30=47'] Exploring Operation: 46+47=93, Resulting Numbers: [93] 93,41 unequal: No Solution Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,41 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 #0,0,0 Current State: 41:[30, 31], Operations: ['28+2=30', '77-46=31'] Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 30+31=61, Resulting Numbers: [61] 61,41 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:[2, 46, 49], Operations: ['77-28=49'] Exploring Operation: 49-2=47, Resulting Numbers: [46, 47] Generated Node #0,1,0: 41:[46, 47] Operation: 49-2=47 Exploring Operation: 46-2=44, Resulting Numbers: [49, 44] Generated Node #0,1,1: 41:[49, 44] Operation: 46-2=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[46, 47], Operations: ['77-28=49', '49-2=47'] Exploring Operation: 46+47=93, Resulting Numbers: [93] 93,41 unequal: No Solution Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,41 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:[49, 44], Operations: ['77-28=49', '46-2=44'] Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,41 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,41 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
mult_heuristic
[ 63, 67, 8, 96 ]
42
[ "63+67=130", "96-8=88", "130-88=42" ]
Current State: 42:[63, 67, 8, 96], Operations: [] Exploring Operation: 63+67=130, Resulting Numbers: [8, 96, 130] Generated Node #2: [8, 96, 130] from Operation: 63+67=130 Current State: 42:[8, 96, 130], Operations: ['63+67=130'] Exploring Operation: 96-8=88, Resulting Numbers: [130, 88] Generated Node #3: [130, 88] from Operation: 96-8=88 Current State: 42:[130, 88], Operations: ['63+67=130', '96-8=88'] Exploring Operation: 130-88=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[63, 67, 8, 96], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [63, 8, 29] Generated Node #0,0: 42:[63, 8, 29] Operation: 96-67=29 Exploring Operation: 67-63=4, Resulting Numbers: [8, 96, 4] Generated Node #0,1: 42:[8, 96, 4] Operation: 67-63=4 Exploring Operation: 96-63=33, Resulting Numbers: [67, 8, 33] Generated Node #0,2: 42:[67, 8, 33] Operation: 96-63=33 Exploring Operation: 96/8=12, Resulting Numbers: [63, 67, 12] Generated Node #0,3: 42:[63, 67, 12] Operation: 96/8=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[63, 8, 29], Operations: ['96-67=29'] Exploring Operation: 8+29=37, Resulting Numbers: [63, 37] Generated Node #0,0,0: 42:[63, 37] Operation: 8+29=37 Exploring Operation: 63-8=55, Resulting Numbers: [29, 55] Generated Node #0,0,1: 42:[29, 55] Operation: 63-8=55 Exploring Operation: 29-8=21, Resulting Numbers: [63, 21] Generated Node #0,0,2: 42:[63, 21] Operation: 29-8=21 Exploring Operation: 63-29=34, Resulting Numbers: [8, 34] Generated Node #0,0,3: 42:[8, 34] Operation: 63-29=34 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 42:[8, 34], Operations: ['96-67=29', '63-29=34'] Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,42 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,42 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[63, 67, 8, 96], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [63, 8, 29] Generated Node #0,0: 42:[63, 8, 29] Operation: 96-67=29 Moving to Node #0,0 Current State: 42:[63, 8, 29], Operations: ['96-67=29'] Exploring Operation: 63-29=34, Resulting Numbers: [8, 34] Generated Node #0,0,3: 42:[8, 34] Operation: 63-29=34 Moving to Node #0,0,3 Current State: 42:[8, 34], Operations: ['96-67=29', '63-29=34'] Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 9, 19, 72, 9 ]
80
[ "19-9=10", "72/9=8", "10*8=80" ]
Current State: 80:[9, 19, 72, 9], Operations: [] Exploring Operation: 19-9=10, Resulting Numbers: [72, 10] Generated Node #2: [72, 10] from Operation: 19-9=10 Current State: 80:[72, 10], Operations: ['19-9=10'] Exploring Operation: 72/9=8, Resulting Numbers: [10, 8] Generated Node #3: [10, 8] from Operation: 72/9=8 Current State: 80:[10, 8], Operations: ['19-9=10', '72/9=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[9, 19, 72, 9], Operations: [] Exploring Operation: 72/9=8, Resulting Numbers: [19, 9, 8] Generated Node #0,0: 80:[19, 9, 8] Operation: 72/9=8 Exploring Operation: 72/9=8, Resulting Numbers: [9, 19, 8] Generated Node #0,1: 80:[9, 19, 8] Operation: 72/9=8 Moving to Node #0,0 Current State: 80:[19, 9, 8], Operations: ['72/9=8'] Exploring Operation: 19-9=10, Resulting Numbers: [8, 10] Generated Node #0,0,0: 80:[8, 10] Operation: 19-9=10 Exploring Operation: 19-8=11, Resulting Numbers: [9, 11] Generated Node #0,0,1: 80:[9, 11] Operation: 19-8=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[8, 10], Operations: ['72/9=8', '19-9=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[9, 19, 72, 9], Operations: [] Exploring Operation: 72/9=8, Resulting Numbers: [19, 9, 8] Generated Node #0,0: 80:[19, 9, 8] Operation: 72/9=8 Moving to Node #0,0 Current State: 80:[19, 9, 8], Operations: ['72/9=8'] Exploring Operation: 19-9=10, Resulting Numbers: [8, 10] Generated Node #0,0,0: 80:[8, 10] Operation: 19-9=10 Moving to Node #0,0,0 Current State: 80:[8, 10], Operations: ['72/9=8', '19-9=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 33, 54, 64, 30 ]
54
[ "64-33=31", "31-30=1", "54*1=54" ]
Current State: 54:[33, 54, 64, 30], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [54, 30, 31] Generated Node #2: [54, 30, 31] from Operation: 64-33=31 Current State: 54:[54, 30, 31], Operations: ['64-33=31'] Exploring Operation: 31-30=1, Resulting Numbers: [54, 1] Generated Node #3: [54, 1] from Operation: 31-30=1 Current State: 54:[54, 1], Operations: ['64-33=31', '31-30=1'] Exploring Operation: 54*1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[33, 54, 64, 30], Operations: [] Exploring Operation: 64-54=10, Resulting Numbers: [33, 30, 10] Generated Node #0,0: 54:[33, 30, 10] Operation: 64-54=10 Exploring Operation: 64-33=31, Resulting Numbers: [54, 30, 31] Generated Node #0,1: 54:[54, 30, 31] Operation: 64-33=31 Exploring Operation: 33-30=3, Resulting Numbers: [54, 64, 3] Generated Node #0,2: 54:[54, 64, 3] Operation: 33-30=3 Moving to Node #0,1 Current State: 54:[54, 30, 31], Operations: ['64-33=31'] Exploring Operation: 54-30=24, Resulting Numbers: [31, 24] Generated Node #0,1,0: 54:[31, 24] Operation: 54-30=24 Exploring Operation: 54-31=23, Resulting Numbers: [30, 23] Generated Node #0,1,1: 54:[30, 23] Operation: 54-31=23 Exploring Operation: 31-30=1, Resulting Numbers: [54, 1] Generated Node #0,1,2: 54:[54, 1] Operation: 31-30=1 Moving to Node #0,0 Current State: 54:[33, 30, 10], Operations: ['64-54=10'] Exploring Operation: 33-10=23, Resulting Numbers: [30, 23] Generated Node #0,0,0: 54:[30, 23] Operation: 33-10=23 Exploring Operation: 30/10=3, Resulting Numbers: [33, 3] Generated Node #0,0,1: 54:[33, 3] Operation: 30/10=3 Exploring Operation: 33-30=3, Resulting Numbers: [10, 3] Generated Node #0,0,2: 54:[10, 3] Operation: 33-30=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 54:[10, 3], Operations: ['64-54=10', '33-30=3'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[33, 3], Operations: ['64-54=10', '30/10=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[30, 23], Operations: ['64-54=10', '33-10=23'] Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 30+23=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 30*23=690, Resulting Numbers: [690] 690,54 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: 54:[54, 64, 3], Operations: ['33-30=3'] Exploring Operation: 54/3=18, Resulting Numbers: [64, 18] Generated Node #0,2,0: 54:[64, 18] Operation: 54/3=18 Exploring Operation: 64-54=10, Resulting Numbers: [3, 10] Generated Node #0,2,1: 54:[3, 10] Operation: 64-54=10 Exploring Operation: 64-3=61, Resulting Numbers: [54, 61] Generated Node #0,2,2: 54:[54, 61] Operation: 64-3=61 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[3, 10], Operations: ['33-30=3', '64-54=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 54:[54, 61], Operations: ['33-30=3', '64-3=61'] Exploring Operation: 61-54=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 54*61=3294, Resulting Numbers: [3294] 3294,54 unequal: No Solution Exploring Operation: 54+61=115, Resulting Numbers: [115] 115,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[64, 18], Operations: ['33-30=3', '54/3=18'] Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 64+18=82, Resulting Numbers: [82] 82,54 unequal: No Solution Exploring Operation: 64*18=1152, Resulting Numbers: [1152] 1152,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 54:[54, 1], Operations: ['64-33=31', '31-30=1'] Exploring Operation: 54+1=55, Resulting Numbers: [55] 55,54 unequal: No Solution Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[33, 54, 64, 30], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [54, 30, 31] Generated Node #0,1: 54:[54, 30, 31] Operation: 64-33=31 Moving to Node #0,1 Current State: 54:[54, 30, 31], Operations: ['64-33=31'] Exploring Operation: 31-30=1, Resulting Numbers: [54, 1] Generated Node #0,1,2: 54:[54, 1] Operation: 31-30=1 Moving to Node #0,1,2 Current State: 54:[54, 1], Operations: ['64-33=31', '31-30=1'] Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.96875
hs_3
mult_heuristic
[ 76, 6, 51, 69 ]
73
[ "69-51=18", "18/6=3", "76-3=73" ]
Current State: 73:[76, 6, 51, 69], Operations: [] Exploring Operation: 69-51=18, Resulting Numbers: [76, 6, 18] Generated Node #2: [76, 6, 18] from Operation: 69-51=18 Current State: 73:[76, 6, 18], Operations: ['69-51=18'] Exploring Operation: 18/6=3, Resulting Numbers: [76, 3] Generated Node #3: [76, 3] from Operation: 18/6=3 Current State: 73:[76, 3], Operations: ['69-51=18', '18/6=3'] Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[76, 6, 51, 69], Operations: [] Exploring Operation: 51-6=45, Resulting Numbers: [76, 69, 45] Generated Node #0,0: 73:[76, 69, 45] Operation: 51-6=45 Exploring Operation: 6+51=57, Resulting Numbers: [76, 69, 57] Generated Node #0,1: 73:[76, 69, 57] Operation: 6+51=57 Exploring Operation: 6+69=75, Resulting Numbers: [76, 51, 75] Generated Node #0,2: 73:[76, 51, 75] Operation: 6+69=75 Exploring Operation: 76+6=82, Resulting Numbers: [51, 69, 82] Generated Node #0,3: 73:[51, 69, 82] Operation: 76+6=82 Exploring Operation: 76-6=70, Resulting Numbers: [51, 69, 70] Generated Node #0,4: 73:[51, 69, 70] Operation: 76-6=70 Moving to Node #0,1 Current State: 73:[76, 69, 57], Operations: ['6+51=57'] Exploring Operation: 76-57=19, Resulting Numbers: [69, 19] Generated Node #0,1,0: 73:[69, 19] Operation: 76-57=19 Exploring Operation: 76+57=133, Resulting Numbers: [69, 133] Generated Node #0,1,1: 73:[69, 133] Operation: 76+57=133 Exploring Operation: 69+57=126, Resulting Numbers: [76, 126] Generated Node #0,1,2: 73:[76, 126] Operation: 69+57=126 Exploring Operation: 76-69=7, Resulting Numbers: [57, 7] Generated Node #0,1,3: 73:[57, 7] Operation: 76-69=7 Exploring Operation: 69-57=12, Resulting Numbers: [76, 12] Generated Node #0,1,4: 73:[76, 12] Operation: 69-57=12 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[76, 126], Operations: ['6+51=57', '69+57=126'] Exploring Operation: 76+126=202, Resulting Numbers: [202] 202,73 unequal: No Solution Exploring Operation: 126-76=50, Resulting Numbers: [50] 50,73 unequal: No Solution Exploring Operation: 76*126=9576, Resulting Numbers: [9576] 9576,73 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 #0,1,0 Current State: 73:[69, 19], Operations: ['6+51=57', '76-57=19'] Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,73 unequal: No Solution Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,73 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,73 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:[69, 133], Operations: ['6+51=57', '76+57=133'] Exploring Operation: 133-69=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 69+133=202, Resulting Numbers: [202] 202,73 unequal: No Solution Exploring Operation: 69*133=9177, Resulting Numbers: [9177] 9177,73 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:[76, 12], Operations: ['6+51=57', '69-57=12'] Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,73 unequal: No Solution Exploring Operation: 76*12=912, Resulting Numbers: [912] 912,73 unequal: No Solution Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,73 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:[57, 7], Operations: ['6+51=57', '76-69=7'] Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,73 unequal: No Solution Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,73 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: 73:[76, 51, 75], Operations: ['6+69=75'] Exploring Operation: 76-75=1, Resulting Numbers: [51, 1] Generated Node #0,2,0: 73:[51, 1] Operation: 76-75=1 Exploring Operation: 76-51=25, Resulting Numbers: [75, 25] Generated Node #0,2,1: 73:[75, 25] Operation: 76-51=25 Exploring Operation: 51+75=126, Resulting Numbers: [76, 126] Generated Node #0,2,2: 73:[76, 126] Operation: 51+75=126 Exploring Operation: 76+51=127, Resulting Numbers: [75, 127] Generated Node #0,2,3: 73:[75, 127] Operation: 76+51=127 Exploring Operation: 75-51=24, Resulting Numbers: [76, 24] Generated Node #0,2,4: 73:[76, 24] Operation: 75-51=24 Moving to Node #0,4 Current State: 73:[51, 69, 70], Operations: ['76-6=70'] Exploring Operation: 69-51=18, Resulting Numbers: [70, 18] Generated Node #0,4,0: 73:[70, 18] Operation: 69-51=18 Exploring Operation: 70-51=19, Resulting Numbers: [69, 19] Generated Node #0,4,1: 73:[69, 19] Operation: 70-51=19 Exploring Operation: 51+70=121, Resulting Numbers: [69, 121] Generated Node #0,4,2: 73:[69, 121] Operation: 51+70=121 Exploring Operation: 69+70=139, Resulting Numbers: [51, 139] Generated Node #0,4,3: 73:[51, 139] Operation: 69+70=139 Exploring Operation: 51+69=120, Resulting Numbers: [70, 120] Generated Node #0,4,4: 73:[70, 120] Operation: 51+69=120 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 73:[70, 120], Operations: ['76-6=70', '51+69=120'] Exploring Operation: 70+120=190, Resulting Numbers: [190] 190,73 unequal: No Solution Exploring Operation: 120-70=50, Resulting Numbers: [50] 50,73 unequal: No Solution Exploring Operation: 70*120=8400, Resulting Numbers: [8400] 8400,73 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 #0,4,2 Current State: 73:[69, 121], Operations: ['76-6=70', '51+70=121'] Exploring Operation: 69+121=190, Resulting Numbers: [190] 190,73 unequal: No Solution Exploring Operation: 121-69=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 69*121=8349, Resulting Numbers: [8349] 8349,73 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 #0,4,0 Current State: 73:[70, 18], Operations: ['76-6=70', '69-51=18'] Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,73 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,73 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 #0,4,1 Current State: 73:[69, 19], Operations: ['76-6=70', '70-51=19'] Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,73 unequal: No Solution Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,73 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,73 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 #0,4,3 Current State: 73:[51, 139], Operations: ['76-6=70', '69+70=139'] Exploring Operation: 139-51=88, Resulting Numbers: [88] 88,73 unequal: No Solution Exploring Operation: 51+139=190, Resulting Numbers: [190] 190,73 unequal: No Solution Exploring Operation: 51*139=7089, Resulting Numbers: [7089] 7089,73 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, 69, 45], Operations: ['51-6=45'] Exploring Operation: 76+45=121, Resulting Numbers: [69, 121] Generated Node #0,0,0: 73:[69, 121] Operation: 76+45=121 Exploring Operation: 76-45=31, Resulting Numbers: [69, 31] Generated Node #0,0,1: 73:[69, 31] Operation: 76-45=31 Exploring Operation: 69-45=24, Resulting Numbers: [76, 24] Generated Node #0,0,2: 73:[76, 24] Operation: 69-45=24 Exploring Operation: 69+45=114, Resulting Numbers: [76, 114] Generated Node #0,0,3: 73:[76, 114] Operation: 69+45=114 Exploring Operation: 76-69=7, Resulting Numbers: [45, 7] Generated Node #0,0,4: 73:[45, 7] Operation: 76-69=7 Moving to Node #0,3 Current State: 73:[51, 69, 82], Operations: ['76+6=82'] Exploring Operation: 69-51=18, Resulting Numbers: [82, 18] Generated Node #0,3,0: 73:[82, 18] Operation: 69-51=18 Exploring Operation: 51+69=120, Resulting Numbers: [82, 120] Generated Node #0,3,1: 73:[82, 120] Operation: 51+69=120 Exploring Operation: 82-69=13, Resulting Numbers: [51, 13] Generated Node #0,3,2: 73:[51, 13] Operation: 82-69=13 Exploring Operation: 51+82=133, Resulting Numbers: [69, 133] Generated Node #0,3,3: 73:[69, 133] Operation: 51+82=133 Exploring Operation: 82-51=31, Resulting Numbers: [69, 31] Generated Node #0,3,4: 73:[69, 31] Operation: 82-51=31 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 73:[69, 31], Operations: ['76+6=82', '82-51=31'] Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,73 unequal: No Solution Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,73 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 #0,3,1 Current State: 73:[82, 120], Operations: ['76+6=82', '51+69=120'] Exploring Operation: 82+120=202, Resulting Numbers: [202] 202,73 unequal: No Solution Exploring Operation: 120-82=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 82*120=9840, Resulting Numbers: [9840] 9840,73 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 #0,3,0 Current State: 73:[82, 18], Operations: ['76+6=82', '69-51=18'] Exploring Operation: 82*18=1476, Resulting Numbers: [1476] 1476,73 unequal: No Solution Exploring Operation: 82+18=100, Resulting Numbers: [100] 100,73 unequal: No Solution Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,73 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 #0,3,3 Current State: 73:[69, 133], Operations: ['76+6=82', '51+82=133'] Exploring Operation: 133-69=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 69+133=202, Resulting Numbers: [202] 202,73 unequal: No Solution Exploring Operation: 69*133=9177, Resulting Numbers: [9177] 9177,73 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 #0,3,2 Current State: 73:[51, 13], Operations: ['76+6=82', '82-69=13'] Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 51+13=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 51*13=663, Resulting Numbers: [663] 663,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 73:[76, 114], Operations: ['51-6=45', '69+45=114'] Exploring Operation: 76+114=190, Resulting Numbers: [190] 190,73 unequal: No Solution Exploring Operation: 76*114=8664, Resulting Numbers: [8664] 8664,73 unequal: No Solution Exploring Operation: 114-76=38, Resulting Numbers: [38] 38,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[69, 31], Operations: ['51-6=45', '76-45=31'] Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,73 unequal: No Solution Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,73 unequal: No Solution Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[75, 25], Operations: ['6+69=75', '76-51=25'] Exploring Operation: 75*25=1875, Resulting Numbers: [1875] 1875,73 unequal: No Solution Exploring Operation: 75+25=100, Resulting Numbers: [100] 100,73 unequal: No Solution Exploring Operation: 75-25=50, Resulting Numbers: [50] 50,73 unequal: No Solution Exploring Operation: 75/25=3, Resulting Numbers: [3] 3,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[76, 24], Operations: ['51-6=45', '69-45=24'] Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,73 unequal: No Solution Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,73 unequal: No Solution Moving to Node #0,2,4 Current State: 73:[76, 24], Operations: ['6+69=75', '75-51=24'] Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,73 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,73 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[69, 121], Operations: ['51-6=45', '76+45=121'] Exploring Operation: 69*121=8349, Resulting Numbers: [8349] 8349,73 unequal: No Solution Exploring Operation: 69+121=190, Resulting Numbers: [190] 190,73 unequal: No Solution Exploring Operation: 121-69=52, Resulting Numbers: [52] 52,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[76, 126], Operations: ['6+69=75', '51+75=126'] Exploring Operation: 76+126=202, Resulting Numbers: [202] 202,73 unequal: No Solution Exploring Operation: 126-76=50, Resulting Numbers: [50] 50,73 unequal: No Solution Exploring Operation: 76*126=9576, Resulting Numbers: [9576] 9576,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[75, 127], Operations: ['6+69=75', '76+51=127'] Exploring Operation: 75+127=202, Resulting Numbers: [202] 202,73 unequal: No Solution Exploring Operation: 127-75=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 75*127=9525, Resulting Numbers: [9525] 9525,73 unequal: No Solution Moving to Node #0,0,4 Current State: 73:[45, 7], Operations: ['51-6=45', '76-69=7'] Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 45*7=315, Resulting Numbers: [315] 315,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[51, 1], Operations: ['6+69=75', '76-75=1'] Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,73 unequal: No Solution Exploring Operation: 51+1=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 51*1=51, Resulting Numbers: [51] 51,73 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,73 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 2, 10, 48, 55 ]
52
[ "2*55=110", "10+48=58", "110-58=52" ]
Current State: 52:[2, 10, 48, 55], Operations: [] Exploring Operation: 2*55=110, Resulting Numbers: [10, 48, 110] Generated Node #2: [10, 48, 110] from Operation: 2*55=110 Current State: 52:[10, 48, 110], Operations: ['2*55=110'] Exploring Operation: 10+48=58, Resulting Numbers: [110, 58] Generated Node #3: [110, 58] from Operation: 10+48=58 Current State: 52:[110, 58], Operations: ['2*55=110', '10+48=58'] Exploring Operation: 110-58=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[2, 10, 48, 55], Operations: [] Exploring Operation: 10/2=5, Resulting Numbers: [48, 55, 5] Generated Node #0,0: 52:[48, 55, 5] Operation: 10/2=5 Exploring Operation: 2+10=12, Resulting Numbers: [48, 55, 12] Generated Node #0,1: 52:[48, 55, 12] Operation: 2+10=12 Exploring Operation: 55-48=7, Resulting Numbers: [2, 10, 7] Generated Node #0,2: 52:[2, 10, 7] Operation: 55-48=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[2, 10, 7], Operations: ['55-48=7'] Exploring Operation: 2+10=12, Resulting Numbers: [7, 12] Generated Node #0,2,0: 52:[7, 12] Operation: 2+10=12 Exploring Operation: 10-7=3, Resulting Numbers: [2, 3] Generated Node #0,2,1: 52:[2, 3] Operation: 10-7=3 Exploring Operation: 10/2=5, Resulting Numbers: [7, 5] Generated Node #0,2,2: 52:[7, 5] Operation: 10/2=5 Moving to Node #0,2,1 Current State: 52:[2, 3], Operations: ['55-48=7', '10-7=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,52 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[7, 12], Operations: ['55-48=7', '2+10=12'] Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,52 unequal: No Solution Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,52 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[7, 5], Operations: ['55-48=7', '10/2=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,52 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[48, 55, 5], Operations: ['10/2=5'] Exploring Operation: 55-5=50, Resulting Numbers: [48, 50] Generated Node #0,0,0: 52:[48, 50] Operation: 55-5=50 Exploring Operation: 48+5=53, Resulting Numbers: [55, 53] Generated Node #0,0,1: 52:[55, 53] Operation: 48+5=53 Exploring Operation: 55-48=7, Resulting Numbers: [5, 7] Generated Node #0,0,2: 52:[5, 7] Operation: 55-48=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[55, 53], Operations: ['10/2=5', '48+5=53'] Exploring Operation: 55-53=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 55+53=108, Resulting Numbers: [108] 108,52 unequal: No Solution Exploring Operation: 55*53=2915, Resulting Numbers: [2915] 2915,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[5, 7], Operations: ['10/2=5', '55-48=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,52 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[48, 50], Operations: ['10/2=5', '55-5=50'] Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,52 unequal: No Solution Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,52 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[48, 55, 12], Operations: ['2+10=12'] Exploring Operation: 48+12=60, Resulting Numbers: [55, 60] Generated Node #0,1,0: 52:[55, 60] Operation: 48+12=60 Exploring Operation: 48/12=4, Resulting Numbers: [55, 4] Generated Node #0,1,1: 52:[55, 4] Operation: 48/12=4 Exploring Operation: 55-48=7, Resulting Numbers: [12, 7] Generated Node #0,1,2: 52:[12, 7] Operation: 55-48=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[55, 4], Operations: ['2+10=12', '48/12=4'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 55+4=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 55*4=220, Resulting Numbers: [220] 220,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[12, 7], Operations: ['2+10=12', '55-48=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,52 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,52 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[55, 60], Operations: ['2+10=12', '48+12=60'] Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,52 unequal: No Solution Exploring Operation: 55*60=3300, Resulting Numbers: [3300] 3300,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 34, 77, 23, 21 ]
