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
[ 54, 13, 18, 22 ]
12
[ "54/18=3", "22-13=9", "3+9=12" ]
Current State: 12:[54, 13, 18, 22], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [13, 22, 3] Generated Node #2: [13, 22, 3] from Operation: 54/18=3 Current State: 12:[13, 22, 3], Operations: ['54/18=3'] Exploring Operation: 22-13=9, Resulting Numbers: [3, 9] Generated Node #3: [3, 9] from Operation: 22-13=9 Current State: 12:[3, 9], Operations: ['54/18=3', '22-13=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[54, 13, 18, 22], Operations: [] Exploring Operation: 54-22=32, Resulting Numbers: [13, 18, 32] Generated Node #0,0: 12:[13, 18, 32] Operation: 54-22=32 Exploring Operation: 54-18=36, Resulting Numbers: [13, 22, 36] Generated Node #0,1: 12:[13, 22, 36] Operation: 54-18=36 Exploring Operation: 54-13=41, Resulting Numbers: [18, 22, 41] Generated Node #0,2: 12:[18, 22, 41] Operation: 54-13=41 Exploring Operation: 22-18=4, Resulting Numbers: [54, 13, 4] Generated Node #0,3: 12:[54, 13, 4] Operation: 22-18=4 Exploring Operation: 54/18=3, Resulting Numbers: [13, 22, 3] Generated Node #0,4: 12:[13, 22, 3] Operation: 54/18=3 Moving to Node #0,4 Current State: 12:[13, 22, 3], Operations: ['54/18=3'] Exploring Operation: 22-3=19, Resulting Numbers: [13, 19] Generated Node #0,4,0: 12:[13, 19] Operation: 22-3=19 Exploring Operation: 13-3=10, Resulting Numbers: [22, 10] Generated Node #0,4,1: 12:[22, 10] Operation: 13-3=10 Exploring Operation: 22+3=25, Resulting Numbers: [13, 25] Generated Node #0,4,2: 12:[13, 25] Operation: 22+3=25 Exploring Operation: 13+3=16, Resulting Numbers: [22, 16] Generated Node #0,4,3: 12:[22, 16] Operation: 13+3=16 Exploring Operation: 22-13=9, Resulting Numbers: [3, 9] Generated Node #0,4,4: 12:[3, 9] Operation: 22-13=9 Moving to Node #0,0 Current State: 12:[13, 18, 32], Operations: ['54-22=32'] Exploring Operation: 32-13=19, Resulting Numbers: [18, 19] Generated Node #0,0,0: 12:[18, 19] Operation: 32-13=19 Exploring Operation: 13+18=31, Resulting Numbers: [32, 31] Generated Node #0,0,1: 12:[32, 31] Operation: 13+18=31 Exploring Operation: 18-13=5, Resulting Numbers: [32, 5] Generated Node #0,0,2: 12:[32, 5] Operation: 18-13=5 Exploring Operation: 13+32=45, Resulting Numbers: [18, 45] Generated Node #0,0,3: 12:[18, 45] Operation: 13+32=45 Exploring Operation: 32-18=14, Resulting Numbers: [13, 14] Generated Node #0,0,4: 12:[13, 14] Operation: 32-18=14 Moving to Node #0,1 Current State: 12:[13, 22, 36], Operations: ['54-18=36'] Exploring Operation: 22-13=9, Resulting Numbers: [36, 9] Generated Node #0,1,0: 12:[36, 9] Operation: 22-13=9 Exploring Operation: 36-13=23, Resulting Numbers: [22, 23] Generated Node #0,1,1: 12:[22, 23] Operation: 36-13=23 Exploring Operation: 36-22=14, Resulting Numbers: [13, 14] Generated Node #0,1,2: 12:[13, 14] Operation: 36-22=14 Exploring Operation: 13+22=35, Resulting Numbers: [36, 35] Generated Node #0,1,3: 12:[36, 35] Operation: 13+22=35 Exploring Operation: 13+36=49, Resulting Numbers: [22, 49] Generated Node #0,1,4: 12:[22, 49] Operation: 13+36=49 Moving to Node #0,3 Current State: 12:[54, 13, 4], Operations: ['22-18=4'] Exploring Operation: 13-4=9, Resulting Numbers: [54, 9] Generated Node #0,3,0: 12:[54, 9] Operation: 13-4=9 Exploring Operation: 54-4=50, Resulting Numbers: [13, 50] Generated Node #0,3,1: 12:[13, 50] Operation: 54-4=50 Exploring Operation: 54+4=58, Resulting Numbers: [13, 58] Generated Node #0,3,2: 12:[13, 58] Operation: 54+4=58 Exploring Operation: 13+4=17, Resulting Numbers: [54, 17] Generated Node #0,3,3: 12:[54, 17] Operation: 13+4=17 Exploring Operation: 54-13=41, Resulting Numbers: [4, 41] Generated Node #0,3,4: 12:[4, 41] Operation: 54-13=41 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 12:[4, 41], Operations: ['22-18=4', '54-13=41'] Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,12 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,12 unequal: No Solution No 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: 12:[13, 50], Operations: ['22-18=4', '54-4=50'] Exploring Operation: 13*50=650, Resulting Numbers: [650] 650,12 unequal: No Solution Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 13+50=63, Resulting Numbers: [63] 63,12 unequal: No Solution No 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: 12:[54, 9], Operations: ['22-18=4', '13-4=9'] Exploring Operation: 54+9=63, Resulting Numbers: [63] 63,12 unequal: No Solution Exploring Operation: 54*9=486, Resulting Numbers: [486] 486,12 unequal: No Solution Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,12 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,12 unequal: No Solution No 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: 12:[13, 58], Operations: ['22-18=4', '54+4=58'] Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,12 unequal: No Solution Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,12 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,12 unequal: No Solution No 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: 12:[54, 17], Operations: ['22-18=4', '13+4=17'] Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 54*17=918, Resulting Numbers: [918] 918,12 unequal: No Solution Exploring Operation: 54+17=71, Resulting Numbers: [71] 71,12 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: 12:[18, 22, 41], Operations: ['54-13=41'] Exploring Operation: 18+41=59, Resulting Numbers: [22, 59] Generated Node #0,2,0: 12:[22, 59] Operation: 18+41=59 Exploring Operation: 18+22=40, Resulting Numbers: [41, 40] Generated Node #0,2,1: 12:[41, 40] Operation: 18+22=40 Exploring Operation: 41-18=23, Resulting Numbers: [22, 23] Generated Node #0,2,2: 12:[22, 23] Operation: 41-18=23 Exploring Operation: 22-18=4, Resulting Numbers: [41, 4] Generated Node #0,2,3: 12:[41, 4] Operation: 22-18=4 Exploring Operation: 41-22=19, Resulting Numbers: [18, 19] Generated Node #0,2,4: 12:[18, 19] Operation: 41-22=19 Moving to Node #0,4,4 Current State: 12:[3, 9], Operations: ['54/18=3', '22-13=9'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[54, 13, 18, 22], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [13, 22, 3] Generated Node #0,4: 12:[13, 22, 3] Operation: 54/18=3 Moving to Node #0,4 Current State: 12:[13, 22, 3], Operations: ['54/18=3'] Exploring Operation: 22-13=9, Resulting Numbers: [3, 9] Generated Node #0,4,4: 12:[3, 9] Operation: 22-13=9 Moving to Node #0,4,4 Current State: 12:[3, 9], Operations: ['54/18=3', '22-13=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.953125
hs_5
sum_heuristic
[ 92, 76, 37, 36 ]
89
[ "92-76=16", "37+36=73", "16+73=89" ]
Current State: 89:[92, 76, 37, 36], Operations: [] Exploring Operation: 92-76=16, Resulting Numbers: [37, 36, 16] Generated Node #2: [37, 36, 16] from Operation: 92-76=16 Current State: 89:[37, 36, 16], Operations: ['92-76=16'] Exploring Operation: 37+36=73, Resulting Numbers: [16, 73] Generated Node #3: [16, 73] from Operation: 37+36=73 Current State: 89:[16, 73], Operations: ['92-76=16', '37+36=73'] Exploring Operation: 16+73=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[92, 76, 37, 36], Operations: [] Exploring Operation: 37+36=73, Resulting Numbers: [92, 76, 73] Generated Node #0,0: 89:[92, 76, 73] Operation: 37+36=73 Exploring Operation: 76+37=113, Resulting Numbers: [92, 36, 113] Generated Node #0,1: 89:[92, 36, 113] Operation: 76+37=113 Exploring Operation: 92-36=56, Resulting Numbers: [76, 37, 56] Generated Node #0,2: 89:[76, 37, 56] Operation: 92-36=56 Exploring Operation: 76+36=112, Resulting Numbers: [92, 37, 112] Generated Node #0,3: 89:[92, 37, 112] Operation: 76+36=112 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[92, 76, 73], Operations: ['37+36=73'] Exploring Operation: 76+73=149, Resulting Numbers: [92, 149] Generated Node #0,0,0: 89:[92, 149] Operation: 76+73=149 Exploring Operation: 92-76=16, Resulting Numbers: [73, 16] Generated Node #0,0,1: 89:[73, 16] Operation: 92-76=16 Exploring Operation: 92+73=165, Resulting Numbers: [76, 165] Generated Node #0,0,2: 89:[76, 165] Operation: 92+73=165 Exploring Operation: 92-73=19, Resulting Numbers: [76, 19] Generated Node #0,0,3: 89:[76, 19] Operation: 92-73=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[92, 149], Operations: ['37+36=73', '76+73=149'] Exploring Operation: 149-92=57, Resulting Numbers: [57] 57,89 unequal: No Solution Exploring Operation: 92+149=241, Resulting Numbers: [241] 241,89 unequal: No Solution Exploring Operation: 92*149=13708, Resulting Numbers: [13708] 13708,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 89:[76, 19], Operations: ['37+36=73', '92-73=19'] Exploring Operation: 76*19=1444, Resulting Numbers: [1444] 1444,89 unequal: No Solution Exploring Operation: 76/19=4, Resulting Numbers: [4] 4,89 unequal: No Solution Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,89 unequal: No Solution Exploring Operation: 76+19=95, Resulting Numbers: [95] 95,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[73, 16], Operations: ['37+36=73', '92-76=16'] Exploring Operation: 73+16=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[92, 76, 37, 36], Operations: [] Exploring Operation: 37+36=73, Resulting Numbers: [92, 76, 73] Generated Node #0,0: 89:[92, 76, 73] Operation: 37+36=73 Moving to Node #0,0 Current State: 89:[92, 76, 73], Operations: ['37+36=73'] Exploring Operation: 92-76=16, Resulting Numbers: [73, 16] Generated Node #0,0,1: 89:[73, 16] Operation: 92-76=16 Moving to Node #0,0,1 Current State: 89:[73, 16], Operations: ['37+36=73', '92-76=16'] Exploring Operation: 73+16=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 21, 27, 3, 24 ]
12
[ "27-21=6", "3*24=72", "72/6=12" ]
Current State: 12:[21, 27, 3, 24], Operations: [] Exploring Operation: 27-21=6, Resulting Numbers: [3, 24, 6] Generated Node #2: [3, 24, 6] from Operation: 27-21=6 Current State: 12:[3, 24, 6], Operations: ['27-21=6'] Exploring Operation: 3*24=72, Resulting Numbers: [6, 72] Generated Node #3: [6, 72] from Operation: 3*24=72 Current State: 12:[6, 72], Operations: ['27-21=6', '3*24=72'] Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[21, 27, 3, 24], Operations: [] Exploring Operation: 27-24=3, Resulting Numbers: [21, 3, 3] Generated Node #0,0: 12:[21, 3, 3] Operation: 27-24=3 Exploring Operation: 24-21=3, Resulting Numbers: [27, 3, 3] Generated Node #0,1: 12:[27, 3, 3] Operation: 24-21=3 Exploring Operation: 27-21=6, Resulting Numbers: [3, 24, 6] Generated Node #0,2: 12:[3, 24, 6] Operation: 27-21=6 Moving to Node #0,0 Current State: 12:[21, 3, 3], Operations: ['27-24=3'] Exploring Operation: 21/3=7, Resulting Numbers: [3, 7] Generated Node #0,0,0: 12:[3, 7] Operation: 21/3=7 Exploring Operation: 21/3=7, Resulting Numbers: [3, 7] Generated Node #0,0,1: 12:[3, 7] Operation: 21/3=7 Exploring Operation: 21-3=18, Resulting Numbers: [3, 18] Generated Node #0,0,2: 12:[3, 18] Operation: 21-3=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[3, 7], Operations: ['27-24=3', '21/3=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,12 unequal: No Solution No 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: 12:[3, 7], Operations: ['27-24=3', '21/3=7'] Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,12 unequal: No Solution No 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: 12:[3, 18], Operations: ['27-24=3', '21-3=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,12 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: 12:[3, 24, 6], Operations: ['27-21=6'] Exploring Operation: 24/3=8, Resulting Numbers: [6, 8] Generated Node #0,2,0: 12:[6, 8] Operation: 24/3=8 Exploring Operation: 24/6=4, Resulting Numbers: [3, 4] Generated Node #0,2,1: 12:[3, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [3, 18] Generated Node #0,2,2: 12:[3, 18] Operation: 24-6=18 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 12:[3, 4], Operations: ['27-21=6', '24/6=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[21, 27, 3, 24], Operations: [] Exploring Operation: 27-21=6, Resulting Numbers: [3, 24, 6] Generated Node #0,2: 12:[3, 24, 6] Operation: 27-21=6 Moving to Node #0,2 Current State: 12:[3, 24, 6], Operations: ['27-21=6'] Exploring Operation: 24/6=4, Resulting Numbers: [3, 4] Generated Node #0,2,1: 12:[3, 4] Operation: 24/6=4 Moving to Node #0,2,1 Current State: 12:[3, 4], Operations: ['27-21=6', '24/6=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 82, 57, 37, 17 ]
85
[ "82+57=139", "37+17=54", "139-54=85" ]
Current State: 85:[82, 57, 37, 17], Operations: [] Exploring Operation: 82+57=139, Resulting Numbers: [37, 17, 139] Generated Node #2: [37, 17, 139] from Operation: 82+57=139 Current State: 85:[37, 17, 139], Operations: ['82+57=139'] Exploring Operation: 37+17=54, Resulting Numbers: [139, 54] Generated Node #3: [139, 54] from Operation: 37+17=54 Current State: 85:[139, 54], Operations: ['82+57=139', '37+17=54'] Exploring Operation: 139-54=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[82, 57, 37, 17], Operations: [] Exploring Operation: 57-37=20, Resulting Numbers: [82, 17, 20] Generated Node #0,0: 85:[82, 17, 20] Operation: 57-37=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[82, 17, 20], Operations: ['57-37=20'] Exploring Operation: 20-17=3, Resulting Numbers: [82, 3] Generated Node #0,0,0: 85:[82, 3] Operation: 20-17=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[82, 3], Operations: ['57-37=20', '20-17=3'] Exploring Operation: 82+3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[82, 57, 37, 17], Operations: [] Exploring Operation: 57-37=20, Resulting Numbers: [82, 17, 20] Generated Node #0,0: 85:[82, 17, 20] Operation: 57-37=20 Moving to Node #0,0 Current State: 85:[82, 17, 20], Operations: ['57-37=20'] Exploring Operation: 20-17=3, Resulting Numbers: [82, 3] Generated Node #0,0,0: 85:[82, 3] Operation: 20-17=3 Moving to Node #0,0,0 Current State: 85:[82, 3], Operations: ['57-37=20', '20-17=3'] Exploring Operation: 82+3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 21, 43, 42, 70 ]
48
[ "21+43=64", "42+70=112", "112-64=48" ]
Current State: 48:[21, 43, 42, 70], Operations: [] Exploring Operation: 21+43=64, Resulting Numbers: [42, 70, 64] Generated Node #2: [42, 70, 64] from Operation: 21+43=64 Current State: 48:[42, 70, 64], Operations: ['21+43=64'] Exploring Operation: 42+70=112, Resulting Numbers: [64, 112] Generated Node #3: [64, 112] from Operation: 42+70=112 Current State: 48:[64, 112], Operations: ['21+43=64', '42+70=112'] Exploring Operation: 112-64=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[21, 43, 42, 70], Operations: [] Exploring Operation: 70-21=49, Resulting Numbers: [43, 42, 49] Generated Node #0,0: 48:[43, 42, 49] Operation: 70-21=49 Exploring Operation: 70-43=27, Resulting Numbers: [21, 42, 27] Generated Node #0,1: 48:[21, 42, 27] Operation: 70-43=27 Exploring Operation: 43-42=1, Resulting Numbers: [21, 70, 1] Generated Node #0,2: 48:[21, 70, 1] Operation: 43-42=1 Exploring Operation: 70-42=28, Resulting Numbers: [21, 43, 28] Generated Node #0,3: 48:[21, 43, 28] Operation: 70-42=28 Moving to Node #0,0 Current State: 48:[43, 42, 49], Operations: ['70-21=49'] Exploring Operation: 49-43=6, Resulting Numbers: [42, 6] Generated Node #0,0,0: 48:[42, 6] Operation: 49-43=6 Exploring Operation: 49-42=7, Resulting Numbers: [43, 7] Generated Node #0,0,1: 48:[43, 7] Operation: 49-42=7 Exploring Operation: 43+42=85, Resulting Numbers: [49, 85] Generated Node #0,0,2: 48:[49, 85] Operation: 43+42=85 Exploring Operation: 43-42=1, Resulting Numbers: [49, 1] Generated Node #0,0,3: 48:[49, 1] Operation: 43-42=1 Moving to Node #0,3 Current State: 48:[21, 43, 28], Operations: ['70-42=28'] Exploring Operation: 43-21=22, Resulting Numbers: [28, 22] Generated Node #0,3,0: 48:[28, 22] Operation: 43-21=22 Exploring Operation: 28-21=7, Resulting Numbers: [43, 7] Generated Node #0,3,1: 48:[43, 7] Operation: 28-21=7 Exploring Operation: 21+28=49, Resulting Numbers: [43, 49] Generated Node #0,3,2: 48:[43, 49] Operation: 21+28=49 Exploring Operation: 43-28=15, Resulting Numbers: [21, 15] Generated Node #0,3,3: 48:[21, 15] Operation: 43-28=15 Moving to Node #0,1 Current State: 48:[21, 42, 27], Operations: ['70-43=27'] Exploring Operation: 21+27=48, Resulting Numbers: [42, 48] Generated Node #0,1,0: 48:[42, 48] Operation: 21+27=48 Exploring Operation: 42-27=15, Resulting Numbers: [21, 15] Generated Node #0,1,1: 48:[21, 15] Operation: 42-27=15 Exploring Operation: 42/21=2, Resulting Numbers: [27, 2] Generated Node #0,1,2: 48:[27, 2] Operation: 42/21=2 Exploring Operation: 42-21=21, Resulting Numbers: [27, 21] Generated Node #0,1,3: 48:[27, 21] Operation: 42-21=21 Moving to Node #0,2 Current State: 48:[21, 70, 1], Operations: ['43-42=1'] Exploring Operation: 21*1=21, Resulting Numbers: [70, 21] Generated Node #0,2,0: 48:[70, 21] Operation: 21*1=21 Exploring Operation: 70-21=49, Resulting Numbers: [1, 49] Generated Node #0,2,1: 48:[1, 49] Operation: 70-21=49 Exploring Operation: 70-1=69, Resulting Numbers: [21, 69] Generated Node #0,2,2: 48:[21, 69] Operation: 70-1=69 Exploring Operation: 21+1=22, Resulting Numbers: [70, 22] Generated Node #0,2,3: 48:[70, 22] Operation: 21+1=22 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[1, 49], Operations: ['43-42=1', '70-21=49'] Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,48 unequal: No Solution Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,48 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,48 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[21, 43, 42, 70], Operations: [] Exploring Operation: 43-42=1, Resulting Numbers: [21, 70, 1] Generated Node #0,2: 48:[21, 70, 1] Operation: 43-42=1 Moving to Node #0,2 Current State: 48:[21, 70, 1], Operations: ['43-42=1'] Exploring Operation: 70-21=49, Resulting Numbers: [1, 49] Generated Node #0,2,1: 48:[1, 49] Operation: 70-21=49 Moving to Node #0,2,1 Current State: 48:[1, 49], Operations: ['43-42=1', '70-21=49'] Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_4
sum_heuristic
[ 37, 30, 54, 6 ]
16
[ "37-30=7", "54/6=9", "7+9=16" ]
Current State: 16:[37, 30, 54, 6], Operations: [] Exploring Operation: 37-30=7, Resulting Numbers: [54, 6, 7] Generated Node #2: [54, 6, 7] from Operation: 37-30=7 Current State: 16:[54, 6, 7], Operations: ['37-30=7'] Exploring Operation: 54/6=9, Resulting Numbers: [7, 9] Generated Node #3: [7, 9] from Operation: 54/6=9 Current State: 16:[7, 9], Operations: ['37-30=7', '54/6=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[37, 30, 54, 6], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [37, 30, 9] Generated Node #0,0: 16:[37, 30, 9] Operation: 54/6=9 Exploring Operation: 54-37=17, Resulting Numbers: [30, 6, 17] Generated Node #0,1: 16:[30, 6, 17] Operation: 54-37=17 Exploring Operation: 54-30=24, Resulting Numbers: [37, 6, 24] Generated Node #0,2: 16:[37, 6, 24] Operation: 54-30=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[30, 6, 17], Operations: ['54-37=17'] Exploring Operation: 30/6=5, Resulting Numbers: [17, 5] Generated Node #0,1,0: 16:[17, 5] Operation: 30/6=5 Exploring Operation: 30-17=13, Resulting Numbers: [6, 13] Generated Node #0,1,1: 16:[6, 13] Operation: 30-17=13 Exploring Operation: 30-6=24, Resulting Numbers: [17, 24] Generated Node #0,1,2: 16:[17, 24] Operation: 30-6=24 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[17, 5], Operations: ['54-37=17', '30/6=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,16 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,16 unequal: No Solution No 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: 16:[6, 13], Operations: ['54-37=17', '30-17=13'] Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,16 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,16 unequal: No Solution No 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: 16:[17, 24], Operations: ['54-37=17', '30-6=24'] Exploring Operation: 17*24=408, Resulting Numbers: [408] 408,16 unequal: No Solution Exploring Operation: 17+24=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,16 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: 16:[37, 6, 24], Operations: ['54-30=24'] Exploring Operation: 37-6=31, Resulting Numbers: [24, 31] Generated Node #0,2,0: 16:[24, 31] Operation: 37-6=31 Exploring Operation: 37-24=13, Resulting Numbers: [6, 13] Generated Node #0,2,1: 16:[6, 13] Operation: 37-24=13 Exploring Operation: 24/6=4, Resulting Numbers: [37, 4] Generated Node #0,2,2: 16:[37, 4] Operation: 24/6=4 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 16:[6, 13], Operations: ['54-30=24', '37-24=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,16 unequal: No Solution No 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: 16:[37, 4], Operations: ['54-30=24', '24/6=4'] Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,16 unequal: No Solution Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,16 unequal: No Solution No 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: 16:[24, 31], Operations: ['54-30=24', '37-6=31'] Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,16 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,16 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: 16:[37, 30, 9], Operations: ['54/6=9'] Exploring Operation: 37-9=28, Resulting Numbers: [30, 28] Generated Node #0,0,0: 16:[30, 28] Operation: 37-9=28 Exploring Operation: 37-30=7, Resulting Numbers: [9, 7] Generated Node #0,0,1: 16:[9, 7] Operation: 37-30=7 Exploring Operation: 30-9=21, Resulting Numbers: [37, 21] Generated Node #0,0,2: 16:[37, 21] Operation: 30-9=21 Moving to Node #0,0,1 Current State: 16:[9, 7], Operations: ['54/6=9', '37-30=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[37, 30, 54, 6], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [37, 30, 9] Generated Node #0,0: 16:[37, 30, 9] Operation: 54/6=9 Moving to Node #0,0 Current State: 16:[37, 30, 9], Operations: ['54/6=9'] Exploring Operation: 37-30=7, Resulting Numbers: [9, 7] Generated Node #0,0,1: 16:[9, 7] Operation: 37-30=7 Moving to Node #0,0,1 Current State: 16:[9, 7], Operations: ['54/6=9', '37-30=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 80, 92, 6, 97 ]
22
[ "97-92=5", "80/5=16", "6+16=22" ]
Current State: 22:[80, 92, 6, 97], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [80, 6, 5] Generated Node #2: [80, 6, 5] from Operation: 97-92=5 Current State: 22:[80, 6, 5], Operations: ['97-92=5'] Exploring Operation: 80/5=16, Resulting Numbers: [6, 16] Generated Node #3: [6, 16] from Operation: 80/5=16 Current State: 22:[6, 16], Operations: ['97-92=5', '80/5=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[80, 92, 6, 97], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [92, 6, 17] Generated Node #0,0: 22:[92, 6, 17] Operation: 97-80=17 Exploring Operation: 92-80=12, Resulting Numbers: [6, 97, 12] Generated Node #0,1: 22:[6, 97, 12] Operation: 92-80=12 Exploring Operation: 92-6=86, Resulting Numbers: [80, 97, 86] Generated Node #0,2: 22:[80, 97, 86] Operation: 92-6=86 Exploring Operation: 80-6=74, Resulting Numbers: [92, 97, 74] Generated Node #0,3: 22:[92, 97, 74] Operation: 80-6=74 Exploring Operation: 97-92=5, Resulting Numbers: [80, 6, 5] Generated Node #0,4: 22:[80, 6, 5] Operation: 97-92=5 Moving to Node #0,4 Current State: 22:[80, 6, 5], Operations: ['97-92=5'] Exploring Operation: 6+5=11, Resulting Numbers: [80, 11] Generated Node #0,4,0: 22:[80, 11] Operation: 6+5=11 Exploring Operation: 80/5=16, Resulting Numbers: [6, 16] Generated Node #0,4,1: 22:[6, 16] Operation: 80/5=16 Exploring Operation: 80-5=75, Resulting Numbers: [6, 75] Generated Node #0,4,2: 22:[6, 75] Operation: 80-5=75 Exploring Operation: 6-5=1, Resulting Numbers: [80, 1] Generated Node #0,4,3: 22:[80, 1] Operation: 6-5=1 Exploring Operation: 80-6=74, Resulting Numbers: [5, 74] Generated Node #0,4,4: 22:[5, 74] Operation: 80-6=74 Moving to Node #0,0 Current State: 22:[92, 6, 17], Operations: ['97-80=17'] Exploring Operation: 6+17=23, Resulting Numbers: [92, 23] Generated Node #0,0,0: 22:[92, 23] Operation: 6+17=23 Exploring Operation: 17-6=11, Resulting Numbers: [92, 11] Generated Node #0,0,1: 22:[92, 11] Operation: 17-6=11 Exploring Operation: 92+6=98, Resulting Numbers: [17, 98] Generated Node #0,0,2: 22:[17, 98] Operation: 92+6=98 Exploring Operation: 92-6=86, Resulting Numbers: [17, 86] Generated Node #0,0,3: 22:[17, 86] Operation: 92-6=86 Exploring Operation: 92-17=75, Resulting Numbers: [6, 75] Generated Node #0,0,4: 22:[6, 75] Operation: 92-17=75 Moving to Node #0,1 Current State: 22:[6, 97, 12], Operations: ['92-80=12'] Exploring Operation: 12-6=6, Resulting Numbers: [97, 6] Generated Node #0,1,0: 22:[97, 6] Operation: 12-6=6 Exploring Operation: 6+12=18, Resulting Numbers: [97, 18] Generated Node #0,1,1: 22:[97, 18] Operation: 6+12=18 Exploring Operation: 12/6=2, Resulting Numbers: [97, 2] Generated Node #0,1,2: 22:[97, 2] Operation: 12/6=2 Exploring Operation: 97-6=91, Resulting Numbers: [12, 91] Generated Node #0,1,3: 22:[12, 91] Operation: 97-6=91 Exploring Operation: 97-12=85, Resulting Numbers: [6, 85] Generated Node #0,1,4: 22:[6, 85] Operation: 97-12=85 Moving to Node #0,2 Current State: 22:[80, 97, 86], Operations: ['92-6=86'] Exploring Operation: 80+86=166, Resulting Numbers: [97, 166] Generated Node #0,2,0: 22:[97, 166] Operation: 80+86=166 Exploring Operation: 80+97=177, Resulting Numbers: [86, 177] Generated Node #0,2,1: 22:[86, 177] Operation: 80+97=177 Exploring Operation: 97-86=11, Resulting Numbers: [80, 11] Generated Node #0,2,2: 22:[80, 11] Operation: 97-86=11 Exploring Operation: 97-80=17, Resulting Numbers: [86, 17] Generated Node #0,2,3: 22:[86, 17] Operation: 97-80=17 Exploring Operation: 86-80=6, Resulting Numbers: [97, 6] Generated Node #0,2,4: 22:[97, 6] Operation: 86-80=6 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[80, 11], Operations: ['92-6=86', '97-86=11'] Exploring Operation: 80*11=880, Resulting Numbers: [880] 880,22 unequal: No Solution Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,22 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 22:[86, 17], Operations: ['92-6=86', '97-80=17'] Exploring Operation: 86*17=1462, Resulting Numbers: [1462] 1462,22 unequal: No Solution Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 86+17=103, Resulting Numbers: [103] 103,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 22:[97, 6], Operations: ['92-6=86', '86-80=6'] Exploring Operation: 97+6=103, Resulting Numbers: [103] 103,22 unequal: No Solution Exploring Operation: 97*6=582, Resulting Numbers: [582] 582,22 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[97, 166], Operations: ['92-6=86', '80+86=166'] Exploring Operation: 166-97=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 97*166=16102, Resulting Numbers: [16102] 16102,22 unequal: No Solution Exploring Operation: 97+166=263, Resulting Numbers: [263] 263,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[86, 177], Operations: ['92-6=86', '80+97=177'] Exploring Operation: 86+177=263, Resulting Numbers: [263] 263,22 unequal: No Solution Exploring Operation: 86*177=15222, Resulting Numbers: [15222] 15222,22 unequal: No Solution Exploring Operation: 177-86=91, Resulting Numbers: [91] 91,22 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: 22:[92, 97, 74], Operations: ['80-6=74'] Exploring Operation: 92+74=166, Resulting Numbers: [97, 166] Generated Node #0,3,0: 22:[97, 166] Operation: 92+74=166 Exploring Operation: 92+97=189, Resulting Numbers: [74, 189] Generated Node #0,3,1: 22:[74, 189] Operation: 92+97=189 Exploring Operation: 97-74=23, Resulting Numbers: [92, 23] Generated Node #0,3,2: 22:[92, 23] Operation: 97-74=23 Exploring Operation: 92-74=18, Resulting Numbers: [97, 18] Generated Node #0,3,3: 22:[97, 18] Operation: 92-74=18 Exploring Operation: 97-92=5, Resulting Numbers: [74, 5] Generated Node #0,3,4: 22:[74, 5] Operation: 97-92=5 Moving to Node #0,4,1 Current State: 22:[6, 16], Operations: ['97-92=5', '80/5=16'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,22 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[80, 92, 6, 97], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [80, 6, 5] Generated Node #0,4: 22:[80, 6, 5] Operation: 97-92=5 Moving to Node #0,4 Current State: 22:[80, 6, 5], Operations: ['97-92=5'] Exploring Operation: 80/5=16, Resulting Numbers: [6, 16] Generated Node #0,4,1: 22:[6, 16] Operation: 80/5=16 Moving to Node #0,4,1 Current State: 22:[6, 16], Operations: ['97-92=5', '80/5=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.954861
hs_5
sum_heuristic
[ 50, 86, 31, 13 ]
65
[ "86-50=36", "36-31=5", "13*5=65" ]
Current State: 65:[50, 86, 31, 13], Operations: [] Exploring Operation: 86-50=36, Resulting Numbers: [31, 13, 36] Generated Node #2: [31, 13, 36] from Operation: 86-50=36 Current State: 65:[31, 13, 36], Operations: ['86-50=36'] Exploring Operation: 36-31=5, Resulting Numbers: [13, 5] Generated Node #3: [13, 5] from Operation: 36-31=5 Current State: 65:[13, 5], Operations: ['86-50=36', '36-31=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[50, 86, 31, 13], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [86, 13, 19] Generated Node #0,0: 65:[86, 13, 19] Operation: 50-31=19 Exploring Operation: 50+13=63, Resulting Numbers: [86, 31, 63] Generated Node #0,1: 65:[86, 31, 63] Operation: 50+13=63 Exploring Operation: 86-50=36, Resulting Numbers: [31, 13, 36] Generated Node #0,2: 65:[31, 13, 36] Operation: 86-50=36 Exploring Operation: 86-31=55, Resulting Numbers: [50, 13, 55] Generated Node #0,3: 65:[50, 13, 55] Operation: 86-31=55 Exploring Operation: 50+31=81, Resulting Numbers: [86, 13, 81] Generated Node #0,4: 65:[86, 13, 81] Operation: 50+31=81 Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[50, 13, 55], Operations: ['86-31=55'] Exploring Operation: 13+55=68, Resulting Numbers: [50, 68] Generated Node #0,3,0: 65:[50, 68] Operation: 13+55=68 Exploring Operation: 55-13=42, Resulting Numbers: [50, 42] Generated Node #0,3,1: 65:[50, 42] Operation: 55-13=42 Exploring Operation: 55-50=5, Resulting Numbers: [13, 5] Generated Node #0,3,2: 65:[13, 5] Operation: 55-50=5 Exploring Operation: 50-13=37, Resulting Numbers: [55, 37] Generated Node #0,3,3: 65:[55, 37] Operation: 50-13=37 Exploring Operation: 50+13=63, Resulting Numbers: [55, 63] Generated Node #0,3,4: 65:[55, 63] Operation: 50+13=63 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 65:[13, 5], Operations: ['86-31=55', '55-50=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[50, 86, 31, 13], Operations: [] Exploring Operation: 86-31=55, Resulting Numbers: [50, 13, 55] Generated Node #0,3: 65:[50, 13, 55] Operation: 86-31=55 Moving to Node #0,3 Current State: 65:[50, 13, 55], Operations: ['86-31=55'] Exploring Operation: 55-50=5, Resulting Numbers: [13, 5] Generated Node #0,3,2: 65:[13, 5] Operation: 55-50=5 Moving to Node #0,3,2 Current State: 65:[13, 5], Operations: ['86-31=55', '55-50=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 42, 10, 50, 22 ]
69
[ "42+22=64", "50/10=5", "64+5=69" ]
Current State: 69:[42, 10, 50, 22], Operations: [] Exploring Operation: 42+22=64, Resulting Numbers: [10, 50, 64] Generated Node #2: [10, 50, 64] from Operation: 42+22=64 Current State: 69:[10, 50, 64], Operations: ['42+22=64'] Exploring Operation: 50/10=5, Resulting Numbers: [64, 5] Generated Node #3: [64, 5] from Operation: 50/10=5 Current State: 69:[64, 5], Operations: ['42+22=64', '50/10=5'] Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[42, 10, 50, 22], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [10, 22, 8] Generated Node #0,0: 69:[10, 22, 8] Operation: 50-42=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[10, 22, 8], Operations: ['50-42=8'] Exploring Operation: 10-8=2, Resulting Numbers: [22, 2] Generated Node #0,0,0: 69:[22, 2] Operation: 10-8=2 Moving to Node #0,0,0 Current State: 69:[22, 2], Operations: ['50-42=8', '10-8=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,69 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
[ 96, 56, 9, 3 ]
99
[ "56+9=65", "3*65=195", "195-96=99" ]
Current State: 99:[96, 56, 9, 3], Operations: [] Exploring Operation: 56+9=65, Resulting Numbers: [96, 3, 65] Generated Node #2: [96, 3, 65] from Operation: 56+9=65 Current State: 99:[96, 3, 65], Operations: ['56+9=65'] Exploring Operation: 3*65=195, Resulting Numbers: [96, 195] Generated Node #3: [96, 195] from Operation: 3*65=195 Current State: 99:[96, 195], Operations: ['56+9=65', '3*65=195'] Exploring Operation: 195-96=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[96, 56, 9, 3], Operations: [] Exploring Operation: 56-9=47, Resulting Numbers: [96, 3, 47] Generated Node #0,0: 99:[96, 3, 47] Operation: 56-9=47 Exploring Operation: 96-56=40, Resulting Numbers: [9, 3, 40] Generated Node #0,1: 99:[9, 3, 40] Operation: 96-56=40 Exploring Operation: 96+3=99, Resulting Numbers: [56, 9, 99] Generated Node #0,2: 99:[56, 9, 99] Operation: 96+3=99 Exploring Operation: 56-3=53, Resulting Numbers: [96, 9, 53] Generated Node #0,3: 99:[96, 9, 53] Operation: 56-3=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[9, 3, 40], Operations: ['96-56=40'] Exploring Operation: 9+3=12, Resulting Numbers: [40, 12] Generated Node #0,1,0: 99:[40, 12] Operation: 9+3=12 Exploring Operation: 40-3=37, Resulting Numbers: [9, 37] Generated Node #0,1,1: 99:[9, 37] Operation: 40-3=37 Exploring Operation: 9/3=3, Resulting Numbers: [40, 3] Generated Node #0,1,2: 99:[40, 3] Operation: 9/3=3 Exploring Operation: 40-9=31, Resulting Numbers: [3, 31] Generated Node #0,1,3: 99:[3, 31] Operation: 40-9=31 Moving to Node #0,1,3 Current State: 99:[3, 31], Operations: ['96-56=40', '40-9=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,99 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[9, 37], Operations: ['96-56=40', '40-3=37'] Exploring Operation: 9*37=333, Resulting Numbers: [333] 333,99 unequal: No Solution Exploring Operation: 9+37=46, Resulting Numbers: [46] 46,99 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[40, 3], Operations: ['96-56=40', '9/3=3'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,99 unequal: No Solution Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[40, 12], Operations: ['96-56=40', '9+3=12'] Exploring Operation: 40*12=480, Resulting Numbers: [480] 480,99 unequal: No Solution Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,99 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[96, 3, 47], Operations: ['56-9=47'] Exploring Operation: 96-47=49, Resulting Numbers: [3, 49] Generated Node #0,0,0: 99:[3, 49] Operation: 96-47=49 Exploring Operation: 96+3=99, Resulting Numbers: [47, 99] Generated Node #0,0,1: 99:[47, 99] Operation: 96+3=99 Exploring Operation: 96/3=32, Resulting Numbers: [47, 32] Generated Node #0,0,2: 99:[47, 32] Operation: 96/3=32 Exploring Operation: 47-3=44, Resulting Numbers: [96, 44] Generated Node #0,0,3: 99:[96, 44] Operation: 47-3=44 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 99:[47, 99], Operations: ['56-9=47', '96+3=99'] Exploring Operation: 47+99=146, Resulting Numbers: [146] 146,99 unequal: No Solution Exploring Operation: 47*99=4653, Resulting Numbers: [4653] 4653,99 unequal: No Solution Exploring Operation: 99-47=52, Resulting Numbers: [52] 52,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 99:[96, 44], Operations: ['56-9=47', '47-3=44'] Exploring Operation: 96*44=4224, Resulting Numbers: [4224] 4224,99 unequal: No Solution Exploring Operation: 96-44=52, Resulting Numbers: [52] 52,99 unequal: No Solution Exploring Operation: 96+44=140, Resulting Numbers: [140] 140,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 99:[47, 32], Operations: ['56-9=47', '96/3=32'] Exploring Operation: 47*32=1504, Resulting Numbers: [1504] 1504,99 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 47+32=79, Resulting Numbers: [79] 79,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[3, 49], Operations: ['56-9=47', '96-47=49'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,99 unequal: No Solution Exploring Operation: 3+49=52, Resulting Numbers: [52] 52,99 unequal: No Solution Exploring Operation: 3*49=147, Resulting Numbers: [147] 147,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[56, 9, 99], Operations: ['96+3=99'] Exploring Operation: 99/9=11, Resulting Numbers: [56, 11] Generated Node #0,2,0: 99:[56, 11] Operation: 99/9=11 Exploring Operation: 99-56=43, Resulting Numbers: [9, 43] Generated Node #0,2,1: 99:[9, 43] Operation: 99-56=43 Exploring Operation: 56-9=47, Resulting Numbers: [99, 47] Generated Node #0,2,2: 99:[99, 47] Operation: 56-9=47 Exploring Operation: 56+9=65, Resulting Numbers: [99, 65] Generated Node #0,2,3: 99:[99, 65] Operation: 56+9=65 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[9, 43], Operations: ['96+3=99', '99-56=43'] Exploring Operation: 9+43=52, Resulting Numbers: [52] 52,99 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 9*43=387, Resulting Numbers: [387] 387,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[99, 47], Operations: ['96+3=99', '56-9=47'] Exploring Operation: 99*47=4653, Resulting Numbers: [4653] 4653,99 unequal: No Solution Exploring Operation: 99+47=146, Resulting Numbers: [146] 146,99 unequal: No Solution Exploring Operation: 99-47=52, Resulting Numbers: [52] 52,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 99:[56, 11], Operations: ['96+3=99', '99/9=11'] Exploring Operation: 56+11=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 56-11=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 56*11=616, Resulting Numbers: [616] 616,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 99:[99, 65], Operations: ['96+3=99', '56+9=65'] Exploring Operation: 99*65=6435, Resulting Numbers: [6435] 6435,99 unequal: No Solution Exploring Operation: 99+65=164, Resulting Numbers: [164] 164,99 unequal: No Solution Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[96, 9, 53], Operations: ['56-3=53'] Exploring Operation: 53-9=44, Resulting Numbers: [96, 44] Generated Node #0,3,0: 99:[96, 44] Operation: 53-9=44 Exploring Operation: 96-53=43, Resulting Numbers: [9, 43] Generated Node #0,3,1: 99:[9, 43] Operation: 96-53=43 Exploring Operation: 96-9=87, Resulting Numbers: [53, 87] Generated Node #0,3,2: 99:[53, 87] Operation: 96-9=87 Exploring Operation: 96+9=105, Resulting Numbers: [53, 105] Generated Node #0,3,3: 99:[53, 105] Operation: 96+9=105 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 99:[9, 43], Operations: ['56-3=53', '96-53=43'] Exploring Operation: 9*43=387, Resulting Numbers: [387] 387,99 unequal: No Solution Exploring Operation: 9+43=52, Resulting Numbers: [52] 52,99 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 99:[96, 44], Operations: ['56-3=53', '53-9=44'] Exploring Operation: 96*44=4224, Resulting Numbers: [4224] 4224,99 unequal: No Solution Exploring Operation: 96-44=52, Resulting Numbers: [52] 52,99 unequal: No Solution Exploring Operation: 96+44=140, Resulting Numbers: [140] 140,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 99:[53, 105], Operations: ['56-3=53', '96+9=105'] Exploring Operation: 105-53=52, Resulting Numbers: [52] 52,99 unequal: No Solution Exploring Operation: 53+105=158, Resulting Numbers: [158] 158,99 unequal: No Solution Exploring Operation: 53*105=5565, Resulting Numbers: [5565] 5565,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 99:[53, 87], Operations: ['56-3=53', '96-9=87'] Exploring Operation: 53*87=4611, Resulting Numbers: [4611] 4611,99 unequal: No Solution Exploring Operation: 87-53=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 53+87=140, Resulting Numbers: [140] 140,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 15, 43, 13, 71 ]
73
[ "43-13=30", "30/15=2", "71+2=73" ]
Current State: 73:[15, 43, 13, 71], Operations: [] Exploring Operation: 43-13=30, Resulting Numbers: [15, 71, 30] Generated Node #2: [15, 71, 30] from Operation: 43-13=30 Current State: 73:[15, 71, 30], Operations: ['43-13=30'] Exploring Operation: 30/15=2, Resulting Numbers: [71, 2] Generated Node #3: [71, 2] from Operation: 30/15=2 Current State: 73:[71, 2], Operations: ['43-13=30', '30/15=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[15, 43, 13, 71], Operations: [] Exploring Operation: 13+71=84, Resulting Numbers: [15, 43, 84] Generated Node #0,0: 73:[15, 43, 84] Operation: 13+71=84 Exploring Operation: 15+13=28, Resulting Numbers: [43, 71, 28] Generated Node #0,1: 73:[43, 71, 28] Operation: 15+13=28 Exploring Operation: 43+13=56, Resulting Numbers: [15, 71, 56] Generated Node #0,2: 73:[15, 71, 56] Operation: 43+13=56 Exploring Operation: 15-13=2, Resulting Numbers: [43, 71, 2] Generated Node #0,3: 73:[43, 71, 2] Operation: 15-13=2 Exploring Operation: 15+43=58, Resulting Numbers: [13, 71, 58] Generated Node #0,4: 73:[13, 71, 58] Operation: 15+43=58 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[43, 71, 28], Operations: ['15+13=28'] Exploring Operation: 43+71=114, Resulting Numbers: [28, 114] Generated Node #0,1,0: 73:[28, 114] Operation: 43+71=114 Exploring Operation: 71+28=99, Resulting Numbers: [43, 99] Generated Node #0,1,1: 73:[43, 99] Operation: 71+28=99 Exploring Operation: 43+28=71, Resulting Numbers: [71, 71] Generated Node #0,1,2: 73:[71, 71] Operation: 43+28=71 Exploring Operation: 71-28=43, Resulting Numbers: [43, 43] Generated Node #0,1,3: 73:[43, 43] Operation: 71-28=43 Exploring Operation: 43-28=15, Resulting Numbers: [71, 15] Generated Node #0,1,4: 73:[71, 15] Operation: 43-28=15 Moving to Node #0,1,2 Current State: 73:[71, 71], Operations: ['15+13=28', '43+28=71'] Exploring Operation: 71+71=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 71-71=0, Resulting Numbers: [0] 0,73 unequal: No Solution Exploring Operation: 71*71=5041, Resulting Numbers: [5041] 5041,73 unequal: No Solution Exploring Operation: 71/71=1, Resulting Numbers: [1] 1,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[43, 99], Operations: ['15+13=28', '71+28=99'] Exploring Operation: 43*99=4257, Resulting Numbers: [4257] 4257,73 unequal: No Solution Exploring Operation: 99-43=56, Resulting Numbers: [56] 56,73 unequal: No Solution Exploring Operation: 43+99=142, Resulting Numbers: [142] 142,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[43, 43], Operations: ['15+13=28', '71-28=43'] Exploring Operation: 43*43=1849, Resulting Numbers: [1849] 1849,73 unequal: No Solution Exploring Operation: 43/43=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,73 unequal: No Solution Exploring Operation: 43-43=0, Resulting Numbers: [0] 0,73 unequal: No Solution Moving to Node #0,1,4 Current State: 73:[71, 15], Operations: ['15+13=28', '43-28=15'] Exploring Operation: 71-15=56, Resulting Numbers: [56] 56,73 unequal: No Solution Exploring Operation: 71*15=1065, Resulting Numbers: [1065] 1065,73 unequal: No Solution Exploring Operation: 71+15=86, Resulting Numbers: [86] 86,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[28, 114], Operations: ['15+13=28', '43+71=114'] Exploring Operation: 114-28=86, Resulting Numbers: [86] 86,73 unequal: No Solution Exploring Operation: 28+114=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 28*114=3192, Resulting Numbers: [3192] 3192,73 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 #0,2 Current State: 73:[15, 71, 56], Operations: ['43+13=56'] Exploring Operation: 15+56=71, Resulting Numbers: [71, 71] Generated Node #0,2,0: 73:[71, 71] Operation: 15+56=71 Exploring Operation: 56-15=41, Resulting Numbers: [71, 41] Generated Node #0,2,1: 73:[71, 41] Operation: 56-15=41 Exploring Operation: 71+56=127, Resulting Numbers: [15, 127] Generated Node #0,2,2: 73:[15, 127] Operation: 71+56=127 Exploring Operation: 15+71=86, Resulting Numbers: [56, 86] Generated Node #0,2,3: 73:[56, 86] Operation: 15+71=86 Exploring Operation: 71-15=56, Resulting Numbers: [56, 56] Generated Node #0,2,4: 73:[56, 56] Operation: 71-15=56 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[71, 71], Operations: ['43+13=56', '15+56=71'] Exploring Operation: 71*71=5041, Resulting Numbers: [5041] 5041,73 unequal: No Solution Exploring Operation: 71-71=0, Resulting Numbers: [0] 0,73 unequal: No Solution Exploring Operation: 71+71=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 71/71=1, Resulting Numbers: [1] 1,73 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 #0,2,3 Current