86
[ "77-34=43", "23-21=2", "43*2=86" ]
Current State: 86:[34, 77, 23, 21], Operations: [] Exploring Operation: 77-34=43, Resulting Numbers: [23, 21, 43] Generated Node #2: [23, 21, 43] from Operation: 77-34=43 Current State: 86:[23, 21, 43], Operations: ['77-34=43'] Exploring Operation: 23-21=2, Resulting Numbers: [43, 2] Generated Node #3: [43, 2] from Operation: 23-21=2 Current State: 86:[43, 2], Operations: ['77-34=43', '23-21=2'] Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[34, 77, 23, 21], Operations: [] Exploring Operation: 23-21=2, Resulting Numbers: [34, 77, 2] Generated Node #0,0: 86:[34, 77, 2] Operation: 23-21=2 Exploring Operation: 23+21=44, Resulting Numbers: [34, 77, 44] Generated Node #0,1: 86:[34, 77, 44] Operation: 23+21=44 Moving to Node #0,0 Current State: 86:[34, 77, 2], Operations: ['23-21=2'] Exploring Operation: 77-34=43, Resulting Numbers: [2, 43] Generated Node #0,0,0: 86:[2, 43] Operation: 77-34=43 Exploring Operation: 34+2=36, Resulting Numbers: [77, 36] Generated Node #0,0,1: 86:[77, 36] Operation: 34+2=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[2, 43], Operations: ['23-21=2', '77-34=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[34, 77, 23, 21], Operations: [] Exploring Operation: 23-21=2, Resulting Numbers: [34, 77, 2] Generated Node #0,0: 86:[34, 77, 2] Operation: 23-21=2 Moving to Node #0,0 Current State: 86:[34, 77, 2], Operations: ['23-21=2'] Exploring Operation: 77-34=43, Resulting Numbers: [2, 43] Generated Node #0,0,0: 86:[2, 43] Operation: 77-34=43 Moving to Node #0,0,0 Current State: 86:[2, 43], Operations: ['23-21=2', '77-34=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 38, 98, 8, 45 ]
62
[ "38+98=136", "136/8=17", "45+17=62" ]
Current State: 62:[38, 98, 8, 45], Operations: [] Exploring Operation: 38+98=136, Resulting Numbers: [8, 45, 136] Generated Node #2: [8, 45, 136] from Operation: 38+98=136 Current State: 62:[8, 45, 136], Operations: ['38+98=136'] Exploring Operation: 136/8=17, Resulting Numbers: [45, 17] Generated Node #3: [45, 17] from Operation: 136/8=17 Current State: 62:[45, 17], Operations: ['38+98=136', '136/8=17'] Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[38, 98, 8, 45], Operations: [] Exploring Operation: 98-38=60, Resulting Numbers: [8, 45, 60] Generated Node #0,0: 62:[8, 45, 60] Operation: 98-38=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[8, 45, 60], Operations: ['98-38=60'] Exploring Operation: 45-8=37, Resulting Numbers: [60, 37] Generated Node #0,0,0: 62:[60, 37] Operation: 45-8=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[60, 37], Operations: ['98-38=60', '45-8=37'] Exploring Operation: 60-37=23, Resulting Numbers: [23] 23,62 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
[ 62, 48, 37, 57 ]
17
[ "62-57=5", "48+37=85", "85/5=17" ]
Current State: 17:[62, 48, 37, 57], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [48, 37, 5] Generated Node #2: [48, 37, 5] from Operation: 62-57=5 Current State: 17:[48, 37, 5], Operations: ['62-57=5'] Exploring Operation: 48+37=85, Resulting Numbers: [5, 85] Generated Node #3: [5, 85] from Operation: 48+37=85 Current State: 17:[5, 85], Operations: ['62-57=5', '48+37=85'] Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[62, 48, 37, 57], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [37, 57, 14] Generated Node #0,0: 17:[37, 57, 14] Operation: 62-48=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[37, 57, 14], Operations: ['62-48=14'] Exploring Operation: 57-37=20, Resulting Numbers: [14, 20] Generated Node #0,0,0: 17:[14, 20] Operation: 57-37=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[14, 20], Operations: ['62-48=14', '57-37=20'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,17 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
[ 3, 27, 27, 73 ]
91
[ "27/3=9", "27+73=100", "100-9=91" ]
Current State: 91:[3, 27, 27, 73], Operations: [] Exploring Operation: 27/3=9, Resulting Numbers: [73, 9] Generated Node #2: [73, 9] from Operation: 27/3=9 Current State: 91:[73, 9], Operations: ['27/3=9'] Exploring Operation: 27+73=100, Resulting Numbers: [9, 100] Generated Node #3: [9, 100] from Operation: 27+73=100 Current State: 91:[9, 100], Operations: ['27/3=9', '27+73=100'] Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[3, 27, 27, 73], Operations: [] Exploring Operation: 27+73=100, Resulting Numbers: [3, 27, 100] Generated Node #0,0: 91:[3, 27, 100] Operation: 27+73=100 Exploring Operation: 27+73=100, Resulting Numbers: [3, 27, 100] Generated Node #0,1: 91:[3, 27, 100] Operation: 27+73=100 Moving to Node #0,0 Current State: 91:[3, 27, 100], Operations: ['27+73=100'] Exploring Operation: 27/3=9, Resulting Numbers: [100, 9] Generated Node #0,0,0: 91:[100, 9] Operation: 27/3=9 Exploring Operation: 3*27=81, Resulting Numbers: [100, 81] Generated Node #0,0,1: 91:[100, 81] Operation: 3*27=81 Moving to Node #0,1 Current State: 91:[3, 27, 100], Operations: ['27+73=100'] Exploring Operation: 27/3=9, Resulting Numbers: [100, 9] Generated Node #0,1,0: 91:[100, 9] Operation: 27/3=9 Exploring Operation: 3*27=81, Resulting Numbers: [100, 81] Generated Node #0,1,1: 91:[100, 81] Operation: 3*27=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[100, 9], Operations: ['27+73=100', '27/3=9'] Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[3, 27, 27, 73], Operations: [] Exploring Operation: 27+73=100, Resulting Numbers: [3, 27, 100] Generated Node #0,1: 91:[3, 27, 100] Operation: 27+73=100 Moving to Node #0,1 Current State: 91:[3, 27, 100], Operations: ['27+73=100'] Exploring Operation: 27/3=9, Resulting Numbers: [100, 9] Generated Node #0,1,0: 91:[100, 9] Operation: 27/3=9 Moving to Node #0,1,0 Current State: 91:[100, 9], Operations: ['27+73=100', '27/3=9'] Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 58, 88, 28, 63 ]
61
[ "88-58=30", "28+63=91", "91-30=61" ]
Current State: 61:[58, 88, 28, 63], Operations: [] Exploring Operation: 88-58=30, Resulting Numbers: [28, 63, 30] Generated Node #2: [28, 63, 30] from Operation: 88-58=30 Current State: 61:[28, 63, 30], Operations: ['88-58=30'] Exploring Operation: 28+63=91, Resulting Numbers: [30, 91] Generated Node #3: [30, 91] from Operation: 28+63=91 Current State: 61:[30, 91], Operations: ['88-58=30', '28+63=91'] Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[58, 88, 28, 63], Operations: [] Exploring Operation: 58+28=86, Resulting Numbers: [88, 63, 86] Generated Node #0,0: 61:[88, 63, 86] Operation: 58+28=86 Exploring Operation: 88+28=116, Resulting Numbers: [58, 63, 116] Generated Node #0,1: 61:[58, 63, 116] Operation: 88+28=116 Exploring Operation: 63-28=35, Resulting Numbers: [58, 88, 35] Generated Node #0,2: 61:[58, 88, 35] Operation: 63-28=35 Exploring Operation: 88-28=60, Resulting Numbers: [58, 63, 60] Generated Node #0,3: 61:[58, 63, 60] Operation: 88-28=60 Exploring Operation: 58-28=30, Resulting Numbers: [88, 63, 30] Generated Node #0,4: 61:[88, 63, 30] Operation: 58-28=30 Moving to Node #0,3 Current State: 61:[58, 63, 60], Operations: ['88-28=60'] Exploring Operation: 63-60=3, Resulting Numbers: [58, 3] Generated Node #0,3,0: 61:[58, 3] Operation: 63-60=3 Exploring Operation: 63-58=5, Resulting Numbers: [60, 5] Generated Node #0,3,1: 61:[60, 5] Operation: 63-58=5 Exploring Operation: 58+60=118, Resulting Numbers: [63, 118] Generated Node #0,3,2: 61:[63, 118] Operation: 58+60=118 Exploring Operation: 60-58=2, Resulting Numbers: [63, 2] Generated Node #0,3,3: 61:[63, 2] Operation: 60-58=2 Exploring Operation: 58+63=121, Resulting Numbers: [60, 121] Generated Node #0,3,4: 61:[60, 121] Operation: 58+63=121 Moving to Node #0,0 Current State: 61:[88, 63, 86], Operations: ['58+28=86'] Exploring Operation: 88-63=25, Resulting Numbers: [86, 25] Generated Node #0,0,0: 61:[86, 25] Operation: 88-63=25 Exploring Operation: 88+63=151, Resulting Numbers: [86, 151] Generated Node #0,0,1: 61:[86, 151] Operation: 88+63=151 Exploring Operation: 86-63=23, Resulting Numbers: [88, 23] Generated Node #0,0,2: 61:[88, 23] Operation: 86-63=23 Exploring Operation: 88+86=174, Resulting Numbers: [63, 174] Generated Node #0,0,3: 61:[63, 174] Operation: 88+86=174 Exploring Operation: 88-86=2, Resulting Numbers: [63, 2] Generated Node #0,0,4: 61:[63, 2] Operation: 88-86=2 Moving to Node #0,2 Current State: 61:[58, 88, 35], Operations: ['63-28=35'] Exploring Operation: 88-58=30, Resulting Numbers: [35, 30] Generated Node #0,2,0: 61:[35, 30] Operation: 88-58=30 Exploring Operation: 88-35=53, Resulting Numbers: [58, 53] Generated Node #0,2,1: 61:[58, 53] Operation: 88-35=53 Exploring Operation: 88+35=123, Resulting Numbers: [58, 123] Generated Node #0,2,2: 61:[58, 123] Operation: 88+35=123 Exploring Operation: 58+35=93, Resulting Numbers: [88, 93] Generated Node #0,2,3: 61:[88, 93] Operation: 58+35=93 Exploring Operation: 58-35=23, Resulting Numbers: [88, 23] Generated Node #0,2,4: 61:[88, 23] Operation: 58-35=23 Moving to Node #0,1 Current State: 61:[58, 63, 116], Operations: ['88+28=116'] Exploring Operation: 63-58=5, Resulting Numbers: [116, 5] Generated Node #0,1,0: 61:[116, 5] Operation: 63-58=5 Exploring Operation: 58+63=121, Resulting Numbers: [116, 121] Generated Node #0,1,1: 61:[116, 121] Operation: 58+63=121 Exploring Operation: 116-63=53, Resulting Numbers: [58, 53] Generated Node #0,1,2: 61:[58, 53] Operation: 116-63=53 Exploring Operation: 116-58=58, Resulting Numbers: [63, 58] Generated Node #0,1,3: 61:[63, 58] Operation: 116-58=58 Exploring Operation: 116/58=2, Resulting Numbers: [63, 2] Generated Node #0,1,4: 61:[63, 2] Operation: 116/58=2 Moving to Node #0,4 Current State: 61:[88, 63, 30], Operations: ['58-28=30'] Exploring Operation: 88+30=118, Resulting Numbers: [63, 118] Generated Node #0,4,0: 61:[63, 118] Operation: 88+30=118 Exploring Operation: 88-63=25, Resulting Numbers: [30, 25] Generated Node #0,4,1: 61:[30, 25] Operation: 88-63=25 Exploring Operation: 63-30=33, Resulting Numbers: [88, 33] Generated Node #0,4,2: 61:[88, 33] Operation: 63-30=33 Exploring Operation: 63+30=93, Resulting Numbers: [88, 93] Generated Node #0,4,3: 61:[88, 93] Operation: 63+30=93 Exploring Operation: 88-30=58, Resulting Numbers: [63, 58] Generated Node #0,4,4: 61:[63, 58] Operation: 88-30=58 Moving to Node #0,1,3 Current State: 61:[63, 58], Operations: ['88+28=116', '116-58=58'] Exploring Operation: 63-58=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 63*58=3654, Resulting Numbers: [3654] 3654,61 unequal: No Solution Exploring Operation: 63+58=121, Resulting Numbers: [121] 121,61 unequal: No Solution Moving to Node #0,4,4 Current State: 61:[63, 58], Operations: ['58-28=30', '88-30=58'] Exploring Operation: 63+58=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 63*58=3654, Resulting Numbers: [3654] 3654,61 unequal: No Solution Exploring Operation: 63-58=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[58, 53], Operations: ['63-28=35', '88-35=53'] Exploring Operation: 58+53=111, Resulting Numbers: [111] 111,61 unequal: No Solution Exploring Operation: 58-53=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 58*53=3074, Resulting Numbers: [3074] 3074,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[58, 53], Operations: ['88+28=116', '116-63=53'] Exploring Operation: 58*53=3074, Resulting Numbers: [3074] 3074,61 unequal: No Solution Exploring Operation: 58+53=111, Resulting Numbers: [111] 111,61 unequal: No Solution Exploring Operation: 58-53=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,4,2 Current State: 61:[88, 33], Operations: ['58-28=30', '63-30=33'] Exploring Operation: 88+33=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 88*33=2904, Resulting Numbers: [2904] 2904,61 unequal: No Solution Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[35, 30], Operations: ['63-28=35', '88-58=30'] Exploring Operation: 35*30=1050, Resulting Numbers: [1050] 1050,61 unequal: No Solution Exploring Operation: 35+30=65, Resulting Numbers: [65] 65,61 unequal: No Solution Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[60, 5], Operations: ['88-28=60', '63-58=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,61 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,61 unequal: No Solution Exploring Operation: 60*5=300, Resulting Numbers: [300] 300,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[88, 93], Operations: ['63-28=35', '58+35=93'] Exploring Operation: 93-88=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 88+93=181, Resulting Numbers: [181] 181,61 unequal: No Solution Exploring Operation: 88*93=8184, Resulting Numbers: [8184] 8184,61 unequal: No Solution Moving to Node #0,4,3 Current State: 61:[88, 93], Operations: ['58-28=30', '63+30=93'] Exploring Operation: 88+93=181, Resulting Numbers: [181] 181,61 unequal: No Solution Exploring Operation: 88*93=8184, Resulting Numbers: [8184] 8184,61 unequal: No Solution Exploring Operation: 93-88=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,4,0 Current State: 61:[63, 118], Operations: ['58-28=30', '88+30=118'] Exploring Operation: 118-63=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 63+118=181, Resulting Numbers: [181] 181,61 unequal: No Solution Exploring Operation: 63*118=7434, Resulting Numbers: [7434] 7434,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[63, 118], Operations: ['88-28=60', '58+60=118'] Exploring Operation: 118-63=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 63+118=181, Resulting Numbers: [181] 181,61 unequal: No Solution Exploring Operation: 63*118=7434, Resulting Numbers: [7434] 7434,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[63, 2], Operations: ['58+28=86', '88-86=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[58, 88, 28, 63], Operations: [] Exploring Operation: 58+28=86, Resulting Numbers: [88, 63, 86] Generated Node #0,0: 61:[88, 63, 86] Operation: 58+28=86 Moving to Node #0,0 Current State: 61:[88, 63, 86], Operations: ['58+28=86'] Exploring Operation: 88-86=2, Resulting Numbers: [63, 2] Generated Node #0,0,4: 61:[63, 2] Operation: 88-86=2 Moving to Node #0,0,4 Current State: 61:[63, 2], Operations: ['58+28=86', '88-86=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.940104
hs_5
mult_heuristic
[ 1, 57, 98, 17 ]
23
[ "1+57=58", "98-17=81", "81-58=23" ]
Current State: 23:[1, 57, 98, 17], Operations: [] Exploring Operation: 1+57=58, Resulting Numbers: [98, 17, 58] Generated Node #2: [98, 17, 58] from Operation: 1+57=58 Current State: 23:[98, 17, 58], Operations: ['1+57=58'] Exploring Operation: 98-17=81, Resulting Numbers: [58, 81] Generated Node #3: [58, 81] from Operation: 98-17=81 Current State: 23:[58, 81], Operations: ['1+57=58', '98-17=81'] Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[1, 57, 98, 17], Operations: [] Exploring Operation: 57-1=56, Resulting Numbers: [98, 17, 56] Generated Node #0,0: 23:[98, 17, 56] Operation: 57-1=56 Exploring Operation: 98-57=41, Resulting Numbers: [1, 17, 41] Generated Node #0,1: 23:[1, 17, 41] Operation: 98-57=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[1, 17, 41], Operations: ['98-57=41'] Exploring Operation: 1+17=18, Resulting Numbers: [41, 18] Generated Node #0,1,0: 23:[41, 18] Operation: 1+17=18 Exploring Operation: 41-1=40, Resulting Numbers: [17, 40] Generated Node #0,1,1: 23:[17, 40] Operation: 41-1=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[41, 18], Operations: ['98-57=41', '1+17=18'] Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[1, 57, 98, 17], Operations: [] Exploring Operation: 98-57=41, Resulting Numbers: [1, 17, 41] Generated Node #0,1: 23:[1, 17, 41] Operation: 98-57=41 Moving to Node #0,1 Current State: 23:[1, 17, 41], Operations: ['98-57=41'] Exploring Operation: 1+17=18, Resulting Numbers: [41, 18] Generated Node #0,1,0: 23:[41, 18] Operation: 1+17=18 Moving to Node #0,1,0 Current State: 23:[41, 18], Operations: ['98-57=41', '1+17=18'] Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 88, 72, 8, 56 ]
64
[ "88-72=16", "56-8=48", "16+48=64" ]
Current State: 64:[88, 72, 8, 56], Operations: [] Exploring Operation: 88-72=16, Resulting Numbers: [8, 56, 16] Generated Node #2: [8, 56, 16] from Operation: 88-72=16 Current State: 64:[8, 56, 16], Operations: ['88-72=16'] Exploring Operation: 56-8=48, Resulting Numbers: [16, 48] Generated Node #3: [16, 48] from Operation: 56-8=48 Current State: 64:[16, 48], Operations: ['88-72=16', '56-8=48'] Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[88, 72, 8, 56], Operations: [] Exploring Operation: 88-72=16, Resulting Numbers: [8, 56, 16] Generated Node #0,0: 64:[8, 56, 16] Operation: 88-72=16 Exploring Operation: 88-56=32, Resulting Numbers: [72, 8, 32] Generated Node #0,1: 64:[72, 8, 32] Operation: 88-56=32 Moving to Node #0,0 Current State: 64:[8, 56, 16], Operations: ['88-72=16'] Exploring Operation: 8+56=64, Resulting Numbers: [16, 64] Generated Node #0,0,0: 64:[16, 64] Operation: 8+56=64 Exploring Operation: 56/8=7, Resulting Numbers: [16, 7] Generated Node #0,0,1: 64:[16, 7] Operation: 56/8=7 Moving to Node #0,1 Current State: 64:[72, 8, 32], Operations: ['88-56=32'] Exploring Operation: 72/8=9, Resulting Numbers: [32, 9] Generated Node #0,1,0: 64:[32, 9] Operation: 72/8=9 Exploring Operation: 72-8=64, Resulting Numbers: [32, 64] Generated Node #0,1,1: 64:[32, 64] Operation: 72-8=64 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[32, 64], Operations: ['88-56=32', '72-8=64'] Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,64 unequal: No Solution Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,64 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 #0,1,0 Current State: 64:[32, 9], Operations: ['88-56=32', '72/8=9'] Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 32+9=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 #0,0,0 Current State: 64:[16, 64], Operations: ['88-72=16', '8+56=64'] Exploring Operation: 16+64=80, Resulting Numbers: [80] 80,64 unequal: No Solution Exploring Operation: 64/16=4, Resulting Numbers: [4] 4,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[16, 7], Operations: ['88-72=16', '56/8=7'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,64 unequal: No Solution Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,64 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 91, 23, 61, 5 ]
12
[ "91-23=68", "61-5=56", "68-56=12" ]
Current State: 12:[91, 23, 61, 5], Operations: [] Exploring Operation: 91-23=68, Resulting Numbers: [61, 5, 68] Generated Node #2: [61, 5, 68] from Operation: 91-23=68 Current State: 12:[61, 5, 68], Operations: ['91-23=68'] Exploring Operation: 61-5=56, Resulting Numbers: [68, 56] Generated Node #3: [68, 56] from Operation: 61-5=56 Current State: 12:[68, 56], Operations: ['91-23=68', '61-5=56'] Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[91, 23, 61, 5], Operations: [] Exploring Operation: 91-61=30, Resulting Numbers: [23, 5, 30] Generated Node #0,0: 12:[23, 5, 30] Operation: 91-61=30 Exploring Operation: 91-23=68, Resulting Numbers: [61, 5, 68] Generated Node #0,1: 12:[61, 5, 68] Operation: 91-23=68 Moving to Node #0,0 Current State: 12:[23, 5, 30], Operations: ['91-61=30'] Exploring Operation: 30-23=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 12:[5, 7] Operation: 30-23=7 Exploring Operation: 30/5=6, Resulting Numbers: [23, 6] Generated Node #0,0,1: 12:[23, 6] Operation: 30/5=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[5, 7], Operations: ['91-61=30', '30-23=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[91, 23, 61, 5], Operations: [] Exploring Operation: 91-61=30, Resulting Numbers: [23, 5, 30] Generated Node #0,0: 12:[23, 5, 30] Operation: 91-61=30 Moving to Node #0,0 Current State: 12:[23, 5, 30], Operations: ['91-61=30'] Exploring Operation: 30-23=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 12:[5, 7] Operation: 30-23=7 Moving to Node #0,0,0 Current State: 12:[5, 7], Operations: ['91-61=30', '30-23=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 36, 71, 10, 30 ]
67
[ "36+71=107", "10+30=40", "107-40=67" ]
Current State: 67:[36, 71, 10, 30], Operations: [] Exploring Operation: 36+71=107, Resulting Numbers: [10, 30, 107] Generated Node #2: [10, 30, 107] from Operation: 36+71=107 Current State: 67:[10, 30, 107], Operations: ['36+71=107'] Exploring Operation: 10+30=40, Resulting Numbers: [107, 40] Generated Node #3: [107, 40] from Operation: 10+30=40 Current State: 67:[107, 40], Operations: ['36+71=107', '10+30=40'] Exploring Operation: 107-40=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[36, 71, 10, 30], Operations: [] Exploring Operation: 36+10=46, Resulting Numbers: [71, 30, 46] Generated Node #0,0: 67:[71, 30, 46] Operation: 36+10=46 Exploring Operation: 36+30=66, Resulting Numbers: [71, 10, 66] Generated Node #0,1: 67:[71, 10, 66] Operation: 36+30=66 Moving to Node #0,0 Current State: 67:[71, 30, 46], Operations: ['36+10=46'] Exploring Operation: 71-30=41, Resulting Numbers: [46, 41] Generated Node #0,0,0: 67:[46, 41] Operation: 71-30=41 Exploring Operation: 30+46=76, Resulting Numbers: [71, 76] Generated Node #0,0,1: 67:[71, 76] Operation: 30+46=76 Moving to Node #0,1 Current State: 67:[71, 10, 66], Operations: ['36+30=66'] Exploring Operation: 71-10=61, Resulting Numbers: [66, 61] Generated Node #0,1,0: 67:[66, 61] Operation: 71-10=61 Exploring Operation: 10+66=76, Resulting Numbers: [71, 76] Generated Node #0,1,1: 67:[71, 76] Operation: 10+66=76 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[66, 61], Operations: ['36+30=66', '71-10=61'] Exploring Operation: 66-61=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 66+61=127, Resulting Numbers: [127] 127,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[71, 76], Operations: ['36+30=66', '10+66=76'] Exploring Operation: 71+76=147, Resulting Numbers: [147] 147,67 unequal: No Solution Exploring Operation: 76-71=5, Resulting Numbers: [5] 5,67 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: 67:[71, 76], Operations: ['36+10=46', '30+46=76'] Exploring Operation: 76-71=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 71+76=147, Resulting Numbers: [147] 147,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[46, 41], Operations: ['36+10=46', '71-30=41'] Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 46+41=87, Resulting Numbers: [87] 87,67 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 61, 63, 36, 60 ]
98
[ "63-61=2", "36+60=96", "2+96=98" ]