State: 73:[56, 86], Operations: ['43+13=56', '15+71=86'] Exploring Operation: 56*86=4816, Resulting Numbers: [4816] 4816,73 unequal: No Solution Exploring Operation: 86-56=30, Resulting Numbers: [30] 30,73 unequal: No Solution Exploring Operation: 56+86=142, Resulting Numbers: [142] 142,73 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 #0,2,1 Current State: 73:[71, 41], Operations: ['43+13=56', '56-15=41'] Exploring Operation: 71*41=2911, Resulting Numbers: [2911] 2911,73 unequal: No Solution Exploring Operation: 71+41=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,73 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 #0,2,4 Current State: 73:[56, 56], Operations: ['43+13=56', '71-15=56'] Exploring Operation: 56*56=3136, Resulting Numbers: [3136] 3136,73 unequal: No Solution Exploring Operation: 56-56=0, Resulting Numbers: [0] 0,73 unequal: No Solution Exploring Operation: 56+56=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 56/56=1, Resulting Numbers: [1] 1,73 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 #0,2,2 Current State: 73:[15, 127], Operations: ['43+13=56', '71+56=127'] Exploring Operation: 15*127=1905, Resulting Numbers: [1905] 1905,73 unequal: No Solution Exploring Operation: 127-15=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 15+127=142, Resulting Numbers: [142] 142,73 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 #0,4 Current State: 73:[13, 71, 58], Operations: ['15+43=58'] Exploring Operation: 58-13=45, Resulting Numbers: [71, 45] Generated Node #0,4,0: 73:[71, 45] Operation: 58-13=45 Exploring Operation: 71+58=129, Resulting Numbers: [13, 129] Generated Node #0,4,1: 73:[13, 129] Operation: 71+58=129 Exploring Operation: 13+58=71, Resulting Numbers: [71, 71] Generated Node #0,4,2: 73:[71, 71] Operation: 13+58=71 Exploring Operation: 71-13=58, Resulting Numbers: [58, 58] Generated Node #0,4,3: 73:[58, 58] Operation: 71-13=58 Exploring Operation: 13+71=84, Resulting Numbers: [58, 84] Generated Node #0,4,4: 73:[58, 84] Operation: 13+71=84 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 73:[71, 71], Operations: ['15+43=58', '13+58=71'] Exploring Operation: 71*71=5041, Resulting Numbers: [5041] 5041,73 unequal: No Solution Exploring Operation: 71-71=0, Resulting Numbers: [0] 0,73 unequal: No Solution Exploring Operation: 71/71=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 71+71=142, Resulting Numbers: [142] 142,73 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 #0,4,4 Current State: 73:[58, 84], Operations: ['15+43=58', '13+71=84'] Exploring Operation: 84-58=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 58+84=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 58*84=4872, Resulting Numbers: [4872] 4872,73 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 #0,4,0 Current State: 73:[71, 45], Operations: ['15+43=58', '58-13=45'] Exploring Operation: 71-45=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 71+45=116, Resulting Numbers: [116] 116,73 unequal: No Solution Exploring Operation: 71*45=3195, Resulting Numbers: [3195] 3195,73 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 #0,4,3 Current State: 73:[58, 58], Operations: ['15+43=58', '71-13=58'] Exploring Operation: 58-58=0, Resulting Numbers: [0] 0,73 unequal: No Solution Exploring Operation: 58/58=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 58*58=3364, Resulting Numbers: [3364] 3364,73 unequal: No Solution Exploring Operation: 58+58=116, Resulting Numbers: [116] 116,73 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 #0,4,1 Current State: 73:[13, 129], Operations: ['15+43=58', '71+58=129'] Exploring Operation: 13+129=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 13*129=1677, Resulting Numbers: [1677] 1677,73 unequal: No Solution Exploring Operation: 129-13=116, Resulting Numbers: [116] 116,73 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 #0,0 Current State: 73:[15, 43, 84], Operations: ['13+71=84'] Exploring Operation: 84-43=41, Resulting Numbers: [15, 41] Generated Node #0,0,0: 73:[15, 41] Operation: 84-43=41 Exploring Operation: 15+43=58, Resulting Numbers: [84, 58] Generated Node #0,0,1: 73:[84, 58] Operation: 15+43=58 Exploring Operation: 15+84=99, Resulting Numbers: [43, 99] Generated Node #0,0,2: 73:[43, 99] Operation: 15+84=99 Exploring Operation: 84-15=69, Resulting Numbers: [43, 69] Generated Node #0,0,3: 73:[43, 69] Operation: 84-15=69 Exploring Operation: 43-15=28, Resulting Numbers: [84, 28] Generated Node #0,0,4: 73:[84, 28] Operation: 43-15=28 Moving to Node #0,0,1 Current State: 73:[84, 58], Operations: ['13+71=84', '15+43=58'] Exploring Operation: 84+58=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 84-58=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 84*58=4872, Resulting Numbers: [4872] 4872,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[43, 69], Operations: ['13+71=84', '84-15=69'] Exploring Operation: 43*69=2967, Resulting Numbers: [2967] 2967,73 unequal: No Solution Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 43+69=112, Resulting Numbers: [112] 112,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[43, 99], Operations: ['13+71=84', '15+84=99'] Exploring Operation: 43*99=4257, Resulting Numbers: [4257] 4257,73 unequal: No Solution Exploring Operation: 43+99=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 99-43=56, Resulting Numbers: [56] 56,73 unequal: No Solution Moving to Node #0,0,4 Current State: 73:[84, 28], Operations: ['13+71=84', '43-15=28'] Exploring Operation: 84/28=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 84*28=2352, Resulting Numbers: [2352] 2352,73 unequal: No Solution Exploring Operation: 84+28=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 84-28=56, Resulting Numbers: [56] 56,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[15, 41], Operations: ['13+71=84', '84-43=41'] Exploring Operation: 15*41=615, Resulting Numbers: [615] 615,73 unequal: No Solution Exploring Operation: 15+41=56, Resulting Numbers: [56] 56,73 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,73 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 Current State: 73:[43, 71, 2], Operations: ['15-13=2'] Exploring Operation: 71+2=73, Resulting Numbers: [43, 73] Generated Node #0,3,0: 73:[43, 73] Operation: 71+2=73 Exploring Operation: 43*2=86, Resulting Numbers: [71, 86] Generated Node #0,3,1: 73:[71, 86] Operation: 43*2=86 Exploring Operation: 43-2=41, Resulting Numbers: [71, 41] Generated Node #0,3,2: 73:[71, 41] Operation: 43-2=41 Exploring Operation: 43+2=45, Resulting Numbers: [71, 45] Generated Node #0,3,3: 73:[71, 45] Operation: 43+2=45 Exploring Operation: 71-2=69, Resulting Numbers: [43, 69] Generated Node #0,3,4: 73:[43, 69] Operation: 71-2=69 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 73:[71, 86], Operations: ['15-13=2', '43*2=86'] Exploring Operation: 71+86=157, Resulting Numbers: [157] 157,73 unequal: No Solution Exploring Operation: 71*86=6106, Resulting Numbers: [6106] 6106,73 unequal: No Solution Exploring Operation: 86-71=15, Resulting Numbers: [15] 15,73 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 #0,3,0 Current State: 73:[43, 73], Operations: ['15-13=2', '71+2=73'] Exploring Operation: 73-43=30, Resulting Numbers: [30] 30,73 unequal: No Solution Exploring Operation: 43+73=116, Resulting Numbers: [116] 116,73 unequal: No Solution Exploring Operation: 43*73=3139, Resulting Numbers: [3139] 3139,73 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 #0,3,3 Current State: 73:[71, 45], Operations: ['15-13=2', '43+2=45'] Exploring Operation: 71*45=3195, Resulting Numbers: [3195] 3195,73 unequal: No Solution Exploring Operation: 71+45=116, Resulting Numbers: [116] 116,73 unequal: No Solution Exploring Operation: 71-45=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 #0,3,2 Current State: 73:[71, 41], Operations: ['15-13=2', '43-2=41'] Exploring Operation: 71+41=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,73 unequal: No Solution Exploring Operation: 71*41=2911, Resulting Numbers: [2911] 2911,73 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 #0,3,4 Current State: 73:[43, 69], Operations: ['15-13=2', '71-2=69'] Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 43+69=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 43*69=2967, Resulting Numbers: [2967] 2967,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 8, 36, 47, 16 ]
81
[ "16/8=2", "36+47=83", "83-2=81" ]
Current State: 81:[8, 36, 47, 16], Operations: [] Exploring Operation: 16/8=2, Resulting Numbers: [36, 47, 2] Generated Node #2: [36, 47, 2] from Operation: 16/8=2 Current State: 81:[36, 47, 2], Operations: ['16/8=2'] Exploring Operation: 36+47=83, Resulting Numbers: [2, 83] Generated Node #3: [2, 83] from Operation: 36+47=83 Current State: 81:[2, 83], Operations: ['16/8=2', '36+47=83'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[8, 36, 47, 16], Operations: [] Exploring Operation: 36+47=83, Resulting Numbers: [8, 16, 83] Generated Node #0,0: 81:[8, 16, 83] Operation: 36+47=83 Exploring Operation: 36-8=28, Resulting Numbers: [47, 16, 28] Generated Node #0,1: 81:[47, 16, 28] Operation: 36-8=28 Exploring Operation: 47-16=31, Resulting Numbers: [8, 36, 31] Generated Node #0,2: 81:[8, 36, 31] Operation: 47-16=31 Exploring Operation: 47-36=11, Resulting Numbers: [8, 16, 11] Generated Node #0,3: 81:[8, 16, 11] Operation: 47-36=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[8, 16, 83], Operations: ['36+47=83'] Exploring Operation: 83-8=75, Resulting Numbers: [16, 75] Generated Node #0,0,0: 81:[16, 75] Operation: 83-8=75 Exploring Operation: 16/8=2, Resulting Numbers: [83, 2] Generated Node #0,0,1: 81:[83, 2] Operation: 16/8=2 Exploring Operation: 16-8=8, Resulting Numbers: [83, 8] Generated Node #0,0,2: 81:[83, 8] Operation: 16-8=8 Exploring Operation: 8+16=24, Resulting Numbers: [83, 24] Generated Node #0,0,3: 81:[83, 24] Operation: 8+16=24 Moving to Node #0,0,1 Current State: 81:[83, 2], Operations: ['36+47=83', '16/8=2'] Exploring Operation: 83*2=166, Resulting Numbers: [166] 166,81 unequal: No Solution Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[8, 36, 47, 16], Operations: [] Exploring Operation: 36+47=83, Resulting Numbers: [8, 16, 83] Generated Node #0,0: 81:[8, 16, 83] Operation: 36+47=83 Moving to Node #0,0 Current State: 81:[8, 16, 83], Operations: ['36+47=83'] Exploring Operation: 16/8=2, Resulting Numbers: [83, 2] Generated Node #0,0,1: 81:[83, 2] Operation: 16/8=2 Moving to Node #0,0,1 Current State: 81:[83, 2], Operations: ['36+47=83', '16/8=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 19, 49, 9, 84 ]
52
[ "19+9=28", "84/28=3", "49+3=52" ]
Current State: 52:[19, 49, 9, 84], Operations: [] Exploring Operation: 19+9=28, Resulting Numbers: [49, 84, 28] Generated Node #2: [49, 84, 28] from Operation: 19+9=28 Current State: 52:[49, 84, 28], Operations: ['19+9=28'] Exploring Operation: 84/28=3, Resulting Numbers: [49, 3] Generated Node #3: [49, 3] from Operation: 84/28=3 Current State: 52:[49, 3], Operations: ['19+9=28', '84/28=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[19, 49, 9, 84], Operations: [] Exploring Operation: 84-9=75, Resulting Numbers: [19, 49, 75] Generated Node #0,0: 52:[19, 49, 75] Operation: 84-9=75 Exploring Operation: 19+9=28, Resulting Numbers: [49, 84, 28] Generated Node #0,1: 52:[49, 84, 28] Operation: 19+9=28 Exploring Operation: 84-19=65, Resulting Numbers: [49, 9, 65] Generated Node #0,2: 52:[49, 9, 65] Operation: 84-19=65 Exploring Operation: 84-49=35, Resulting Numbers: [19, 9, 35] Generated Node #0,3: 52:[19, 9, 35] Operation: 84-49=35 Moving to Node #0,3 Current State: 52:[19, 9, 35], Operations: ['84-49=35'] Exploring Operation: 35-19=16, Resulting Numbers: [9, 16] Generated Node #0,3,0: 52:[9, 16] Operation: 35-19=16 Exploring Operation: 19+35=54, Resulting Numbers: [9, 54] Generated Node #0,3,1: 52:[9, 54] Operation: 19+35=54 Exploring Operation: 19+9=28, Resulting Numbers: [35, 28] Generated Node #0,3,2: 52:[35, 28] Operation: 19+9=28 Exploring Operation: 35-9=26, Resulting Numbers: [19, 26] Generated Node #0,3,3: 52:[19, 26] Operation: 35-9=26 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 52:[9, 54], Operations: ['84-49=35', '19+35=54'] Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,52 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,52 unequal: No Solution Exploring Operation: 9+54=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 9*54=486, Resulting Numbers: [486] 486,52 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 #0,3,3 Current State: 52:[19, 26], Operations: ['84-49=35', '35-9=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,52 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,52 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 #0,3,0 Current State: 52:[9, 16], Operations: ['84-49=35', '35-19=16'] Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,52 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,52 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 #0,3,2 Current State: 52:[35, 28], Operations: ['84-49=35', '19+9=28'] Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,52 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:[49, 9, 65], Operations: ['84-19=65'] Exploring Operation: 49-9=40, Resulting Numbers: [65, 40] Generated Node #0,2,0: 52:[65, 40] Operation: 49-9=40 Exploring Operation: 65-49=16, Resulting Numbers: [9, 16] Generated Node #0,2,1: 52:[9, 16] Operation: 65-49=16 Exploring Operation: 49+9=58, Resulting Numbers: [65, 58] Generated Node #0,2,2: 52:[65, 58] Operation: 49+9=58 Exploring Operation: 65-9=56, Resulting Numbers: [49, 56] Generated Node #0,2,3: 52:[49, 56] Operation: 65-9=56 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[9, 16], Operations: ['84-19=65', '65-49=16'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,52 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:[49, 56], Operations: ['84-19=65', '65-9=56'] Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,52 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[65, 58], Operations: ['84-19=65', '49+9=58'] Exploring Operation: 65+58=123, Resulting Numbers: [123] 123,52 unequal: No Solution Exploring Operation: 65-58=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 65*58=3770, Resulting Numbers: [3770] 3770,52 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:[65, 40], Operations: ['84-19=65', '49-9=40'] Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 65+40=105, Resulting Numbers: [105] 105,52 unequal: No Solution Exploring Operation: 65*40=2600, Resulting Numbers: [2600] 2600,52 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: 52:[19, 49, 75], Operations: ['84-9=75'] Exploring Operation: 75-19=56, Resulting Numbers: [49, 56] Generated Node #0,0,0: 52:[49, 56] Operation: 75-19=56 Exploring Operation: 49-19=30, Resulting Numbers: [75, 30] Generated Node #0,0,1: 52:[75, 30] Operation: 49-19=30 Exploring Operation: 19+49=68, Resulting Numbers: [75, 68] Generated Node #0,0,2: 52:[75, 68] Operation: 19+49=68 Exploring Operation: 75-49=26, Resulting Numbers: [19, 26] Generated Node #0,0,3: 52:[19, 26] Operation: 75-49=26 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 52:[19, 26], Operations: ['84-9=75', '75-49=26'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,52 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,52 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 #0,0,0 Current State: 52:[49, 56], Operations: ['84-9=75', '75-19=56'] Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,52 unequal: No Solution Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,52 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:[75, 30], Operations: ['84-9=75', '49-19=30'] Exploring Operation: 75+30=105, Resulting Numbers: [105] 105,52 unequal: No Solution Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,52 unequal: No Solution Exploring Operation: 75*30=2250, Resulting Numbers: [2250] 2250,52 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:[75, 68], Operations: ['84-9=75', '19+49=68'] Exploring Operation: 75+68=143, Resulting Numbers: [143] 143,52 unequal: No Solution Exploring Operation: 75-68=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 75*68=5100, Resulting Numbers: [5100] 5100,52 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: 52:[49, 84, 28], Operations: ['19+9=28'] Exploring Operation: 49-28=21, Resulting Numbers: [84, 21] Generated Node #0,1,0: 52:[84, 21] Operation: 49-28=21 Exploring Operation: 84-28=56, Resulting Numbers: [49, 56] Generated Node #0,1,1: 52:[49, 56] Operation: 84-28=56 Exploring Operation: 84/28=3, Resulting Numbers: [49, 3] Generated Node #0,1,2: 52:[49, 3] Operation: 84/28=3 Exploring Operation: 84-49=35, Resulting Numbers: [28, 35] Generated Node #0,1,3: 52:[28, 35] Operation: 84-49=35 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 52:[49, 3], Operations: ['19+9=28', '84/28=3'] Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,52 unequal: No Solution Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[19, 49, 9, 84], Operations: [] Exploring Operation: 19+9=28, Resulting Numbers: [49, 84, 28] Generated Node #0,1: 52:[49, 84, 28] Operation: 19+9=28 Moving to Node #0,1 Current State: 52:[49, 84, 28], Operations: ['19+9=28'] Exploring Operation: 84/28=3, Resulting Numbers: [49, 3] Generated Node #0,1,2: 52:[49, 3] Operation: 84/28=3 Moving to Node #0,1,2 Current State: 52:[49, 3], Operations: ['19+9=28', '84/28=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_4
sum_heuristic
[ 56, 42, 13, 30 ]
100
[ "42-30=12", "13*12=156", "156-56=100" ]
Current State: 100:[56, 42, 13, 30], Operations: [] Exploring Operation: 42-30=12, Resulting Numbers: [56, 13, 12] Generated Node #2: [56, 13, 12] from Operation: 42-30=12 Current State: 100:[56, 13, 12], Operations: ['42-30=12'] Exploring Operation: 13*12=156, Resulting Numbers: [56, 156] Generated Node #3: [56, 156] from Operation: 13*12=156 Current State: 100:[56, 156], Operations: ['42-30=12', '13*12=156'] Exploring Operation: 156-56=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[56, 42, 13, 30], Operations: [] Exploring Operation: 56-30=26, Resulting Numbers: [42, 13, 26] Generated Node #0,0: 100:[42, 13, 26] Operation: 56-30=26 Exploring Operation: 56+42=98, Resulting Numbers: [13, 30, 98] Generated Node #0,1: 100:[13, 30, 98] Operation: 56+42=98 Exploring Operation: 42-30=12, Resulting Numbers: [56, 13, 12] Generated Node #0,2: 100:[56, 13, 12] Operation: 42-30=12 Exploring Operation: 56-42=14, Resulting Numbers: [13, 30, 14] Generated Node #0,3: 100:[13, 30, 14] Operation: 56-42=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[13, 30, 98], Operations: ['56+42=98'] Exploring Operation: 13+98=111, Resulting Numbers: [30, 111] Generated Node #0,1,0: 100:[30, 111] Operation: 13+98=111 Exploring Operation: 30-13=17, Resulting Numbers: [98, 17] Generated Node #0,1,1: 100:[98, 17] Operation: 30-13=17 Exploring Operation: 13+30=43, Resulting Numbers: [98, 43] Generated Node #0,1,2: 100:[98, 43] Operation: 13+30=43 Exploring Operation: 98-13=85, Resulting Numbers: [30, 85] Generated Node #0,1,3: 100:[30, 85] Operation: 98-13=85 Moving to Node #0,1,1 Current State: 100:[98, 17], Operations: ['56+42=98', '30-13=17'] Exploring Operation: 98*17=1666, Resulting Numbers: [1666] 1666,100 unequal: No Solution Exploring Operation: 98+17=115, Resulting Numbers: [115] 115,100 unequal: No Solution Exploring Operation: 98-17=81, Resulting Numbers: [81] 81,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[98, 43], Operations: ['56+42=98', '13+30=43'] Exploring Operation: 98-43=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 98*43=4214, Resulting Numbers: [4214] 4214,100 unequal: No Solution Exploring Operation: 98+43=141, Resulting Numbers: [141] 141,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[30, 111], Operations: ['56+42=98', '13+98=111'] Exploring Operation: 30*111=3330, Resulting Numbers: [3330] 3330,100 unequal: No Solution Exploring Operation: 111-30=81, Resulting Numbers: [81] 81,100 unequal: No Solution Exploring Operation: 30+111=141, Resulting Numbers: [141] 141,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[30, 85], Operations: ['56+42=98', '98-13=85'] Exploring Operation: 30+85=115, Resulting Numbers: [115] 115,100 unequal: No Solution Exploring Operation: 30*85=2550, Resulting Numbers: [2550] 2550,100 unequal: No Solution Exploring Operation: 85-30=55, Resulting Numbers: [55] 55,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[56, 13, 12], Operations: ['42-30=12'] Exploring Operation: 56-12=44, Resulting Numbers: [13, 44] Generated Node #0,2,0: 100:[13, 44] Operation: 56-12=44 Exploring Operation: 56-13=43, Resulting Numbers: [12, 43] Generated Node #0,2,1: 100:[12, 43] Operation: 56-13=43 Exploring Operation: 13+12=25, Resulting Numbers: [56, 25] Generated Node #0,2,2: 100:[56, 25] Operation: 13+12=25 Exploring Operation: 13-12=1, Resulting Numbers: [56, 1] Generated Node #0,2,3: 100:[56, 1] Operation: 13-12=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 100:[56, 25], Operations: ['42-30=12', '13+12=25'] Exploring Operation: 56*25=1400, Resulting Numbers: [1400] 1400,100 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 56+25=81, Resulting Numbers: [81] 81,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 100:[56, 1], Operations: ['42-30=12', '13-12=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,100 unequal: No Solution Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 100:[13, 44], Operations: ['42-30=12', '56-12=44'] Exploring Operation: 13*44=572, Resulting Numbers: [572] 572,100 unequal: No Solution Exploring Operation: 13+44=57, Resulting Numbers: [57] 57,100 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 100:[12, 43], Operations: ['42-30=12', '56-13=43'] Exploring Operation: 12+43=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 12*43=516, Resulting Numbers: [516] 516,100 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[42, 13, 26], Operations: ['56-30=26'] Exploring Operation: 26/13=2, Resulting Numbers: [42, 2] Generated Node #0,0,0: 100:[42, 2] Operation: 26/13=2 Exploring Operation: 42-13=29, Resulting Numbers: [26, 29] Generated Node #0,0,1: 100:[26, 29] Operation: 42-13=29 Exploring Operation: 42-26=16, Resulting Numbers: [13, 16] Generated Node #0,0,2: 100:[13, 16] Operation: 42-26=16 Exploring Operation: 42+13=55, Resulting Numbers: [26, 55] Generated Node #0,0,3: 100:[26, 55] Operation: 42+13=55 Moving to Node #0,0,1 Current State: 100:[26, 29], Operations: ['56-30=26', '42-13=29'] Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,100 unequal: No Solution Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,100 unequal: No Solution Moving to Node #0,0,3 Current State: 100:[26, 55], Operations: ['56-30=26', '42+13=55'] Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 26*55=1430, Resulting Numbers: [1430] 1430,100 unequal: No Solution Exploring Operation: 26+55=81, Resulting Numbers: [81] 81,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[13, 16], Operations: ['56-30=26', '42-26=16'] Exploring Operation: 13*16=208, Resulting Numbers: [208] 208,100 unequal: No Solution Exploring Operation: 13+16=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[42, 2], Operations: ['56-30=26', '26/13=2'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,100 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,100 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[13, 30, 14], Operations: ['56-42=14'] Exploring Operation: 13+14=27, Resulting Numbers: [30, 27] Generated Node #0,3,0: 100:[30, 27] Operation: 13+14=27 Exploring Operation: 14-13=1, Resulting Numbers: [30, 1] Generated Node #0,3,1: 100:[30, 1] Operation: 14-13=1 Exploring Operation: 30-14=16, Resulting Numbers: [13, 16] Generated Node #0,3,2: 100:[13, 16] Operation: 30-14=16 Exploring Operation: 30-13=17, Resulting Numbers: [14, 17] Generated Node #0,3,3: 100:[14, 17] Operation: 30-13=17 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 100:[30, 1], Operations: ['56-42=14', '14-13=1'] Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 30*1=30, Resulting Numbers: [30] 30,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 100:[30, 27], Operations: ['56-42=14', '13+14=27'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 30*27=810, Resulting Numbers: [810] 810,100 unequal: No Solution Exploring Operation: 30+27=57, Resulting Numbers: [57] 57,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 100:[13, 16], Operations: ['56-42=14', '30-14=16'] Exploring Operation: 13*16=208, Resulting Numbers: [208] 208,100 unequal: No Solution Exploring Operation: 13+16=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 100:[14, 17], Operations: ['56-42=14', '30-13=17'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,100 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 82, 90, 1, 48 ]