Current State: 98:[61, 63, 36, 60], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [36, 60, 2] Generated Node #2: [36, 60, 2] from Operation: 63-61=2 Current State: 98:[36, 60, 2], Operations: ['63-61=2'] Exploring Operation: 36+60=96, Resulting Numbers: [2, 96] Generated Node #3: [2, 96] from Operation: 36+60=96 Current State: 98:[2, 96], Operations: ['63-61=2', '36+60=96'] Exploring Operation: 2+96=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[61, 63, 36, 60], Operations: [] Exploring Operation: 61+36=97, Resulting Numbers: [63, 60, 97] Generated Node #0,0: 98:[63, 60, 97] Operation: 61+36=97 Exploring Operation: 63+36=99, Resulting Numbers: [61, 60, 99] Generated Node #0,1: 98:[61, 60, 99] Operation: 63+36=99 Exploring Operation: 63-61=2, Resulting Numbers: [36, 60, 2] Generated Node #0,2: 98:[36, 60, 2] Operation: 63-61=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[61, 60, 99], Operations: ['63+36=99'] Exploring Operation: 99-60=39, Resulting Numbers: [61, 39] Generated Node #0,1,0: 98:[61, 39] Operation: 99-60=39 Exploring Operation: 99-61=38, Resulting Numbers: [60, 38] Generated Node #0,1,1: 98:[60, 38] Operation: 99-61=38 Exploring Operation: 61-60=1, Resulting Numbers: [99, 1] Generated Node #0,1,2: 98:[99, 1] Operation: 61-60=1 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[99, 1], Operations: ['63+36=99', '61-60=1'] Exploring Operation: 99/1=99, Resulting Numbers: [99] 99,98 unequal: No Solution Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[61, 63, 36, 60], Operations: [] Exploring Operation: 63+36=99, Resulting Numbers: [61, 60, 99] Generated Node #0,1: 98:[61, 60, 99] Operation: 63+36=99 Moving to Node #0,1 Current State: 98:[61, 60, 99], Operations: ['63+36=99'] Exploring Operation: 61-60=1, Resulting Numbers: [99, 1] Generated Node #0,1,2: 98:[99, 1] Operation: 61-60=1 Moving to Node #0,1,2 Current State: 98:[99, 1], Operations: ['63+36=99', '61-60=1'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 67, 7, 33, 76 ]
49
[ "67-7=60", "33+76=109", "109-60=49" ]
Current State: 49:[67, 7, 33, 76], Operations: [] Exploring Operation: 67-7=60, Resulting Numbers: [33, 76, 60] Generated Node #2: [33, 76, 60] from Operation: 67-7=60 Current State: 49:[33, 76, 60], Operations: ['67-7=60'] Exploring Operation: 33+76=109, Resulting Numbers: [60, 109] Generated Node #3: [60, 109] from Operation: 33+76=109 Current State: 49:[60, 109], Operations: ['67-7=60', '33+76=109'] Exploring Operation: 109-60=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[67, 7, 33, 76], Operations: [] Exploring Operation: 76-67=9, Resulting Numbers: [7, 33, 9] Generated Node #0,0: 49:[7, 33, 9] Operation: 76-67=9 Exploring Operation: 76-33=43, Resulting Numbers: [67, 7, 43] Generated Node #0,1: 49:[67, 7, 43] Operation: 76-33=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[7, 33, 9], Operations: ['76-67=9'] Exploring Operation: 7+33=40, Resulting Numbers: [9, 40] Generated Node #0,0,0: 49:[9, 40] Operation: 7+33=40 Exploring Operation: 33+9=42, Resulting Numbers: [7, 42] Generated Node #0,0,1: 49:[7, 42] Operation: 33+9=42 Moving to Node #0,0,1 Current State: 49:[7, 42], Operations: ['76-67=9', '33+9=42'] Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[67, 7, 33, 76], Operations: [] Exploring Operation: 76-67=9, Resulting Numbers: [7, 33, 9] Generated Node #0,0: 49:[7, 33, 9] Operation: 76-67=9 Moving to Node #0,0 Current State: 49:[7, 33, 9], Operations: ['76-67=9'] Exploring Operation: 33+9=42, Resulting Numbers: [7, 42] Generated Node #0,0,1: 49:[7, 42] Operation: 33+9=42 Moving to Node #0,0,1 Current State: 49:[7, 42], Operations: ['76-67=9', '33+9=42'] Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 20, 54, 58, 65 ]
89
[ "54-20=34", "58+65=123", "123-34=89" ]
Current State: 89:[20, 54, 58, 65], Operations: [] Exploring Operation: 54-20=34, Resulting Numbers: [58, 65, 34] Generated Node #2: [58, 65, 34] from Operation: 54-20=34 Current State: 89:[58, 65, 34], Operations: ['54-20=34'] Exploring Operation: 58+65=123, Resulting Numbers: [34, 123] Generated Node #3: [34, 123] from Operation: 58+65=123 Current State: 89:[34, 123], Operations: ['54-20=34', '58+65=123'] Exploring Operation: 123-34=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[20, 54, 58, 65], Operations: [] Exploring Operation: 20+54=74, Resulting Numbers: [58, 65, 74] Generated Node #0,0: 89:[58, 65, 74] Operation: 20+54=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[58, 65, 74], Operations: ['20+54=74'] Exploring Operation: 58+65=123, Resulting Numbers: [74, 123] Generated Node #0,0,0: 89:[74, 123] Operation: 58+65=123 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[74, 123], Operations: ['20+54=74', '58+65=123'] Exploring Operation: 123-74=49, Resulting Numbers: [49] 49,89 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_1
sum_heuristic
[ 83, 13, 7, 3 ]
74
[ "83-13=70", "7-3=4", "70+4=74" ]
Current State: 74:[83, 13, 7, 3], Operations: [] Exploring Operation: 83-13=70, Resulting Numbers: [7, 3, 70] Generated Node #2: [7, 3, 70] from Operation: 83-13=70 Current State: 74:[7, 3, 70], Operations: ['83-13=70'] Exploring Operation: 7-3=4, Resulting Numbers: [70, 4] Generated Node #3: [70, 4] from Operation: 7-3=4 Current State: 74:[70, 4], Operations: ['83-13=70', '7-3=4'] Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[83, 13, 7, 3], Operations: [] Exploring Operation: 83-13=70, Resulting Numbers: [7, 3, 70] Generated Node #0,0: 74:[7, 3, 70] Operation: 83-13=70 Exploring Operation: 83-7=76, Resulting Numbers: [13, 3, 76] Generated Node #0,1: 74:[13, 3, 76] Operation: 83-7=76 Moving to Node #0,0 Current State: 74:[7, 3, 70], Operations: ['83-13=70'] Exploring Operation: 7-3=4, Resulting Numbers: [70, 4] Generated Node #0,0,0: 74:[70, 4] Operation: 7-3=4 Exploring Operation: 7+70=77, Resulting Numbers: [3, 77] Generated Node #0,0,1: 74:[3, 77] Operation: 7+70=77 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[3, 77], Operations: ['83-13=70', '7+70=77'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[83, 13, 7, 3], Operations: [] Exploring Operation: 83-13=70, Resulting Numbers: [7, 3, 70] Generated Node #0,0: 74:[7, 3, 70] Operation: 83-13=70 Moving to Node #0,0 Current State: 74:[7, 3, 70], Operations: ['83-13=70'] Exploring Operation: 7+70=77, Resulting Numbers: [3, 77] Generated Node #0,0,1: 74:[3, 77] Operation: 7+70=77 Moving to Node #0,0,1 Current State: 74:[3, 77], Operations: ['83-13=70', '7+70=77'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 44, 63, 46, 52 ]
79
[ "63-44=19", "46+52=98", "98-19=79" ]
Current State: 79:[44, 63, 46, 52], Operations: [] Exploring Operation: 63-44=19, Resulting Numbers: [46, 52, 19] Generated Node #2: [46, 52, 19] from Operation: 63-44=19 Current State: 79:[46, 52, 19], Operations: ['63-44=19'] Exploring Operation: 46+52=98, Resulting Numbers: [19, 98] Generated Node #3: [19, 98] from Operation: 46+52=98 Current State: 79:[19, 98], Operations: ['63-44=19', '46+52=98'] Exploring Operation: 98-19=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[44, 63, 46, 52], Operations: [] Exploring Operation: 44+46=90, Resulting Numbers: [63, 52, 90] Generated Node #0,0: 79:[63, 52, 90] Operation: 44+46=90 Exploring Operation: 44+52=96, Resulting Numbers: [63, 46, 96] Generated Node #0,1: 79:[63, 46, 96] Operation: 44+52=96 Exploring Operation: 46+52=98, Resulting Numbers: [44, 63, 98] Generated Node #0,2: 79:[44, 63, 98] Operation: 46+52=98 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[63, 52, 90], Operations: ['44+46=90'] Exploring Operation: 90-52=38, Resulting Numbers: [63, 38] Generated Node #0,0,0: 79:[63, 38] Operation: 90-52=38 Exploring Operation: 63+52=115, Resulting Numbers: [90, 115] Generated Node #0,0,1: 79:[90, 115] Operation: 63+52=115 Exploring Operation: 63-52=11, Resulting Numbers: [90, 11] Generated Node #0,0,2: 79:[90, 11] Operation: 63-52=11 Moving to Node #0,0,1 Current State: 79:[90, 115], Operations: ['44+46=90', '63+52=115'] Exploring Operation: 90+115=205, Resulting Numbers: [205] 205,79 unequal: No Solution Exploring Operation: 90*115=10350, Resulting Numbers: [10350] 10350,79 unequal: No Solution Exploring Operation: 115-90=25, Resulting Numbers: [25] 25,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[63, 38], Operations: ['44+46=90', '90-52=38'] Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 63*38=2394, Resulting Numbers: [2394] 2394,79 unequal: No Solution Exploring Operation: 63+38=101, Resulting Numbers: [101] 101,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[90, 11], Operations: ['44+46=90', '63-52=11'] Exploring Operation: 90-11=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[44, 63, 46, 52], Operations: [] Exploring Operation: 44+46=90, Resulting Numbers: [63, 52, 90] Generated Node #0,0: 79:[63, 52, 90] Operation: 44+46=90 Moving to Node #0,0 Current State: 79:[63, 52, 90], Operations: ['44+46=90'] Exploring Operation: 63-52=11, Resulting Numbers: [90, 11] Generated Node #0,0,2: 79:[90, 11] Operation: 63-52=11 Moving to Node #0,0,2 Current State: 79:[90, 11], Operations: ['44+46=90', '63-52=11'] Exploring Operation: 90-11=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 72, 50, 1, 30 ]
92
[ "72+50=122", "1*30=30", "122-30=92" ]
Current State: 92:[72, 50, 1, 30], Operations: [] Exploring Operation: 72+50=122, Resulting Numbers: [1, 30, 122] Generated Node #2: [1, 30, 122] from Operation: 72+50=122 Current State: 92:[1, 30, 122], Operations: ['72+50=122'] Exploring Operation: 1*30=30, Resulting Numbers: [122, 30] Generated Node #3: [122, 30] from Operation: 1*30=30 Current State: 92:[122, 30], Operations: ['72+50=122', '1*30=30'] Exploring Operation: 122-30=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[72, 50, 1, 30], Operations: [] Exploring Operation: 50-30=20, Resulting Numbers: [72, 1, 20] Generated Node #0,0: 92:[72, 1, 20] Operation: 50-30=20 Exploring Operation: 72+1=73, Resulting Numbers: [50, 30, 73] Generated Node #0,1: 92:[50, 30, 73] Operation: 72+1=73 Exploring Operation: 72-30=42, Resulting Numbers: [50, 1, 42] Generated Node #0,2: 92:[50, 1, 42] Operation: 72-30=42 Exploring Operation: 72+30=102, Resulting Numbers: [50, 1, 102] Generated Node #0,3: 92:[50, 1, 102] Operation: 72+30=102 Exploring Operation: 72-50=22, Resulting Numbers: [1, 30, 22] Generated Node #0,4: 92:[1, 30, 22] Operation: 72-50=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[50, 1, 42], Operations: ['72-30=42'] Exploring Operation: 50-1=49, Resulting Numbers: [42, 49] Generated Node #0,2,0: 92:[42, 49] Operation: 50-1=49 Exploring Operation: 1+42=43, Resulting Numbers: [50, 43] Generated Node #0,2,1: 92:[50, 43] Operation: 1+42=43 Exploring Operation: 50*1=50, Resulting Numbers: [42, 50] Generated Node #0,2,2: 92:[42, 50] Operation: 50*1=50 Exploring Operation: 50-42=8, Resulting Numbers: [1, 8] Generated Node #0,2,3: 92:[1, 8] Operation: 50-42=8 Exploring Operation: 50+42=92, Resulting Numbers: [1, 92] Generated Node #0,2,4: 92:[1, 92] Operation: 50+42=92 Moving to Node #0,2,4 Current State: 92:[1, 92], Operations: ['72-30=42', '50+42=92'] Exploring Operation: 1*92=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[72, 50, 1, 30], Operations: [] Exploring Operation: 72-30=42, Resulting Numbers: [50, 1, 42] Generated Node #0,2: 92:[50, 1, 42] Operation: 72-30=42 Moving to Node #0,2 Current State: 92:[50, 1, 42], Operations: ['72-30=42'] Exploring Operation: 50+42=92, Resulting Numbers: [1, 92] Generated Node #0,2,4: 92:[1, 92] Operation: 50+42=92 Moving to Node #0,2,4 Current State: 92:[1, 92], Operations: ['72-30=42', '50+42=92'] Exploring Operation: 1*92=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 79, 98, 16, 23 ]
58
[ "98-79=19", "16+23=39", "19+39=58" ]
Current State: 58:[79, 98, 16, 23], Operations: [] Exploring Operation: 98-79=19, Resulting Numbers: [16, 23, 19] Generated Node #2: [16, 23, 19] from Operation: 98-79=19 Current State: 58:[16, 23, 19], Operations: ['98-79=19'] Exploring Operation: 16+23=39, Resulting Numbers: [19, 39] Generated Node #3: [19, 39] from Operation: 16+23=39 Current State: 58:[19, 39], Operations: ['98-79=19', '16+23=39'] Exploring Operation: 19+39=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[79, 98, 16, 23], Operations: [] Exploring Operation: 98-79=19, Resulting Numbers: [16, 23, 19] Generated Node #0,0: 58:[16, 23, 19] Operation: 98-79=19 Exploring Operation: 79-16=63, Resulting Numbers: [98, 23, 63] Generated Node #0,1: 58:[98, 23, 63] Operation: 79-16=63 Exploring Operation: 79-23=56, Resulting Numbers: [98, 16, 56] Generated Node #0,2: 58:[98, 16, 56] Operation: 79-23=56 Exploring Operation: 98-23=75, Resulting Numbers: [79, 16, 75] Generated Node #0,3: 58:[79, 16, 75] Operation: 98-23=75 Exploring Operation: 98-16=82, Resulting Numbers: [79, 23, 82] Generated Node #0,4: 58:[79, 23, 82] Operation: 98-16=82 Moving to Node #0,0 Current State: 58:[16, 23, 19], Operations: ['98-79=19'] Exploring Operation: 16+23=39, Resulting Numbers: [19, 39] Generated Node #0,0,0: 58:[19, 39] Operation: 16+23=39 Exploring Operation: 19-16=3, Resulting Numbers: [23, 3] Generated Node #0,0,1: 58:[23, 3] Operation: 19-16=3 Exploring Operation: 16+19=35, Resulting Numbers: [23, 35] Generated Node #0,0,2: 58:[23, 35] Operation: 16+19=35 Exploring Operation: 23-16=7, Resulting Numbers: [19, 7] Generated Node #0,0,3: 58:[19, 7] Operation: 23-16=7 Exploring Operation: 23-19=4, Resulting Numbers: [16, 4] Generated Node #0,0,4: 58:[16, 4] Operation: 23-19=4 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 58:[23, 3], Operations: ['98-79=19', '19-16=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,58 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 58:[23, 35], Operations: ['98-79=19', '16+19=35'] Exploring Operation: 23*35=805, Resulting Numbers: [805] 805,58 unequal: No Solution Exploring Operation: 23+35=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[79, 98, 16, 23], Operations: [] Exploring Operation: 98-79=19, Resulting Numbers: [16, 23, 19] Generated Node #0,0: 58:[16, 23, 19] Operation: 98-79=19 Moving to Node #0,0 Current State: 58:[16, 23, 19], Operations: ['98-79=19'] Exploring Operation: 16+19=35, Resulting Numbers: [23, 35] Generated Node #0,0,2: 58:[23, 35] Operation: 16+19=35 Moving to Node #0,0,2 Current State: 58:[23, 35], Operations: ['98-79=19', '16+19=35'] Exploring Operation: 23+35=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 17, 78, 76, 79 ]
31
[ "79-17=62", "78-76=2", "62/2=31" ]
Current State: 31:[17, 78, 76, 79], Operations: [] Exploring Operation: 79-17=62, Resulting Numbers: [78, 76, 62] Generated Node #2: [78, 76, 62] from Operation: 79-17=62 Current State: 31:[78, 76, 62], Operations: ['79-17=62'] Exploring Operation: 78-76=2, Resulting Numbers: [62, 2] Generated Node #3: [62, 2] from Operation: 78-76=2 Current State: 31:[62, 2], Operations: ['79-17=62', '78-76=2'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[17, 78, 76, 79], Operations: [] Exploring Operation: 76-17=59, Resulting Numbers: [78, 79, 59] Generated Node #0,0: 31:[78, 79, 59] Operation: 76-17=59 Exploring Operation: 79-78=1, Resulting Numbers: [17, 76, 1] Generated Node #0,1: 31:[17, 76, 1] Operation: 79-78=1 Exploring Operation: 78-17=61, Resulting Numbers: [76, 79, 61] Generated Node #0,2: 31:[76, 79, 61] Operation: 78-17=61 Exploring Operation: 79-76=3, Resulting Numbers: [17, 78, 3] Generated Node #0,3: 31:[17, 78, 3] Operation: 79-76=3 Exploring Operation: 78-76=2, Resulting Numbers: [17, 79, 2] Generated Node #0,4: 31:[17, 79, 2] Operation: 78-76=2 Moving to Node #0,1 Current State: 31:[17, 76, 1], Operations: ['79-78=1'] Exploring Operation: 76-17=59, Resulting Numbers: [1, 59] Generated Node #0,1,0: 31:[1, 59] Operation: 76-17=59 Exploring Operation: 17/1=17, Resulting Numbers: [76, 17] Generated Node #0,1,1: 31:[76, 17] Operation: 17/1=17 Exploring Operation: 17*1=17, Resulting Numbers: [76, 17] Generated Node #0,1,2: 31:[76, 17] Operation: 17*1=17 Exploring Operation: 17+1=18, Resulting Numbers: [76, 18] Generated Node #0,1,3: 31:[76, 18] Operation: 17+1=18 Exploring Operation: 76-1=75, Resulting Numbers: [17, 75] Generated Node #0,1,4: 31:[17, 75] Operation: 76-1=75 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[1, 59], Operations: ['79-78=1', '76-17=59'] Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 1*59=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 #0,1,3 Current State: 31:[76, 18], Operations: ['79-78=1', '17+1=18'] Exploring Operation: 76*18=1368, Resulting Numbers: [1368] 1368,31 unequal: No Solution Exploring Operation: 76+18=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 76-18=58, Resulting Numbers: [58] 58,31 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:[17, 75], Operations: ['79-78=1', '76-1=75'] Exploring Operation: 17*75=1275, Resulting Numbers: [1275] 1275,31 unequal: No Solution Exploring Operation: 17+75=92, Resulting Numbers: [92] 92,31 unequal: No Solution Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,31 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:[76, 17], Operations: ['79-78=1', '17/1=17'] Exploring Operation: 76+17=93, Resulting Numbers: [93] 93,31 unequal: No Solution Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 76*17=1292, Resulting Numbers: [1292] 1292,31 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:[76, 17], Operations: ['79-78=1', '17*1=17'] Exploring Operation: 76*17=1292, Resulting Numbers: [1292] 1292,31 unequal: No Solution Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 76+17=93, Resulting Numbers: [93] 93,31 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:[17, 78, 3], Operations: ['79-76=3'] Exploring Operation: 78-17=61, Resulting Numbers: [3, 61] Generated Node #0,3,0: 31:[3, 61] Operation: 78-17=61 Exploring Operation: 78-3=75, Resulting Numbers: [17, 75] Generated Node #0,3,1: 31:[17, 75] Operation: 78-3=75 Exploring Operation: 78/3=26, Resulting Numbers: [17, 26] Generated Node #0,3,2: 31:[17, 26] Operation: 78/3=26 Exploring Operation: 17+3=20, Resulting Numbers: [78, 20] Generated Node #0,3,3: 31:[78, 20] Operation: 17+3=20 Exploring Operation: 17-3=14, Resulting Numbers: [78, 14] Generated Node #0,3,4: 31:[78, 14] Operation: 17-3=14 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[17, 26], Operations: ['79-76=3', '78/3=26'] Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,31 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,31 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,31 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 #0,3,0 Current State: 31:[3, 61], Operations: ['79-76=3', '78-17=61'] Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,31 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 #0,3,1 Current State: 31:[17, 75], Operations: ['79-76=3', '78-3=75'] Exploring Operation: 17*75=1275, Resulting Numbers: [1275] 1275,31 unequal: No Solution Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 17+75=92, Resulting Numbers: [92] 92,31 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 #0,3,3 Current State: 31:[78, 20], Operations: ['79-76=3', '17+3=20'] Exploring Operation: 78+20=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 78*20=1560, Resulting Numbers: [1560] 1560,31 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 #0,3,4 Current State: 31:[78, 14], Operations: ['79-76=3', '17-3=14'] Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,31 unequal: No Solution Exploring Operation: 78*14=1092, Resulting Numbers: [1092] 1092,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 31:[17, 79, 2], Operations: ['78-76=2'] Exploring Operation: 79-17=62, Resulting Numbers: [2, 62] Generated Node #0,4,0: 31:[2, 62] Operation: 79-17=62 Exploring Operation: 79-2=77, Resulting Numbers: [17, 77] Generated Node #0,4,1: 31:[17, 77] Operation: 79-2=77 Exploring Operation: 17-2=15, Resulting Numbers: [79, 15] Generated Node #0,4,2: 31:[79, 15] Operation: 17-2=15 Exploring Operation: 17+2=19, Resulting Numbers: [79, 19] Generated Node #0,4,3: 31:[79, 19] Operation: 17+2=19 Exploring Operation: 17*2=34, Resulting Numbers: [79, 34] Generated Node #0,4,4: 31:[79, 34] Operation: 17*2=34 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 31:[79, 34], Operations: ['78-76=2', '17*2=34'] Exploring Operation: 79+34=113, Resulting Numbers: [113] 113,31 unequal: No Solution Exploring Operation: 79-34=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 79*34=2686, Resulting Numbers: [2686] 2686,31 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 #0,4,0 Current State: 31:[2, 62], Operations: ['78-76=2', '79-17=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,31 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[17, 78, 76, 79], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [17, 79, 2] Generated Node #0,4: 31:[17, 79, 2] Operation: 78-76=2 Moving to Node #0,4 Current State: 31:[17, 79, 2], Operations: ['78-76=2'] Exploring Operation: 79-17=62, Resulting Numbers: [2, 62] Generated Node #0,4,0: 31:[2, 62] Operation: 79-17=62 Moving to Node #0,4,0 Current State: 31:[2, 62], Operations: ['78-76=2', '79-17=62'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_5
sum_heuristic
[ 27, 5, 32, 2 ]
42
[ "27-5=22", "32*2=64", "64-22=42" ]
Current State: 42:[27, 5, 32, 2], Operations: [] Exploring Operation: 27-5=22, Resulting Numbers: [32, 2, 22] Generated Node #2: [32, 2, 22] from Operation: 27-5=22 Current State: 42:[32, 2, 22], Operations: ['27-5=22'] Exploring Operation: 32*2=64, Resulting Numbers: [22, 64] Generated Node #3: [22, 64] from Operation: 32*2=64 Current State: 42:[22, 64], Operations: ['27-5=22', '32*2=64'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[27, 5, 32, 2], Operations: [] Exploring Operation: 32-27=5, Resulting Numbers: [5, 2, 5] Generated Node #0,0: 42:[5, 2, 5] Operation: 32-27=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[5, 2, 5], Operations: ['32-27=5'] Exploring Operation: 5+2=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 42:[5, 7] Operation: 5+2=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[5, 7], Operations: ['32-27=5', '5+2=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 12, 90, 8, 23 ]
18
[ "23-8=15", "90/15=6", "12+6=18" ]
Current State: 18:[12, 90, 8, 23], Operations: [] Exploring Operation: 23-8=15, Resulting Numbers: [12, 90, 15] Generated Node #2: [12, 90, 15] from Operation: 23-8=15 Current State: 18:[12, 90, 15], Operations: ['23-8=15'] Exploring Operation: 90/15=6, Resulting Numbers: [12, 6] Generated Node #3: [12, 6] from Operation: 90/15=6 Current State: 18:[12, 6], Operations: ['23-8=15', '90/15=6'] Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[12, 90, 8, 23], Operations: [] Exploring Operation: 90-23=67, Resulting Numbers: [12, 8, 67] Generated Node #0,0: 18:[12, 8, 67] Operation: 90-23=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[12, 8, 67], Operations: ['90-23=67'] Exploring Operation: 67-12=55, Resulting Numbers: [8, 55] Generated Node #0,0,0: 18:[8, 55] Operation: 67-12=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[8, 55], Operations: ['90-23=67', '67-12=55'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,18 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
[ 47, 29, 71, 32 ]
57
[ "47-29=18", "71-32=39", "18+39=57" ]