41
[ "90-82=8", "1+48=49", "49-8=41" ]
Current State: 41:[82, 90, 1, 48], Operations: [] Exploring Operation: 90-82=8, Resulting Numbers: [1, 48, 8] Generated Node #2: [1, 48, 8] from Operation: 90-82=8 Current State: 41:[1, 48, 8], Operations: ['90-82=8'] Exploring Operation: 1+48=49, Resulting Numbers: [8, 49] Generated Node #3: [8, 49] from Operation: 1+48=49 Current State: 41:[8, 49], Operations: ['90-82=8', '1+48=49'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[82, 90, 1, 48], Operations: [] Exploring Operation: 82-48=34, Resulting Numbers: [90, 1, 34] Generated Node #0,0: 41:[90, 1, 34] Operation: 82-48=34 Exploring Operation: 90-82=8, Resulting Numbers: [1, 48, 8] Generated Node #0,1: 41:[1, 48, 8] Operation: 90-82=8 Exploring Operation: 82-1=81, Resulting Numbers: [90, 48, 81] Generated Node #0,2: 41:[90, 48, 81] Operation: 82-1=81 Exploring Operation: 90-48=42, Resulting Numbers: [82, 1, 42] Generated Node #0,3: 41:[82, 1, 42] Operation: 90-48=42 Moving to Node #0,1 Current State: 41:[1, 48, 8], Operations: ['90-82=8'] Exploring Operation: 48/1=48, Resulting Numbers: [8, 48] Generated Node #0,1,0: 41:[8, 48] Operation: 48/1=48 Exploring Operation: 1*48=48, Resulting Numbers: [8, 48] Generated Node #0,1,1: 41:[8, 48] Operation: 1*48=48 Exploring Operation: 48-1=47, Resulting Numbers: [8, 47] Generated Node #0,1,2: 41:[8, 47] Operation: 48-1=47 Exploring Operation: 1+8=9, Resulting Numbers: [48, 9] Generated Node #0,1,3: 41:[48, 9] Operation: 1+8=9 Moving to Node #0,3 Current State: 41:[82, 1, 42], Operations: ['90-48=42'] Exploring Operation: 42-1=41, Resulting Numbers: [82, 41] Generated Node #0,3,0: 41:[82, 41] Operation: 42-1=41 Exploring Operation: 82-1=81, Resulting Numbers: [42, 81] Generated Node #0,3,1: 41:[42, 81] Operation: 82-1=81 Exploring Operation: 82*1=82, Resulting Numbers: [42, 82] Generated Node #0,3,2: 41:[42, 82] Operation: 82*1=82 Exploring Operation: 82-42=40, Resulting Numbers: [1, 40] Generated Node #0,3,3: 41:[1, 40] Operation: 82-42=40 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[82, 41], Operations: ['90-48=42', '42-1=41'] Exploring Operation: 82*41=3362, Resulting Numbers: [3362] 3362,41 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[82, 90, 1, 48], Operations: [] Exploring Operation: 90-48=42, Resulting Numbers: [82, 1, 42] Generated Node #0,3: 41:[82, 1, 42] Operation: 90-48=42 Moving to Node #0,3 Current State: 41:[82, 1, 42], Operations: ['90-48=42'] Exploring Operation: 42-1=41, Resulting Numbers: [82, 41] Generated Node #0,3,0: 41:[82, 41] Operation: 42-1=41 Moving to Node #0,3,0 Current State: 41:[82, 41], Operations: ['90-48=42', '42-1=41'] Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 3, 63, 98, 55 ]
72
[ "63+98=161", "55+161=216", "216/3=72" ]
Current State: 72:[3, 63, 98, 55], Operations: [] Exploring Operation: 63+98=161, Resulting Numbers: [3, 55, 161] Generated Node #2: [3, 55, 161] from Operation: 63+98=161 Current State: 72:[3, 55, 161], Operations: ['63+98=161'] Exploring Operation: 55+161=216, Resulting Numbers: [3, 216] Generated Node #3: [3, 216] from Operation: 55+161=216 Current State: 72:[3, 216], Operations: ['63+98=161', '55+161=216'] Exploring Operation: 216/3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[3, 63, 98, 55], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [3, 98, 8] Generated Node #0,0: 72:[3, 98, 8] Operation: 63-55=8 Exploring Operation: 63/3=21, Resulting Numbers: [98, 55, 21] Generated Node #0,1: 72:[98, 55, 21] Operation: 63/3=21 Exploring Operation: 98-55=43, Resulting Numbers: [3, 63, 43] Generated Node #0,2: 72:[3, 63, 43] Operation: 98-55=43 Exploring Operation: 98-63=35, Resulting Numbers: [3, 55, 35] Generated Node #0,3: 72:[3, 55, 35] Operation: 98-63=35 Moving to Node #0,2 Current State: 72:[3, 63, 43], Operations: ['98-55=43'] Exploring Operation: 3+63=66, Resulting Numbers: [43, 66] Generated Node #0,2,0: 72:[43, 66] Operation: 3+63=66 Exploring Operation: 63-43=20, Resulting Numbers: [3, 20] Generated Node #0,2,1: 72:[3, 20] Operation: 63-43=20 Exploring Operation: 43-3=40, Resulting Numbers: [63, 40] Generated Node #0,2,2: 72:[63, 40] Operation: 43-3=40 Exploring Operation: 63/3=21, Resulting Numbers: [43, 21] Generated Node #0,2,3: 72:[43, 21] Operation: 63/3=21 Moving to Node #0,3 Current State: 72:[3, 55, 35], Operations: ['98-63=35'] Exploring Operation: 55+35=90, Resulting Numbers: [3, 90] Generated Node #0,3,0: 72:[3, 90] Operation: 55+35=90 Exploring Operation: 55-3=52, Resulting Numbers: [35, 52] Generated Node #0,3,1: 72:[35, 52] Operation: 55-3=52 Exploring Operation: 55-35=20, Resulting Numbers: [3, 20] Generated Node #0,3,2: 72:[3, 20] Operation: 55-35=20 Exploring Operation: 3+55=58, Resulting Numbers: [35, 58] Generated Node #0,3,3: 72:[35, 58] Operation: 3+55=58 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 72:[3, 20], Operations: ['98-63=35', '55-35=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,72 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,72 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:[35, 58], Operations: ['98-63=35', '3+55=58'] Exploring Operation: 35+58=93, Resulting Numbers: [93] 93,72 unequal: No Solution Exploring Operation: 58-35=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 35*58=2030, Resulting Numbers: [2030] 2030,72 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 #0,3,1 Current State: 72:[35, 52], Operations: ['98-63=35', '55-3=52'] Exploring Operation: 35+52=87, Resulting Numbers: [87] 87,72 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,72 unequal: No Solution Exploring Operation: 35*52=1820, Resulting Numbers: [1820] 1820,72 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:[3, 90], Operations: ['98-63=35', '55+35=90'] Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,72 unequal: No Solution Exploring Operation: 3*90=270, Resulting Numbers: [270] 270,72 unequal: No Solution Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,72 unequal: No Solution Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,72 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: 72:[3, 98, 8], Operations: ['63-55=8'] Exploring Operation: 3*8=24, Resulting Numbers: [98, 24] Generated Node #0,0,0: 72:[98, 24] Operation: 3*8=24 Exploring Operation: 98-8=90, Resulting Numbers: [3, 90] Generated Node #0,0,1: 72:[3, 90] Operation: 98-8=90 Exploring Operation: 3+8=11, Resulting Numbers: [98, 11] Generated Node #0,0,2: 72:[98, 11] Operation: 3+8=11 Exploring Operation: 98-3=95, Resulting Numbers: [8, 95] Generated Node #0,0,3: 72:[8, 95] Operation: 98-3=95 Moving to Node #0,1 Current State: 72:[98, 55, 21], Operations: ['63/3=21'] Exploring Operation: 55+21=76, Resulting Numbers: [98, 76] Generated Node #0,1,0: 72:[98, 76] Operation: 55+21=76 Exploring Operation: 98-55=43, Resulting Numbers: [21, 43] Generated Node #0,1,1: 72:[21, 43] Operation: 98-55=43 Exploring Operation: 98-21=77, Resulting Numbers: [55, 77] Generated Node #0,1,2: 72:[55, 77] Operation: 98-21=77 Exploring Operation: 55-21=34, Resulting Numbers: [98, 34] Generated Node #0,1,3: 72:[98, 34] Operation: 55-21=34 Moving to Node #0,2,1 Current State: 72:[3, 20], Operations: ['98-55=43', '63-43=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,72 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[43, 21], Operations: ['98-55=43', '63/3=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,72 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[21, 43], Operations: ['63/3=21', '98-55=43'] Exploring Operation: 21*43=903, Resulting Numbers: [903] 903,72 unequal: No Solution Exploring Operation: 21+43=64, Resulting Numbers: [64] 64,72 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[43, 66], Operations: ['98-55=43', '3+63=66'] Exploring Operation: 43+66=109, Resulting Numbers: [109] 109,72 unequal: No Solution Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 43*66=2838, Resulting Numbers: [2838] 2838,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[63, 40], Operations: ['98-55=43', '43-3=40'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 63+40=103, Resulting Numbers: [103] 103,72 unequal: No Solution Exploring Operation: 63*40=2520, Resulting Numbers: [2520] 2520,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[3, 90], Operations: ['63-55=8', '98-8=90'] Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,72 unequal: No Solution Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,72 unequal: No Solution Exploring Operation: 3*90=270, Resulting Numbers: [270] 270,72 unequal: No Solution Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[55, 77], Operations: ['63/3=21', '98-21=77'] Exploring Operation: 55*77=4235, Resulting Numbers: [4235] 4235,72 unequal: No Solution Exploring Operation: 77-55=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 55+77=132, Resulting Numbers: [132] 132,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[8, 95], Operations: ['63-55=8', '98-3=95'] Exploring Operation: 8*95=760, Resulting Numbers: [760] 760,72 unequal: No Solution Exploring Operation: 8+95=103, Resulting Numbers: [103] 103,72 unequal: No Solution Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[98, 24], Operations: ['63-55=8', '3*8=24'] Exploring Operation: 98*24=2352, Resulting Numbers: [2352] 2352,72 unequal: No Solution Exploring Operation: 98+24=122, Resulting Numbers: [122] 122,72 unequal: No Solution Exploring Operation: 98-24=74, Resulting Numbers: [74] 74,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[98, 11], Operations: ['63-55=8', '3+8=11'] Exploring Operation: 98-11=87, Resulting Numbers: [87] 87,72 unequal: No Solution Exploring Operation: 98+11=109, Resulting Numbers: [109] 109,72 unequal: No Solution Exploring Operation: 98*11=1078, Resulting Numbers: [1078] 1078,72 unequal: No Solution Moving to Node #0,1,3 Current State: 72:[98, 34], Operations: ['63/3=21', '55-21=34'] Exploring Operation: 98+34=132, Resulting Numbers: [132] 132,72 unequal: No Solution Exploring Operation: 98-34=64, Resulting Numbers: [64] 64,72 unequal: No Solution Exploring Operation: 98*34=3332, Resulting Numbers: [3332] 3332,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[98, 76], Operations: ['63/3=21', '55+21=76'] Exploring Operation: 98-76=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 98+76=174, Resulting Numbers: [174] 174,72 unequal: No Solution Exploring Operation: 98*76=7448, Resulting Numbers: [7448] 7448,72 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 57, 97, 84, 48 ]
70
[ "97-57=40", "84*40=3360", "3360/48=70" ]
Current State: 70:[57, 97, 84, 48], Operations: [] Exploring Operation: 97-57=40, Resulting Numbers: [84, 48, 40] Generated Node #2: [84, 48, 40] from Operation: 97-57=40 Current State: 70:[84, 48, 40], Operations: ['97-57=40'] Exploring Operation: 84*40=3360, Resulting Numbers: [48, 3360] Generated Node #3: [48, 3360] from Operation: 84*40=3360 Current State: 70:[48, 3360], Operations: ['97-57=40', '84*40=3360'] Exploring Operation: 3360/48=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[57, 97, 84, 48], Operations: [] Exploring Operation: 97-57=40, Resulting Numbers: [84, 48, 40] Generated Node #0,0: 70:[84, 48, 40] Operation: 97-57=40 Exploring Operation: 97-48=49, Resulting Numbers: [57, 84, 49] Generated Node #0,1: 70:[57, 84, 49] Operation: 97-48=49 Exploring Operation: 97-84=13, Resulting Numbers: [57, 48, 13] Generated Node #0,2: 70:[57, 48, 13] Operation: 97-84=13 Moving to Node #0,2 Current State: 70:[57, 48, 13], Operations: ['97-84=13'] Exploring Operation: 57+13=70, Resulting Numbers: [48, 70] Generated Node #0,2,0: 70:[48, 70] Operation: 57+13=70 Exploring Operation: 48-13=35, Resulting Numbers: [57, 35] Generated Node #0,2,1: 70:[57, 35] Operation: 48-13=35 Exploring Operation: 57-48=9, Resulting Numbers: [13, 9] Generated Node #0,2,2: 70:[13, 9] Operation: 57-48=9 Moving to Node #0,0 Current State: 70:[84, 48, 40], Operations: ['97-57=40'] Exploring Operation: 84-40=44, Resulting Numbers: [48, 44] Generated Node #0,0,0: 70:[48, 44] Operation: 84-40=44 Exploring Operation: 84-48=36, Resulting Numbers: [40, 36] Generated Node #0,0,1: 70:[40, 36] Operation: 84-48=36 Exploring Operation: 48-40=8, Resulting Numbers: [84, 8] Generated Node #0,0,2: 70:[84, 8] Operation: 48-40=8 Moving to Node #0,1 Current State: 70:[57, 84, 49], Operations: ['97-48=49'] Exploring Operation: 84-49=35, Resulting Numbers: [57, 35] Generated Node #0,1,0: 70:[57, 35] Operation: 84-49=35 Exploring Operation: 57-49=8, Resulting Numbers: [84, 8] Generated Node #0,1,1: 70:[84, 8] Operation: 57-49=8 Exploring Operation: 84-57=27, Resulting Numbers: [49, 27] Generated Node #0,1,2: 70:[49, 27] Operation: 84-57=27 Moving to Node #0,2,2 Current State: 70:[13, 9], Operations: ['97-84=13', '57-48=9'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,70 unequal: No Solution Exploring Operation: 13*9=117, Resulting Numbers: [117] 117,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[40, 36], Operations: ['97-57=40', '84-48=36'] Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,70 unequal: No Solution Exploring Operation: 40*36=1440, Resulting Numbers: [1440] 1440,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[57, 35], Operations: ['97-84=13', '48-13=35'] Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,70 unequal: No Solution Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,70 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[57, 35], Operations: ['97-48=49', '84-49=35'] Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,70 unequal: No Solution Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,70 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[48, 70], Operations: ['97-84=13', '57+13=70'] Exploring Operation: 48*70=3360, Resulting Numbers: [3360] 3360,70 unequal: No Solution Exploring Operation: 48+70=118, Resulting Numbers: [118] 118,70 unequal: No Solution Exploring Operation: 70-48=22, Resulting Numbers: [22] 22,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[84, 8], Operations: ['97-57=40', '48-40=8'] Exploring Operation: 84*8=672, Resulting Numbers: [672] 672,70 unequal: No Solution Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,70 unequal: No Solution Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[84, 8], Operations: ['97-48=49', '57-49=8'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,70 unequal: No Solution Exploring Operation: 84*8=672, Resulting Numbers: [672] 672,70 unequal: No Solution Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[49, 27], Operations: ['97-48=49', '84-57=27'] Exploring Operation: 49*27=1323, Resulting Numbers: [1323] 1323,70 unequal: No Solution Exploring Operation: 49+27=76, Resulting Numbers: [76] 76,70 unequal: No Solution Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[48, 44], Operations: ['97-57=40', '84-40=44'] Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,70 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,70 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 21, 26, 83, 24 ]
64
[ "26-21=5", "83-24=59", "5+59=64" ]
Current State: 64:[21, 26, 83, 24], Operations: [] Exploring Operation: 26-21=5, Resulting Numbers: [83, 24, 5] Generated Node #2: [83, 24, 5] from Operation: 26-21=5 Current State: 64:[83, 24, 5], Operations: ['26-21=5'] Exploring Operation: 83-24=59, Resulting Numbers: [5, 59] Generated Node #3: [5, 59] from Operation: 83-24=59 Current State: 64:[5, 59], Operations: ['26-21=5', '83-24=59'] Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[21, 26, 83, 24], Operations: [] Exploring Operation: 83-21=62, Resulting Numbers: [26, 24, 62] Generated Node #0,0: 64:[26, 24, 62] Operation: 83-21=62 Exploring Operation: 83-24=59, Resulting Numbers: [21, 26, 59] Generated Node #0,1: 64:[21, 26, 59] Operation: 83-24=59 Exploring Operation: 83-26=57, Resulting Numbers: [21, 24, 57] Generated Node #0,2: 64:[21, 24, 57] Operation: 83-26=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[26, 24, 62], Operations: ['83-21=62'] Exploring Operation: 26-24=2, Resulting Numbers: [62, 2] Generated Node #0,0,0: 64:[62, 2] Operation: 26-24=2 Exploring Operation: 62-24=38, Resulting Numbers: [26, 38] Generated Node #0,0,1: 64:[26, 38] Operation: 62-24=38 Exploring Operation: 62-26=36, Resulting Numbers: [24, 36] Generated Node #0,0,2: 64:[24, 36] Operation: 62-26=36 Moving to Node #0,0,0 Current State: 64:[62, 2], Operations: ['83-21=62', '26-24=2'] Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[21, 26, 83, 24], Operations: [] Exploring Operation: 83-21=62, Resulting Numbers: [26, 24, 62] Generated Node #0,0: 64:[26, 24, 62] Operation: 83-21=62 Moving to Node #0,0 Current State: 64:[26, 24, 62], Operations: ['83-21=62'] Exploring Operation: 26-24=2, Resulting Numbers: [62, 2] Generated Node #0,0,0: 64:[62, 2] Operation: 26-24=2 Moving to Node #0,0,0 Current State: 64:[62, 2], Operations: ['83-21=62', '26-24=2'] Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 69, 54, 74, 71 ]
12
[ "69-54=15", "74-71=3", "15-3=12" ]
Current State: 12:[69, 54, 74, 71], Operations: [] Exploring Operation: 69-54=15, Resulting Numbers: [74, 71, 15] Generated Node #2: [74, 71, 15] from Operation: 69-54=15 Current State: 12:[74, 71, 15], Operations: ['69-54=15'] Exploring Operation: 74-71=3, Resulting Numbers: [15, 3] Generated Node #3: [15, 3] from Operation: 74-71=3 Current State: 12:[15, 3], Operations: ['69-54=15', '74-71=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[69, 54, 74, 71], Operations: [] Exploring Operation: 69-54=15, Resulting Numbers: [74, 71, 15] Generated Node #0,0: 12:[74, 71, 15] Operation: 69-54=15 Exploring Operation: 74-71=3, Resulting Numbers: [69, 54, 3] Generated Node #0,1: 12:[69, 54, 3] Operation: 74-71=3 Exploring Operation: 71-69=2, Resulting Numbers: [54, 74, 2] Generated Node #0,2: 12:[54, 74, 2] Operation: 71-69=2 Exploring Operation: 74-69=5, Resulting Numbers: [54, 71, 5] Generated Node #0,3: 12:[54, 71, 5] Operation: 74-69=5 Moving to Node #0,1 Current State: 12:[69, 54, 3], Operations: ['74-71=3'] Exploring Operation: 69/3=23, Resulting Numbers: [54, 23] Generated Node #0,1,0: 12:[54, 23] Operation: 69/3=23 Exploring Operation: 69-54=15, Resulting Numbers: [3, 15] Generated Node #0,1,1: 12:[3, 15] Operation: 69-54=15 Exploring Operation: 69-3=66, Resulting Numbers: [54, 66] Generated Node #0,1,2: 12:[54, 66] Operation: 69-3=66 Exploring Operation: 54/3=18, Resulting Numbers: [69, 18] Generated Node #0,1,3: 12:[69, 18] Operation: 54/3=18 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[3, 15], Operations: ['74-71=3', '69-54=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,12 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[69, 54, 74, 71], Operations: [] Exploring Operation: 74-71=3, Resulting Numbers: [69, 54, 3] Generated Node #0,1: 12:[69, 54, 3] Operation: 74-71=3 Moving to Node #0,1 Current State: 12:[69, 54, 3], Operations: ['74-71=3'] Exploring Operation: 69-54=15, Resulting Numbers: [3, 15] Generated Node #0,1,1: 12:[3, 15] Operation: 69-54=15 Moving to Node #0,1,1 Current State: 12:[3, 15], Operations: ['74-71=3', '69-54=15'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 5, 37, 45, 60 ]
14
[ "45/5=9", "60-37=23", "23-9=14" ]
Current State: 14:[5, 37, 45, 60], Operations: [] Exploring Operation: 45/5=9, Resulting Numbers: [37, 60, 9] Generated Node #2: [37, 60, 9] from Operation: 45/5=9 Current State: 14:[37, 60, 9], Operations: ['45/5=9'] Exploring Operation: 60-37=23, Resulting Numbers: [9, 23] Generated Node #3: [9, 23] from Operation: 60-37=23 Current State: 14:[9, 23], Operations: ['45/5=9', '60-37=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[5, 37, 45, 60], Operations: [] Exploring Operation: 60-45=15, Resulting Numbers: [5, 37, 15] Generated Node #0,0: 14:[5, 37, 15] Operation: 60-45=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[5, 37, 15], Operations: ['60-45=15'] Exploring Operation: 37-15=22, Resulting Numbers: [5, 22] Generated Node #0,0,0: 14:[5, 22] Operation: 37-15=22 Moving to Node #0,0,0 Current State: 14:[5, 22], Operations: ['60-45=15', '37-15=22'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,14 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
[ 27, 41, 56, 98 ]
63
[ "41-27=14", "98/14=7", "56+7=63" ]
Current State: 63:[27, 41, 56, 98], Operations: [] Exploring Operation: 41-27=14, Resulting Numbers: [56, 98, 14] Generated Node #2: [56, 98, 14] from Operation: 41-27=14 Current State: 63:[56, 98, 14], Operations: ['41-27=14'] Exploring Operation: 98/14=7, Resulting Numbers: [56, 7] Generated Node #3: [56, 7] from Operation: 98/14=7 Current State: 63:[56, 7], Operations: ['41-27=14', '98/14=7'] Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[27, 41, 56, 98], Operations: [] Exploring Operation: 98-27=71, Resulting Numbers: [41, 56, 71] Generated Node #0,0: 63:[41, 56, 71] Operation: 98-27=71 Exploring Operation: 98-41=57, Resulting Numbers: [27, 56, 57] Generated Node #0,1: 63:[27, 56, 57] Operation: 98-41=57 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[27, 56, 57], Operations: ['98-41=57'] Exploring Operation: 57-56=1, Resulting Numbers: [27, 1] Generated Node #0,1,0: 63:[27, 1] Operation: 57-56=1 Exploring Operation: 56-27=29, Resulting Numbers: [57, 29] Generated Node #0,1,1: 63:[57, 29] Operation: 56-27=29 Moving to Node #0,1,0 Current State: 63:[27, 1], Operations: ['98-41=57', '57-56=1'] Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,63 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[57, 29], Operations: ['98-41=57', '56-27=29'] Exploring Operation: 57+29=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 57-29=28, Resulting Numbers: [28] 28,63 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:[41, 56, 71], Operations: ['98-27=71'] Exploring Operation: 71-41=30, Resulting Numbers: [56, 30] Generated Node #0,0,0: 63:[56, 30] Operation: 71-41=30 Exploring Operation: 56-41=15, Resulting Numbers: [71, 15] Generated Node #0,0,1: 63:[71, 15] Operation: 56-41=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[71, 15], Operations: ['98-27=71', '56-41=15'] Exploring Operation: 71+15=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 71-15=56, Resulting Numbers: [56] 56,63 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:[56, 30], Operations: ['98-27=71', '71-41=30'] Exploring Operation: 56+30=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,63 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
[ 10, 76, 62, 22 ]
80
[ "76-62=14", "22-14=8", "10*8=80" ]
Current State: 80:[10, 76, 62, 22], Operations: [] Exploring Operation: 76-62=14, Resulting Numbers: [10, 22, 14] Generated Node #2: [10, 22, 14] from Operation: 76-62=14 Current State: 80:[10, 22, 14], Operations: ['76-62=14'] Exploring Operation: 22-14=8, Resulting Numbers: [10, 8] Generated Node #3: [10, 8] from Operation: 22-14=8 Current State: 80:[10, 8], Operations: ['76-62=14', '22-14=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[10, 76, 62, 22], Operations: [] Exploring Operation: 76-62=14, Resulting Numbers: [10, 22, 14] Generated Node #0,0: 80:[10, 22, 14] Operation: 76-62=14 Exploring Operation: 62-22=40, Resulting Numbers: [10, 76, 40] Generated Node #0,1: 80:[10, 76, 40] Operation: 62-22=40 Exploring Operation: 62+22=84, Resulting Numbers: [10, 76, 84] Generated Node #0,2: 80:[10, 76, 84] Operation: 62+22=84 Moving to Node #0,0 Current State: 80:[10, 22, 14], Operations: ['76-62=14'] Exploring Operation: 22-14=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 22-14=8 Exploring Operation: 14-10=4, Resulting Numbers: [22, 4] Generated Node #0,0,1: 80:[22, 4] Operation: 14-10=4 Exploring Operation: 22-10=12, Resulting Numbers: [14, 12] Generated Node #0,0,2: 80:[14, 12] Operation: 22-10=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['76-62=14', '22-14=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[10, 76, 62, 22], Operations: [] Exploring Operation: 76-62=14, Resulting Numbers: [10, 22, 14] Generated Node #0,0: 80:[10, 22, 14] Operation: 76-62=14 Moving to Node #0,0 Current State: 80:[10, 22, 14], Operations: ['76-62=14'] Exploring Operation: 22-14=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 22-14=8 Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['76-62=14', '22-14=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 66, 95, 2, 15 ]
77
[ "66/2=33", "95+15=110", "110-33=77" ]
Current State: 77:[66, 95, 2, 15], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [95, 15, 33] Generated Node #2: [95, 15, 33] from Operation: 66/2=33 Current State: 77:[95, 15, 33], Operations: ['66/2=33'] Exploring Operation: 95+15=110, Resulting Numbers: [33, 110] Generated Node #3: [33, 110] from Operation: 95+15=110 Current State: 77:[33, 110], Operations: ['66/2=33', '95+15=110'] Exploring Operation: 110-33=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[66, 95, 2, 15], Operations: [] Exploring Operation: 95-15=80, Resulting Numbers: [66, 2, 80] Generated Node #0,0: 77:[66, 2, 80] Operation: 95-15=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[66, 2, 80], Operations: ['95-15=80'] Exploring Operation: 80-66=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 77:[2, 14] Operation: 80-66=14 Moving to Node #0,0,0 Current State: 77:[2, 14], Operations: ['95-15=80', '80-66=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 88, 3, 95, 1 ]
28
[ "95-88=7", "3+1=4", "7*4=28" ]
Current State: 28:[88, 3, 95, 1], Operations: [] Exploring Operation: 95-88=7, Resulting Numbers: [3, 1, 7] Generated Node #2: [3, 1, 7] from Operation: 95-88=7 Current State: 28:[3, 1, 7], Operations: ['95-88=7'] Exploring Operation: 3+1=4, Resulting Numbers: [7, 4] Generated Node #3: [7, 4] from Operation: 3+1=4 Current State: 28:[7, 4], Operations: ['95-88=7', '3+1=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[88, 3, 95, 1], Operations: [] Exploring Operation: 95-3=92, Resulting Numbers: [88, 1, 92] Generated Node #0,0: 28:[88, 1, 92] Operation: 95-3=92 Exploring Operation: 88-3=85, Resulting Numbers: [95, 1, 85] Generated Node #0,1: 28:[95, 1, 85] Operation: 88-3=85 Exploring Operation: 95-88=7, Resulting Numbers: [3, 1, 7] Generated Node #0,2: 28:[3, 1, 7] Operation: 95-88=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[3, 1, 7], Operations: ['95-88=7'] Exploring Operation: 3-1=2, Resulting Numbers: [7, 2] Generated Node #0,2,0: 28:[7, 2] Operation: 3-1=2 Exploring Operation: 3+1=4, Resulting Numbers: [7, 4] Generated Node #0,2,1: 28:[7, 4] Operation: 3+1=4 Exploring Operation: 3*1=3, Resulting Numbers: [7, 3] Generated Node #0,2,2: 28:[7, 3] Operation: 3*1=3 Moving to Node #0,2,0 Current State: 28:[7, 2], Operations: ['95-88=7', '3-1=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,28 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,28 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,28 unequal: No Solution Moving to Node #0,2,1 Current State: 28:[7, 4], Operations: ['95-88=7', '3+1=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,28 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[88, 3, 95, 1], Operations: [] Exploring Operation: 95-88=7, Resulting Numbers: [3, 1, 7] Generated Node #0,2: 28:[3, 1, 7] Operation: 95-88=7 Moving to Node #0,2 Current State: 28:[3, 1, 7], Operations: ['95-88=7'] Exploring Operation: 3+1=4, Resulting Numbers: [7, 4] Generated Node #0,2,1: 28:[7, 4] Operation: 3+1=4 Moving to Node #0,2,1 Current State: 28:[7, 4], Operations: ['95-88=7', '3+1=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 15, 75, 3, 24 ]
69
[ "15+75=90", "24-3=21", "90-21=69" ]
Current State: 69:[15, 75, 3, 24], Operations: [] Exploring Operation: 15+75=90, Resulting Numbers: [3, 24, 90] Generated Node #2: [3, 24, 90] from Operation: 15+75=90 Current State: 69:[3, 24, 90], Operations: ['15+75=90'] Exploring Operation: 24-3=21, Resulting Numbers: [90, 21] Generated Node #3: [90, 21] from Operation: 24-3=21 Current State: 69:[90, 21], Operations: ['15+75=90', '24-3=21'] Exploring Operation: 90-21=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[15, 75, 3, 24], Operations: [] Exploring Operation: 15/3=5, Resulting Numbers: [75, 24, 5] Generated Node #0,0: 69:[75, 24, 5] Operation: 15/3=5 Exploring Operation: 75/15=5, Resulting Numbers: [3, 24, 5] Generated Node #0,1: 69:[3, 24, 5] Operation: 75/15=5 Exploring Operation: 75-15=60, Resulting Numbers: [3, 24, 60] Generated Node #0,2: 69:[3, 24, 60] Operation: 75-15=60 Exploring Operation: 75/3=25, Resulting Numbers: [15, 24, 25] Generated Node #0,3: 69:[15, 24, 25] Operation: 75/3=25 Exploring Operation: 15+3=18, Resulting Numbers: [75, 24, 18] Generated Node #0,4: 69:[75, 24, 18] Operation: 15+3=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[3, 24, 5], Operations: ['75/15=5'] Exploring Operation: 24-5=19, Resulting Numbers: [3, 19] Generated Node #0,1,0: 69:[3, 19] Operation: 24-5=19 Exploring Operation: 24-3=21, Resulting Numbers: [5, 21] Generated Node #0,1,1: 69:[5, 21] Operation: 24-3=21 Exploring Operation: 3*24=72, Resulting Numbers: [5, 72] Generated Node #0,1,2: 69:[5, 72] Operation: 3*24=72 Exploring Operation: 3+24=27, Resulting Numbers: [5, 27] Generated Node #0,1,3: 69:[5, 27] Operation: 3+24=27 Exploring Operation: 5-3=2, Resulting Numbers: [24, 2] Generated Node #0,1,4: 69:[24, 2] Operation: 5-3=2 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 69:[24, 2], Operations: ['75/15=5', '5-3=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,69 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,69 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 #0,1,0 Current State: 69:[3, 19], Operations: ['75/15=5', '24-5=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 3*19=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 #0,1,1 Current State: 69:[5, 21], Operations: ['75/15=5', '24-3=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 21-5=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 #0,1,2 Current State: 69:[5, 72], Operations: ['75/15=5', '3*24=72'] Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,69 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,69 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,69 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 #0,1,3 Current State: 69:[5, 27], Operations: ['75/15=5', '3+24=27'] Exploring Operation: 5+27=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 5*27=135, Resulting Numbers: [135] 135,69 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[75, 24, 5], Operations: ['15/3=5'] Exploring Operation: 75/5=15, Resulting Numbers: [24, 15] Generated Node #0,0,0: 69:[24, 15] Operation: 75/5=15 Exploring Operation: 75-5=70, Resulting Numbers: [24, 70] Generated Node #0,0,1: 69:[24, 70] Operation: 75-5=70 Exploring Operation: 24-5=19, Resulting Numbers: [75, 19] Generated Node #0,0,2: 69:[75, 19] Operation: 24-5=19 Exploring Operation: 24+5=29, Resulting Numbers: [75, 29] Generated Node #0,0,3: 69:[75, 29] Operation: 24+5=29 Exploring Operation: 75+5=80, Resulting Numbers: [24, 80] Generated Node #0,0,4: 69:[24, 80] Operation: 75+5=80 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[24, 70], Operations: ['15/3=5', '75-5=70'] Exploring Operation: 24+70=94, Resulting Numbers: [94] 94,69 unequal: No Solution Exploring Operation: 24*70=1680, Resulting Numbers: [1680] 1680,69 unequal: No Solution Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,69 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:[24, 15], Operations: ['15/3=5', '75/5=15'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,69 unequal: No Solution Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,69 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:[75, 19], Operations: ['15/3=5', '24-5=19'] Exploring Operation: 75-19=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 75+19=94, Resulting Numbers: [94] 94,69 unequal: No Solution Exploring Operation: 75*19=1425, Resulting Numbers: [1425] 1425,69 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:[75, 29], Operations: ['15/3=5', '24+5=29'] Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,69 unequal: No Solution Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,69 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,69 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:[24, 80], Operations: ['15/3=5', '75+5=80'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 24*80=1920, Resulting Numbers: [1920] 1920,69 unequal: No Solution Exploring Operation: 24+80=104, Resulting Numbers: [104] 104,69 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:[3, 24, 60], Operations: ['75-15=60'] Exploring Operation: 60/3=20, Resulting Numbers: [24, 20] Generated Node #0,2,0: 69:[24, 20] Operation: 60/3=20 Exploring Operation: 3*24=72, Resulting Numbers: [60, 72] Generated Node #0,2,1: 69:[60, 72] Operation: 3*24=72 Exploring Operation: 24-3=21, Resulting Numbers: [60, 21] Generated Node #0,2,2: 69:[60, 21] Operation: 24-3=21 Exploring Operation: 3+60=63, Resulting Numbers: [24, 63] Generated Node #0,2,3: 69:[24, 63] Operation: 3+60=63 Exploring Operation: 3+24=27, Resulting Numbers: [60, 27] Generated Node #0,2,4: 69:[60, 27] Operation: 3+24=27 Moving to Node #0,2,0 Current State: 69:[24, 20], Operations: ['75-15=60', '60/3=20'] Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,69 unequal: No Solution Exploring Operation: 24*20=480, Resulting Numbers: [480] 480,69 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[24, 63], Operations: ['75-15=60', '3+60=63'] Exploring Operation: 24+63=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,69 unequal: No Solution Exploring Operation: 24*63=1512, Resulting Numbers: [1512] 1512,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[60, 21], Operations: ['75-15=60', '24-3=21'] Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,69 unequal: No Solution Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,69 unequal: No Solution Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[60, 72], Operations: ['75-15=60', '3*24=72'] Exploring Operation: 72-60=12, Resulting Numbers: [12] 12,69 unequal: No Solution Exploring Operation: 60+72=132, Resulting Numbers: [132] 132,69 unequal: No Solution Exploring Operation: 60*72=4320, Resulting Numbers: [4320] 4320,69 unequal: No Solution Moving to Node #0,2,4 Current State: 69:[60, 27], Operations: ['75-15=60', '3+24=27'] Exploring Operation: 60+27=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 60*27=1620, Resulting Numbers: [1620] 1620,69 unequal: No Solution Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,69 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 #0,3 Current State: 69:[15, 24, 25], Operations: ['75/3=25'] Exploring Operation: 15+24=39, Resulting Numbers: [25, 39] Generated Node #0,3,0: 69:[25, 39] Operation: 15+24=39 Exploring Operation: 25-15=10, Resulting Numbers: [24, 10] Generated Node #0,3,1: 69:[24, 10] Operation: 25-15=10 Exploring Operation: 15+25=40, Resulting Numbers: [24, 40] Generated Node #0,3,2: 69:[24, 40] Operation: 15+25=40 Exploring Operation: 25-24=1, Resulting Numbers: [15, 1] Generated Node #0,3,3: 69:[15, 1] Operation: 25-24=1 Exploring Operation: 24-15=9, Resulting Numbers: [25, 9] Generated Node #0,3,4: 69:[25, 9] Operation: 24-15=9 Moving to Node #0,3,1 Current State: 69:[24, 10], Operations: ['75/3=25', '25-15=10'] Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,69 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[25, 9], Operations: ['75/3=25', '24-15=9'] Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,69 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[15, 1], Operations: ['75/3=25', '25-24=1'] Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[25, 39], Operations: ['75/3=25', '15+24=39'] Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,69 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[24, 40], Operations: ['75/3=25', '15+25=40'] Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,69 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,69 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 #0,4 Current State: 69:[75, 24, 18], Operations: ['15+3=18'] Exploring Operation: 24+18=42, Resulting Numbers: [75, 42] Generated Node #0,4,0: 69:[75, 42] Operation: 24+18=42 Exploring Operation: 75-18=57, Resulting Numbers: [24, 57] Generated Node #0,4,1: 69:[24, 57] Operation: 75-18=57 Exploring Operation: 75+18=93, Resulting Numbers: [24, 93] Generated Node #0,4,2: 69:[24, 93] Operation: 75+18=93 Exploring Operation: 24-18=6, Resulting Numbers: [75, 6] Generated Node #0,4,3: 69:[75, 6] Operation: 24-18=6 Exploring Operation: 75-24=51, Resulting Numbers: [18, 51] Generated Node #0,4,4: 69:[18, 51] Operation: 75-24=51 Moving to Node #0,4,3 Current State: 69:[75, 6], Operations: ['15+3=18', '24-18=6'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[15, 75, 3, 24], Operations: [] Exploring Operation: 15+3=18, Resulting Numbers: [75, 24, 18] Generated Node #0,4: 69:[75, 24, 18] Operation: 15+3=18 Moving to Node #0,4 Current State: 69:[75, 24, 18], Operations: ['15+3=18'] Exploring Operation: 24-18=6, Resulting Numbers: [75, 6] Generated Node #0,4,3: 69:[75, 6] Operation: 24-18=6 Moving to Node #0,4,3 Current State: 69:[75, 6], Operations: ['15+3=18', '24-18=6'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.915799
hs_5
sum_heuristic
[ 69, 79, 20, 56 ]
46
[ "79-69=10", "56-20=36", "10+36=46" ]
Current State: 46:[69, 79, 20, 56], Operations: [] Exploring Operation: 79-69=10, Resulting Numbers: [20, 56, 10] Generated Node #2: [20, 56, 10] from Operation: 79-69=10 Current State: 46:[20, 56, 10], Operations: ['79-69=10'] Exploring Operation: 56-20=36, Resulting Numbers: [10, 36] Generated Node #3: [10, 36] from Operation: 56-20=36 Current State: 46:[10, 36], Operations: ['79-69=10', '56-20=36'] Exploring Operation: 10+36=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[69, 79, 20, 56], Operations: [] Exploring Operation: 79-69=10, Resulting Numbers: [20, 56, 10] Generated Node #0,0: 46:[20, 56, 10] Operation: 79-69=10 Exploring Operation: 79-56=23, Resulting Numbers: [69, 20, 23] Generated Node #0,1: 46:[69, 20, 23] Operation: 79-56=23 Exploring Operation: 69-20=49, Resulting Numbers: [79, 56, 49] Generated Node #0,2: 46:[79, 56, 49] Operation: 69-20=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[20, 56, 10], Operations: ['79-69=10'] Exploring Operation: 20+10=30, Resulting Numbers: [56, 30] Generated Node #0,0,0: 46:[56, 30] Operation: 20+10=30 Exploring Operation: 20/10=2, Resulting Numbers: [56, 2] Generated Node #0,0,1: 46:[56, 2] Operation: 20/10=2 Exploring Operation: 56-10=46, Resulting Numbers: [20, 46] Generated Node #0,0,2: 46:[20, 46] Operation: 56-10=46 Moving to Node #0,0,2 Current State: 46:[20, 46], Operations: ['79-69=10', '56-10=46'] Exploring Operation: 20*46=920, Resulting Numbers: [920] 920,46 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 20+46=66, Resulting Numbers: [66] 66,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[56, 2], Operations: ['79-69=10', '20/10=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,46 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,46 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[56, 30], Operations: ['79-69=10', '20+10=30'] Exploring Operation: 56*30=1680, Resulting Numbers: [1680] 1680,46 unequal: No Solution Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 56+30=86, Resulting Numbers: [86] 86,46 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 Current State: 46:[69, 20, 23], Operations: ['79-56=23'] Exploring Operation: 69-23=46, Resulting Numbers: [20, 46] Generated Node #0,1,0: 46:[20, 46] Operation: 69-23=46 Exploring Operation: 69-20=49, Resulting Numbers: [23, 49] Generated Node #0,1,1: 46:[23, 49] Operation: 69-20=49 Exploring Operation: 69/23=3, Resulting Numbers: [20, 3] Generated Node #0,1,2: 46:[20, 3] Operation: 69/23=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[20, 46], Operations: ['79-56=23', '69-23=46'] Exploring Operation: 20+46=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 20*46=920, Resulting Numbers: [920] 920,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[23, 49], Operations: ['79-56=23', '69-20=49'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 23+49=72, Resulting Numbers: [72] 72,46 unequal: No Solution Exploring Operation: 23*49=1127, Resulting Numbers: [1127] 1127,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[20, 3], Operations: ['79-56=23', '69/23=3'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,46 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[79, 56, 49], Operations: ['69-20=49'] Exploring Operation: 56-49=7, Resulting Numbers: [79, 7] Generated Node #0,2,0: 46:[79, 7] Operation: 56-49=7 Exploring Operation: 79-56=23, Resulting Numbers: [49, 23] Generated Node #0,2,1: 46:[49, 23] Operation: 79-56=23 Exploring Operation: 79-49=30, Resulting Numbers: [56, 30] Generated Node #0,2,2: 46:[56, 30] Operation: 79-49=30 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 46:[49, 23], Operations: ['69-20=49', '79-56=23'] Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,46 unequal: No Solution Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,46 unequal: No Solution Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 46:[56, 30], Operations: ['69-20=49', '79-49=30'] Exploring Operation: 56*30=1680, Resulting Numbers: [1680] 1680,46 unequal: No Solution Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 56+30=86, Resulting Numbers: [86] 86,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 46:[79, 7], Operations: ['69-20=49', '56-49=7'] Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,46 unequal: No Solution Exploring Operation: 79*7=553, Resulting Numbers: [553] 553,46 unequal: No Solution Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 94, 71, 51, 91 ]