Current State: 57:[47, 29, 71, 32], Operations: [] Exploring Operation: 47-29=18, Resulting Numbers: [71, 32, 18] Generated Node #2: [71, 32, 18] from Operation: 47-29=18 Current State: 57:[71, 32, 18], Operations: ['47-29=18'] Exploring Operation: 71-32=39, Resulting Numbers: [18, 39] Generated Node #3: [18, 39] from Operation: 71-32=39 Current State: 57:[18, 39], Operations: ['47-29=18', '71-32=39'] Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[47, 29, 71, 32], Operations: [] Exploring Operation: 47-29=18, Resulting Numbers: [71, 32, 18] Generated Node #0,0: 57:[71, 32, 18] Operation: 47-29=18 Exploring Operation: 32-29=3, Resulting Numbers: [47, 71, 3] Generated Node #0,1: 57:[47, 71, 3] Operation: 32-29=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[47, 71, 3], Operations: ['32-29=3'] Exploring Operation: 71-47=24, Resulting Numbers: [3, 24] Generated Node #0,1,0: 57:[3, 24] Operation: 71-47=24 Exploring Operation: 47+3=50, Resulting Numbers: [71, 50] Generated Node #0,1,1: 57:[71, 50] Operation: 47+3=50 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[3, 24], Operations: ['32-29=3', '71-47=24'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 57:[71, 50], Operations: ['32-29=3', '47+3=50'] Exploring Operation: 71-50=21, Resulting Numbers: [21] 21,57 unequal: No Solution Exploring Operation: 71+50=121, Resulting Numbers: [121] 121,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[71, 32, 18], Operations: ['47-29=18'] Exploring Operation: 71-32=39, Resulting Numbers: [18, 39] Generated Node #0,0,0: 57:[18, 39] Operation: 71-32=39 Exploring Operation: 71-18=53, Resulting Numbers: [32, 53] Generated Node #0,0,1: 57:[32, 53] Operation: 71-18=53 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[32, 53], Operations: ['47-29=18', '71-18=53'] Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,57 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[18, 39], Operations: ['47-29=18', '71-32=39'] Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,57 unequal: No Solution Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[47, 29, 71, 32], Operations: [] Exploring Operation: 47-29=18, Resulting Numbers: [71, 32, 18] Generated Node #0,0: 57:[71, 32, 18] Operation: 47-29=18 Moving to Node #0,0 Current State: 57:[71, 32, 18], Operations: ['47-29=18'] Exploring Operation: 71-32=39, Resulting Numbers: [18, 39] Generated Node #0,0,0: 57:[18, 39] Operation: 71-32=39 Moving to Node #0,0,0 Current State: 57:[18, 39], Operations: ['47-29=18', '71-32=39'] Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 22, 53, 8, 36 ]
55
[ "8+36=44", "44/22=2", "53+2=55" ]
Current State: 55:[22, 53, 8, 36], Operations: [] Exploring Operation: 8+36=44, Resulting Numbers: [22, 53, 44] Generated Node #2: [22, 53, 44] from Operation: 8+36=44 Current State: 55:[22, 53, 44], Operations: ['8+36=44'] Exploring Operation: 44/22=2, Resulting Numbers: [53, 2] Generated Node #3: [53, 2] from Operation: 44/22=2 Current State: 55:[53, 2], Operations: ['8+36=44', '44/22=2'] Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[22, 53, 8, 36], Operations: [] Exploring Operation: 36-22=14, Resulting Numbers: [53, 8, 14] Generated Node #0,0: 55:[53, 8, 14] Operation: 36-22=14 Exploring Operation: 22+36=58, Resulting Numbers: [53, 8, 58] Generated Node #0,1: 55:[53, 8, 58] Operation: 22+36=58 Exploring Operation: 53-36=17, Resulting Numbers: [22, 8, 17] Generated Node #0,2: 55:[22, 8, 17] Operation: 53-36=17 Exploring Operation: 22-8=14, Resulting Numbers: [53, 36, 14] Generated Node #0,3: 55:[53, 36, 14] Operation: 22-8=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[53, 8, 14], Operations: ['36-22=14'] Exploring Operation: 53-8=45, Resulting Numbers: [14, 45] Generated Node #0,0,0: 55:[14, 45] Operation: 53-8=45 Exploring Operation: 53+8=61, Resulting Numbers: [14, 61] Generated Node #0,0,1: 55:[14, 61] Operation: 53+8=61 Exploring Operation: 14-8=6, Resulting Numbers: [53, 6] Generated Node #0,0,2: 55:[53, 6] Operation: 14-8=6 Exploring Operation: 8+14=22, Resulting Numbers: [53, 22] Generated Node #0,0,3: 55:[53, 22] Operation: 8+14=22 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 55:[53, 6], Operations: ['36-22=14', '14-8=6'] Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,55 unequal: No Solution Exploring Operation: 53*6=318, Resulting Numbers: [318] 318,55 unequal: No Solution Exploring Operation: 53+6=59, Resulting Numbers: [59] 59,55 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 #0,0,1 Current State: 55:[14, 61], Operations: ['36-22=14', '53+8=61'] Exploring Operation: 14+61=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 14*61=854, Resulting Numbers: [854] 854,55 unequal: No Solution Exploring Operation: 61-14=47, Resulting Numbers: [47] 47,55 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 #0,0,0 Current State: 55:[14, 45], Operations: ['36-22=14', '53-8=45'] Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,55 unequal: No Solution Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,55 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 #0,0,3 Current State: 55:[53, 22], Operations: ['36-22=14', '8+14=22'] Exploring Operation: 53-22=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 53*22=1166, Resulting Numbers: [1166] 1166,55 unequal: No Solution Exploring Operation: 53+22=75, Resulting Numbers: [75] 75,55 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 #0,1 Current State: 55:[53, 8, 58], Operations: ['22+36=58'] Exploring Operation: 58-53=5, Resulting Numbers: [8, 5] Generated Node #0,1,0: 55:[8, 5] Operation: 58-53=5 Exploring Operation: 53+8=61, Resulting Numbers: [58, 61] Generated Node #0,1,1: 55:[58, 61] Operation: 53+8=61 Exploring Operation: 53-8=45, Resulting Numbers: [58, 45] Generated Node #0,1,2: 55:[58, 45] Operation: 53-8=45 Exploring Operation: 58-8=50, Resulting Numbers: [53, 50] Generated Node #0,1,3: 55:[53, 50] Operation: 58-8=50 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[8, 5], Operations: ['22+36=58', '58-53=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,55 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:[53, 50], Operations: ['22+36=58', '58-8=50'] Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,55 unequal: No Solution Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,55 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:[58, 61], Operations: ['22+36=58', '53+8=61'] Exploring Operation: 58+61=119, Resulting Numbers: [119] 119,55 unequal: No Solution Exploring Operation: 58*61=3538, Resulting Numbers: [3538] 3538,55 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,55 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:[58, 45], Operations: ['22+36=58', '53-8=45'] Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 58+45=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 58*45=2610, Resulting Numbers: [2610] 2610,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[22, 8, 17], Operations: ['53-36=17'] Exploring Operation: 17-8=9, Resulting Numbers: [22, 9] Generated Node #0,2,0: 55:[22, 9] Operation: 17-8=9 Exploring Operation: 22+17=39, Resulting Numbers: [8, 39] Generated Node #0,2,1: 55:[8, 39] Operation: 22+17=39 Exploring Operation: 22-8=14, Resulting Numbers: [17, 14] Generated Node #0,2,2: 55:[17, 14] Operation: 22-8=14 Exploring Operation: 22-17=5, Resulting Numbers: [8, 5] Generated Node #0,2,3: 55:[8, 5] Operation: 22-17=5 Moving to Node #0,2,3 Current State: 55:[8, 5], Operations: ['53-36=17', '22-17=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[17, 14], Operations: ['53-36=17', '22-8=14'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 17*14=238, Resulting Numbers: [238] 238,55 unequal: No Solution Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,55 unequal: No Solution Moving to Node #0,2,0 Current State: 55:[22, 9], Operations: ['53-36=17', '17-8=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,55 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[8, 39], Operations: ['53-36=17', '22+17=39'] Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 8*39=312, Resulting Numbers: [312] 312,55 unequal: No Solution Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,55 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 #0,3 Current State: 55:[53, 36, 14], Operations: ['22-8=14'] Exploring Operation: 36-14=22, Resulting Numbers: [53, 22] Generated Node #0,3,0: 55:[53, 22] Operation: 36-14=22 Exploring Operation: 36+14=50, Resulting Numbers: [53, 50] Generated Node #0,3,1: 55:[53, 50] Operation: 36+14=50 Exploring Operation: 53+14=67, Resulting Numbers: [36, 67] Generated Node #0,3,2: 55:[36, 67] Operation: 53+14=67 Exploring Operation: 53-36=17, Resulting Numbers: [14, 17] Generated Node #0,3,3: 55:[14, 17] Operation: 53-36=17 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 55:[53, 50], Operations: ['22-8=14', '36+14=50'] Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,55 unequal: No Solution Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,55 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 #0,3,3 Current State: 55:[14, 17], Operations: ['22-8=14', '53-36=17'] Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,55 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,55 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 #0,3,0 Current State: 55:[53, 22], Operations: ['22-8=14', '36-14=22'] Exploring Operation: 53*22=1166, Resulting Numbers: [1166] 1166,55 unequal: No Solution Exploring Operation: 53-22=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 53+22=75, Resulting Numbers: [75] 75,55 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 #0,3,2 Current State: 55:[36, 67], Operations: ['22-8=14', '53+14=67'] Exploring Operation: 36*67=2412, Resulting Numbers: [2412] 2412,55 unequal: No Solution Exploring Operation: 36+67=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 67-36=31, Resulting Numbers: [31] 31,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 33, 32, 32, 8 ]
25
[ "33+32=65", "32+8=40", "65-40=25" ]
Current State: 25:[33, 32, 32, 8], Operations: [] Exploring Operation: 33+32=65, Resulting Numbers: [8, 65] Generated Node #2: [8, 65] from Operation: 33+32=65 Current State: 25:[8, 65], Operations: ['33+32=65'] Exploring Operation: 32+8=40, Resulting Numbers: [65, 40] Generated Node #3: [65, 40] from Operation: 32+8=40 Current State: 25:[65, 40], Operations: ['33+32=65', '32+8=40'] Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[33, 32, 32, 8], Operations: [] Exploring Operation: 33-32=1, Resulting Numbers: [32, 8, 1] Generated Node #0,0: 25:[32, 8, 1] Operation: 33-32=1 Exploring Operation: 33-8=25, Resulting Numbers: [32, 32, 25] Generated Node #0,1: 25:[32, 32, 25] Operation: 33-8=25 Exploring Operation: 33-32=1, Resulting Numbers: [32, 8, 1] Generated Node #0,2: 25:[32, 8, 1] Operation: 33-32=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[32, 8, 1], Operations: ['33-32=1'] Exploring Operation: 32-1=31, Resulting Numbers: [8, 31] Generated Node #0,0,0: 25:[8, 31] Operation: 32-1=31 Exploring Operation: 32/8=4, Resulting Numbers: [1, 4] Generated Node #0,0,1: 25:[1, 4] Operation: 32/8=4 Exploring Operation: 32-8=24, Resulting Numbers: [1, 24] Generated Node #0,0,2: 25:[1, 24] Operation: 32-8=24 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[1, 4], Operations: ['33-32=1', '32/8=4'] Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,25 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 25:[1, 24], Operations: ['33-32=1', '32-8=24'] Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[33, 32, 32, 8], Operations: [] Exploring Operation: 33-32=1, Resulting Numbers: [32, 8, 1] Generated Node #0,0: 25:[32, 8, 1] Operation: 33-32=1 Moving to Node #0,0 Current State: 25:[32, 8, 1], Operations: ['33-32=1'] Exploring Operation: 32-8=24, Resulting Numbers: [1, 24] Generated Node #0,0,2: 25:[1, 24] Operation: 32-8=24 Moving to Node #0,0,2 Current State: 25:[1, 24], Operations: ['33-32=1', '32-8=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 77, 41, 20, 79 ]
42
[ "79-77=2", "41-20=21", "2*21=42" ]
Current State: 42:[77, 41, 20, 79], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [41, 20, 2] Generated Node #2: [41, 20, 2] from Operation: 79-77=2 Current State: 42:[41, 20, 2], Operations: ['79-77=2'] Exploring Operation: 41-20=21, Resulting Numbers: [2, 21] Generated Node #3: [2, 21] from Operation: 41-20=21 Current State: 42:[2, 21], Operations: ['79-77=2', '41-20=21'] Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[77, 41, 20, 79], Operations: [] Exploring Operation: 79-41=38, Resulting Numbers: [77, 20, 38] Generated Node #0,0: 42:[77, 20, 38] Operation: 79-41=38 Exploring Operation: 79-77=2, Resulting Numbers: [41, 20, 2] Generated Node #0,1: 42:[41, 20, 2] Operation: 79-77=2 Moving to Node #0,1 Current State: 42:[41, 20, 2], Operations: ['79-77=2'] Exploring Operation: 41+2=43, Resulting Numbers: [20, 43] Generated Node #0,1,0: 42:[20, 43] Operation: 41+2=43 Exploring Operation: 41-20=21, Resulting Numbers: [2, 21] Generated Node #0,1,1: 42:[2, 21] Operation: 41-20=21 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[2, 21], Operations: ['79-77=2', '41-20=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[77, 41, 20, 79], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [41, 20, 2] Generated Node #0,1: 42:[41, 20, 2] Operation: 79-77=2 Moving to Node #0,1 Current State: 42:[41, 20, 2], Operations: ['79-77=2'] Exploring Operation: 41-20=21, Resulting Numbers: [2, 21] Generated Node #0,1,1: 42:[2, 21] Operation: 41-20=21 Moving to Node #0,1,1 Current State: 42:[2, 21], Operations: ['79-77=2', '41-20=21'] Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 35, 35, 72, 42 ]
29
[ "35/35=1", "72-42=30", "30-1=29" ]
Current State: 29:[35, 35, 72, 42], Operations: [] Exploring Operation: 35/35=1, Resulting Numbers: [72, 42, 1] Generated Node #2: [72, 42, 1] from Operation: 35/35=1 Current State: 29:[72, 42, 1], Operations: ['35/35=1'] Exploring Operation: 72-42=30, Resulting Numbers: [1, 30] Generated Node #3: [1, 30] from Operation: 72-42=30 Current State: 29:[1, 30], Operations: ['35/35=1', '72-42=30'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[35, 35, 72, 42], Operations: [] Exploring Operation: 72-35=37, Resulting Numbers: [35, 42, 37] Generated Node #0,0: 29:[35, 42, 37] Operation: 72-35=37 Exploring Operation: 72-42=30, Resulting Numbers: [35, 35, 30] Generated Node #0,1: 29:[35, 35, 30] Operation: 72-42=30 Moving to Node #0,1 Current State: 29:[35, 35, 30], Operations: ['72-42=30'] Exploring Operation: 35-35=0, Resulting Numbers: [30, 0] Generated Node #0,1,0: 29:[30, 0] Operation: 35-35=0 Exploring Operation: 35/35=1, Resulting Numbers: [30, 1] Generated Node #0,1,1: 29:[30, 1] Operation: 35/35=1 Moving to Node #0,0 Current State: 29:[35, 42, 37], Operations: ['72-35=37'] Exploring Operation: 42-37=5, Resulting Numbers: [35, 5] Generated Node #0,0,0: 29:[35, 5] Operation: 42-37=5 Exploring Operation: 42-35=7, Resulting Numbers: [37, 7] Generated Node #0,0,1: 29:[37, 7] Operation: 42-35=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[35, 5], Operations: ['72-35=37', '42-37=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[37, 7], Operations: ['72-35=37', '42-35=7'] Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 29:[30, 1], Operations: ['72-42=30', '35/35=1'] Exploring Operation: 30*1=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[35, 35, 72, 42], Operations: [] Exploring Operation: 72-42=30, Resulting Numbers: [35, 35, 30] Generated Node #0,1: 29:[35, 35, 30] Operation: 72-42=30 Moving to Node #0,1 Current State: 29:[35, 35, 30], Operations: ['72-42=30'] Exploring Operation: 35/35=1, Resulting Numbers: [30, 1] Generated Node #0,1,1: 29:[30, 1] Operation: 35/35=1 Moving to Node #0,1,1 Current State: 29:[30, 1], Operations: ['72-42=30', '35/35=1'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 62, 73, 49, 27 ]
59
[ "62+73=135", "49+27=76", "135-76=59" ]
Current State: 59:[62, 73, 49, 27], Operations: [] Exploring Operation: 62+73=135, Resulting Numbers: [49, 27, 135] Generated Node #2: [49, 27, 135] from Operation: 62+73=135 Current State: 59:[49, 27, 135], Operations: ['62+73=135'] Exploring Operation: 49+27=76, Resulting Numbers: [135, 76] Generated Node #3: [135, 76] from Operation: 49+27=76 Current State: 59:[135, 76], Operations: ['62+73=135', '49+27=76'] Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[62, 73, 49, 27], Operations: [] Exploring Operation: 73-27=46, Resulting Numbers: [62, 49, 46] Generated Node #0,0: 59:[62, 49, 46] Operation: 73-27=46 Exploring Operation: 73+27=100, Resulting Numbers: [62, 49, 100] Generated Node #0,1: 59:[62, 49, 100] Operation: 73+27=100 Exploring Operation: 62+27=89, Resulting Numbers: [73, 49, 89] Generated Node #0,2: 59:[73, 49, 89] Operation: 62+27=89 Exploring Operation: 49+27=76, Resulting Numbers: [62, 73, 76] Generated Node #0,3: 59:[62, 73, 76] Operation: 49+27=76 Exploring Operation: 62-27=35, Resulting Numbers: [73, 49, 35] Generated Node #0,4: 59:[73, 49, 35] Operation: 62-27=35 Moving to Node #0,0 Current State: 59:[62, 49, 46], Operations: ['73-27=46'] Exploring Operation: 49+46=95, Resulting Numbers: [62, 95] Generated Node #0,0,0: 59:[62, 95] Operation: 49+46=95 Exploring Operation: 62-49=13, Resulting Numbers: [46, 13] Generated Node #0,0,1: 59:[46, 13] Operation: 62-49=13 Exploring Operation: 62-46=16, Resulting Numbers: [49, 16] Generated Node #0,0,2: 59:[49, 16] Operation: 62-46=16 Exploring Operation: 49-46=3, Resulting Numbers: [62, 3] Generated Node #0,0,3: 59:[62, 3] Operation: 49-46=3 Exploring Operation: 62+46=108, Resulting Numbers: [49, 108] Generated Node #0,0,4: 59:[49, 108] Operation: 62+46=108 Moving to Node #0,3 Current State: 59:[62, 73, 76], Operations: ['49+27=76'] Exploring Operation: 76-73=3, Resulting Numbers: [62, 3] Generated Node #0,3,0: 59:[62, 3] Operation: 76-73=3 Exploring Operation: 73-62=11, Resulting Numbers: [76, 11] Generated Node #0,3,1: 59:[76, 11] Operation: 73-62=11 Exploring Operation: 62+76=138, Resulting Numbers: [73, 138] Generated Node #0,3,2: 59:[73, 138] Operation: 62+76=138 Exploring Operation: 62+73=135, Resulting Numbers: [76, 135] Generated Node #0,3,3: 59:[76, 135] Operation: 62+73=135 Exploring Operation: 76-62=14, Resulting Numbers: [73, 14] Generated Node #0,3,4: 59:[73, 14] Operation: 76-62=14 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[62, 3], Operations: ['49+27=76', '76-73=3'] Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,59 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[62, 73, 49, 27], Operations: [] Exploring Operation: 49+27=76, Resulting Numbers: [62, 73, 76] Generated Node #0,3: 59:[62, 73, 76] Operation: 49+27=76 Moving to Node #0,3 Current State: 59:[62, 73, 76], Operations: ['49+27=76'] Exploring Operation: 76-73=3, Resulting Numbers: [62, 3] Generated Node #0,3,0: 59:[62, 3] Operation: 76-73=3 Moving to Node #0,3,0 Current State: 59:[62, 3], Operations: ['49+27=76', '76-73=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 36, 45, 65, 61 ]
85
[ "36+45=81", "65-61=4", "81+4=85" ]
Current State: 85:[36, 45, 65, 61], Operations: [] Exploring Operation: 36+45=81, Resulting Numbers: [65, 61, 81] Generated Node #2: [65, 61, 81] from Operation: 36+45=81 Current State: 85:[65, 61, 81], Operations: ['36+45=81'] Exploring Operation: 65-61=4, Resulting Numbers: [81, 4] Generated Node #3: [81, 4] from Operation: 65-61=4 Current State: 85:[81, 4], Operations: ['36+45=81', '65-61=4'] Exploring Operation: 81+4=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[36, 45, 65, 61], Operations: [] Exploring Operation: 65-61=4, Resulting Numbers: [36, 45, 4] Generated Node #0,0: 85:[36, 45, 4] Operation: 65-61=4 Exploring Operation: 45-36=9, Resulting Numbers: [65, 61, 9] Generated Node #0,1: 85:[65, 61, 9] Operation: 45-36=9 Exploring Operation: 36+45=81, Resulting Numbers: [65, 61, 81] Generated Node #0,2: 85:[65, 61, 81] Operation: 36+45=81 Exploring Operation: 61-45=16, Resulting Numbers: [36, 65, 16] Generated Node #0,3: 85:[36, 65, 16] Operation: 61-45=16 Exploring Operation: 65-45=20, Resulting Numbers: [36, 61, 20] Generated Node #0,4: 85:[36, 61, 20] Operation: 65-45=20 Moving to Node #0,3 Current State: 85:[36, 65, 16], Operations: ['61-45=16'] Exploring Operation: 65-36=29, Resulting Numbers: [16, 29] Generated Node #0,3,0: 85:[16, 29] Operation: 65-36=29 Exploring Operation: 65+16=81, Resulting Numbers: [36, 81] Generated Node #0,3,1: 85:[36, 81] Operation: 65+16=81 Exploring Operation: 36-16=20, Resulting Numbers: [65, 20] Generated Node #0,3,2: 85:[65, 20] Operation: 36-16=20 Exploring Operation: 65-16=49, Resulting Numbers: [36, 49] Generated Node #0,3,3: 85:[36, 49] Operation: 65-16=49 Exploring Operation: 36+65=101, Resulting Numbers: [16, 101] Generated Node #0,3,4: 85:[16, 101] Operation: 36+65=101 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 85:[16, 29], Operations: ['61-45=16', '65-36=29'] Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,85 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 85:[16, 101], Operations: ['61-45=16', '36+65=101'] Exploring Operation: 16+101=117, Resulting Numbers: [117] 117,85 unequal: No Solution Exploring Operation: 101-16=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[36, 45, 65, 61], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [36, 65, 16] Generated Node #0,3: 85:[36, 65, 16] Operation: 61-45=16 Moving to Node #0,3 Current State: 85:[36, 65, 16], Operations: ['61-45=16'] Exploring Operation: 36+65=101, Resulting Numbers: [16, 101] Generated Node #0,3,4: 85:[16, 101] Operation: 36+65=101 Moving to Node #0,3,4 Current State: 85:[16, 101], Operations: ['61-45=16', '36+65=101'] Exploring Operation: 101-16=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 97, 92, 10, 88 ]
86
[ "97-92=5", "10/5=2", "88-2=86" ]
Current State: 86:[97, 92, 10, 88], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [10, 88, 5] Generated Node #2: [10, 88, 5] from Operation: 97-92=5 Current State: 86:[10, 88, 5], Operations: ['97-92=5'] Exploring Operation: 10/5=2, Resulting Numbers: [88, 2] Generated Node #3: [88, 2] from Operation: 10/5=2 Current State: 86:[88, 2], Operations: ['97-92=5', '10/5=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[97, 92, 10, 88], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [10, 88, 5] Generated Node #0,0: 86:[10, 88, 5] Operation: 97-92=5 Exploring Operation: 92-10=82, Resulting Numbers: [97, 88, 82] Generated Node #0,1: 86:[97, 88, 82] Operation: 92-10=82 Exploring Operation: 97-88=9, Resulting Numbers: [92, 10, 9] Generated Node #0,2: 86:[92, 10, 9] Operation: 97-88=9 Exploring Operation: 97-10=87, Resulting Numbers: [92, 88, 87] Generated Node #0,3: 86:[92, 88, 87] Operation: 97-10=87 Exploring Operation: 92-88=4, Resulting Numbers: [97, 10, 4] Generated Node #0,4: 86:[97, 10, 4] Operation: 92-88=4 Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[92, 88, 87], Operations: ['97-10=87'] Exploring Operation: 92-87=5, Resulting Numbers: [88, 5] Generated Node #0,3,0: 86:[88, 5] Operation: 92-87=5 Exploring Operation: 92-88=4, Resulting Numbers: [87, 4] Generated Node #0,3,1: 86:[87, 4] Operation: 92-88=4 Exploring Operation: 92+87=179, Resulting Numbers: [88, 179] Generated Node #0,3,2: 86:[88, 179] Operation: 92+87=179 Exploring Operation: 92+88=180, Resulting Numbers: [87, 180] Generated Node #0,3,3: 86:[87, 180] Operation: 92+88=180 Exploring Operation: 88-87=1, Resulting Numbers: [92, 1] Generated Node #0,3,4: 86:[92, 1] Operation: 88-87=1 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 86:[87, 4], Operations: ['97-10=87', '92-88=4'] Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,86 unequal: No Solution Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,86 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,86 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 #0,3,0 Current State: 86:[88, 5], Operations: ['97-10=87', '92-87=5'] Exploring Operation: 88+5=93, Resulting Numbers: [93] 93,86 unequal: No Solution Exploring Operation: 88*5=440, Resulting Numbers: [440] 440,86 unequal: No Solution Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,86 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 #0,3,4 Current State: 86:[92, 1], Operations: ['97-10=87', '88-87=1'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,86 unequal: No Solution Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,86 unequal: No Solution Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,86 unequal: No Solution Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,86 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 #0,3,2 Current State: 86:[88, 179], Operations: ['97-10=87', '92+87=179'] Exploring Operation: 179-88=91, Resulting Numbers: [91] 91,86 unequal: No Solution Exploring Operation: 88*179=15752, Resulting Numbers: [15752] 15752,86 unequal: No Solution Exploring Operation: 88+179=267, Resulting Numbers: [267] 267,86 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 #0,3,3 Current State: 86:[87, 180], Operations: ['97-10=87', '92+88=180'] Exploring Operation: 87+180=267, Resulting Numbers: [267] 267,86 unequal: No Solution Exploring Operation: 180-87=93, Resulting Numbers: [93] 93,86 unequal: No Solution Exploring Operation: 87*180=15660, Resulting Numbers: [15660] 15660,86 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 #0,0 Current State: 86:[10, 88, 5], Operations: ['97-92=5'] Exploring Operation: 88-10=78, Resulting Numbers: [5, 78] Generated Node #0,0,0: 86:[5, 78] Operation: 88-10=78 Exploring Operation: 10/5=2, Resulting Numbers: [88, 2] Generated Node #0,0,1: 86:[88, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [88, 5] Generated Node #0,0,2: 86:[88, 5] Operation: 10-5=5 Exploring Operation: 88-5=83, Resulting Numbers: [10, 83] Generated Node #0,0,3: 86:[10, 83] Operation: 88-5=83 Exploring Operation: 10*5=50, Resulting Numbers: [88, 50] Generated Node #0,0,4: 86:[88, 50] Operation: 10*5=50 Moving to Node #0,0,1 Current State: 86:[88, 2], Operations: ['97-92=5', '10/5=2'] Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,86 unequal: No Solution Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,86 unequal: No Solution Exploring Operation: 88*2=176, Resulting Numbers: [176] 176,86 unequal: No Solution Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[97, 92, 10, 88], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [10, 88, 5] Generated Node #0,0: 86:[10, 88, 5] Operation: 97-92=5 Moving to Node #0,0 Current State: 86:[10, 88, 5], Operations: ['97-92=5'] Exploring Operation: 10/5=2, Resulting Numbers: [88, 2] Generated Node #0,0,1: 86:[88, 2] Operation: 10/5=2 Moving to Node #0,0,1 Current State: 86:[88, 2], Operations: ['97-92=5', '10/5=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