23
[ "94+71=165", "51+91=142", "165-142=23" ]
Current State: 23:[94, 71, 51, 91], Operations: [] Exploring Operation: 94+71=165, Resulting Numbers: [51, 91, 165] Generated Node #2: [51, 91, 165] from Operation: 94+71=165 Current State: 23:[51, 91, 165], Operations: ['94+71=165'] Exploring Operation: 51+91=142, Resulting Numbers: [165, 142] Generated Node #3: [165, 142] from Operation: 51+91=142 Current State: 23:[165, 142], Operations: ['94+71=165', '51+91=142'] Exploring Operation: 165-142=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[94, 71, 51, 91], Operations: [] Exploring Operation: 94-71=23, Resulting Numbers: [51, 91, 23] Generated Node #0,0: 23:[51, 91, 23] Operation: 94-71=23 Exploring Operation: 94-91=3, Resulting Numbers: [71, 51, 3] Generated Node #0,1: 23:[71, 51, 3] Operation: 94-91=3 Exploring Operation: 91-71=20, Resulting Numbers: [94, 51, 20] Generated Node #0,2: 23:[94, 51, 20] Operation: 91-71=20 Moving to Node #0,0 Current State: 23:[51, 91, 23], Operations: ['94-71=23'] Exploring Operation: 91-51=40, Resulting Numbers: [23, 40] Generated Node #0,0,0: 23:[23, 40] Operation: 91-51=40 Exploring Operation: 51-23=28, Resulting Numbers: [91, 28] Generated Node #0,0,1: 23:[91, 28] Operation: 51-23=28 Exploring Operation: 91-23=68, Resulting Numbers: [51, 68] Generated Node #0,0,2: 23:[51, 68] Operation: 91-23=68 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[23, 40], Operations: ['94-71=23', '91-51=40'] Exploring Operation: 23+40=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 23*40=920, Resulting Numbers: [920] 920,23 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 #0,0,1 Current State: 23:[91, 28], Operations: ['94-71=23', '51-23=28'] Exploring Operation: 91*28=2548, Resulting Numbers: [2548] 2548,23 unequal: No Solution Exploring Operation: 91+28=119, Resulting Numbers: [119] 119,23 unequal: No Solution Exploring Operation: 91-28=63, Resulting Numbers: [63] 63,23 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 #0,0,2 Current State: 23:[51, 68], Operations: ['94-71=23', '91-23=68'] Exploring Operation: 51*68=3468, Resulting Numbers: [3468] 3468,23 unequal: No Solution Exploring Operation: 51+68=119, Resulting Numbers: [119] 119,23 unequal: No Solution Exploring Operation: 68-51=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:[71, 51, 3], Operations: ['94-91=3'] Exploring Operation: 51/3=17, Resulting Numbers: [71, 17] Generated Node #0,1,0: 23:[71, 17] Operation: 51/3=17 Exploring Operation: 71-51=20, Resulting Numbers: [3, 20] Generated Node #0,1,1: 23:[3, 20] Operation: 71-51=20 Exploring Operation: 71-3=68, Resulting Numbers: [51, 68] Generated Node #0,1,2: 23:[51, 68] Operation: 71-3=68 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[3, 20], Operations: ['94-91=3', '71-51=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[94, 71, 51, 91], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [71, 51, 3] Generated Node #0,1: 23:[71, 51, 3] Operation: 94-91=3 Moving to Node #0,1 Current State: 23:[71, 51, 3], Operations: ['94-91=3'] Exploring Operation: 71-51=20, Resulting Numbers: [3, 20] Generated Node #0,1,1: 23:[3, 20] Operation: 71-51=20 Moving to Node #0,1,1 Current State: 23:[3, 20], Operations: ['94-91=3', '71-51=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 92, 48, 8, 72 ]
14
[ "92-72=20", "48/8=6", "20-6=14" ]
Current State: 14:[92, 48, 8, 72], Operations: [] Exploring Operation: 92-72=20, Resulting Numbers: [48, 8, 20] Generated Node #2: [48, 8, 20] from Operation: 92-72=20 Current State: 14:[48, 8, 20], Operations: ['92-72=20'] Exploring Operation: 48/8=6, Resulting Numbers: [20, 6] Generated Node #3: [20, 6] from Operation: 48/8=6 Current State: 14:[20, 6], Operations: ['92-72=20', '48/8=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[92, 48, 8, 72], Operations: [] Exploring Operation: 92-72=20, Resulting Numbers: [48, 8, 20] Generated Node #0,0: 14:[48, 8, 20] Operation: 92-72=20 Exploring Operation: 92-48=44, Resulting Numbers: [8, 72, 44] Generated Node #0,1: 14:[8, 72, 44] Operation: 92-48=44 Exploring Operation: 72-48=24, Resulting Numbers: [92, 8, 24] Generated Node #0,2: 14:[92, 8, 24] Operation: 72-48=24 Exploring Operation: 72/8=9, Resulting Numbers: [92, 48, 9] Generated Node #0,3: 14:[92, 48, 9] Operation: 72/8=9 Moving to Node #0,0 Current State: 14:[48, 8, 20], Operations: ['92-72=20'] Exploring Operation: 20-8=12, Resulting Numbers: [48, 12] Generated Node #0,0,0: 14:[48, 12] Operation: 20-8=12 Exploring Operation: 48-8=40, Resulting Numbers: [20, 40] Generated Node #0,0,1: 14:[20, 40] Operation: 48-8=40 Exploring Operation: 48-20=28, Resulting Numbers: [8, 28] Generated Node #0,0,2: 14:[8, 28] Operation: 48-20=28 Exploring Operation: 48/8=6, Resulting Numbers: [20, 6] Generated Node #0,0,3: 14:[20, 6] Operation: 48/8=6 Moving to Node #0,2 Current State: 14:[92, 8, 24], Operations: ['72-48=24'] Exploring Operation: 92-24=68, Resulting Numbers: [8, 68] Generated Node #0,2,0: 14:[8, 68] Operation: 92-24=68 Exploring Operation: 24-8=16, Resulting Numbers: [92, 16] Generated Node #0,2,1: 14:[92, 16] Operation: 24-8=16 Exploring Operation: 24/8=3, Resulting Numbers: [92, 3] Generated Node #0,2,2: 14:[92, 3] Operation: 24/8=3 Exploring Operation: 92-8=84, Resulting Numbers: [24, 84] Generated Node #0,2,3: 14:[24, 84] Operation: 92-8=84 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[8, 68], Operations: ['72-48=24', '92-24=68'] Exploring Operation: 8*68=544, Resulting Numbers: [544] 544,14 unequal: No Solution Exploring Operation: 68-8=60, Resulting Numbers: [60] 60,14 unequal: No Solution Exploring Operation: 8+68=76, Resulting Numbers: [76] 76,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 14:[92, 3], Operations: ['72-48=24', '24/8=3'] Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,14 unequal: No Solution Exploring Operation: 92*3=276, Resulting Numbers: [276] 276,14 unequal: No Solution Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[92, 16], Operations: ['72-48=24', '24-8=16'] Exploring Operation: 92+16=108, Resulting Numbers: [108] 108,14 unequal: No Solution Exploring Operation: 92-16=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 92*16=1472, Resulting Numbers: [1472] 1472,14 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 #0,2,3 Current State: 14:[24, 84], Operations: ['72-48=24', '92-8=84'] Exploring Operation: 24*84=2016, Resulting Numbers: [2016] 2016,14 unequal: No Solution Exploring Operation: 84-24=60, Resulting Numbers: [60] 60,14 unequal: No Solution Exploring Operation: 24+84=108, Resulting Numbers: [108] 108,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 14:[8, 72, 44], Operations: ['92-48=44'] Exploring Operation: 44-8=36, Resulting Numbers: [72, 36] Generated Node #0,1,0: 14:[72, 36] Operation: 44-8=36 Exploring Operation: 72-44=28, Resulting Numbers: [8, 28] Generated Node #0,1,1: 14:[8, 28] Operation: 72-44=28 Exploring Operation: 72-8=64, Resulting Numbers: [44, 64] Generated Node #0,1,2: 14:[44, 64] Operation: 72-8=64 Exploring Operation: 72/8=9, Resulting Numbers: [44, 9] Generated Node #0,1,3: 14:[44, 9] Operation: 72/8=9 Moving to Node #0,3 Current State: 14:[92, 48, 9], Operations: ['72/8=9'] Exploring Operation: 92-48=44, Resulting Numbers: [9, 44] Generated Node #0,3,0: 14:[9, 44] Operation: 92-48=44 Exploring Operation: 92-9=83, Resulting Numbers: [48, 83] Generated Node #0,3,1: 14:[48, 83] Operation: 92-9=83 Exploring Operation: 48-9=39, Resulting Numbers: [92, 39] Generated Node #0,3,2: 14:[92, 39] Operation: 48-9=39 Exploring Operation: 92+9=101, Resulting Numbers: [48, 101] Generated Node #0,3,3: 14:[48, 101] Operation: 92+9=101 Moving to Node #0,0,3 Current State: 14:[20, 6], Operations: ['92-72=20', '48/8=6'] Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,14 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[92, 48, 8, 72], Operations: [] Exploring Operation: 92-72=20, Resulting Numbers: [48, 8, 20] Generated Node #0,0: 14:[48, 8, 20] Operation: 92-72=20 Moving to Node #0,0 Current State: 14:[48, 8, 20], Operations: ['92-72=20'] Exploring Operation: 48/8=6, Resulting Numbers: [20, 6] Generated Node #0,0,3: 14:[20, 6] Operation: 48/8=6 Moving to Node #0,0,3 Current State: 14:[20, 6], Operations: ['92-72=20', '48/8=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 68, 46, 20, 21 ]
73
[ "68+46=114", "20+21=41", "114-41=73" ]
Current State: 73:[68, 46, 20, 21], Operations: [] Exploring Operation: 68+46=114, Resulting Numbers: [20, 21, 114] Generated Node #2: [20, 21, 114] from Operation: 68+46=114 Current State: 73:[20, 21, 114], Operations: ['68+46=114'] Exploring Operation: 20+21=41, Resulting Numbers: [114, 41] Generated Node #3: [114, 41] from Operation: 20+21=41 Current State: 73:[114, 41], Operations: ['68+46=114', '20+21=41'] Exploring Operation: 114-41=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[68, 46, 20, 21], Operations: [] Exploring Operation: 46+20=66, Resulting Numbers: [68, 21, 66] Generated Node #0,0: 73:[68, 21, 66] Operation: 46+20=66 Moving to Node #0,0 Current State: 73:[68, 21, 66], Operations: ['46+20=66'] Exploring Operation: 21+66=87, Resulting Numbers: [68, 87] Generated Node #0,0,0: 73:[68, 87] Operation: 21+66=87 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[68, 87], Operations: ['46+20=66', '21+66=87'] Exploring Operation: 87-68=19, Resulting Numbers: [19] 19,73 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, 5, 50, 88 ]
87
[ "54-5=49", "88-50=38", "49+38=87" ]
Current State: 87:[54, 5, 50, 88], Operations: [] Exploring Operation: 54-5=49, Resulting Numbers: [50, 88, 49] Generated Node #2: [50, 88, 49] from Operation: 54-5=49 Current State: 87:[50, 88, 49], Operations: ['54-5=49'] Exploring Operation: 88-50=38, Resulting Numbers: [49, 38] Generated Node #3: [49, 38] from Operation: 88-50=38 Current State: 87:[49, 38], Operations: ['54-5=49', '88-50=38'] Exploring Operation: 49+38=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[54, 5, 50, 88], Operations: [] Exploring Operation: 50/5=10, Resulting Numbers: [54, 88, 10] Generated Node #0,0: 87:[54, 88, 10] Operation: 50/5=10 Exploring Operation: 54-50=4, Resulting Numbers: [5, 88, 4] Generated Node #0,1: 87:[5, 88, 4] Operation: 54-50=4 Exploring Operation: 54+50=104, Resulting Numbers: [5, 88, 104] Generated Node #0,2: 87:[5, 88, 104] Operation: 54+50=104 Exploring Operation: 88-54=34, Resulting Numbers: [5, 50, 34] Generated Node #0,3: 87:[5, 50, 34] Operation: 88-54=34 Exploring Operation: 88-50=38, Resulting Numbers: [54, 5, 38] Generated Node #0,4: 87:[54, 5, 38] Operation: 88-50=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[5, 88, 4], Operations: ['54-50=4'] Exploring Operation: 5+4=9, Resulting Numbers: [88, 9] Generated Node #0,1,0: 87:[88, 9] Operation: 5+4=9 Exploring Operation: 88-4=84, Resulting Numbers: [5, 84] Generated Node #0,1,1: 87:[5, 84] Operation: 88-4=84 Exploring Operation: 5-4=1, Resulting Numbers: [88, 1] Generated Node #0,1,2: 87:[88, 1] Operation: 5-4=1 Exploring Operation: 5+88=93, Resulting Numbers: [4, 93] Generated Node #0,1,3: 87:[4, 93] Operation: 5+88=93 Exploring Operation: 88-5=83, Resulting Numbers: [4, 83] Generated Node #0,1,4: 87:[4, 83] Operation: 88-5=83 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[88, 1], Operations: ['54-50=4', '5-4=1'] Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[54, 5, 50, 88], Operations: [] Exploring Operation: 54-50=4, Resulting Numbers: [5, 88, 4] Generated Node #0,1: 87:[5, 88, 4] Operation: 54-50=4 Moving to Node #0,1 Current State: 87:[5, 88, 4], Operations: ['54-50=4'] Exploring Operation: 5-4=1, Resulting Numbers: [88, 1] Generated Node #0,1,2: 87:[88, 1] Operation: 5-4=1 Moving to Node #0,1,2 Current State: 87:[88, 1], Operations: ['54-50=4', '5-4=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 33, 13, 48, 95 ]
97
[ "33+13=46", "48+95=143", "143-46=97" ]
Current State: 97:[33, 13, 48, 95], Operations: [] Exploring Operation: 33+13=46, Resulting Numbers: [48, 95, 46] Generated Node #2: [48, 95, 46] from Operation: 33+13=46 Current State: 97:[48, 95, 46], Operations: ['33+13=46'] Exploring Operation: 48+95=143, Resulting Numbers: [46, 143] Generated Node #3: [46, 143] from Operation: 48+95=143 Current State: 97:[46, 143], Operations: ['33+13=46', '48+95=143'] Exploring Operation: 143-46=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[33, 13, 48, 95], Operations: [] Exploring Operation: 33+48=81, Resulting Numbers: [13, 95, 81] Generated Node #0,0: 97:[13, 95, 81] Operation: 33+48=81 Exploring Operation: 33+13=46, Resulting Numbers: [48, 95, 46] Generated Node #0,1: 97:[48, 95, 46] Operation: 33+13=46 Moving to Node #0,0 Current State: 97:[13, 95, 81], Operations: ['33+48=81'] Exploring Operation: 13+95=108, Resulting Numbers: [81, 108] Generated Node #0,0,0: 97:[81, 108] Operation: 13+95=108 Exploring Operation: 13+81=94, Resulting Numbers: [95, 94] Generated Node #0,0,1: 97:[95, 94] Operation: 13+81=94 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[95, 94], Operations: ['33+48=81', '13+81=94'] Exploring Operation: 95-94=1, Resulting Numbers: [1] 1,97 unequal: No Solution Exploring Operation: 95+94=189, Resulting Numbers: [189] 189,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[81, 108], Operations: ['33+48=81', '13+95=108'] Exploring Operation: 81+108=189, Resulting Numbers: [189] 189,97 unequal: No Solution Exploring Operation: 108-81=27, Resulting Numbers: [27] 27,97 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: 97:[48, 95, 46], Operations: ['33+13=46'] Exploring Operation: 95+46=141, Resulting Numbers: [48, 141] Generated Node #0,1,0: 97:[48, 141] Operation: 95+46=141 Exploring Operation: 48+46=94, Resulting Numbers: [95, 94] Generated Node #0,1,1: 97:[95, 94] Operation: 48+46=94 Moving to Node #0,1,1 Current State: 97:[95, 94], Operations: ['33+13=46', '48+46=94'] Exploring Operation: 95-94=1, Resulting Numbers: [1] 1,97 unequal: No Solution Exploring Operation: 95+94=189, Resulting Numbers: [189] 189,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[48, 141], Operations: ['33+13=46', '95+46=141'] Exploring Operation: 141-48=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 48+141=189, Resulting Numbers: [189] 189,97 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 23, 85, 50, 48 ]
36
[ "85-23=62", "50+48=98", "98-62=36" ]
Current State: 36:[23, 85, 50, 48], Operations: [] Exploring Operation: 85-23=62, Resulting Numbers: [50, 48, 62] Generated Node #2: [50, 48, 62] from Operation: 85-23=62 Current State: 36:[50, 48, 62], Operations: ['85-23=62'] Exploring Operation: 50+48=98, Resulting Numbers: [62, 98] Generated Node #3: [62, 98] from Operation: 50+48=98 Current State: 36:[62, 98], Operations: ['85-23=62', '50+48=98'] Exploring Operation: 98-62=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[23, 85, 50, 48], Operations: [] Exploring Operation: 50-23=27, Resulting Numbers: [85, 48, 27] Generated Node #0,0: 36:[85, 48, 27] Operation: 50-23=27 Exploring Operation: 85-23=62, Resulting Numbers: [50, 48, 62] Generated Node #0,1: 36:[50, 48, 62] Operation: 85-23=62 Exploring Operation: 85-50=35, Resulting Numbers: [23, 48, 35] Generated Node #0,2: 36:[23, 48, 35] Operation: 85-50=35 Exploring Operation: 50-48=2, Resulting Numbers: [23, 85, 2] Generated Node #0,3: 36:[23, 85, 2] Operation: 50-48=2 Exploring Operation: 85-48=37, Resulting Numbers: [23, 50, 37] Generated Node #0,4: 36:[23, 50, 37] Operation: 85-48=37 Moving to Node #0,2 Current State: 36:[23, 48, 35], Operations: ['85-50=35'] Exploring Operation: 35-23=12, Resulting Numbers: [48, 12] Generated Node #0,2,0: 36:[48, 12] Operation: 35-23=12 Exploring Operation: 23+35=58, Resulting Numbers: [48, 58] Generated Node #0,2,1: 36:[48, 58] Operation: 23+35=58 Exploring Operation: 48-23=25, Resulting Numbers: [35, 25] Generated Node #0,2,2: 36:[35, 25] Operation: 48-23=25 Exploring Operation: 48-35=13, Resulting Numbers: [23, 13] Generated Node #0,2,3: 36:[23, 13] Operation: 48-35=13 Exploring Operation: 23+48=71, Resulting Numbers: [35, 71] Generated Node #0,2,4: 36:[35, 71] Operation: 23+48=71 Moving to Node #0,4 Current State: 36:[23, 50, 37], Operations: ['85-48=37'] Exploring Operation: 50-23=27, Resulting Numbers: [37, 27] Generated Node #0,4,0: 36:[37, 27] Operation: 50-23=27 Exploring Operation: 37-23=14, Resulting Numbers: [50, 14] Generated Node #0,4,1: 36:[50, 14] Operation: 37-23=14 Exploring Operation: 50-37=13, Resulting Numbers: [23, 13] Generated Node #0,4,2: 36:[23, 13] Operation: 50-37=13 Exploring Operation: 23+50=73, Resulting Numbers: [37, 73] Generated Node #0,4,3: 36:[37, 73] Operation: 23+50=73 Exploring Operation: 23+37=60, Resulting Numbers: [50, 60] Generated Node #0,4,4: 36:[50, 60] Operation: 23+37=60 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 36:[23, 13], Operations: ['85-48=37', '50-37=13'] Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,36 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[23, 85, 50, 48], Operations: [] Exploring Operation: 85-48=37, Resulting Numbers: [23, 50, 37] Generated Node #0,4: 36:[23, 50, 37] Operation: 85-48=37 Moving to Node #0,4 Current State: 36:[23, 50, 37], Operations: ['85-48=37'] Exploring Operation: 50-37=13, Resulting Numbers: [23, 13] Generated Node #0,4,2: 36:[23, 13] Operation: 50-37=13 Moving to Node #0,4,2 Current State: 36:[23, 13], Operations: ['85-48=37', '50-37=13'] Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 95, 90, 25, 27 ]
10
[ "95-90=5", "27-25=2", "5*2=10" ]
Current State: 10:[95, 90, 25, 27], Operations: [] Exploring Operation: 95-90=5, Resulting Numbers: [25, 27, 5] Generated Node #2: [25, 27, 5] from Operation: 95-90=5 Current State: 10:[25, 27, 5], Operations: ['95-90=5'] Exploring Operation: 27-25=2, Resulting Numbers: [5, 2] Generated Node #3: [5, 2] from Operation: 27-25=2 Current State: 10:[5, 2], Operations: ['95-90=5', '27-25=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[95, 90, 25, 27], Operations: [] Exploring Operation: 95-27=68, Resulting Numbers: [90, 25, 68] Generated Node #0,0: 10:[90, 25, 68] Operation: 95-27=68 Exploring Operation: 90-27=63, Resulting Numbers: [95, 25, 63] Generated Node #0,1: 10:[95, 25, 63] Operation: 90-27=63 Exploring Operation: 95-90=5, Resulting Numbers: [25, 27, 5] Generated Node #0,2: 10:[25, 27, 5] Operation: 95-90=5 Moving to Node #0,2 Current State: 10:[25, 27, 5], Operations: ['95-90=5'] Exploring Operation: 25/5=5, Resulting Numbers: [27, 5] Generated Node #0,2,0: 10:[27, 5] Operation: 25/5=5 Exploring Operation: 27-25=2, Resulting Numbers: [5, 2] Generated Node #0,2,1: 10:[5, 2] Operation: 27-25=2 Exploring Operation: 25-5=20, Resulting Numbers: [27, 20] Generated Node #0,2,2: 10:[27, 20] Operation: 25-5=20 Moving to Node #0,0 Current State: 10:[90, 25, 68], Operations: ['95-27=68'] Exploring Operation: 90-25=65, Resulting Numbers: [68, 65] Generated Node #0,0,0: 10:[68, 65] Operation: 90-25=65 Exploring Operation: 90-68=22, Resulting Numbers: [25, 22] Generated Node #0,0,1: 10:[25, 22] Operation: 90-68=22 Exploring Operation: 68-25=43, Resulting Numbers: [90, 43] Generated Node #0,0,2: 10:[90, 43] Operation: 68-25=43 Moving to Node #0,1 Current State: 10:[95, 25, 63], Operations: ['90-27=63'] Exploring Operation: 95-63=32, Resulting Numbers: [25, 32] Generated Node #0,1,0: 10:[25, 32] Operation: 95-63=32 Exploring Operation: 95-25=70, Resulting Numbers: [63, 70] Generated Node #0,1,1: 10:[63, 70] Operation: 95-25=70 Exploring Operation: 63-25=38, Resulting Numbers: [95, 38] Generated Node #0,1,2: 10:[95, 38] Operation: 63-25=38 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[25, 32], Operations: ['90-27=63', '95-63=32'] Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,10 unequal: No Solution Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[63, 70], Operations: ['90-27=63', '95-25=70'] Exploring Operation: 63*70=4410, Resulting Numbers: [4410] 4410,10 unequal: No Solution Exploring Operation: 63+70=133, Resulting Numbers: [133] 133,10 unequal: No Solution Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[95, 38], Operations: ['90-27=63', '63-25=38'] Exploring Operation: 95+38=133, Resulting Numbers: [133] 133,10 unequal: No Solution Exploring Operation: 95-38=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 95*38=3610, Resulting Numbers: [3610] 3610,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 10:[5, 2], Operations: ['95-90=5', '27-25=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[95, 90, 25, 27], Operations: [] Exploring Operation: 95-90=5, Resulting Numbers: [25, 27, 5] Generated Node #0,2: 10:[25, 27, 5] Operation: 95-90=5 Moving to Node #0,2 Current State: 10:[25, 27, 5], Operations: ['95-90=5'] Exploring Operation: 27-25=2, Resulting Numbers: [5, 2] Generated Node #0,2,1: 10:[5, 2] Operation: 27-25=2 Moving to Node #0,2,1 Current State: 10:[5, 2], Operations: ['95-90=5', '27-25=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 87, 20, 10, 73 ]
44
[ "87+20=107", "73-10=63", "107-63=44" ]
Current State: 44:[87, 20, 10, 73], Operations: [] Exploring Operation: 87+20=107, Resulting Numbers: [10, 73, 107] Generated Node #2: [10, 73, 107] from Operation: 87+20=107 Current State: 44:[10, 73, 107], Operations: ['87+20=107'] Exploring Operation: 73-10=63, Resulting Numbers: [107, 63] Generated Node #3: [107, 63] from Operation: 73-10=63 Current State: 44:[107, 63], Operations: ['87+20=107', '73-10=63'] Exploring Operation: 107-63=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[87, 20, 10, 73], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [20, 10, 14] Generated Node #0,0: 44:[20, 10, 14] Operation: 87-73=14 Moving to Node #0,0 Current State: 44:[20, 10, 14], Operations: ['87-73=14'] Exploring Operation: 14-10=4, Resulting Numbers: [20, 4] Generated Node #0,0,0: 44:[20, 4] Operation: 14-10=4 Moving to Node #0,0,0 Current State: 44:[20, 4], Operations: ['87-73=14', '14-10=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,44 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 10, 50, 37, 39 ]