sum_heuristic
[ 98, 19, 54, 97 ]
89
[ "98+54=152", "152/19=8", "97-8=89" ]
Current State: 89:[98, 19, 54, 97], Operations: [] Exploring Operation: 98+54=152, Resulting Numbers: [19, 97, 152] Generated Node #2: [19, 97, 152] from Operation: 98+54=152 Current State: 89:[19, 97, 152], Operations: ['98+54=152'] Exploring Operation: 152/19=8, Resulting Numbers: [97, 8] Generated Node #3: [97, 8] from Operation: 152/19=8 Current State: 89:[97, 8], Operations: ['98+54=152', '152/19=8'] Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[98, 19, 54, 97], Operations: [] Exploring Operation: 98-19=79, Resulting Numbers: [54, 97, 79] Generated Node #0,0: 89:[54, 97, 79] Operation: 98-19=79 Exploring Operation: 97-19=78, Resulting Numbers: [98, 54, 78] Generated Node #0,1: 89:[98, 54, 78] Operation: 97-19=78 Exploring Operation: 19+54=73, Resulting Numbers: [98, 97, 73] Generated Node #0,2: 89:[98, 97, 73] Operation: 19+54=73 Moving to Node #0,2 Current State: 89:[98, 97, 73], Operations: ['19+54=73'] Exploring Operation: 98-73=25, Resulting Numbers: [97, 25] Generated Node #0,2,0: 89:[97, 25] Operation: 98-73=25 Exploring Operation: 97-73=24, Resulting Numbers: [98, 24] Generated Node #0,2,1: 89:[98, 24] Operation: 97-73=24 Exploring Operation: 98+73=171, Resulting Numbers: [97, 171] Generated Node #0,2,2: 89:[97, 171] Operation: 98+73=171 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[97, 25], Operations: ['19+54=73', '98-73=25'] Exploring Operation: 97*25=2425, Resulting Numbers: [2425] 2425,89 unequal: No Solution Exploring Operation: 97-25=72, Resulting Numbers: [72] 72,89 unequal: No Solution Exploring Operation: 97+25=122, Resulting Numbers: [122] 122,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[98, 24], Operations: ['19+54=73', '97-73=24'] Exploring Operation: 98-24=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 98*24=2352, Resulting Numbers: [2352] 2352,89 unequal: No Solution Exploring Operation: 98+24=122, Resulting Numbers: [122] 122,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[97, 171], Operations: ['19+54=73', '98+73=171'] Exploring Operation: 97*171=16587, Resulting Numbers: [16587] 16587,89 unequal: No Solution Exploring Operation: 171-97=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 97+171=268, Resulting Numbers: [268] 268,89 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: 89:[54, 97, 79], Operations: ['98-19=79'] Exploring Operation: 97-54=43, Resulting Numbers: [79, 43] Generated Node #0,0,0: 89:[79, 43] Operation: 97-54=43 Exploring Operation: 54+79=133, Resulting Numbers: [97, 133] Generated Node #0,0,1: 89:[97, 133] Operation: 54+79=133 Exploring Operation: 54+97=151, Resulting Numbers: [79, 151] Generated Node #0,0,2: 89:[79, 151] Operation: 54+97=151 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[97, 133], Operations: ['98-19=79', '54+79=133'] Exploring Operation: 133-97=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 97*133=12901, Resulting Numbers: [12901] 12901,89 unequal: No Solution Exploring Operation: 97+133=230, Resulting Numbers: [230] 230,89 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 #0,0,0 Current State: 89:[79, 43], Operations: ['98-19=79', '97-54=43'] Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,89 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,89 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 #0,0,2 Current State: 89:[79, 151], Operations: ['98-19=79', '54+97=151'] Exploring Operation: 79*151=11929, Resulting Numbers: [11929] 11929,89 unequal: No Solution Exploring Operation: 79+151=230, Resulting Numbers: [230] 230,89 unequal: No Solution Exploring Operation: 151-79=72, Resulting Numbers: [72] 72,89 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: 89:[98, 54, 78], Operations: ['97-19=78'] Exploring Operation: 98+54=152, Resulting Numbers: [78, 152] Generated Node #0,1,0: 89:[78, 152] Operation: 98+54=152 Exploring Operation: 54+78=132, Resulting Numbers: [98, 132] Generated Node #0,1,1: 89:[98, 132] Operation: 54+78=132 Exploring Operation: 98-54=44, Resulting Numbers: [78, 44] Generated Node #0,1,2: 89:[78, 44] Operation: 98-54=44 Moving to Node #0,1,1 Current State: 89:[98, 132], Operations: ['97-19=78', '54+78=132'] Exploring Operation: 98+132=230, Resulting Numbers: [230] 230,89 unequal: No Solution Exploring Operation: 132-98=34, Resulting Numbers: [34] 34,89 unequal: No Solution Exploring Operation: 98*132=12936, Resulting Numbers: [12936] 12936,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[78, 44], Operations: ['97-19=78', '98-54=44'] Exploring Operation: 78+44=122, Resulting Numbers: [122] 122,89 unequal: No Solution Exploring Operation: 78*44=3432, Resulting Numbers: [3432] 3432,89 unequal: No Solution Exploring Operation: 78-44=34, Resulting Numbers: [34] 34,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[78, 152], Operations: ['97-19=78', '98+54=152'] Exploring Operation: 78*152=11856, Resulting Numbers: [11856] 11856,89 unequal: No Solution Exploring Operation: 152-78=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 78+152=230, Resulting Numbers: [230] 230,89 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 14, 1, 23, 76 ]
67
[ "14*1=14", "76-23=53", "14+53=67" ]
Current State: 67:[14, 1, 23, 76], Operations: [] Exploring Operation: 14*1=14, Resulting Numbers: [23, 76, 14] Generated Node #2: [23, 76, 14] from Operation: 14*1=14 Current State: 67:[23, 76, 14], Operations: ['14*1=14'] Exploring Operation: 76-23=53, Resulting Numbers: [14, 53] Generated Node #3: [14, 53] from Operation: 76-23=53 Current State: 67:[14, 53], Operations: ['14*1=14', '76-23=53'] Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[14, 1, 23, 76], Operations: [] Exploring Operation: 14+1=15, Resulting Numbers: [23, 76, 15] Generated Node #0,0: 67:[23, 76, 15] Operation: 14+1=15 Exploring Operation: 14+23=37, Resulting Numbers: [1, 76, 37] Generated Node #0,1: 67:[1, 76, 37] Operation: 14+23=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[23, 76, 15], Operations: ['14+1=15'] Exploring Operation: 23+15=38, Resulting Numbers: [76, 38] Generated Node #0,0,0: 67:[76, 38] Operation: 23+15=38 Exploring Operation: 76-15=61, Resulting Numbers: [23, 61] Generated Node #0,0,1: 67:[23, 61] Operation: 76-15=61 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[76, 38], Operations: ['14+1=15', '23+15=38'] Exploring Operation: 76+38=114, Resulting Numbers: [114] 114,67 unequal: No Solution Exploring Operation: 76-38=38, Resulting Numbers: [38] 38,67 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:[23, 61], Operations: ['14+1=15', '76-15=61'] Exploring Operation: 23+61=84, Resulting Numbers: [84] 84,67 unequal: No Solution Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,67 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:[1, 76, 37], Operations: ['14+23=37'] Exploring Operation: 76-1=75, Resulting Numbers: [37, 75] Generated Node #0,1,0: 67:[37, 75] Operation: 76-1=75 Exploring Operation: 1+37=38, Resulting Numbers: [76, 38] Generated Node #0,1,1: 67:[76, 38] Operation: 1+37=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 67:[37, 75], Operations: ['14+23=37', '76-1=75'] Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 37+75=112, Resulting Numbers: [112] 112,67 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 #0,1,1 Current State: 67:[76, 38], Operations: ['14+23=37', '1+37=38'] Exploring Operation: 76-38=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 76+38=114, Resulting Numbers: [114] 114,67 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 No solution found.
0
hs_2
sum_heuristic
[ 32, 20, 45, 19 ]
76
[ "32-20=12", "45+19=64", "12+64=76" ]
Current State: 76:[32, 20, 45, 19], Operations: [] Exploring Operation: 32-20=12, Resulting Numbers: [45, 19, 12] Generated Node #2: [45, 19, 12] from Operation: 32-20=12 Current State: 76:[45, 19, 12], Operations: ['32-20=12'] Exploring Operation: 45+19=64, Resulting Numbers: [12, 64] Generated Node #3: [12, 64] from Operation: 45+19=64 Current State: 76:[12, 64], Operations: ['32-20=12', '45+19=64'] Exploring Operation: 12+64=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[32, 20, 45, 19], Operations: [] Exploring Operation: 32+45=77, Resulting Numbers: [20, 19, 77] Generated Node #0,0: 76:[20, 19, 77] Operation: 32+45=77 Exploring Operation: 45-32=13, Resulting Numbers: [20, 19, 13] Generated Node #0,1: 76:[20, 19, 13] Operation: 45-32=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[20, 19, 77], Operations: ['32+45=77'] Exploring Operation: 20+19=39, Resulting Numbers: [77, 39] Generated Node #0,0,0: 76:[77, 39] Operation: 20+19=39 Exploring Operation: 20-19=1, Resulting Numbers: [77, 1] Generated Node #0,0,1: 76:[77, 1] Operation: 20-19=1 Moving to Node #0,0,0 Current State: 76:[77, 39], Operations: ['32+45=77', '20+19=39'] Exploring Operation: 77+39=116, Resulting Numbers: [116] 116,76 unequal: No Solution Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[77, 1], Operations: ['32+45=77', '20-19=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[32, 20, 45, 19], Operations: [] Exploring Operation: 32+45=77, Resulting Numbers: [20, 19, 77] Generated Node #0,0: 76:[20, 19, 77] Operation: 32+45=77 Moving to Node #0,0 Current State: 76:[20, 19, 77], Operations: ['32+45=77'] Exploring Operation: 20-19=1, Resulting Numbers: [77, 1] Generated Node #0,0,1: 76:[77, 1] Operation: 20-19=1 Moving to Node #0,0,1 Current State: 76:[77, 1], Operations: ['32+45=77', '20-19=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 82, 42, 66, 5 ]
49
[ "82-5=77", "42*77=3234", "3234/66=49" ]
Current State: 49:[82, 42, 66, 5], Operations: [] Exploring Operation: 82-5=77, Resulting Numbers: [42, 66, 77] Generated Node #2: [42, 66, 77] from Operation: 82-5=77 Current State: 49:[42, 66, 77], Operations: ['82-5=77'] Exploring Operation: 42*77=3234, Resulting Numbers: [66, 3234] Generated Node #3: [66, 3234] from Operation: 42*77=3234 Current State: 49:[66, 3234], Operations: ['82-5=77', '42*77=3234'] Exploring Operation: 3234/66=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[82, 42, 66, 5], Operations: [] Exploring Operation: 66-42=24, Resulting Numbers: [82, 5, 24] Generated Node #0,0: 49:[82, 5, 24] Operation: 66-42=24 Exploring Operation: 82-42=40, Resulting Numbers: [66, 5, 40] Generated Node #0,1: 49:[66, 5, 40] Operation: 82-42=40 Exploring Operation: 82-5=77, Resulting Numbers: [42, 66, 77] Generated Node #0,2: 49:[42, 66, 77] Operation: 82-5=77 Exploring Operation: 42+5=47, Resulting Numbers: [82, 66, 47] Generated Node #0,3: 49:[82, 66, 47] Operation: 42+5=47 Exploring Operation: 82-66=16, Resulting Numbers: [42, 5, 16] Generated Node #0,4: 49:[42, 5, 16] Operation: 82-66=16 Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[42, 5, 16], Operations: ['82-66=16'] Exploring Operation: 42-5=37, Resulting Numbers: [16, 37] Generated Node #0,4,0: 49:[16, 37] Operation: 42-5=37 Exploring Operation: 16-5=11, Resulting Numbers: [42, 11] Generated Node #0,4,1: 49:[42, 11] Operation: 16-5=11 Exploring Operation: 42-16=26, Resulting Numbers: [5, 26] Generated Node #0,4,2: 49:[5, 26] Operation: 42-16=26 Exploring Operation: 42+16=58, Resulting Numbers: [5, 58] Generated Node #0,4,3: 49:[5, 58] Operation: 42+16=58 Exploring Operation: 42+5=47, Resulting Numbers: [16, 47] Generated Node #0,4,4: 49:[16, 47] Operation: 42+5=47 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 49:[42, 11], Operations: ['82-66=16', '16-5=11'] Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,49 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 49:[5, 58], Operations: ['82-66=16', '42+16=58'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 5*58=290, Resulting Numbers: [290] 290,49 unequal: No Solution Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 49:[16, 47], Operations: ['82-66=16', '42+5=47'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 16+47=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 16*47=752, Resulting Numbers: [752] 752,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 49:[16, 37], Operations: ['82-66=16', '42-5=37'] Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 16*37=592, Resulting Numbers: [592] 592,49 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 49:[5, 26], Operations: ['82-66=16', '42-16=26'] Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,49 unequal: No Solution Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[66, 5, 40], Operations: ['82-42=40'] Exploring Operation: 40/5=8, Resulting Numbers: [66, 8] Generated Node #0,1,0: 49:[66, 8] Operation: 40/5=8 Exploring Operation: 66-5=61, Resulting Numbers: [40, 61] Generated Node #0,1,1: 49:[40, 61] Operation: 66-5=61 Exploring Operation: 66-40=26, Resulting Numbers: [5, 26] Generated Node #0,1,2: 49:[5, 26] Operation: 66-40=26 Exploring Operation: 5+40=45, Resulting Numbers: [66, 45] Generated Node #0,1,3: 49:[66, 45] Operation: 5+40=45 Exploring Operation: 66+5=71, Resulting Numbers: [40, 71] Generated Node #0,1,4: 49:[40, 71] Operation: 66+5=71 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[66, 8], Operations: ['82-42=40', '40/5=8'] Exploring Operation: 66+8=74, Resulting Numbers: [74] 74,49 unequal: No Solution Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,49 unequal: No Solution Exploring Operation: 66*8=528, Resulting Numbers: [528] 528,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[40, 61], Operations: ['82-42=40', '66-5=61'] Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 40+61=101, Resulting Numbers: [101] 101,49 unequal: No Solution Exploring Operation: 40*61=2440, Resulting Numbers: [2440] 2440,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 49:[5, 26], Operations: ['82-42=40', '66-40=26'] Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,49 unequal: No Solution Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 49:[66, 45], Operations: ['82-42=40', '5+40=45'] Exploring Operation: 66*45=2970, Resulting Numbers: [2970] 2970,49 unequal: No Solution Exploring Operation: 66+45=111, Resulting Numbers: [111] 111,49 unequal: No Solution Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 49:[40, 71], Operations: ['82-42=40', '66+5=71'] Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 40+71=111, Resulting Numbers: [111] 111,49 unequal: No Solution Exploring Operation: 40*71=2840, Resulting Numbers: [2840] 2840,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[82, 5, 24], Operations: ['66-42=24'] Exploring Operation: 82-5=77, Resulting Numbers: [24, 77] Generated Node #0,0,0: 49:[24, 77] Operation: 82-5=77 Exploring Operation: 82+5=87, Resulting Numbers: [24, 87] Generated Node #0,0,1: 49:[24, 87] Operation: 82+5=87 Exploring Operation: 5+24=29, Resulting Numbers: [82, 29] Generated Node #0,0,2: 49:[82, 29] Operation: 5+24=29 Exploring Operation: 24-5=19, Resulting Numbers: [82, 19] Generated Node #0,0,3: 49:[82, 19] Operation: 24-5=19 Exploring Operation: 82-24=58, Resulting Numbers: [5, 58] Generated Node #0,0,4: 49:[5, 58] Operation: 82-24=58 Moving to Node #0,0,4 Current State: 49:[5, 58], Operations: ['66-42=24', '82-24=58'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 5*58=290, Resulting Numbers: [290] 290,49 unequal: No Solution Moving to Node #0,0,3 Current State: 49:[82, 19], Operations: ['66-42=24', '24-5=19'] Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 82*19=1558, Resulting Numbers: [1558] 1558,49 unequal: No Solution Exploring Operation: 82+19=101, Resulting Numbers: [101] 101,49 unequal: No Solution Moving to Node #0,0,0 Current State: 49:[24, 77], Operations: ['66-42=24', '82-5=77'] Exploring Operation: 24+77=101, Resulting Numbers: [101] 101,49 unequal: No Solution Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 24*77=1848, Resulting Numbers: [1848] 1848,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[82, 29], Operations: ['66-42=24', '5+24=29'] Exploring Operation: 82*29=2378, Resulting Numbers: [2378] 2378,49 unequal: No Solution Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 82+29=111, Resulting Numbers: [111] 111,49 unequal: No Solution Moving to Node #0,0,1 Current State: 49:[24, 87], Operations: ['66-42=24', '82+5=87'] Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 24+87=111, Resulting Numbers: [111] 111,49 unequal: No Solution Exploring Operation: 24*87=2088, Resulting Numbers: [2088] 2088,49 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 #0,2 Current State: 49:[42, 66, 77], Operations: ['82-5=77'] Exploring Operation: 77-66=11, Resulting Numbers: [42, 11] Generated Node #0,2,0: 49:[42, 11] Operation: 77-66=11 Exploring Operation: 66-42=24, Resulting Numbers: [77, 24] Generated Node #0,2,1: 49:[77, 24] Operation: 66-42=24 Exploring Operation: 77-42=35, Resulting Numbers: [66, 35] Generated Node #0,2,2: 49:[66, 35] Operation: 77-42=35 Exploring Operation: 42+77=119, Resulting Numbers: [66, 119] Generated Node #0,2,3: 49:[66, 119] Operation: 42+77=119 Exploring Operation: 42+66=108, Resulting Numbers: [77, 108] Generated Node #0,2,4: 49:[77, 108] Operation: 42+66=108 Moving to Node #0,2,0 Current State: 49:[42, 11], Operations: ['82-5=77', '77-66=11'] Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[66, 35], Operations: ['82-5=77', '77-42=35'] Exploring Operation: 66*35=2310, Resulting Numbers: [2310] 2310,49 unequal: No Solution Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 66+35=101, Resulting Numbers: [101] 101,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[77, 24], Operations: ['82-5=77', '66-42=24'] Exploring Operation: 77*24=1848, Resulting Numbers: [1848] 1848,49 unequal: No Solution Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 77+24=101, Resulting Numbers: [101] 101,49 unequal: No Solution Moving to Node #0,2,3 Current State: 49:[66, 119], Operations: ['82-5=77', '42+77=119'] Exploring Operation: 119-66=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 66+119=185, Resulting Numbers: [185] 185,49 unequal: No Solution Exploring Operation: 66*119=7854, Resulting Numbers: [7854] 7854,49 unequal: No Solution Moving to Node #0,2,4 Current State: 49:[77, 108], Operations: ['82-5=77', '42+66=108'] Exploring Operation: 108-77=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 77*108=8316, Resulting Numbers: [8316] 8316,49 unequal: No Solution Exploring Operation: 77+108=185, Resulting Numbers: [185] 185,49 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 #0,3 Current State: 49:[82, 66, 47], Operations: ['42+5=47'] Exploring Operation: 82+47=129, Resulting Numbers: [66, 129] Generated Node #0,3,0: 49:[66, 129] Operation: 82+47=129 Exploring Operation: 66+47=113, Resulting Numbers: [82, 113] Generated Node #0,3,1: 49:[82, 113] Operation: 66+47=113 Exploring Operation: 66-47=19, Resulting Numbers: [82, 19] Generated Node #0,3,2: 49:[82, 19] Operation: 66-47=19 Exploring Operation: 82-66=16, Resulting Numbers: [47, 16] Generated Node #0,3,3: 49:[47, 16] Operation: 82-66=16 Exploring Operation: 82-47=35, Resulting Numbers: [66, 35] Generated Node #0,3,4: 49:[66, 35] Operation: 82-47=35 Moving to Node #0,3,3 Current State: 49:[47, 16], Operations: ['42+5=47', '82-66=16'] Exploring Operation: 47*16=752, Resulting Numbers: [752] 752,49 unequal: No Solution Exploring Operation: 47+16=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,49 unequal: No Solution Moving to Node #0,3,4 Current State: 49:[66, 35], Operations: ['42+5=47', '82-47=35'] Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 66+35=101, Resulting Numbers: [101] 101,49 unequal: No Solution Exploring Operation: 66*35=2310, Resulting Numbers: [2310] 2310,49 unequal: No Solution Moving to Node #0,3,2 Current State: 49:[82, 19], Operations: ['42+5=47', '66-47=19'] Exploring Operation: 82*19=1558, Resulting Numbers: [1558] 1558,49 unequal: No Solution Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 82+19=101, Resulting Numbers: [101] 101,49 unequal: No Solution Moving to Node #0,3,0 Current State: 49:[66, 129], Operations: ['42+5=47', '82+47=129'] Exploring Operation: 129-66=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 66+129=195, Resulting Numbers: [195] 195,49 unequal: No Solution Exploring Operation: 66*129=8514, Resulting Numbers: [8514] 8514,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[82, 113], Operations: ['42+5=47', '66+47=113'] Exploring Operation: 82*113=9266, Resulting Numbers: [9266] 9266,49 unequal: No Solution Exploring Operation: 113-82=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 82+113=195, Resulting Numbers: [195] 195,49 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
[ 87, 4, 46, 30 ]
13
[ "87+46=133", "4*30=120", "133-120=13" ]
Current State: 13:[87, 4, 46, 30], Operations: [] Exploring Operation: 87+46=133, Resulting Numbers: [4, 30, 133] Generated Node #2: [4, 30, 133] from Operation: 87+46=133 Current State: 13:[4, 30, 133], Operations: ['87+46=133'] Exploring Operation: 4*30=120, Resulting Numbers: [133, 120] Generated Node #3: [133, 120] from Operation: 4*30=120 Current State: 13:[133, 120], Operations: ['87+46=133', '4*30=120'] Exploring Operation: 133-120=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[87, 4, 46, 30], Operations: [] Exploring Operation: 87-46=41, Resulting Numbers: [4, 30, 41] Generated Node #0,0: 13:[4, 30, 41] Operation: 87-46=41 Moving to Node #0,0 Current State: 13:[4, 30, 41], Operations: ['87-46=41'] Exploring Operation: 41-30=11, Resulting Numbers: [4, 11] Generated Node #0,0,0: 13:[4, 11] Operation: 41-30=11 Moving to Node #0,0,0 Current State: 13:[4, 11], Operations: ['87-46=41', '41-30=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,13 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 91, 45, 35, 88 ]
13
[ "91+45=136", "35+88=123", "136-123=13" ]