62
[ "10+50=60", "39-37=2", "60+2=62" ]
Current State: 62:[10, 50, 37, 39], Operations: [] Exploring Operation: 10+50=60, Resulting Numbers: [37, 39, 60] Generated Node #2: [37, 39, 60] from Operation: 10+50=60 Current State: 62:[37, 39, 60], Operations: ['10+50=60'] Exploring Operation: 39-37=2, Resulting Numbers: [60, 2] Generated Node #3: [60, 2] from Operation: 39-37=2 Current State: 62:[60, 2], Operations: ['10+50=60', '39-37=2'] Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[10, 50, 37, 39], Operations: [] Exploring Operation: 10+50=60, Resulting Numbers: [37, 39, 60] Generated Node #0,0: 62:[37, 39, 60] Operation: 10+50=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[37, 39, 60], Operations: ['10+50=60'] Exploring Operation: 39-37=2, Resulting Numbers: [60, 2] Generated Node #0,0,0: 62:[60, 2] Operation: 39-37=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[60, 2], Operations: ['10+50=60', '39-37=2'] Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[10, 50, 37, 39], Operations: [] Exploring Operation: 10+50=60, Resulting Numbers: [37, 39, 60] Generated Node #0,0: 62:[37, 39, 60] Operation: 10+50=60 Moving to Node #0,0 Current State: 62:[37, 39, 60], Operations: ['10+50=60'] Exploring Operation: 39-37=2, Resulting Numbers: [60, 2] Generated Node #0,0,0: 62:[60, 2] Operation: 39-37=2 Moving to Node #0,0,0 Current State: 62:[60, 2], Operations: ['10+50=60', '39-37=2'] Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 35, 92, 77, 35 ]
99
[ "92-35=57", "77-35=42", "57+42=99" ]
Current State: 99:[35, 92, 77, 35], Operations: [] Exploring Operation: 92-35=57, Resulting Numbers: [77, 57] Generated Node #2: [77, 57] from Operation: 92-35=57 Current State: 99:[77, 57], Operations: ['92-35=57'] Exploring Operation: 77-35=42, Resulting Numbers: [57, 42] Generated Node #3: [57, 42] from Operation: 77-35=42 Current State: 99:[57, 42], Operations: ['92-35=57', '77-35=42'] Exploring Operation: 57+42=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[35, 92, 77, 35], Operations: [] Exploring Operation: 35+77=112, Resulting Numbers: [92, 35, 112] Generated Node #0,0: 99:[92, 35, 112] Operation: 35+77=112 Exploring Operation: 77-35=42, Resulting Numbers: [92, 35, 42] Generated Node #0,1: 99:[92, 35, 42] Operation: 77-35=42 Exploring Operation: 77-35=42, Resulting Numbers: [35, 92, 42] Generated Node #0,2: 99:[35, 92, 42] Operation: 77-35=42 Exploring Operation: 92-77=15, Resulting Numbers: [35, 35, 15] Generated Node #0,3: 99:[35, 35, 15] Operation: 92-77=15 Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[35, 35, 15], Operations: ['92-77=15'] Exploring Operation: 35-15=20, Resulting Numbers: [35, 20] Generated Node #0,3,0: 99:[35, 20] Operation: 35-15=20 Exploring Operation: 35-15=20, Resulting Numbers: [35, 20] Generated Node #0,3,1: 99:[35, 20] Operation: 35-15=20 Exploring Operation: 35/35=1, Resulting Numbers: [15, 1] Generated Node #0,3,2: 99:[15, 1] Operation: 35/35=1 Exploring Operation: 35-35=0, Resulting Numbers: [15, 0] Generated Node #0,3,3: 99:[15, 0] Operation: 35-35=0 Moving to Node #0,3,2 Current State: 99:[15, 1], Operations: ['92-77=15', '35/35=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,99 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,99 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,99 unequal: No Solution Moving to Node #0,3,3 Current State: 99:[15, 0], Operations: ['92-77=15', '35-35=0'] Exploring Operation: 15+0=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 15-0=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 15*0=0, Resulting Numbers: [0] 0,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[35, 20], Operations: ['92-77=15', '35-15=20'] Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,99 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,99 unequal: No Solution Moving to Node #0,3,0 Current State: 99:[35, 20], Operations: ['92-77=15', '35-15=20'] Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,99 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[92, 35, 42], Operations: ['77-35=42'] Exploring Operation: 92-35=57, Resulting Numbers: [42, 57] Generated Node #0,1,0: 99:[42, 57] Operation: 92-35=57 Exploring Operation: 42-35=7, Resulting Numbers: [92, 7] Generated Node #0,1,1: 99:[92, 7] Operation: 42-35=7 Exploring Operation: 92-42=50, Resulting Numbers: [35, 50] Generated Node #0,1,2: 99:[35, 50] Operation: 92-42=50 Exploring Operation: 35+42=77, Resulting Numbers: [92, 77] Generated Node #0,1,3: 99:[92, 77] Operation: 35+42=77 Moving to Node #0,1,1 Current State: 99:[92, 7], Operations: ['77-35=42', '42-35=7'] Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,99 unequal: No Solution Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[35, 92, 77, 35], Operations: [] Exploring Operation: 77-35=42, Resulting Numbers: [92, 35, 42] Generated Node #0,1: 99:[92, 35, 42] Operation: 77-35=42 Moving to Node #0,1 Current State: 99:[92, 35, 42], Operations: ['77-35=42'] Exploring Operation: 42-35=7, Resulting Numbers: [92, 7] Generated Node #0,1,1: 99:[92, 7] Operation: 42-35=7 Moving to Node #0,1,1 Current State: 99:[92, 7], Operations: ['77-35=42', '42-35=7'] Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 90, 52, 45, 88 ]
95
[ "90-52=38", "45+88=133", "133-38=95" ]
Current State: 95:[90, 52, 45, 88], Operations: [] Exploring Operation: 90-52=38, Resulting Numbers: [45, 88, 38] Generated Node #2: [45, 88, 38] from Operation: 90-52=38 Current State: 95:[45, 88, 38], Operations: ['90-52=38'] Exploring Operation: 45+88=133, Resulting Numbers: [38, 133] Generated Node #3: [38, 133] from Operation: 45+88=133 Current State: 95:[38, 133], Operations: ['90-52=38', '45+88=133'] Exploring Operation: 133-38=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[90, 52, 45, 88], Operations: [] Exploring Operation: 90/45=2, Resulting Numbers: [52, 88, 2] Generated Node #0,0: 95:[52, 88, 2] Operation: 90/45=2 Exploring Operation: 52+45=97, Resulting Numbers: [90, 88, 97] Generated Node #0,1: 95:[90, 88, 97] Operation: 52+45=97 Exploring Operation: 52-45=7, Resulting Numbers: [90, 88, 7] Generated Node #0,2: 95:[90, 88, 7] Operation: 52-45=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[90, 88, 97], Operations: ['52+45=97'] Exploring Operation: 97-88=9, Resulting Numbers: [90, 9] Generated Node #0,1,0: 95:[90, 9] Operation: 97-88=9 Exploring Operation: 97-90=7, Resulting Numbers: [88, 7] Generated Node #0,1,1: 95:[88, 7] Operation: 97-90=7 Exploring Operation: 90-88=2, Resulting Numbers: [97, 2] Generated Node #0,1,2: 95:[97, 2] Operation: 90-88=2 Moving to Node #0,1,2 Current State: 95:[97, 2], Operations: ['52+45=97', '90-88=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,95 unequal: No Solution Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[90, 52, 45, 88], Operations: [] Exploring Operation: 52+45=97, Resulting Numbers: [90, 88, 97] Generated Node #0,1: 95:[90, 88, 97] Operation: 52+45=97 Moving to Node #0,1 Current State: 95:[90, 88, 97], Operations: ['52+45=97'] Exploring Operation: 90-88=2, Resulting Numbers: [97, 2] Generated Node #0,1,2: 95:[97, 2] Operation: 90-88=2 Moving to Node #0,1,2 Current State: 95:[97, 2], Operations: ['52+45=97', '90-88=2'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 8, 6, 83, 79 ]
19
[ "83+79=162", "162/6=27", "27-8=19" ]
Current State: 19:[8, 6, 83, 79], Operations: [] Exploring Operation: 83+79=162, Resulting Numbers: [8, 6, 162] Generated Node #2: [8, 6, 162] from Operation: 83+79=162 Current State: 19:[8, 6, 162], Operations: ['83+79=162'] Exploring Operation: 162/6=27, Resulting Numbers: [8, 27] Generated Node #3: [8, 27] from Operation: 162/6=27 Current State: 19:[8, 27], Operations: ['83+79=162', '162/6=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[8, 6, 83, 79], Operations: [] Exploring Operation: 83-79=4, Resulting Numbers: [8, 6, 4] Generated Node #0,0: 19:[8, 6, 4] Operation: 83-79=4 Exploring Operation: 83-8=75, Resulting Numbers: [6, 79, 75] Generated Node #0,1: 19:[6, 79, 75] Operation: 83-8=75 Exploring Operation: 8+6=14, Resulting Numbers: [83, 79, 14] Generated Node #0,2: 19:[83, 79, 14] Operation: 8+6=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[8, 6, 4], Operations: ['83-79=4'] Exploring Operation: 6*4=24, Resulting Numbers: [8, 24] Generated Node #0,0,0: 19:[8, 24] Operation: 6*4=24 Exploring Operation: 8+4=12, Resulting Numbers: [6, 12] Generated Node #0,0,1: 19:[6, 12] Operation: 8+4=12 Exploring Operation: 8+6=14, Resulting Numbers: [4, 14] Generated Node #0,0,2: 19:[4, 14] Operation: 8+6=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[8, 24], Operations: ['83-79=4', '6*4=24'] Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 19:[6, 12], Operations: ['83-79=4', '8+4=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 19:[4, 14], Operations: ['83-79=4', '8+6=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[6, 79, 75], Operations: ['83-8=75'] Exploring Operation: 79-75=4, Resulting Numbers: [6, 4] Generated Node #0,1,0: 19:[6, 4] Operation: 79-75=4 Exploring Operation: 79-6=73, Resulting Numbers: [75, 73] Generated Node #0,1,1: 19:[75, 73] Operation: 79-6=73 Exploring Operation: 75-6=69, Resulting Numbers: [79, 69] Generated Node #0,1,2: 19:[79, 69] Operation: 75-6=69 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[6, 4], Operations: ['83-8=75', '79-75=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[75, 73], Operations: ['83-8=75', '79-6=73'] Exploring Operation: 75*73=5475, Resulting Numbers: [5475] 5475,19 unequal: No Solution Exploring Operation: 75+73=148, Resulting Numbers: [148] 148,19 unequal: No Solution Exploring Operation: 75-73=2, Resulting Numbers: [2] 2,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 19:[79, 69], Operations: ['83-8=75', '75-6=69'] Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 79+69=148, Resulting Numbers: [148] 148,19 unequal: No Solution Exploring Operation: 79*69=5451, Resulting Numbers: [5451] 5451,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[83, 79, 14], Operations: ['8+6=14'] Exploring Operation: 79-14=65, Resulting Numbers: [83, 65] Generated Node #0,2,0: 19:[83, 65] Operation: 79-14=65 Exploring Operation: 83-79=4, Resulting Numbers: [14, 4] Generated Node #0,2,1: 19:[14, 4] Operation: 83-79=4 Exploring Operation: 83-14=69, Resulting Numbers: [79, 69] Generated Node #0,2,2: 19:[79, 69] Operation: 83-14=69 Moving to Node #0,2,1 Current State: 19:[14, 4], Operations: ['8+6=14', '83-79=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,19 unequal: No Solution Moving to Node #0,2,0 Current State: 19:[83, 65], Operations: ['8+6=14', '79-14=65'] Exploring Operation: 83*65=5395, Resulting Numbers: [5395] 5395,19 unequal: No Solution Exploring Operation: 83+65=148, Resulting Numbers: [148] 148,19 unequal: No Solution Exploring Operation: 83-65=18, Resulting Numbers: [18] 18,19 unequal: No Solution Moving to Node #0,2,2 Current State: 19:[79, 69], Operations: ['8+6=14', '83-14=69'] Exploring Operation: 79*69=5451, Resulting Numbers: [5451] 5451,19 unequal: No Solution Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 79+69=148, Resulting Numbers: [148] 148,19 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
[ 4, 23, 2, 58 ]
56
[ "4+23=27", "58/2=29", "27+29=56" ]
Current State: 56:[4, 23, 2, 58], Operations: [] Exploring Operation: 4+23=27, Resulting Numbers: [2, 58, 27] Generated Node #2: [2, 58, 27] from Operation: 4+23=27 Current State: 56:[2, 58, 27], Operations: ['4+23=27'] Exploring Operation: 58/2=29, Resulting Numbers: [27, 29] Generated Node #3: [27, 29] from Operation: 58/2=29 Current State: 56:[27, 29], Operations: ['4+23=27', '58/2=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[4, 23, 2, 58], Operations: [] Exploring Operation: 4+23=27, Resulting Numbers: [2, 58, 27] Generated Node #0,0: 56:[2, 58, 27] Operation: 4+23=27 Exploring Operation: 58-2=56, Resulting Numbers: [4, 23, 56] Generated Node #0,1: 56:[4, 23, 56] Operation: 58-2=56 Exploring Operation: 58/2=29, Resulting Numbers: [4, 23, 29] Generated Node #0,2: 56:[4, 23, 29] Operation: 58/2=29 Exploring Operation: 23-4=19, Resulting Numbers: [2, 58, 19] Generated Node #0,3: 56:[2, 58, 19] Operation: 23-4=19 Exploring Operation: 23+2=25, Resulting Numbers: [4, 58, 25] Generated Node #0,4: 56:[4, 58, 25] Operation: 23+2=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[2, 58, 27], Operations: ['4+23=27'] Exploring Operation: 58-27=31, Resulting Numbers: [2, 31] Generated Node #0,0,0: 56:[2, 31] Operation: 58-27=31 Exploring Operation: 2+27=29, Resulting Numbers: [58, 29] Generated Node #0,0,1: 56:[58, 29] Operation: 2+27=29 Exploring Operation: 58/2=29, Resulting Numbers: [27, 29] Generated Node #0,0,2: 56:[27, 29] Operation: 58/2=29 Exploring Operation: 58-2=56, Resulting Numbers: [27, 56] Generated Node #0,0,3: 56:[27, 56] Operation: 58-2=56 Exploring Operation: 2*27=54, Resulting Numbers: [58, 54] Generated Node #0,0,4: 56:[58, 54] Operation: 2*27=54 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 56:[27, 56], Operations: ['4+23=27', '58-2=56'] Exploring Operation: 27+56=83, Resulting Numbers: [83] 83,56 unequal: No Solution Exploring Operation: 27*56=1512, Resulting Numbers: [1512] 1512,56 unequal: No Solution Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,56 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:[27, 29], Operations: ['4+23=27', '58/2=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[4, 23, 2, 58], Operations: [] Exploring Operation: 4+23=27, Resulting Numbers: [2, 58, 27] Generated Node #0,0: 56:[2, 58, 27] Operation: 4+23=27 Moving to Node #0,0 Current State: 56:[2, 58, 27], Operations: ['4+23=27'] Exploring Operation: 58/2=29, Resulting Numbers: [27, 29] Generated Node #0,0,2: 56:[27, 29] Operation: 58/2=29 Moving to Node #0,0,2 Current State: 56:[27, 29], Operations: ['4+23=27', '58/2=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 83, 22, 2, 44 ]
82
[ "22*2=44", "44/44=1", "83-1=82" ]
Current State: 82:[83, 22, 2, 44], Operations: [] Exploring Operation: 22*2=44, Resulting Numbers: [83, 44, 44] Generated Node #2: [83, 44, 44] from Operation: 22*2=44 Current State: 82:[83, 44, 44], Operations: ['22*2=44'] Exploring Operation: 44/44=1, Resulting Numbers: [83, 1] Generated Node #3: [83, 1] from Operation: 44/44=1 Current State: 82:[83, 1], Operations: ['22*2=44', '44/44=1'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[83, 22, 2, 44], Operations: [] Exploring Operation: 44/22=2, Resulting Numbers: [83, 2, 2] Generated Node #0,0: 82:[83, 2, 2] Operation: 44/22=2 Exploring Operation: 22+44=66, Resulting Numbers: [83, 2, 66] Generated Node #0,1: 82:[83, 2, 66] Operation: 22+44=66 Exploring Operation: 22/2=11, Resulting Numbers: [83, 44, 11] Generated Node #0,2: 82:[83, 44, 11] Operation: 22/2=11 Exploring Operation: 22*2=44, Resulting Numbers: [83, 44, 44] Generated Node #0,3: 82:[83, 44, 44] Operation: 22*2=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[83, 2, 2], Operations: ['44/22=2'] Exploring Operation: 83+2=85, Resulting Numbers: [2, 85] Generated Node #0,0,0: 82:[2, 85] Operation: 83+2=85 Exploring Operation: 83-2=81, Resulting Numbers: [2, 81] Generated Node #0,0,1: 82:[2, 81] Operation: 83-2=81 Exploring Operation: 2/2=1, Resulting Numbers: [83, 1] Generated Node #0,0,2: 82:[83, 1] Operation: 2/2=1 Exploring Operation: 83-2=81, Resulting Numbers: [2, 81] Generated Node #0,0,3: 82:[2, 81] Operation: 83-2=81 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[2, 81], Operations: ['44/22=2', '83-2=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,82 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,82 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 82:[2, 81], Operations: ['44/22=2', '83-2=81'] Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,82 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,82 unequal: No Solution Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[83, 1], Operations: ['44/22=2', '2/2=1'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[83, 22, 2, 44], Operations: [] Exploring Operation: 44/22=2, Resulting Numbers: [83, 2, 2] Generated Node #0,0: 82:[83, 2, 2] Operation: 44/22=2 Moving to Node #0,0 Current State: 82:[83, 2, 2], Operations: ['44/22=2'] Exploring Operation: 2/2=1, Resulting Numbers: [83, 1] Generated Node #0,0,2: 82:[83, 1] Operation: 2/2=1 Moving to Node #0,0,2 Current State: 82:[83, 1], Operations: ['44/22=2', '2/2=1'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 37, 69, 52, 52 ]
33
[ "69-37=32", "52/52=1", "32+1=33" ]
Current State: 33:[37, 69, 52, 52], Operations: [] Exploring Operation: 69-37=32, Resulting Numbers: [52, 52, 32] Generated Node #2: [52, 52, 32] from Operation: 69-37=32 Current State: 33:[52, 52, 32], Operations: ['69-37=32'] Exploring Operation: 52/52=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 52/52=1 Current State: 33:[32, 1], Operations: ['69-37=32', '52/52=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[37, 69, 52, 52], Operations: [] Exploring Operation: 69-52=17, Resulting Numbers: [37, 52, 17] Generated Node #0,0: 33:[37, 52, 17] Operation: 69-52=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[37, 52, 17], Operations: ['69-52=17'] Exploring Operation: 52-17=35, Resulting Numbers: [37, 35] Generated Node #0,0,0: 33:[37, 35] Operation: 52-17=35 Moving to Node #0,0,0 Current State: 33:[37, 35], Operations: ['69-52=17', '52-17=35'] Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 43, 39, 99, 66 ]
17
[ "39*66=2574", "2574/99=26", "43-26=17" ]
Current State: 17:[43, 39, 99, 66], Operations: [] Exploring Operation: 39*66=2574, Resulting Numbers: [43, 99, 2574] Generated Node #2: [43, 99, 2574] from Operation: 39*66=2574 Current State: 17:[43, 99, 2574], Operations: ['39*66=2574'] Exploring Operation: 2574/99=26, Resulting Numbers: [43, 26] Generated Node #3: [43, 26] from Operation: 2574/99=26 Current State: 17:[43, 26], Operations: ['39*66=2574', '2574/99=26'] Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[43, 39, 99, 66], Operations: [] Exploring Operation: 99-43=56, Resulting Numbers: [39, 66, 56] Generated Node #0,0: 17:[39, 66, 56] Operation: 99-43=56 Exploring Operation: 99-66=33, Resulting Numbers: [43, 39, 33] Generated Node #0,1: 17:[43, 39, 33] Operation: 99-66=33 Exploring Operation: 66-43=23, Resulting Numbers: [39, 99, 23] Generated Node #0,2: 17:[39, 99, 23] Operation: 66-43=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[43, 39, 33], Operations: ['99-66=33'] Exploring Operation: 39-33=6, Resulting Numbers: [43, 6] Generated Node #0,1,0: 17:[43, 6] Operation: 39-33=6 Exploring Operation: 43-39=4, Resulting Numbers: [33, 4] Generated Node #0,1,1: 17:[33, 4] Operation: 43-39=4 Exploring Operation: 43-33=10, Resulting Numbers: [39, 10] Generated Node #0,1,2: 17:[39, 10] Operation: 43-33=10 Moving to Node #0,1,1 Current State: 17:[33, 4], Operations: ['99-66=33', '43-39=4'] Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,17 unequal: No Solution Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,17 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[39, 10], Operations: ['99-66=33', '43-33=10'] Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,17 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,17 unequal: No Solution Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[43, 6], Operations: ['99-66=33', '39-33=6'] Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,17 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,17 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:[39, 66, 56], Operations: ['99-43=56'] Exploring Operation: 56-39=17, Resulting Numbers: [66, 17] Generated Node #0,0,0: 17:[66, 17] Operation: 56-39=17 Exploring Operation: 66-39=27, Resulting Numbers: [56, 27] Generated Node #0,0,1: 17:[56, 27] Operation: 66-39=27 Exploring Operation: 66-56=10, Resulting Numbers: [39, 10] Generated Node #0,0,2: 17:[39, 10] Operation: 66-56=10 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 17:[39, 10], Operations: ['99-43=56', '66-56=10'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,17 unequal: No Solution Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,17 unequal: No Solution Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,17 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:[66, 17], Operations: ['99-43=56', '56-39=17'] Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 66+17=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 66*17=1122, Resulting Numbers: [1122] 1122,17 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:[56, 27], Operations: ['99-43=56', '66-39=27'] Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 56*27=1512, Resulting Numbers: [1512] 1512,17 unequal: No Solution Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,17 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[39, 99, 23], Operations: ['66-43=23'] Exploring Operation: 99-39=60, Resulting Numbers: [23, 60] Generated Node #0,2,0: 17:[23, 60] Operation: 99-39=60 Exploring Operation: 99-23=76, Resulting Numbers: [39, 76] Generated Node #0,2,1: 17:[39, 76] Operation: 99-23=76 Exploring Operation: 39-23=16, Resulting Numbers: [99, 16] Generated Node #0,2,2: 17:[99, 16] Operation: 39-23=16 Moving to Node #0,2,0 Current State: 17:[23, 60], Operations: ['66-43=23', '99-39=60'] Exploring Operation: 23*60=1380, Resulting Numbers: [1380] 1380,17 unequal: No Solution Exploring Operation: 23+60=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[39, 76], Operations: ['66-43=23', '99-23=76'] Exploring Operation: 39*76=2964, Resulting Numbers: [2964] 2964,17 unequal: No Solution Exploring Operation: 39+76=115, Resulting Numbers: [115] 115,17 unequal: No Solution Exploring Operation: 76-39=37, Resulting Numbers: [37] 37,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[99, 16], Operations: ['66-43=23', '39-23=16'] Exploring Operation: 99*16=1584, Resulting Numbers: [1584] 1584,17 unequal: No Solution Exploring Operation: 99+16=115, Resulting Numbers: [115] 115,17 unequal: No Solution Exploring Operation: 99-16=83, Resulting Numbers: [83] 83,17 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