Current State: 13:[91, 45, 35, 88], Operations: [] Exploring Operation: 91+45=136, Resulting Numbers: [35, 88, 136] Generated Node #2: [35, 88, 136] from Operation: 91+45=136 Current State: 13:[35, 88, 136], Operations: ['91+45=136'] Exploring Operation: 35+88=123, Resulting Numbers: [136, 123] Generated Node #3: [136, 123] from Operation: 35+88=123 Current State: 13:[136, 123], Operations: ['91+45=136', '35+88=123'] Exploring Operation: 136-123=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[91, 45, 35, 88], Operations: [] Exploring Operation: 91-88=3, Resulting Numbers: [45, 35, 3] Generated Node #0,0: 13:[45, 35, 3] Operation: 91-88=3 Exploring Operation: 91-35=56, Resulting Numbers: [45, 88, 56] Generated Node #0,1: 13:[45, 88, 56] Operation: 91-35=56 Exploring Operation: 91-45=46, Resulting Numbers: [35, 88, 46] Generated Node #0,2: 13:[35, 88, 46] Operation: 91-45=46 Exploring Operation: 88-45=43, Resulting Numbers: [91, 35, 43] Generated Node #0,3: 13:[91, 35, 43] Operation: 88-45=43 Moving to Node #0,0 Current State: 13:[45, 35, 3], Operations: ['91-88=3'] Exploring Operation: 45-3=42, Resulting Numbers: [35, 42] Generated Node #0,0,0: 13:[35, 42] Operation: 45-3=42 Exploring Operation: 35-3=32, Resulting Numbers: [45, 32] Generated Node #0,0,1: 13:[45, 32] Operation: 35-3=32 Exploring Operation: 45/3=15, Resulting Numbers: [35, 15] Generated Node #0,0,2: 13:[35, 15] Operation: 45/3=15 Exploring Operation: 45-35=10, Resulting Numbers: [3, 10] Generated Node #0,0,3: 13:[3, 10] Operation: 45-35=10 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 13:[3, 10], Operations: ['91-88=3', '45-35=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[91, 45, 35, 88], Operations: [] Exploring Operation: 91-88=3, Resulting Numbers: [45, 35, 3] Generated Node #0,0: 13:[45, 35, 3] Operation: 91-88=3 Moving to Node #0,0 Current State: 13:[45, 35, 3], Operations: ['91-88=3'] Exploring Operation: 45-35=10, Resulting Numbers: [3, 10] Generated Node #0,0,3: 13:[3, 10] Operation: 45-35=10 Moving to Node #0,0,3 Current State: 13:[3, 10], Operations: ['91-88=3', '45-35=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 10, 42, 7, 3 ]
56
[ "10+42=52", "7-3=4", "52+4=56" ]
Current State: 56:[10, 42, 7, 3], Operations: [] Exploring Operation: 10+42=52, Resulting Numbers: [7, 3, 52] Generated Node #2: [7, 3, 52] from Operation: 10+42=52 Current State: 56:[7, 3, 52], Operations: ['10+42=52'] Exploring Operation: 7-3=4, Resulting Numbers: [52, 4] Generated Node #3: [52, 4] from Operation: 7-3=4 Current State: 56:[52, 4], Operations: ['10+42=52', '7-3=4'] Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[10, 42, 7, 3], Operations: [] Exploring Operation: 42/3=14, Resulting Numbers: [10, 7, 14] Generated Node #0,0: 56:[10, 7, 14] Operation: 42/3=14 Exploring Operation: 42-10=32, Resulting Numbers: [7, 3, 32] Generated Node #0,1: 56:[7, 3, 32] Operation: 42-10=32 Exploring Operation: 10+42=52, Resulting Numbers: [7, 3, 52] Generated Node #0,2: 56:[7, 3, 52] Operation: 10+42=52 Exploring Operation: 42/7=6, Resulting Numbers: [10, 3, 6] Generated Node #0,3: 56:[10, 3, 6] Operation: 42/7=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[10, 7, 14], Operations: ['42/3=14'] Exploring Operation: 14/7=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 56:[10, 2] Operation: 14/7=2 Exploring Operation: 14-10=4, Resulting Numbers: [7, 4] Generated Node #0,0,1: 56:[7, 4] Operation: 14-10=4 Exploring Operation: 14-7=7, Resulting Numbers: [10, 7] Generated Node #0,0,2: 56:[10, 7] Operation: 14-7=7 Exploring Operation: 10-7=3, Resulting Numbers: [14, 3] Generated Node #0,0,3: 56:[14, 3] Operation: 10-7=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[7, 4], Operations: ['42/3=14', '14-10=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 56:[14, 3], Operations: ['42/3=14', '10-7=3'] Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[10, 2], Operations: ['42/3=14', '14/7=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 56:[10, 7], Operations: ['42/3=14', '14-7=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[10, 3, 6], Operations: ['42/7=6'] Exploring Operation: 6/3=2, Resulting Numbers: [10, 2] Generated Node #0,3,0: 56:[10, 2] Operation: 6/3=2 Exploring Operation: 10+3=13, Resulting Numbers: [6, 13] Generated Node #0,3,1: 56:[6, 13] Operation: 10+3=13 Exploring Operation: 10-6=4, Resulting Numbers: [3, 4] Generated Node #0,3,2: 56:[3, 4] Operation: 10-6=4 Exploring Operation: 10-3=7, Resulting Numbers: [6, 7] Generated Node #0,3,3: 56:[6, 7] Operation: 10-3=7 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 56:[3, 4], Operations: ['42/7=6', '10-6=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 56:[6, 7], Operations: ['42/7=6', '10-3=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 56:[10, 2], Operations: ['42/7=6', '6/3=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 56:[6, 13], Operations: ['42/7=6', '10+3=13'] Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[7, 3, 32], Operations: ['42-10=32'] Exploring Operation: 7+3=10, Resulting Numbers: [32, 10] Generated Node #0,1,0: 56:[32, 10] Operation: 7+3=10 Exploring Operation: 32-3=29, Resulting Numbers: [7, 29] Generated Node #0,1,1: 56:[7, 29] Operation: 32-3=29 Exploring Operation: 7-3=4, Resulting Numbers: [32, 4] Generated Node #0,1,2: 56:[32, 4] Operation: 7-3=4 Exploring Operation: 32-7=25, Resulting Numbers: [3, 25] Generated Node #0,1,3: 56:[3, 25] Operation: 32-7=25 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 56:[7, 29], Operations: ['42-10=32', '32-3=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,56 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 56:[32, 4], Operations: ['42-10=32', '7-3=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,56 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,56 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 56:[3, 25], Operations: ['42-10=32', '32-7=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,56 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 56:[32, 10], Operations: ['42-10=32', '7+3=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,56 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[7, 3, 52], Operations: ['10+42=52'] Exploring Operation: 7-3=4, Resulting Numbers: [52, 4] Generated Node #0,2,0: 56:[52, 4] Operation: 7-3=4 Exploring Operation: 7+52=59, Resulting Numbers: [3, 59] Generated Node #0,2,1: 56:[3, 59] Operation: 7+52=59 Exploring Operation: 3+52=55, Resulting Numbers: [7, 55] Generated Node #0,2,2: 56:[7, 55] Operation: 3+52=55 Exploring Operation: 7+3=10, Resulting Numbers: [52, 10] Generated Node #0,2,3: 56:[52, 10] Operation: 7+3=10 Moving to Node #0,2,2 Current State: 56:[7, 55], Operations: ['10+42=52', '3+52=55'] Exploring Operation: 7+55=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 7*55=385, Resulting Numbers: [385] 385,56 unequal: No Solution Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[3, 59], Operations: ['10+42=52', '7+52=59'] Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,56 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[10, 42, 7, 3], Operations: [] Exploring Operation: 10+42=52, Resulting Numbers: [7, 3, 52] Generated Node #0,2: 56:[7, 3, 52] Operation: 10+42=52 Moving to Node #0,2 Current State: 56:[7, 3, 52], Operations: ['10+42=52'] Exploring Operation: 7+52=59, Resulting Numbers: [3, 59] Generated Node #0,2,1: 56:[3, 59] Operation: 7+52=59 Moving to Node #0,2,1 Current State: 56:[3, 59], Operations: ['10+42=52', '7+52=59'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.940972
hs_4
sum_heuristic
[ 64, 2, 17, 76 ]
12
[ "64*2=128", "76+128=204", "204/17=12" ]
Current State: 12:[64, 2, 17, 76], Operations: [] Exploring Operation: 64*2=128, Resulting Numbers: [17, 76, 128] Generated Node #2: [17, 76, 128] from Operation: 64*2=128 Current State: 12:[17, 76, 128], Operations: ['64*2=128'] Exploring Operation: 76+128=204, Resulting Numbers: [17, 204] Generated Node #3: [17, 204] from Operation: 76+128=204 Current State: 12:[17, 204], Operations: ['64*2=128', '76+128=204'] Exploring Operation: 204/17=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[64, 2, 17, 76], Operations: [] Exploring Operation: 76-64=12, Resulting Numbers: [2, 17, 12] Generated Node #0,0: 12:[2, 17, 12] Operation: 76-64=12 Moving to Node #0,0 Current State: 12:[2, 17, 12], Operations: ['76-64=12'] Exploring Operation: 17-12=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 12:[2, 5] Operation: 17-12=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[2, 5], Operations: ['76-64=12', '17-12=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 51, 27, 87, 44 ]
53
[ "51+27=78", "87+44=131", "131-78=53" ]
Current State: 53:[51, 27, 87, 44], Operations: [] Exploring Operation: 51+27=78, Resulting Numbers: [87, 44, 78] Generated Node #2: [87, 44, 78] from Operation: 51+27=78 Current State: 53:[87, 44, 78], Operations: ['51+27=78'] Exploring Operation: 87+44=131, Resulting Numbers: [78, 131] Generated Node #3: [78, 131] from Operation: 87+44=131 Current State: 53:[78, 131], Operations: ['51+27=78', '87+44=131'] Exploring Operation: 131-78=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[51, 27, 87, 44], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [51, 27, 43] Generated Node #0,0: 53:[51, 27, 43] Operation: 87-44=43 Exploring Operation: 87-51=36, Resulting Numbers: [27, 44, 36] Generated Node #0,1: 53:[27, 44, 36] Operation: 87-51=36 Exploring Operation: 87-27=60, Resulting Numbers: [51, 44, 60] Generated Node #0,2: 53:[51, 44, 60] Operation: 87-27=60 Moving to Node #0,2 Current State: 53:[51, 44, 60], Operations: ['87-27=60'] Exploring Operation: 51+44=95, Resulting Numbers: [60, 95] Generated Node #0,2,0: 53:[60, 95] Operation: 51+44=95 Exploring Operation: 51-44=7, Resulting Numbers: [60, 7] Generated Node #0,2,1: 53:[60, 7] Operation: 51-44=7 Exploring Operation: 60-44=16, Resulting Numbers: [51, 16] Generated Node #0,2,2: 53:[51, 16] Operation: 60-44=16 Moving to Node #0,0 Current State: 53:[51, 27, 43], Operations: ['87-44=43'] Exploring Operation: 51+27=78, Resulting Numbers: [43, 78] Generated Node #0,0,0: 53:[43, 78] Operation: 51+27=78 Exploring Operation: 51-27=24, Resulting Numbers: [43, 24] Generated Node #0,0,1: 53:[43, 24] Operation: 51-27=24 Exploring Operation: 27+43=70, Resulting Numbers: [51, 70] Generated Node #0,0,2: 53:[51, 70] Operation: 27+43=70 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[51, 70], Operations: ['87-44=43', '27+43=70'] Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,53 unequal: No Solution Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,53 unequal: No Solution Exploring Operation: 70-51=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 #0,0,0 Current State: 53:[43, 78], Operations: ['87-44=43', '51+27=78'] Exploring Operation: 43+78=121, Resulting Numbers: [121] 121,53 unequal: No Solution Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 43*78=3354, Resulting Numbers: [3354] 3354,53 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 #0,0,1 Current State: 53:[43, 24], Operations: ['87-44=43', '51-27=24'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,53 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,53 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: 53:[27, 44, 36], Operations: ['87-51=36'] Exploring Operation: 27+36=63, Resulting Numbers: [44, 63] Generated Node #0,1,0: 53:[44, 63] Operation: 27+36=63 Exploring Operation: 44-27=17, Resulting Numbers: [36, 17] Generated Node #0,1,1: 53:[36, 17] Operation: 44-27=17 Exploring Operation: 27+44=71, Resulting Numbers: [36, 71] Generated Node #0,1,2: 53:[36, 71] Operation: 27+44=71 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[44, 63], Operations: ['87-51=36', '27+36=63'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 44*63=2772, Resulting Numbers: [2772] 2772,53 unequal: No Solution Exploring Operation: 44+63=107, Resulting Numbers: [107] 107,53 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 #0,1,2 Current State: 53:[36, 71], Operations: ['87-51=36', '27+44=71'] Exploring Operation: 36*71=2556, Resulting Numbers: [2556] 2556,53 unequal: No Solution Exploring Operation: 36+71=107, Resulting Numbers: [107] 107,53 unequal: No Solution Exploring Operation: 71-36=35, Resulting Numbers: [35] 35,53 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 #0,1,1 Current State: 53:[36, 17], Operations: ['87-51=36', '44-27=17'] Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[51, 27, 87, 44], Operations: [] Exploring Operation: 87-51=36, Resulting Numbers: [27, 44, 36] Generated Node #0,1: 53:[27, 44, 36] Operation: 87-51=36 Moving to Node #0,1 Current State: 53:[27, 44, 36], Operations: ['87-51=36'] Exploring Operation: 44-27=17, Resulting Numbers: [36, 17] Generated Node #0,1,1: 53:[36, 17] Operation: 44-27=17 Moving to Node #0,1,1 Current State: 53:[36, 17], Operations: ['87-51=36', '44-27=17'] Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_3
mult_heuristic
[ 67, 45, 18, 50 ]
17
[ "67+18=85", "50-45=5", "85/5=17" ]
Current State: 17:[67, 45, 18, 50], Operations: [] Exploring Operation: 67+18=85, Resulting Numbers: [45, 50, 85] Generated Node #2: [45, 50, 85] from Operation: 67+18=85 Current State: 17:[45, 50, 85], Operations: ['67+18=85'] Exploring Operation: 50-45=5, Resulting Numbers: [85, 5] Generated Node #3: [85, 5] from Operation: 50-45=5 Current State: 17:[85, 5], Operations: ['67+18=85', '50-45=5'] Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[67, 45, 18, 50], Operations: [] Exploring Operation: 50-45=5, Resulting Numbers: [67, 18, 5] Generated Node #0,0: 17:[67, 18, 5] Operation: 50-45=5 Exploring Operation: 67-50=17, Resulting Numbers: [45, 18, 17] Generated Node #0,1: 17:[45, 18, 17] Operation: 67-50=17 Exploring Operation: 67-45=22, Resulting Numbers: [18, 50, 22] Generated Node #0,2: 17:[18, 50, 22] Operation: 67-45=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[45, 18, 17], Operations: ['67-50=17'] Exploring Operation: 45-17=28, Resulting Numbers: [18, 28] Generated Node #0,1,0: 17:[18, 28] Operation: 45-17=28 Exploring Operation: 18-17=1, Resulting Numbers: [45, 1] Generated Node #0,1,1: 17:[45, 1] Operation: 18-17=1 Exploring Operation: 45-18=27, Resulting Numbers: [17, 27] Generated Node #0,1,2: 17:[17, 27] Operation: 45-18=27 Moving to Node #0,1,2 Current State: 17:[17, 27], Operations: ['67-50=17', '45-18=27'] Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[18, 28], Operations: ['67-50=17', '45-17=28'] Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 18*28=504, Resulting Numbers: [504] 504,17 unequal: No Solution Exploring Operation: 18+28=46, Resulting Numbers: [46] 46,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[45, 1], Operations: ['67-50=17', '18-17=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[18, 50, 22], Operations: ['67-45=22'] Exploring Operation: 50-18=32, Resulting Numbers: [22, 32] Generated Node #0,2,0: 17:[22, 32] Operation: 50-18=32 Exploring Operation: 22-18=4, Resulting Numbers: [50, 4] Generated Node #0,2,1: 17:[50, 4] Operation: 22-18=4 Exploring Operation: 50-22=28, Resulting Numbers: [18, 28] Generated Node #0,2,2: 17:[18, 28] Operation: 50-22=28 Moving to Node #0,2,2 Current State: 17:[18, 28], Operations: ['67-45=22', '50-22=28'] Exploring Operation: 18*28=504, Resulting Numbers: [504] 504,17 unequal: No Solution Exploring Operation: 18+28=46, Resulting Numbers: [46] 46,17 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[22, 32], Operations: ['67-45=22', '50-18=32'] Exploring Operation: 22+32=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 22*32=704, Resulting Numbers: [704] 704,17 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[50, 4], Operations: ['67-45=22', '22-18=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,17 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[67, 18, 5], Operations: ['50-45=5'] Exploring Operation: 18-5=13, Resulting Numbers: [67, 13] Generated Node #0,0,0: 17:[67, 13] Operation: 18-5=13 Exploring Operation: 67-5=62, Resulting Numbers: [18, 62] Generated Node #0,0,1: 17:[18, 62] Operation: 67-5=62 Exploring Operation: 67-18=49, Resulting Numbers: [5, 49] Generated Node #0,0,2: 17:[5, 49] Operation: 67-18=49 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 17:[5, 49], Operations: ['50-45=5', '67-18=49'] Exploring Operation: 5*49=245, Resulting Numbers: [245] 245,17 unequal: No Solution Exploring Operation: 5+49=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,17 unequal: No Solution No 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: 17:[18, 62], Operations: ['50-45=5', '67-5=62'] Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 18*62=1116, Resulting Numbers: [1116] 1116,17 unequal: No Solution Exploring Operation: 18+62=80, Resulting Numbers: [80] 80,17 unequal: No Solution No 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: 17:[67, 13], Operations: ['50-45=5', '18-5=13'] Exploring Operation: 67-13=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 67+13=80, Resulting Numbers: [80] 80,17 unequal: No Solution Exploring Operation: 67*13=871, Resulting Numbers: [871] 871,17 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
[ 7, 34, 25, 76 ]
19
[ "76-34=42", "42/7=6", "25-6=19" ]
Current State: 19:[7, 34, 25, 76], Operations: [] Exploring Operation: 76-34=42, Resulting Numbers: [7, 25, 42] Generated Node #2: [7, 25, 42] from Operation: 76-34=42 Current State: 19:[7, 25, 42], Operations: ['76-34=42'] Exploring Operation: 42/7=6, Resulting Numbers: [25, 6] Generated Node #3: [25, 6] from Operation: 42/7=6 Current State: 19:[25, 6], Operations: ['76-34=42', '42/7=6'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[7, 34, 25, 76], Operations: [] Exploring Operation: 76-34=42, Resulting Numbers: [7, 25, 42] Generated Node #0,0: 19:[7, 25, 42] Operation: 76-34=42 Moving to Node #0,0 Current State: 19:[7, 25, 42], Operations: ['76-34=42'] Exploring Operation: 42-25=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 19:[7, 17] Operation: 42-25=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[7, 17], Operations: ['76-34=42', '42-25=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,19 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
[ 54, 6, 53, 41 ]
36
[ "54-6=48", "53-41=12", "48-12=36" ]
Current State: 36:[54, 6, 53, 41], Operations: [] Exploring Operation: 54-6=48, Resulting Numbers: [53, 41, 48] Generated Node #2: [53, 41, 48] from Operation: 54-6=48 Current State: 36:[53, 41, 48], Operations: ['54-6=48'] Exploring Operation: 53-41=12, Resulting Numbers: [48, 12] Generated Node #3: [48, 12] from Operation: 53-41=12 Current State: 36:[48, 12], Operations: ['54-6=48', '53-41=12'] Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[54, 6, 53, 41], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [6, 53, 13] Generated Node #0,0: 36:[6, 53, 13] Operation: 54-41=13 Exploring Operation: 53-41=12, Resulting Numbers: [54, 6, 12] Generated Node #0,1: 36:[54, 6, 12] Operation: 53-41=12 Exploring Operation: 54-6=48, Resulting Numbers: [53, 41, 48] Generated Node #0,2: 36:[53, 41, 48] Operation: 54-6=48 Exploring Operation: 54-53=1, Resulting Numbers: [6, 41, 1] Generated Node #0,3: 36:[6, 41, 1] Operation: 54-53=1 Exploring Operation: 54/6=9, Resulting Numbers: [53, 41, 9] Generated Node #0,4: 36:[53, 41, 9] Operation: 54/6=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 36:[6, 41, 1], Operations: ['54-53=1'] Exploring Operation: 6*1=6, Resulting Numbers: [41, 6] Generated Node #0,3,0: 36:[41, 6] Operation: 6*1=6 Exploring Operation: 41*1=41, Resulting Numbers: [6, 41] Generated Node #0,3,1: 36:[6, 41] Operation: 41*1=41 Exploring Operation: 41-6=35, Resulting Numbers: [1, 35] Generated Node #0,3,2: 36:[1, 35] Operation: 41-6=35 Exploring Operation: 6/1=6, Resulting Numbers: [41, 6] Generated Node #0,3,3: 36:[41, 6] Operation: 6/1=6 Exploring Operation: 41-1=40, Resulting Numbers: [6, 40] Generated Node #0,3,4: 36:[6, 40] Operation: 41-1=40 Moving to Node #0,3,2 Current State: 36:[1, 35], Operations: ['54-53=1', '41-6=35'] Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,36 unequal: No Solution Exploring Operation: 1+35=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[54, 6, 53, 41], Operations: [] Exploring Operation: 54-53=1, Resulting Numbers: [6, 41, 1] Generated Node #0,3: 36:[6, 41, 1] Operation: 54-53=1 Moving to Node #0,3 Current State: 36:[6, 41, 1], Operations: ['54-53=1'] Exploring Operation: 41-6=35, Resulting Numbers: [1, 35] Generated Node #0,3,2: 36:[1, 35] Operation: 41-6=35 Moving to Node #0,3,2 Current State: 36:[1, 35], Operations: ['54-53=1', '41-6=35'] Exploring Operation: 1+35=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 55, 46, 48, 10 ]
49
[ "55-46=9", "48+10=58", "58-9=49" ]
Current State: 49:[55, 46, 48, 10], Operations: [] Exploring Operation: 55-46=9, Resulting Numbers: [48, 10, 9] Generated Node #2: [48, 10, 9] from Operation: 55-46=9 Current State: 49:[48, 10, 9], Operations: ['55-46=9'] Exploring Operation: 48+10=58, Resulting Numbers: [9, 58] Generated Node #3: [9, 58] from Operation: 48+10=58 Current State: 49:[9, 58], Operations: ['55-46=9', '48+10=58'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[55, 46, 48, 10], Operations: [] Exploring Operation: 48-46=2, Resulting Numbers: [55, 10, 2] Generated Node #0,0: 49:[55, 10, 2] Operation: 48-46=2 Exploring Operation: 55-46=9, Resulting Numbers: [48, 10, 9] Generated Node #0,1: 49:[48, 10, 9] Operation: 55-46=9 Exploring Operation: 55-10=45, Resulting Numbers: [46, 48, 45] Generated Node #0,2: 49:[46, 48, 45] Operation: 55-10=45 Exploring Operation: 55-48=7, Resulting Numbers: [46, 10, 7] Generated Node #0,3: 49:[46, 10, 7] Operation: 55-48=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[48, 10, 9], Operations: ['55-46=9'] Exploring Operation: 48-10=38, Resulting Numbers: [9, 38] Generated Node #0,1,0: 49:[9, 38] Operation: 48-10=38 Exploring Operation: 10-9=1, Resulting Numbers: [48, 1] Generated Node #0,1,1: 49:[48, 1] Operation: 10-9=1 Exploring Operation: 48+9=57, Resulting Numbers: [10, 57] Generated Node #0,1,2: 49:[10, 57] Operation: 48+9=57 Exploring Operation: 48+10=58, Resulting Numbers: [9, 58] Generated Node #0,1,3: 49:[9, 58] Operation: 48+10=58 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[48, 1], Operations: ['55-46=9', '10-9=1'] Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,49 unequal: No Solution Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[55, 46, 48, 10], Operations: [] Exploring Operation: 55-46=9, Resulting Numbers: [48, 10, 9] Generated Node #0,1: 49:[48, 10, 9] Operation: 55-46=9 Moving to Node #0,1 Current State: 49:[48, 10, 9], Operations: ['55-46=9'] Exploring Operation: 10-9=1, Resulting Numbers: [48, 1] Generated Node #0,1,1: 49:[48, 1] Operation: 10-9=1 Moving to Node #0,1,1 Current State: 49:[48, 1], Operations: ['55-46=9', '10-9=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 73, 6, 15, 78 ]
24
[ "73*6=438", "438-78=360", "360/15=24" ]
Current State: 24:[73, 6, 15, 78], Operations: [] Exploring Operation: 73*6=438, Resulting Numbers: [15, 78, 438] Generated Node #2: [15, 78, 438] from Operation: 73*6=438 Current State: 24:[15, 78, 438], Operations: ['73*6=438'] Exploring Operation: 438-78=360, Resulting Numbers: [15, 360] Generated Node #3: [15, 360] from Operation: 438-78=360 Current State: 24:[15, 360], Operations: ['73*6=438', '438-78=360'] Exploring Operation: 360/15=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[73, 6, 15, 78], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [73, 15, 13] Generated Node #0,0: 24:[73, 15, 13] Operation: 78/6=13 Exploring Operation: 73-15=58, Resulting Numbers: [6, 78, 58] Generated Node #0,1: 24:[6, 78, 58] Operation: 73-15=58 Exploring Operation: 78-73=5, Resulting Numbers: [6, 15, 5] Generated Node #0,2: 24:[6, 15, 5] Operation: 78-73=5 Moving to Node #0,2 Current State: 24:[6, 15, 5], Operations: ['78-73=5'] Exploring Operation: 15/5=3, Resulting Numbers: [6, 3] Generated Node #0,2,0: 24:[6, 3] Operation: 15/5=3 Exploring Operation: 15-6=9, Resulting Numbers: [5, 9] Generated Node #0,2,1: 24:[5, 9] Operation: 15-6=9 Exploring Operation: 15-5=10, Resulting Numbers: [6, 10] Generated Node #0,2,2: 24:[6, 10] Operation: 15-5=10 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 24:[6, 3], Operations: ['78-73=5', '15/5=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 24:[5, 9], Operations: ['78-73=5', '15-6=9'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 24:[6, 10], Operations: ['78-73=5', '15-5=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 24:[73, 15, 13], Operations: ['78/6=13'] Exploring Operation: 73-13=60, Resulting Numbers: [15, 60] Generated Node #0,0,0: 24:[15, 60] Operation: 73-13=60 Exploring Operation: 15-13=2, Resulting Numbers: [73, 2] Generated Node #0,0,1: 24:[73, 2] Operation: 15-13=2 Exploring Operation: 73-15=58, Resulting Numbers: [13, 58] Generated Node #0,0,2: 24:[13, 58] Operation: 73-15=58 Moving to Node #0,1 Current State: 24:[6, 78, 58], Operations: ['73-15=58'] Exploring Operation: 78-6=72, Resulting Numbers: [58, 72] Generated Node #0,1,0: 24:[58, 72] Operation: 78-6=72 Exploring Operation: 78-58=20, Resulting Numbers: [6, 20] Generated Node #0,1,1: 24:[6, 20] Operation: 78-58=20 Exploring Operation: 78/6=13, Resulting Numbers: [58, 13] Generated Node #0,1,2: 24:[58, 13] Operation: 78/6=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[6, 20], Operations: ['73-15=58', '78-58=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,24 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[58, 13], Operations: ['73-15=58', '78/6=13'] Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,24 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[58, 72], Operations: ['73-15=58', '78-6=72'] Exploring Operation: 58+72=130, Resulting Numbers: [130] 130,24 unequal: No Solution Exploring Operation: 58*72=4176, Resulting Numbers: [4176] 4176,24 unequal: No Solution Exploring Operation: 72-58=14, Resulting Numbers: [14] 14,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 24:[13, 58], Operations: ['78/6=13', '73-15=58'] Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,24 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[15, 60], Operations: ['78/6=13', '73-13=60'] Exploring Operation: 15+60=75, Resulting Numbers: [75] 75,24 unequal: No Solution Exploring Operation: 60/15=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 60-15=45, Resulting Numbers: [45] 45,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[73, 2], Operations: ['78/6=13', '15-13=2'] Exploring Operation: 73*2=146, Resulting Numbers: [146] 146,24 unequal: No Solution Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,24 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,24 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 35, 5, 18, 9 ]
100
[ "18+9=27", "5*27=135", "135-35=100" ]
Current State: 100:[35, 5, 18, 9], Operations: [] Exploring Operation: 18+9=27, Resulting Numbers: [35, 5, 27] Generated Node #2: [35, 5, 27] from Operation: 18+9=27 Current State: 100:[35, 5, 27], Operations: ['18+9=27'] Exploring Operation: 5*27=135, Resulting Numbers: [35, 135] Generated Node #3: [35, 135] from Operation: 5*27=135 Current State: 100:[35, 135], Operations: ['18+9=27', '5*27=135'] Exploring Operation: 135-35=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[35, 5, 18, 9], Operations: [] Exploring Operation: 35-9=26, Resulting Numbers: [5, 18, 26] Generated Node #0,0: 100:[5, 18, 26] Operation: 35-9=26 Moving to Node #0,0 Current State: 100:[5, 18, 26], Operations: ['35-9=26'] Exploring Operation: 26-18=8, Resulting Numbers: [5, 8] Generated Node #0,0,0: 100:[5, 8] Operation: 26-18=8 Moving to Node #0,0,0 Current State: 100:[5, 8], Operations: ['35-9=26', '26-18=8'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,100 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 62, 53, 2, 70 ]
77
[ "62-53=9", "70-2=68", "9+68=77" ]
Current State: 77:[62, 53, 2, 70], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [2, 70, 9] Generated Node #2: [2, 70, 9] from Operation: 62-53=9 Current State: 77:[2, 70, 9], Operations: ['62-53=9'] Exploring Operation: 70-2=68, Resulting Numbers: [9, 68] Generated Node #3: [9, 68] from Operation: 70-2=68 Current State: 77:[9, 68], Operations: ['62-53=9', '70-2=68'] Exploring Operation: 9+68=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[62, 53, 2, 70], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [2, 70, 9] Generated Node #0,0: 77:[2, 70, 9] Operation: 62-53=9 Exploring Operation: 70-53=17, Resulting Numbers: [62, 2, 17] Generated Node #0,1: 77:[62, 2, 17] Operation: 70-53=17 Exploring Operation: 70-62=8, Resulting Numbers: [53, 2, 8] Generated Node #0,2: 77:[53, 2, 8] Operation: 70-62=8 Exploring Operation: 62+2=64, Resulting Numbers: [53, 70, 64] Generated Node #0,3: 77:[53, 70, 64] Operation: 62+2=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[2, 70, 9], Operations: ['62-53=9'] Exploring Operation: 2+9=11, Resulting Numbers: [70, 11] Generated Node #0,0,0: 77:[70, 11] Operation: 2+9=11 Exploring Operation: 70+9=79, Resulting Numbers: [2, 79] Generated Node #0,0,1: 77:[2, 79] Operation: 70+9=79 Exploring Operation: 9-2=7, Resulting Numbers: [70, 7] Generated Node #0,0,2: 77:[70, 7] Operation: 9-2=7 Exploring Operation: 2+70=72, Resulting Numbers: [9, 72] Generated Node #0,0,3: 77:[9, 72] Operation: 2+70=72 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[70, 11], Operations: ['62-53=9', '2+9=11'] Exploring Operation: 70-11=59, Resulting Numbers: [59] 59,77 unequal: No Solution Exploring Operation: 70+11=81, Resulting Numbers: [81] 81,77 unequal: No Solution Exploring Operation: 70*11=770, Resulting Numbers: [770] 770,77 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 #0,0,1 Current State: 77:[2, 79], Operations: ['62-53=9', '70+9=79'] Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,77 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,77 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[62, 53, 2, 70], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [2, 70, 9] Generated Node #0,0: 77:[2, 70, 9] Operation: 62-53=9 Moving to Node #0,0 Current State: 77:[2, 70, 9], Operations: ['62-53=9'] Exploring Operation: 70+9=79, Resulting Numbers: [2, 79] Generated Node #0,0,1: 77:[2, 79] Operation: 70+9=79 Moving to Node #0,0,1 Current State: 77:[2, 79], Operations: ['62-53=9', '70+9=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 6, 10, 35, 77 ]
73
[ "35-10=25", "6*25=150", "150-77=73" ]
Current State: 73:[6, 10, 35, 77], Operations: [] Exploring Operation: 35-10=25, Resulting Numbers: [6, 77, 25] Generated Node #2: [6, 77, 25] from Operation: 35-10=25 Current State: 73:[6, 77, 25], Operations: ['35-10=25'] Exploring Operation: 6*25=150, Resulting Numbers: [77, 150] Generated Node #3: [77, 150] from Operation: 6*25=150 Current State: 73:[77, 150], Operations: ['35-10=25', '6*25=150'] Exploring Operation: 150-77=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[6, 10, 35, 77], Operations: [] Exploring Operation: 6+35=41, Resulting Numbers: [10, 77, 41] Generated Node #0,0: 73:[10, 77, 41] Operation: 6+35=41 Exploring Operation: 6*10=60, Resulting Numbers: [35, 77, 60] Generated Node #0,1: 73:[35, 77, 60] Operation: 6*10=60 Exploring Operation: 6+10=16, Resulting Numbers: [35, 77, 16] Generated Node #0,2: 73:[35, 77, 16] Operation: 6+10=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[35, 77, 60], Operations: ['6*10=60'] Exploring Operation: 35+60=95, Resulting Numbers: [77, 95] Generated Node #0,1,0: 73:[77, 95] Operation: 35+60=95 Exploring Operation: 77-35=42, Resulting Numbers: [60, 42] Generated Node #0,1,1: 73:[60, 42] Operation: 77-35=42 Exploring Operation: 35+77=112, Resulting Numbers: [60, 112] Generated Node #0,1,2: 73:[60, 112] Operation: 35+77=112 Moving to Node #0,1,0 Current State: 73:[77, 95], Operations: ['6*10=60', '35+60=95'] Exploring Operation: 77*95=7315, Resulting Numbers: [7315] 7315,73 unequal: No Solution Exploring Operation: 77+95=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 95-77=18, Resulting Numbers: [18] 18,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[60, 42], Operations: ['6*10=60', '77-35=42'] Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,73 unequal: No Solution Exploring Operation: 60+42=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 60*42=2520, Resulting Numbers: [2520] 2520,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[60, 112], Operations: ['6*10=60', '35+77=112'] Exploring Operation: 60+112=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 112-60=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 60*112=6720, Resulting Numbers: [6720] 6720,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[10, 77, 41], Operations: ['6+35=41'] Exploring Operation: 10+41=51, Resulting Numbers: [77, 51] Generated Node #0,0,0: 73:[77, 51] Operation: 10+41=51 Exploring Operation: 77-10=67, Resulting Numbers: [41, 67] Generated Node #0,0,1: 73:[41, 67] Operation: 77-10=67 Exploring Operation: 10+77=87, Resulting Numbers: [41, 87] Generated Node #0,0,2: 73:[41, 87] Operation: 10+77=87 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[77, 51], Operations: ['6+35=41', '10+41=51'] Exploring Operation: 77+51=128, Resulting Numbers: [128] 128,73 unequal: No Solution Exploring Operation: 77*51=3927, Resulting Numbers: [3927] 3927,73 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[41, 67], Operations: ['6+35=41', '77-10=67'] Exploring Operation: 41*67=2747, Resulting Numbers: [2747] 2747,73 unequal: No Solution Exploring Operation: 41+67=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[41, 87], Operations: ['6+35=41', '10+77=87'] Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 41*87=3567, Resulting Numbers: [3567] 3567,73 unequal: No Solution Exploring Operation: 41+87=128, Resulting Numbers: [128] 128,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[35, 77, 16], Operations: ['6+10=16'] Exploring Operation: 77-16=61, Resulting Numbers: [35, 61] Generated Node #0,2,0: 73:[35, 61] Operation: 77-16=61 Exploring Operation: 35-16=19, Resulting Numbers: [77, 19] Generated Node #0,2,1: 73:[77, 19] Operation: 35-16=19 Exploring Operation: 35+16=51, Resulting Numbers: [77, 51] Generated Node #0,2,2: 73:[77, 51] Operation: 35+16=51 Moving to Node #0,2,2 Current State: 73:[77, 51], Operations: ['6+10=16', '35+16=51'] Exploring Operation: 77*51=3927, Resulting Numbers: [3927] 3927,73 unequal: No Solution Exploring Operation: 77+51=128, Resulting Numbers: [128] 128,73 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[35, 61], Operations: ['6+10=16', '77-16=61'] Exploring Operation: 35*61=2135, Resulting Numbers: [2135] 2135,73 unequal: No Solution Exploring Operation: 61-35=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 35+61=96, Resulting Numbers: [96] 96,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[77, 19], Operations: ['6+10=16', '35-16=19'] Exploring Operation: 77-19=58, Resulting Numbers: [58] 58,73 unequal: No Solution Exploring Operation: 77*19=1463, Resulting Numbers: [1463] 1463,73 unequal: No Solution Exploring Operation: 77+19=96, Resulting Numbers: [96] 96,73 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
[ 42, 20, 38, 64 ]
48
[ "42-20=22", "64-38=26", "22+26=48" ]
Current State: 48:[42, 20, 38, 64], Operations: [] Exploring Operation: 42-20=22, Resulting Numbers: [38, 64, 22] Generated Node #2: [38, 64, 22] from Operation: 42-20=22 Current State: 48:[38, 64, 22], Operations: ['42-20=22'] Exploring Operation: 64-38=26, Resulting Numbers: [22, 26] Generated Node #3: [22, 26] from Operation: 64-38=26 Current State: 48:[22, 26], Operations: ['42-20=22', '64-38=26'] Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[42, 20, 38, 64], Operations: [] Exploring Operation: 38-20=18, Resulting Numbers: [42, 64, 18] Generated Node #0,0: 48:[42, 64, 18] Operation: 38-20=18 Exploring Operation: 64-42=22, Resulting Numbers: [20, 38, 22] Generated Node #0,1: 48:[20, 38, 22] Operation: 64-42=22 Exploring Operation: 42-38=4, Resulting Numbers: [20, 64, 4] Generated Node #0,2: 48:[20, 64, 4] Operation: 42-38=4 Exploring Operation: 64-38=26, Resulting Numbers: [42, 20, 26] Generated Node #0,3: 48:[42, 20, 26] Operation: 64-38=26 Exploring Operation: 64-20=44, Resulting Numbers: [42, 38, 44] Generated Node #0,4: 48:[42, 38, 44] Operation: 64-20=44 Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[42, 20, 26], Operations: ['64-38=26'] Exploring Operation: 42-26=16, Resulting Numbers: [20, 16] Generated Node #0,3,0: 48:[20, 16] Operation: 42-26=16 Exploring Operation: 42+20=62, Resulting Numbers: [26, 62] Generated Node #0,3,1: 48:[26, 62] Operation: 42+20=62 Exploring Operation: 20+26=46, Resulting Numbers: [42, 46] Generated Node #0,3,2: 48:[42, 46] Operation: 20+26=46 Exploring Operation: 26-20=6, Resulting Numbers: [42, 6] Generated Node #0,3,3: 48:[42, 6] Operation: 26-20=6 Exploring Operation: 42-20=22, Resulting Numbers: [26, 22] Generated Node #0,3,4: 48:[26, 22] Operation: 42-20=22 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 48:[20, 16], Operations: ['64-38=26', '42-26=16'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,48 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,48 unequal: No Solution No 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: 48:[26, 22], Operations: ['64-38=26', '42-20=22'] Exploring Operation: 26*22=572, Resulting Numbers: [572] 572,48 unequal: No Solution Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[42, 20, 38, 64], Operations: [] Exploring Operation: 64-38=26, Resulting Numbers: [42, 20, 26] Generated Node #0,3: 48:[42, 20, 26] Operation: 64-38=26 Moving to Node #0,3 Current State: 48:[42, 20, 26], Operations: ['64-38=26'] Exploring Operation: 42-20=22, Resulting Numbers: [26, 22] Generated Node #0,3,4: 48:[26, 22] Operation: 42-20=22 Moving to Node #0,3,4 Current State: 48:[26, 22], Operations: ['64-38=26', '42-20=22'] Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 65, 51, 2, 96 ]
84
[ "65-51=14", "2+96=98", "98-14=84" ]
Current State: 84:[65, 51, 2, 96], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [2, 96, 14] Generated Node #2: [2, 96, 14] from Operation: 65-51=14 Current State: 84:[2, 96, 14], Operations: ['65-51=14'] Exploring Operation: 2+96=98, Resulting Numbers: [14, 98] Generated Node #3: [14, 98] from Operation: 2+96=98 Current State: 84:[14, 98], Operations: ['65-51=14', '2+96=98'] Exploring Operation: 98-14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[65, 51, 2, 96], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [2, 96, 14] Generated Node #0,0: 84:[2, 96, 14] Operation: 65-51=14 Exploring Operation: 96-65=31, Resulting Numbers: [51, 2, 31] Generated Node #0,1: 84:[51, 2, 31] Operation: 96-65=31 Exploring Operation: 96-51=45, Resulting Numbers: [65, 2, 45] Generated Node #0,2: 84:[65, 2, 45] Operation: 96-51=45 Exploring Operation: 65+2=67, Resulting Numbers: [51, 96, 67] Generated Node #0,3: 84:[51, 96, 67] Operation: 65+2=67 Exploring Operation: 96/2=48, Resulting Numbers: [65, 51, 48] Generated Node #0,4: 84:[65, 51, 48] Operation: 96/2=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[2, 96, 14], Operations: ['65-51=14'] Exploring Operation: 2*14=28, Resulting Numbers: [96, 28] Generated Node #0,0,0: 84:[96, 28] Operation: 2*14=28 Exploring Operation: 96-14=82, Resulting Numbers: [2, 82] Generated Node #0,0,1: 84:[2, 82] Operation: 96-14=82 Exploring Operation: 96/2=48, Resulting Numbers: [14, 48] Generated Node #0,0,2: 84:[14, 48] Operation: 96/2=48 Exploring Operation: 14-2=12, Resulting Numbers: [96, 12] Generated Node #0,0,3: 84:[96, 12] Operation: 14-2=12 Exploring Operation: 96-2=94, Resulting Numbers: [14, 94] Generated Node #0,0,4: 84:[14, 94] Operation: 96-2=94 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 84:[2, 82], Operations: ['65-51=14', '96-14=82'] Exploring Operation: 2*82=164, Resulting Numbers: [164] 164,84 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[65, 51, 2, 96], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [2, 96, 14] Generated Node #0,0: 84:[2, 96, 14] Operation: 65-51=14 Moving to Node #0,0 Current State: 84:[2, 96, 14], Operations: ['65-51=14'] Exploring Operation: 96-14=82, Resulting Numbers: [2, 82] Generated Node #0,0,1: 84:[2, 82] Operation: 96-14=82 Moving to Node #0,0,1 Current State: 84:[2, 82], Operations: ['65-51=14', '96-14=82'] Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 88, 43, 44, 5 ]
46
[ "88/44=2", "43+5=48", "48-2=46" ]
Current State: 46:[88, 43, 44, 5], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [43, 5, 2] Generated Node #2: [43, 5, 2] from Operation: 88/44=2 Current State: 46:[43, 5, 2], Operations: ['88/44=2'] Exploring Operation: 43+5=48, Resulting Numbers: [2, 48] Generated Node #3: [2, 48] from Operation: 43+5=48 Current State: 46:[2, 48], Operations: ['88/44=2', '43+5=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[88, 43, 44, 5], Operations: [] Exploring Operation: 88-44=44, Resulting Numbers: [43, 5, 44] Generated Node #0,0: 46:[43, 5, 44] Operation: 88-44=44 Exploring Operation: 88-43=45, Resulting Numbers: [44, 5, 45] Generated Node #0,1: 46:[44, 5, 45] Operation: 88-43=45 Exploring Operation: 88/44=2, Resulting Numbers: [43, 5, 2] Generated Node #0,2: 46:[43, 5, 2] Operation: 88/44=2 Moving to Node #0,1 Current State: 46:[44, 5, 45], Operations: ['88-43=45'] Exploring Operation: 45-44=1, Resulting Numbers: [5, 1] Generated Node #0,1,0: 46:[5, 1] Operation: 45-44=1 Exploring Operation: 44+5=49, Resulting Numbers: [45, 49] Generated Node #0,1,1: 46:[45, 49] Operation: 44+5=49 Exploring Operation: 5+45=50, Resulting Numbers: [44, 50] Generated Node #0,1,2: 46:[44, 50] Operation: 5+45=50 Moving to Node #0,2 Current State: 46:[43, 5, 2], Operations: ['88/44=2'] Exploring Operation: 43+5=48, Resulting Numbers: [2, 48] Generated Node #0,2,0: 46:[2, 48] Operation: 43+5=48 Exploring Operation: 43+2=45, Resulting Numbers: [5, 45] Generated Node #0,2,1: 46:[5, 45] Operation: 43+2=45 Exploring Operation: 5-2=3, Resulting Numbers: [43, 3] Generated Node #0,2,2: 46:[43, 3] Operation: 5-2=3 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 46:[2, 48], Operations: ['88/44=2', '43+5=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[88, 43, 44, 5], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [43, 5, 2] Generated Node #0,2: 46:[43, 5, 2] Operation: 88/44=2 Moving to Node #0,2 Current State: 46:[43, 5, 2], Operations: ['88/44=2'] Exploring Operation: 43+5=48, Resulting Numbers: [2, 48] Generated Node #0,2,0: 46:[2, 48] Operation: 43+5=48 Moving to Node #0,2,0 Current State: 46:[2, 48], Operations: ['88/44=2', '43+5=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 52, 81, 57, 23 ]
52
[ "81-57=24", "24-23=1", "52*1=52" ]
Current State: 52:[52, 81, 57, 23], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [52, 23, 24] Generated Node #2: [52, 23, 24] from Operation: 81-57=24 Current State: 52:[52, 23, 24], Operations: ['81-57=24'] Exploring Operation: 24-23=1, Resulting Numbers: [52, 1] Generated Node #3: [52, 1] from Operation: 24-23=1 Current State: 52:[52, 1], Operations: ['81-57=24', '24-23=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[52, 81, 57, 23], Operations: [] Exploring Operation: 81-52=29, Resulting Numbers: [57, 23, 29] Generated Node #0,0: 52:[57, 23, 29] Operation: 81-52=29 Exploring Operation: 81-23=58, Resulting Numbers: [52, 57, 58] Generated Node #0,1: 52:[52, 57, 58] Operation: 81-23=58 Exploring Operation: 57-52=5, Resulting Numbers: [81, 23, 5] Generated Node #0,2: 52:[81, 23, 5] Operation: 57-52=5 Exploring Operation: 81-57=24, Resulting Numbers: [52, 23, 24] Generated Node #0,3: 52:[52, 23, 24] Operation: 81-57=24 Moving to Node #0,3 Current State: 52:[52, 23, 24], Operations: ['81-57=24'] Exploring Operation: 23+24=47, Resulting Numbers: [52, 47] Generated Node #0,3,0: 52:[52, 47] Operation: 23+24=47 Exploring Operation: 24-23=1, Resulting Numbers: [52, 1] Generated Node #0,3,1: 52:[52, 1] Operation: 24-23=1 Exploring Operation: 52-24=28, Resulting Numbers: [23, 28] Generated Node #0,3,2: 52:[23, 28] Operation: 52-24=28 Exploring Operation: 52-23=29, Resulting Numbers: [24, 29] Generated Node #0,3,3: 52:[24, 29] Operation: 52-23=29 Moving to Node #0,1 Current State: 52:[52, 57, 58], Operations: ['81-23=58'] Exploring Operation: 57-52=5, Resulting Numbers: [58, 5] Generated Node #0,1,0: 52:[58, 5] Operation: 57-52=5 Exploring Operation: 52+57=109, Resulting Numbers: [58, 109] Generated Node #0,1,1: 52:[58, 109] Operation: 52+57=109 Exploring Operation: 58-57=1, Resulting Numbers: [52, 1] Generated Node #0,1,2: 52:[52, 1] Operation: 58-57=1 Exploring Operation: 58-52=6, Resulting Numbers: [57, 6] Generated Node #0,1,3: 52:[57, 6] Operation: 58-52=6 Moving to Node #0,0 Current State: 52:[57, 23, 29], Operations: ['81-52=29'] Exploring Operation: 23+29=52, Resulting Numbers: [57, 52] Generated Node #0,0,0: 52:[57, 52] Operation: 23+29=52 Exploring Operation: 57-29=28, Resulting Numbers: [23, 28] Generated Node #0,0,1: 52:[23, 28] Operation: 57-29=28 Exploring Operation: 29-23=6, Resulting Numbers: [57, 6] Generated Node #0,0,2: 52:[57, 6] Operation: 29-23=6 Exploring Operation: 57-23=34, Resulting Numbers: [29, 34] Generated Node #0,0,3: 52:[29, 34] Operation: 57-23=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[57, 52], Operations: ['81-52=29', '23+29=52'] Exploring Operation: 57+52=109, Resulting Numbers: [109] 109,52 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 57*52=2964, Resulting Numbers: [2964] 2964,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[23, 28], Operations: ['81-52=29', '57-29=28'] Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,52 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 52:[57, 6], Operations: ['81-52=29', '29-23=6'] Exploring Operation: 57*6=342, Resulting Numbers: [342] 342,52 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 52:[29, 34], Operations: ['81-52=29', '57-23=34'] Exploring Operation: 29*34=986, Resulting Numbers: [986] 986,52 unequal: No Solution Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 52:[81, 23, 5], Operations: ['57-52=5'] Exploring Operation: 23-5=18, Resulting Numbers: [81, 18] Generated Node #0,2,0: 52:[81, 18] Operation: 23-5=18 Exploring Operation: 81-5=76, Resulting Numbers: [23, 76] Generated Node #0,2,1: 52:[23, 76] Operation: 81-5=76 Exploring Operation: 81-23=58, Resulting Numbers: [5, 58] Generated Node #0,2,2: 52:[5, 58] Operation: 81-23=58 Exploring Operation: 23+5=28, Resulting Numbers: [81, 28] Generated Node #0,2,3: 52:[81, 28] Operation: 23+5=28 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[5, 58], Operations: ['57-52=5', '81-23=58'] Exploring Operation: 5*58=290, Resulting Numbers: [290] 290,52 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[23, 76], Operations: ['57-52=5', '81-5=76'] Exploring Operation: 23*76=1748, Resulting Numbers: [1748] 1748,52 unequal: No Solution Exploring Operation: 23+76=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 52:[81, 28], Operations: ['57-52=5', '23+5=28'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 81*28=2268, Resulting Numbers: [2268] 2268,52 unequal: No Solution Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[81, 18], Operations: ['57-52=5', '23-5=18'] Exploring Operation: 81-18=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 81+18=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 81*18=1458, Resulting Numbers: [1458] 1458,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 52:[52, 1], Operations: ['81-57=24', '24-23=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[52, 81, 57, 23], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [52, 23, 24] Generated Node #0,3: 52:[52, 23, 24] Operation: 81-57=24 Moving to Node #0,3 Current State: 52:[52, 23, 24], Operations: ['81-57=24'] Exploring Operation: 24-23=1, Resulting Numbers: [52, 1] Generated Node #0,3,1: 52:[52, 1] Operation: 24-23=1 Moving to Node #0,3,1 Current State: 52:[52, 1], Operations: ['81-57=24', '24-23=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.957465
hs_4
sum_heuristic
[ 37, 2, 43, 25 ]
46
[ "43-25=18", "18/2=9", "37+9=46" ]
Current State: 46:[37, 2, 43, 25], Operations: [] Exploring Operation: 43-25=18, Resulting Numbers: [37, 2, 18] Generated Node #2: [37, 2, 18] from Operation: 43-25=18 Current State: 46:[37, 2, 18], Operations: ['43-25=18'] Exploring Operation: 18/2=9, Resulting Numbers: [37, 9] Generated Node #3: [37, 9] from Operation: 18/2=9 Current State: 46:[37, 9], Operations: ['43-25=18', '18/2=9'] Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[37, 2, 43, 25], Operations: [] Exploring Operation: 2+43=45, Resulting Numbers: [37, 25, 45] Generated Node #0,0: 46:[37, 25, 45] Operation: 2+43=45 Exploring Operation: 37+2=39, Resulting Numbers: [43, 25, 39] Generated Node #0,1: 46:[43, 25, 39] Operation: 37+2=39 Exploring Operation: 25-2=23, Resulting Numbers: [37, 43, 23] Generated Node #0,2: 46:[37, 43, 23] Operation: 25-2=23 Exploring Operation: 37-25=12, Resulting Numbers: [2, 43, 12] Generated Node #0,3: 46:[2, 43, 12] Operation: 37-25=12 Exploring Operation: 43-37=6, Resulting Numbers: [2, 25, 6] Generated Node #0,4: 46:[2, 25, 6] Operation: 43-37=6 Moving to Node #0,4 Current State: 46:[2, 25, 6], Operations: ['43-37=6'] Exploring Operation: 2+25=27, Resulting Numbers: [6, 27] Generated Node #0,4,0: 46:[6, 27] Operation: 2+25=27 Exploring Operation: 25-2=23, Resulting Numbers: [6, 23] Generated Node #0,4,1: 46:[6, 23] Operation: 25-2=23 Exploring Operation: 6/2=3, Resulting Numbers: [25, 3] Generated Node #0,4,2: 46:[25, 3] Operation: 6/2=3 Exploring Operation: 25-6=19, Resulting Numbers: [2, 19] Generated Node #0,4,3: 46:[2, 19] Operation: 25-6=19 Exploring Operation: 6-2=4, Resulting Numbers: [25, 4] Generated Node #0,4,4: 46:[25, 4] Operation: 6-2=4 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 46:[25, 3], Operations: ['43-37=6', '6/2=3'] Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,46 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,46 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,46 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 #0,4,1 Current State: 46:[6, 23], Operations: ['43-37=6', '25-2=23'] Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,46 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,46 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 #0,4,3 Current State: 46:[2, 19], Operations: ['43-37=6', '25-6=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,46 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,46 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,46 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 #0,4,4 Current State: 46:[25, 4], Operations: ['43-37=6', '6-2=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,46 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 #0,4,0 Current State: 46:[6, 27], Operations: ['43-37=6', '2+25=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 6*27=162, Resulting Numbers: [162] 162,46 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: 46:[43, 25, 39], Operations: ['37+2=39'] Exploring Operation: 43+25=68, Resulting Numbers: [39, 68] Generated Node #0,1,0: 46:[39, 68] Operation: 43+25=68 Exploring Operation: 25+39=64, Resulting Numbers: [43, 64] Generated Node #0,1,1: 46:[43, 64] Operation: 25+39=64 Exploring Operation: 43-25=18, Resulting Numbers: [39, 18] Generated Node #0,1,2: 46:[39, 18] Operation: 43-25=18 Exploring Operation: 39-25=14, Resulting Numbers: [43, 14] Generated Node #0,1,3: 46:[43, 14] Operation: 39-25=14 Exploring Operation: 43-39=4, Resulting Numbers: [25, 4] Generated Node #0,1,4: 46:[25, 4] Operation: 43-39=4 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 46:[25, 4], Operations: ['37+2=39', '43-39=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,46 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 #0,1,2 Current State: 46:[39, 18], Operations: ['37+2=39', '43-25=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,46 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 #0,1,3 Current State: 46:[43, 14], Operations: ['37+2=39', '39-25=14'] Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 43*14=602, Resulting Numbers: [602] 602,46 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,46 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 #0,1,1 Current State: 46:[43, 64], Operations: ['37+2=39', '25+39=64'] Exploring Operation: 43*64=2752, Resulting Numbers: [2752] 2752,46 unequal: No Solution Exploring Operation: 43+64=107, Resulting Numbers: [107] 107,46 unequal: No Solution Exploring Operation: 64-43=21, Resulting Numbers: [21] 21,46 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 #0,1,0 Current State: 46:[39, 68], Operations: ['37+2=39', '43+25=68'] Exploring Operation: 39+68=107, Resulting Numbers: [107] 107,46 unequal: No Solution Exploring Operation: 39*68=2652, Resulting Numbers: [2652] 2652,46 unequal: No Solution Exploring Operation: 68-39=29, Resulting Numbers: [29] 29,46 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: 46:[37, 25, 45], Operations: ['2+43=45'] Exploring Operation: 45-37=8, Resulting Numbers: [25, 8] Generated Node #0,0,0: 46:[25, 8] Operation: 45-37=8 Exploring Operation: 37-25=12, Resulting Numbers: [45, 12] Generated Node #0,0,1: 46:[45, 12] Operation: 37-25=12 Exploring Operation: 25+45=70, Resulting Numbers: [37, 70] Generated Node #0,0,2: 46:[37, 70] Operation: 25+45=70 Exploring Operation: 45-25=20, Resulting Numbers: [37, 20] Generated Node #0,0,3: 46:[37, 20] Operation: 45-25=20 Exploring Operation: 37+25=62, Resulting Numbers: [45, 62] Generated Node #0,0,4: 46:[45, 62] Operation: 37+25=62 Moving to Node #0,2 Current State: 46:[37, 43, 23], Operations: ['25-2=23'] Exploring Operation: 43-23=20, Resulting Numbers: [37, 20] Generated Node #0,2,0: 46:[37, 20] Operation: 43-23=20 Exploring Operation: 37+23=60, Resulting Numbers: [43, 60] Generated Node #0,2,1: 46:[43, 60] Operation: 37+23=60 Exploring Operation: 43+23=66, Resulting Numbers: [37, 66] Generated Node #0,2,2: 46:[37, 66] Operation: 43+23=66 Exploring Operation: 43-37=6, Resulting Numbers: [23, 6] Generated Node #0,2,3: 46:[23, 6] Operation: 43-37=6 Exploring Operation: 37-23=14, Resulting Numbers: [43, 14] Generated Node #0,2,4: 46:[43, 14] Operation: 37-23=14 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 46:[23, 6], Operations: ['25-2=23', '43-37=6'] Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,46 unequal: No Solution Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,46 unequal: No Solution Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,46 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 #0,2,0 Current State: 46:[37, 20], Operations: ['25-2=23', '43-23=20'] Exploring Operation: 37*20=740, Resulting Numbers: [740] 740,46 unequal: No Solution Exploring Operation: 37+20=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,46 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 #0,2,4 Current State: 46:[43, 14], Operations: ['25-2=23', '37-23=14'] Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 43*14=602, Resulting Numbers: [602] 602,46 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 #0,2,1 Current State: 46:[43, 60], Operations: ['25-2=23', '37+23=60'] Exploring Operation: 43+60=103, Resulting Numbers: [103] 103,46 unequal: No Solution Exploring Operation: 43*60=2580, Resulting Numbers: [2580] 2580,46 unequal: No Solution Exploring Operation: 60-43=17, Resulting Numbers: [17] 17,46 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 #0,2,2 Current State: 46:[37, 66], Operations: ['25-2=23', '43+23=66'] Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 37*66=2442, Resulting Numbers: [2442] 2442,46 unequal: No Solution Exploring Operation: 37+66=103, Resulting Numbers: [103] 103,46 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: 46:[2, 43, 12], Operations: ['37-25=12'] Exploring Operation: 2*12=24, Resulting Numbers: [43, 24] Generated Node #0,3,0: 46:[43, 24] Operation: 2*12=24 Exploring Operation: 12/2=6, Resulting Numbers: [43, 6] Generated Node #0,3,1: 46:[43, 6] Operation: 12/2=6 Exploring Operation: 43-12=31, Resulting Numbers: [2, 31] Generated Node #0,3,2: 46:[2, 31] Operation: 43-12=31 Exploring Operation: 43+12=55, Resulting Numbers: [2, 55] Generated Node #0,3,3: 46:[2, 55] Operation: 43+12=55 Exploring Operation: 2+43=45, Resulting Numbers: [12, 45] Generated Node #0,3,4: 46:[12, 45] Operation: 2+43=45 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 46:[43, 24], Operations: ['37-25=12', '2*12=24'] Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,46 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,46 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 #0,3,1 Current State: 46:[43, 6], Operations: ['37-25=12', '12/2=6'] Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,46 unequal: No Solution Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,46 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 #0,3,2 Current State: 46:[2, 31], Operations: ['37-25=12', '43-12=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,46 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,46 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 #0,3,3 Current State: 46:[2, 55], Operations: ['37-25=12', '43+12=55'] Exploring Operation: 2*55=110, Resulting Numbers: [110] 110,46 unequal: No Solution Exploring Operation: 2+55=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,46 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 #0,3,4 Current State: 46:[12, 45], Operations: ['37-25=12', '2+43=45'] Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 12*45=540, Resulting Numbers: [540] 540,46 unequal: No Solution Exploring Operation: 12+45=57, Resulting Numbers: [57] 57,46 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: 46:[25, 8], Operations: ['2+43=45', '45-37=8'] Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,46 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,46 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[45, 12], Operations: ['2+43=45', '37-25=12'] Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,46 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[37, 20], Operations: ['2+43=45', '45-25=20'] Exploring Operation: 37*20=740, Resulting Numbers: [740] 740,46 unequal: No Solution Exploring Operation: 37+20=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[45, 62], Operations: ['2+43=45', '37+25=62'] Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,46 unequal: No Solution Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,46 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[37, 70], Operations: ['2+43=45', '25+45=70'] Exploring Operation: 70-37=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 37*70=2590, Resulting Numbers: [2590] 2590,46 unequal: No Solution Exploring Operation: 37+70=107, Resulting Numbers: [107] 107,46 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 10, 39, 4, 84 ]
18
[ "84-39=45", "4*45=180", "180/10=18" ]
Current State: 18:[10, 39, 4, 84], Operations: [] Exploring Operation: 84-39=45, Resulting Numbers: [10, 4, 45] Generated Node #2: [10, 4, 45] from Operation: 84-39=45 Current State: 18:[10, 4, 45], Operations: ['84-39=45'] Exploring Operation: 4*45=180, Resulting Numbers: [10, 180] Generated Node #3: [10, 180] from Operation: 4*45=180 Current State: 18:[10, 180], Operations: ['84-39=45', '4*45=180'] Exploring Operation: 180/10=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[10, 39, 4, 84], Operations: [] Exploring Operation: 84-10=74, Resulting Numbers: [39, 4, 74] Generated Node #0,0: 18:[39, 4, 74] Operation: 84-10=74 Exploring Operation: 84/4=21, Resulting Numbers: [10, 39, 21] Generated Node #0,1: 18:[10, 39, 21] Operation: 84/4=21 Exploring Operation: 84-39=45, Resulting Numbers: [10, 4, 45] Generated Node #0,2: 18:[10, 4, 45] Operation: 84-39=45 Exploring Operation: 39-10=29, Resulting Numbers: [4, 84, 29] Generated Node #0,3: 18:[4, 84, 29] Operation: 39-10=29 Moving to Node #0,1 Current State: 18:[10, 39, 21], Operations: ['84/4=21'] Exploring Operation: 21-10=11, Resulting Numbers: [39, 11] Generated Node #0,1,0: 18:[39, 11] Operation: 21-10=11 Exploring Operation: 39-10=29, Resulting Numbers: [21, 29] Generated Node #0,1,1: 18:[21, 29] Operation: 39-10=29 Exploring Operation: 39-21=18, Resulting Numbers: [10, 18] Generated Node #0,1,2: 18:[10, 18] Operation: 39-21=18 Exploring Operation: 10+39=49, Resulting Numbers: [21, 49] Generated Node #0,1,3: 18:[21, 49] Operation: 10+39=49 Moving to Node #0,2 Current State: 18:[10, 4, 45], Operations: ['84-39=45'] Exploring Operation: 45-10=35, Resulting Numbers: [4, 35] Generated Node #0,2,0: 18:[4, 35] Operation: 45-10=35 Exploring Operation: 45-4=41, Resulting Numbers: [10, 41] Generated Node #0,2,1: 18:[10, 41] Operation: 45-4=41 Exploring Operation: 10-4=6, Resulting Numbers: [45, 6] Generated Node #0,2,2: 18:[45, 6] Operation: 10-4=6 Exploring Operation: 10+4=14, Resulting Numbers: [45, 14] Generated Node #0,2,3: 18:[45, 14] Operation: 10+4=14 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[4, 35], Operations: ['84-39=45', '45-10=35'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,18 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:[10, 41], Operations: ['84-39=45', '45-4=41'] Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,18 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,18 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:[45, 6], Operations: ['84-39=45', '10-4=6'] Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,18 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,18 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:[45, 14], Operations: ['84-39=45', '10+4=14'] Exploring Operation: 45*14=630, Resulting Numbers: [630] 630,18 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,18 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, 84, 29], Operations: ['39-10=29'] Exploring Operation: 84-4=80, Resulting Numbers: [29, 80] Generated Node #0,3,0: 18:[29, 80] Operation: 84-4=80 Exploring Operation: 84-29=55, Resulting Numbers: [4, 55] Generated Node #0,3,1: 18:[4, 55] Operation: 84-29=55 Exploring Operation: 84/4=21, Resulting Numbers: [29, 21] Generated Node #0,3,2: 18:[29, 21] Operation: 84/4=21 Exploring Operation: 29-4=25, Resulting Numbers: [84, 25] Generated Node #0,3,3: 18:[84, 25] Operation: 29-4=25 Moving to Node #0,0 Current State: 18:[39, 4, 74], Operations: ['84-10=74'] Exploring Operation: 74-39=35, Resulting Numbers: [4, 35] Generated Node #0,0,0: 18:[4, 35] Operation: 74-39=35 Exploring Operation: 39+4=43, Resulting Numbers: [74, 43] Generated Node #0,0,1: 18:[74, 43] Operation: 39+4=43 Exploring Operation: 39-4=35, Resulting Numbers: [74, 35] Generated Node #0,0,2: 18:[74, 35] Operation: 39-4=35 Exploring Operation: 74-4=70, Resulting Numbers: [39, 70] Generated Node #0,0,3: 18:[39, 70] Operation: 74-4=70 Moving to Node #0,1,2 Current State: 18:[10, 18], Operations: ['84/4=21', '39-21=18'] Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,18 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[21, 29], Operations: ['84/4=21', '39-10=29'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[29, 21], Operations: ['39-10=29', '84/4=21'] Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,18 unequal: No Solution Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[4, 35], Operations: ['84-10=74', '74-39=35'] Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,18 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[39, 11], Operations: ['84/4=21', '21-10=11'] Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,18 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,18 unequal: No Solution Moving to Node #0,1,3 Current State: 18:[21, 49], Operations: ['84/4=21', '10+39=49'] Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 21*49=1029, Resulting Numbers: [1029] 1029,18 unequal: No Solution Exploring Operation: 21+49=70, Resulting Numbers: [70] 70,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[4, 55], Operations: ['39-10=29', '84-29=55'] Exploring Operation: 4*55=220, Resulting Numbers: [220] 220,18 unequal: No Solution Exploring Operation: 4+55=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[29, 80], Operations: ['39-10=29', '84-4=80'] Exploring Operation: 29+80=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 29*80=2320, Resulting Numbers: [2320] 2320,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[39, 70], Operations: ['84-10=74', '74-4=70'] Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 39+70=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 39*70=2730, Resulting Numbers: [2730] 2730,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[84, 25], Operations: ['39-10=29', '29-4=25'] Exploring Operation: 84+25=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 84*25=2100, Resulting Numbers: [2100] 2100,18 unequal: No Solution Exploring Operation: 84-25=59, Resulting Numbers: [59] 59,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[74, 35], Operations: ['84-10=74', '39-4=35'] Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 74+35=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 74*35=2590, Resulting Numbers: [2590] 2590,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[74, 43], Operations: ['84-10=74', '39+4=43'] Exploring Operation: 74-43=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 74*43=3182, Resulting Numbers: [3182] 3182,18 unequal: No Solution Exploring Operation: 74+43=117, Resulting Numbers: [117] 117,18 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 35, 11, 8, 97 ]
81
[ "35-11=24", "8+97=105", "105-24=81" ]
Current State: 81:[35, 11, 8, 97], Operations: [] Exploring Operation: 35-11=24, Resulting Numbers: [8, 97, 24] Generated Node #2: [8, 97, 24] from Operation: 35-11=24 Current State: 81:[8, 97, 24], Operations: ['35-11=24'] Exploring Operation: 8+97=105, Resulting Numbers: [24, 105] Generated Node #3: [24, 105] from Operation: 8+97=105 Current State: 81:[24, 105], Operations: ['35-11=24', '8+97=105'] Exploring Operation: 105-24=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[35, 11, 8, 97], Operations: [] Exploring Operation: 97-8=89, Resulting Numbers: [35, 11, 89] Generated Node #0,0: 81:[35, 11, 89] Operation: 97-8=89 Exploring Operation: 35-8=27, Resulting Numbers: [11, 97, 27] Generated Node #0,1: 81:[11, 97, 27] Operation: 35-8=27 Exploring Operation: 35-11=24, Resulting Numbers: [8, 97, 24] Generated Node #0,2: 81:[8, 97, 24] Operation: 35-11=24 Exploring Operation: 97-11=86, Resulting Numbers: [35, 8, 86] Generated Node #0,3: 81:[35, 8, 86] Operation: 97-11=86 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[35, 8, 86], Operations: ['97-11=86'] Exploring Operation: 35-8=27, Resulting Numbers: [86, 27] Generated Node #0,3,0: 81:[86, 27] Operation: 35-8=27 Exploring Operation: 8+86=94, Resulting Numbers: [35, 94] Generated Node #0,3,1: 81:[35, 94] Operation: 8+86=94 Exploring Operation: 35+8=43, Resulting Numbers: [86, 43] Generated Node #0,3,2: 81:[86, 43] Operation: 35+8=43 Exploring Operation: 86-8=78, Resulting Numbers: [35, 78] Generated Node #0,3,3: 81:[35, 78] Operation: 86-8=78 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 81:[86, 27], Operations: ['97-11=86', '35-8=27'] Exploring Operation: 86+27=113, Resulting Numbers: [113] 113,81 unequal: No Solution Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,81 unequal: No Solution Exploring Operation: 86*27=2322, Resulting Numbers: [2322] 2322,81 unequal: No Solution No 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: 81:[35, 78], Operations: ['97-11=86', '86-8=78'] Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 35+78=113, Resulting Numbers: [113] 113,81 unequal: No Solution Exploring Operation: 35*78=2730, Resulting Numbers: [2730] 2730,81 unequal: No Solution No 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: 81:[35, 94], Operations: ['97-11=86', '8+86=94'] Exploring Operation: 35+94=129, Resulting Numbers: [129] 129,81 unequal: No Solution Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,81 unequal: No Solution Exploring Operation: 35*94=3290, Resulting Numbers: [3290] 3290,81 unequal: No Solution No 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: 81:[86, 43], Operations: ['97-11=86', '35+8=43'] Exploring Operation: 86+43=129, Resulting Numbers: [129] 129,81 unequal: No Solution Exploring Operation: 86-43=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 86/43=2, Resulting Numbers: [2] 2,81 unequal: No Solution Exploring Operation: 86*43=3698, Resulting Numbers: [3698] 3698,81 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: 81:[35, 11, 89], Operations: ['97-8=89'] Exploring Operation: 35+11=46, Resulting Numbers: [89, 46] Generated Node #0,0,0: 81:[89, 46] Operation: 35+11=46 Exploring Operation: 35-11=24, Resulting Numbers: [89, 24] Generated Node #0,0,1: 81:[89, 24] Operation: 35-11=24 Exploring Operation: 89-11=78, Resulting Numbers: [35, 78] Generated Node #0,0,2: 81:[35, 78] Operation: 89-11=78 Exploring Operation: 11+89=100, Resulting Numbers: [35, 100] Generated Node #0,0,3: 81:[35, 100] Operation: 11+89=100 Moving to Node #0,0,1 Current State: 81:[89, 24], Operations: ['97-8=89', '35-11=24'] Exploring Operation: 89+24=113, Resulting Numbers: [113] 113,81 unequal: No Solution Exploring Operation: 89*24=2136, Resulting Numbers: [2136] 2136,81 unequal: No Solution Exploring Operation: 89-24=65, Resulting Numbers: [65] 65,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[35, 78], Operations: ['97-8=89', '89-11=78'] Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 35*78=2730, Resulting Numbers: [2730] 2730,81 unequal: No Solution Exploring Operation: 35+78=113, Resulting Numbers: [113] 113,81 unequal: No Solution Moving to Node #0,0,3 Current State: 81:[35, 100], Operations: ['97-8=89', '11+89=100'] Exploring Operation: 35*100=3500, Resulting Numbers: [3500] 3500,81 unequal: No Solution Exploring Operation: 35+100=135, Resulting Numbers: [135] 135,81 unequal: No Solution Exploring Operation: 100-35=65, Resulting Numbers: [65] 65,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[89, 46], Operations: ['97-8=89', '35+11=46'] Exploring Operation: 89+46=135, Resulting Numbers: [135] 135,81 unequal: No Solution Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 89*46=4094, Resulting Numbers: [4094] 4094,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[11, 97, 27], Operations: ['35-8=27'] Exploring Operation: 97-11=86, Resulting Numbers: [27, 86] Generated Node #0,1,0: 81:[27, 86] Operation: 97-11=86 Exploring Operation: 27-11=16, Resulting Numbers: [97, 16] Generated Node #0,1,1: 81:[97, 16] Operation: 27-11=16 Exploring Operation: 97-27=70, Resulting Numbers: [11, 70] Generated Node #0,1,2: 81:[11, 70] Operation: 97-27=70 Exploring Operation: 11+97=108, Resulting Numbers: [27, 108] Generated Node #0,1,3: 81:[27, 108] Operation: 11+97=108 Moving to Node #0,1,0 Current State: 81:[27, 86], Operations: ['35-8=27', '97-11=86'] Exploring Operation: 27*86=2322, Resulting Numbers: [2322] 2322,81 unequal: No Solution Exploring Operation: 27+86=113, Resulting Numbers: [113] 113,81 unequal: No Solution Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[11, 70], Operations: ['35-8=27', '97-27=70'] Exploring Operation: 11*70=770, Resulting Numbers: [770] 770,81 unequal: No Solution Exploring Operation: 11+70=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[35, 11, 8, 97], Operations: [] Exploring Operation: 35-8=27, Resulting Numbers: [11, 97, 27] Generated Node #0,1: 81:[11, 97, 27] Operation: 35-8=27 Moving to Node #0,1 Current State: 81:[11, 97, 27], Operations: ['35-8=27'] Exploring Operation: 97-27=70, Resulting Numbers: [11, 70] Generated Node #0,1,2: 81:[11, 70] Operation: 97-27=70 Moving to Node #0,1,2 Current State: 81:[11, 70], Operations: ['35-8=27', '97-27=70'] Exploring Operation: 11+70=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.956597
hs_4
mult_heuristic