[ 87, 16, 68, 33 ]
36
[ "87-16=71", "68-33=35", "71-35=36" ]
Current State: 36:[87, 16, 68, 33], Operations: [] Exploring Operation: 87-16=71, Resulting Numbers: [68, 33, 71] Generated Node #2: [68, 33, 71] from Operation: 87-16=71 Current State: 36:[68, 33, 71], Operations: ['87-16=71'] Exploring Operation: 68-33=35, Resulting Numbers: [71, 35] Generated Node #3: [71, 35] from Operation: 68-33=35 Current State: 36:[71, 35], Operations: ['87-16=71', '68-33=35'] Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[87, 16, 68, 33], Operations: [] Exploring Operation: 68-33=35, Resulting Numbers: [87, 16, 35] Generated Node #0,0: 36:[87, 16, 35] Operation: 68-33=35 Exploring Operation: 87-68=19, Resulting Numbers: [16, 33, 19] Generated Node #0,1: 36:[16, 33, 19] Operation: 87-68=19 Exploring Operation: 87-33=54, Resulting Numbers: [16, 68, 54] Generated Node #0,2: 36:[16, 68, 54] Operation: 87-33=54 Moving to Node #0,1 Current State: 36:[16, 33, 19], Operations: ['87-68=19'] Exploring Operation: 16+19=35, Resulting Numbers: [33, 35] Generated Node #0,1,0: 36:[33, 35] Operation: 16+19=35 Exploring Operation: 33-16=17, Resulting Numbers: [19, 17] Generated Node #0,1,1: 36:[19, 17] Operation: 33-16=17 Exploring Operation: 19-16=3, Resulting Numbers: [33, 3] Generated Node #0,1,2: 36:[33, 3] Operation: 19-16=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 36:[19, 17], Operations: ['87-68=19', '33-16=17'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[87, 16, 68, 33], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [16, 33, 19] Generated Node #0,1: 36:[16, 33, 19] Operation: 87-68=19 Moving to Node #0,1 Current State: 36:[16, 33, 19], Operations: ['87-68=19'] Exploring Operation: 33-16=17, Resulting Numbers: [19, 17] Generated Node #0,1,1: 36:[19, 17] Operation: 33-16=17 Moving to Node #0,1,1 Current State: 36:[19, 17], Operations: ['87-68=19', '33-16=17'] Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 32, 31, 45, 90 ]
45
[ "32-31=1", "90-45=45", "1*45=45" ]
Current State: 45:[32, 31, 45, 90], Operations: [] Exploring Operation: 32-31=1, Resulting Numbers: [45, 90, 1] Generated Node #2: [45, 90, 1] from Operation: 32-31=1 Current State: 45:[45, 90, 1], Operations: ['32-31=1'] Exploring Operation: 90-45=45, Resulting Numbers: [1, 45] Generated Node #3: [1, 45] from Operation: 90-45=45 Current State: 45:[1, 45], Operations: ['32-31=1', '90-45=45'] Exploring Operation: 1*45=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[32, 31, 45, 90], Operations: [] Exploring Operation: 90-31=59, Resulting Numbers: [32, 45, 59] Generated Node #0,0: 45:[32, 45, 59] Operation: 90-31=59 Exploring Operation: 90-32=58, Resulting Numbers: [31, 45, 58] Generated Node #0,1: 45:[31, 45, 58] Operation: 90-32=58 Exploring Operation: 90-45=45, Resulting Numbers: [32, 31, 45] Generated Node #0,2: 45:[32, 31, 45] Operation: 90-45=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[32, 45, 59], Operations: ['90-31=59'] Exploring Operation: 59-32=27, Resulting Numbers: [45, 27] Generated Node #0,0,0: 45:[45, 27] Operation: 59-32=27 Exploring Operation: 59-45=14, Resulting Numbers: [32, 14] Generated Node #0,0,1: 45:[32, 14] Operation: 59-45=14 Exploring Operation: 45-32=13, Resulting Numbers: [59, 13] Generated Node #0,0,2: 45:[59, 13] Operation: 45-32=13 Moving to Node #0,0,0 Current State: 45:[45, 27], Operations: ['90-31=59', '59-32=27'] Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,45 unequal: No Solution Exploring Operation: 45*27=1215, Resulting Numbers: [1215] 1215,45 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[32, 14], Operations: ['90-31=59', '59-45=14'] Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,45 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[59, 13], Operations: ['90-31=59', '45-32=13'] Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,45 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[31, 45, 58], Operations: ['90-32=58'] Exploring Operation: 58-31=27, Resulting Numbers: [45, 27] Generated Node #0,1,0: 45:[45, 27] Operation: 58-31=27 Exploring Operation: 45-31=14, Resulting Numbers: [58, 14] Generated Node #0,1,1: 45:[58, 14] Operation: 45-31=14 Exploring Operation: 58-45=13, Resulting Numbers: [31, 13] Generated Node #0,1,2: 45:[31, 13] Operation: 58-45=13 Moving to Node #0,1,0 Current State: 45:[45, 27], Operations: ['90-32=58', '58-31=27'] Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,45 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 45*27=1215, Resulting Numbers: [1215] 1215,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[58, 14], Operations: ['90-32=58', '45-31=14'] Exploring Operation: 58+14=72, Resulting Numbers: [72] 72,45 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 58*14=812, Resulting Numbers: [812] 812,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[31, 13], Operations: ['90-32=58', '58-45=13'] Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,45 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[32, 31, 45], Operations: ['90-45=45'] Exploring Operation: 32-31=1, Resulting Numbers: [45, 1] Generated Node #0,2,0: 45:[45, 1] Operation: 32-31=1 Exploring Operation: 45-32=13, Resulting Numbers: [31, 13] Generated Node #0,2,1: 45:[31, 13] Operation: 45-32=13 Exploring Operation: 45-31=14, Resulting Numbers: [32, 14] Generated Node #0,2,2: 45:[32, 14] Operation: 45-31=14 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 45:[45, 1], Operations: ['90-45=45', '32-31=1'] Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[32, 31, 45, 90], Operations: [] Exploring Operation: 90-45=45, Resulting Numbers: [32, 31, 45] Generated Node #0,2: 45:[32, 31, 45] Operation: 90-45=45 Moving to Node #0,2 Current State: 45:[32, 31, 45], Operations: ['90-45=45'] Exploring Operation: 32-31=1, Resulting Numbers: [45, 1] Generated Node #0,2,0: 45:[45, 1] Operation: 32-31=1 Moving to Node #0,2,0 Current State: 45:[45, 1], Operations: ['90-45=45', '32-31=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 48, 37, 41, 61 ]
91
[ "48-37=11", "41+61=102", "102-11=91" ]
Current State: 91:[48, 37, 41, 61], Operations: [] Exploring Operation: 48-37=11, Resulting Numbers: [41, 61, 11] Generated Node #2: [41, 61, 11] from Operation: 48-37=11 Current State: 91:[41, 61, 11], Operations: ['48-37=11'] Exploring Operation: 41+61=102, Resulting Numbers: [11, 102] Generated Node #3: [11, 102] from Operation: 41+61=102 Current State: 91:[11, 102], Operations: ['48-37=11', '41+61=102'] Exploring Operation: 102-11=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[48, 37, 41, 61], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [37, 41, 13] Generated Node #0,0: 91:[37, 41, 13] Operation: 61-48=13 Exploring Operation: 48+37=85, Resulting Numbers: [41, 61, 85] Generated Node #0,1: 91:[41, 61, 85] Operation: 48+37=85 Exploring Operation: 48-41=7, Resulting Numbers: [37, 61, 7] Generated Node #0,2: 91:[37, 61, 7] Operation: 48-41=7 Exploring Operation: 48+41=89, Resulting Numbers: [37, 61, 89] Generated Node #0,3: 91:[37, 61, 89] Operation: 48+41=89 Exploring Operation: 48-37=11, Resulting Numbers: [41, 61, 11] Generated Node #0,4: 91:[41, 61, 11] Operation: 48-37=11 Moving to Node #0,0 Current State: 91:[37, 41, 13], Operations: ['61-48=13'] Exploring Operation: 41-37=4, Resulting Numbers: [13, 4] Generated Node #0,0,0: 91:[13, 4] Operation: 41-37=4 Exploring Operation: 41+13=54, Resulting Numbers: [37, 54] Generated Node #0,0,1: 91:[37, 54] Operation: 41+13=54 Exploring Operation: 37-13=24, Resulting Numbers: [41, 24] Generated Node #0,0,2: 91:[41, 24] Operation: 37-13=24 Exploring Operation: 41-13=28, Resulting Numbers: [37, 28] Generated Node #0,0,3: 91:[37, 28] Operation: 41-13=28 Exploring Operation: 37+41=78, Resulting Numbers: [13, 78] Generated Node #0,0,4: 91:[13, 78] Operation: 37+41=78 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[13, 4], Operations: ['61-48=13', '41-37=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 91:[13, 78], Operations: ['61-48=13', '37+41=78'] Exploring Operation: 13*78=1014, Resulting Numbers: [1014] 1014,91 unequal: No Solution Exploring Operation: 78/13=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 13+78=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[48, 37, 41, 61], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [37, 41, 13] Generated Node #0,0: 91:[37, 41, 13] Operation: 61-48=13 Moving to Node #0,0 Current State: 91:[37, 41, 13], Operations: ['61-48=13'] Exploring Operation: 37+41=78, Resulting Numbers: [13, 78] Generated Node #0,0,4: 91:[13, 78] Operation: 37+41=78 Moving to Node #0,0,4 Current State: 91:[13, 78], Operations: ['61-48=13', '37+41=78'] Exploring Operation: 13+78=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 31, 66, 24, 72 ]
83
[ "66-31=35", "72-24=48", "35+48=83" ]
Current State: 83:[31, 66, 24, 72], Operations: [] Exploring Operation: 66-31=35, Resulting Numbers: [24, 72, 35] Generated Node #2: [24, 72, 35] from Operation: 66-31=35 Current State: 83:[24, 72, 35], Operations: ['66-31=35'] Exploring Operation: 72-24=48, Resulting Numbers: [35, 48] Generated Node #3: [35, 48] from Operation: 72-24=48 Current State: 83:[35, 48], Operations: ['66-31=35', '72-24=48'] Exploring Operation: 35+48=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[31, 66, 24, 72], Operations: [] Exploring Operation: 66+24=90, Resulting Numbers: [31, 72, 90] Generated Node #0,0: 83:[31, 72, 90] Operation: 66+24=90 Exploring Operation: 31+24=55, Resulting Numbers: [66, 72, 55] Generated Node #0,1: 83:[66, 72, 55] Operation: 31+24=55 Exploring Operation: 24+72=96, Resulting Numbers: [31, 66, 96] Generated Node #0,2: 83:[31, 66, 96] Operation: 24+72=96 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[66, 72, 55], Operations: ['31+24=55'] Exploring Operation: 72+55=127, Resulting Numbers: [66, 127] Generated Node #0,1,0: 83:[66, 127] Operation: 72+55=127 Exploring Operation: 66+72=138, Resulting Numbers: [55, 138] Generated Node #0,1,1: 83:[55, 138] Operation: 66+72=138 Exploring Operation: 66+55=121, Resulting Numbers: [72, 121] Generated Node #0,1,2: 83:[72, 121] Operation: 66+55=121 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 83:[72, 121], Operations: ['31+24=55', '66+55=121'] Exploring Operation: 121-72=49, Resulting Numbers: [49] 49,83 unequal: No Solution Exploring Operation: 72+121=193, Resulting Numbers: [193] 193,83 unequal: No Solution Exploring Operation: 72*121=8712, Resulting Numbers: [8712] 8712,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[66, 127], Operations: ['31+24=55', '72+55=127'] Exploring Operation: 127-66=61, Resulting Numbers: [61] 61,83 unequal: No Solution Exploring Operation: 66*127=8382, Resulting Numbers: [8382] 8382,83 unequal: No Solution Exploring Operation: 66+127=193, Resulting Numbers: [193] 193,83 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:[55, 138], Operations: ['31+24=55', '66+72=138'] Exploring Operation: 55+138=193, Resulting Numbers: [193] 193,83 unequal: No Solution Exploring Operation: 138-55=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[31, 66, 24, 72], Operations: [] Exploring Operation: 31+24=55, Resulting Numbers: [66, 72, 55] Generated Node #0,1: 83:[66, 72, 55] Operation: 31+24=55 Moving to Node #0,1 Current State: 83:[66, 72, 55], Operations: ['31+24=55'] Exploring Operation: 66+72=138, Resulting Numbers: [55, 138] Generated Node #0,1,1: 83:[55, 138] Operation: 66+72=138 Moving to Node #0,1,1 Current State: 83:[55, 138], Operations: ['31+24=55', '66+72=138'] Exploring Operation: 138-55=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 60, 20, 1, 51 ]
55
[ "60/20=3", "1+51=52", "3+52=55" ]
Current State: 55:[60, 20, 1, 51], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [1, 51, 3] Generated Node #2: [1, 51, 3] from Operation: 60/20=3 Current State: 55:[1, 51, 3], Operations: ['60/20=3'] Exploring Operation: 1+51=52, Resulting Numbers: [3, 52] Generated Node #3: [3, 52] from Operation: 1+51=52 Current State: 55:[3, 52], Operations: ['60/20=3', '1+51=52'] Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[60, 20, 1, 51], Operations: [] Exploring Operation: 60-51=9, Resulting Numbers: [20, 1, 9] Generated Node #0,0: 55:[20, 1, 9] Operation: 60-51=9 Exploring Operation: 60/20=3, Resulting Numbers: [1, 51, 3] Generated Node #0,1: 55:[1, 51, 3] Operation: 60/20=3 Exploring Operation: 20-1=19, Resulting Numbers: [60, 51, 19] Generated Node #0,2: 55:[60, 51, 19] Operation: 20-1=19 Exploring Operation: 60-1=59, Resulting Numbers: [20, 51, 59] Generated Node #0,3: 55:[20, 51, 59] Operation: 60-1=59 Moving to Node #0,1 Current State: 55:[1, 51, 3], Operations: ['60/20=3'] Exploring Operation: 1+51=52, Resulting Numbers: [3, 52] Generated Node #0,1,0: 55:[3, 52] Operation: 1+51=52 Exploring Operation: 1*51=51, Resulting Numbers: [3, 51] Generated Node #0,1,1: 55:[3, 51] Operation: 1*51=51 Exploring Operation: 1+3=4, Resulting Numbers: [51, 4] Generated Node #0,1,2: 55:[51, 4] Operation: 1+3=4 Exploring Operation: 51+3=54, Resulting Numbers: [1, 54] Generated Node #0,1,3: 55:[1, 54] Operation: 51+3=54 Moving to Node #0,0 Current State: 55:[20, 1, 9], Operations: ['60-51=9'] Exploring Operation: 20-9=11, Resulting Numbers: [1, 11] Generated Node #0,0,0: 55:[1, 11] Operation: 20-9=11 Exploring Operation: 20*1=20, Resulting Numbers: [9, 20] Generated Node #0,0,1: 55:[9, 20] Operation: 20*1=20 Exploring Operation: 1+9=10, Resulting Numbers: [20, 10] Generated Node #0,0,2: 55:[20, 10] Operation: 1+9=10 Exploring Operation: 20-1=19, Resulting Numbers: [9, 19] Generated Node #0,0,3: 55:[9, 19] Operation: 20-1=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[1, 11], Operations: ['60-51=9', '20-9=11'] Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,55 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 #0,0,2 Current State: 55:[20, 10], Operations: ['60-51=9', '1+9=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,55 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,55 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 #0,0,3 Current State: 55:[9, 19], Operations: ['60-51=9', '20-1=19'] Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,55 unequal: No Solution Exploring Operation: 9*19=171, Resulting Numbers: [171] 171,55 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 #0,0,1 Current State: 55:[9, 20], Operations: ['60-51=9', '20*1=20'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 9+20=29, Resulting Numbers: [29] 29,55 unequal: No Solution Exploring Operation: 9*20=180, Resulting Numbers: [180] 180,55 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: 55:[20, 51, 59], Operations: ['60-1=59'] Exploring Operation: 20+51=71, Resulting Numbers: [59, 71] Generated Node #0,3,0: 55:[59, 71] Operation: 20+51=71 Exploring Operation: 59-20=39, Resulting Numbers: [51, 39] Generated Node #0,3,1: 55:[51, 39] Operation: 59-20=39 Exploring Operation: 51-20=31, Resulting Numbers: [59, 31] Generated Node #0,3,2: 55:[59, 31] Operation: 51-20=31 Exploring Operation: 59-51=8, Resulting Numbers: [20, 8] Generated Node #0,3,3: 55:[20, 8] Operation: 59-51=8 Moving to Node #0,2 Current State: 55:[60, 51, 19], Operations: ['20-1=19'] Exploring Operation: 60-51=9, Resulting Numbers: [19, 9] Generated Node #0,2,0: 55:[19, 9] Operation: 60-51=9 Exploring Operation: 51-19=32, Resulting Numbers: [60, 32] Generated Node #0,2,1: 55:[60, 32] Operation: 51-19=32 Exploring Operation: 60-19=41, Resulting Numbers: [51, 41] Generated Node #0,2,2: 55:[51, 41] Operation: 60-19=41 Exploring Operation: 51+19=70, Resulting Numbers: [60, 70] Generated Node #0,2,3: 55:[60, 70] Operation: 51+19=70 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 55:[19, 9], Operations: ['20-1=19', '60-51=9'] Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,55 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,55 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 #0,2,2 Current State: 55:[51, 41], Operations: ['20-1=19', '60-19=41'] Exploring Operation: 51*41=2091, Resulting Numbers: [2091] 2091,55 unequal: No Solution Exploring Operation: 51-41=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 51+41=92, Resulting Numbers: [92] 92,55 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 #0,2,3 Current State: 55:[60, 70], Operations: ['20-1=19', '51+19=70'] Exploring Operation: 60+70=130, Resulting Numbers: [130] 130,55 unequal: No Solution Exploring Operation: 60*70=4200, Resulting Numbers: [4200] 4200,55 unequal: No Solution Exploring Operation: 70-60=10, Resulting Numbers: [10] 10,55 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 #0,2,1 Current State: 55:[60, 32], Operations: ['20-1=19', '51-19=32'] Exploring Operation: 60-32=28, Resulting Numbers: [28] 28,55 unequal: No Solution Exploring Operation: 60+32=92, Resulting Numbers: [92] 92,55 unequal: No Solution Exploring Operation: 60*32=1920, Resulting Numbers: [1920] 1920,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 55:[3, 52], Operations: ['60/20=3', '1+51=52'] Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,55 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[60, 20, 1, 51], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [1, 51, 3] Generated Node #0,1: 55:[1, 51, 3] Operation: 60/20=3 Moving to Node #0,1 Current State: 55:[1, 51, 3], Operations: ['60/20=3'] Exploring Operation: 1+51=52, Resulting Numbers: [3, 52] Generated Node #0,1,0: 55:[3, 52] Operation: 1+51=52 Moving to Node #0,1,0 Current State: 55:[3, 52], Operations: ['60/20=3', '1+51=52'] Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.954861
hs_4
mult_heuristic
[ 75, 11, 3, 75 ]
30
[ "75/75=1", "11-1=10", "3*10=30" ]
Current State: 30:[75, 11, 3, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [11, 3, 1] Generated Node #2: [11, 3, 1] from Operation: 75/75=1 Current State: 30:[11, 3, 1], Operations: ['75/75=1'] Exploring Operation: 11-1=10, Resulting Numbers: [3, 10] Generated Node #3: [3, 10] from Operation: 11-1=10 Current State: 30:[3, 10], Operations: ['75/75=1', '11-1=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[75, 11, 3, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [11, 3, 1] Generated Node #0,0: 30:[11, 3, 1] Operation: 75/75=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[11, 3, 1], Operations: ['75/75=1'] Exploring Operation: 11-1=10, Resulting Numbers: [3, 10] Generated Node #0,0,0: 30:[3, 10] Operation: 11-1=10 Moving to Node #0,0,0 Current State: 30:[3, 10], Operations: ['75/75=1', '11-1=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[75, 11, 3, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [11, 3, 1] Generated Node #0,0: 30:[11, 3, 1] Operation: 75/75=1 Moving to Node #0,0 Current State: 30:[11, 3, 1], Operations: ['75/75=1'] Exploring Operation: 11-1=10, Resulting Numbers: [3, 10] Generated Node #0,0,0: 30:[3, 10] Operation: 11-1=10 Moving to Node #0,0,0 Current State: 30:[3, 10], Operations: ['75/75=1', '11-1=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 88, 55, 80, 11 ]
82
[ "55-11=44", "88/44=2", "80+2=82" ]
Current State: 82:[88, 55, 80, 11], Operations: [] Exploring Operation: 55-11=44, Resulting Numbers: [88, 80, 44] Generated Node #2: [88, 80, 44] from Operation: 55-11=44 Current State: 82:[88, 80, 44], Operations: ['55-11=44'] Exploring Operation: 88/44=2, Resulting Numbers: [80, 2] Generated Node #3: [80, 2] from Operation: 88/44=2 Current State: 82:[80, 2], Operations: ['55-11=44', '88/44=2'] Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[88, 55, 80, 11], Operations: [] Exploring Operation: 55/11=5, Resulting Numbers: [88, 80, 5] Generated Node #0,0: 82:[88, 80, 5] Operation: 55/11=5 Exploring Operation: 55-11=44, Resulting Numbers: [88, 80, 44] Generated Node #0,1: 82:[88, 80, 44] Operation: 55-11=44 Moving to Node #0,0 Current State: 82:[88, 80, 5], Operations: ['55/11=5'] Exploring Operation: 88-5=83, Resulting Numbers: [80, 83] Generated Node #0,0,0: 82:[80, 83] Operation: 88-5=83 Exploring Operation: 88-80=8, Resulting Numbers: [5, 8] Generated Node #0,0,1: 82:[5, 8] Operation: 88-80=8 Moving to Node #0,1 Current State: 82:[88, 80, 44], Operations: ['55-11=44'] Exploring Operation: 88/44=2, Resulting Numbers: [80, 2] Generated Node #0,1,0: 82:[80, 2] Operation: 88/44=2 Exploring Operation: 88-44=44, Resulting Numbers: [80, 44] Generated Node #0,1,1: 82:[80, 44] Operation: 88-44=44 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[80, 2], Operations: ['55-11=44', '88/44=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[88, 55, 80, 11], Operations: [] Exploring Operation: 55-11=44, Resulting Numbers: [88, 80, 44] Generated Node #0,1: 82:[88, 80, 44] Operation: 55-11=44 Moving to Node #0,1 Current State: 82:[88, 80, 44], Operations: ['55-11=44'] Exploring Operation: 88/44=2, Resulting Numbers: [80, 2] Generated Node #0,1,0: 82:[80, 2] Operation: 88/44=2 Moving to Node #0,1,0 Current State: 82:[80, 2], Operations: ['55-11=44', '88/44=2'] Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 13, 21, 19, 3 ]
12
[ "13+21=34", "19+3=22", "34-22=12" ]
Current State: 12:[13, 21, 19, 3], Operations: [] Exploring Operation: 13+21=34, Resulting Numbers: [19, 3, 34] Generated Node #2: [19, 3, 34] from Operation: 13+21=34 Current State: 12:[19, 3, 34], Operations: ['13+21=34'] Exploring Operation: 19+3=22, Resulting Numbers: [34, 22] Generated Node #3: [34, 22] from Operation: 19+3=22 Current State: 12:[34, 22], Operations: ['13+21=34', '19+3=22'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[13, 21, 19, 3], Operations: [] Exploring Operation: 21-13=8, Resulting Numbers: [19, 3, 8] Generated Node #0,0: 12:[19, 3, 8] Operation: 21-13=8 Exploring Operation: 21-19=2, Resulting Numbers: [13, 3, 2] Generated Node #0,1: 12:[13, 3, 2] Operation: 21-19=2 Moving to Node #0,1 Current State: 12:[13, 3, 2], Operations: ['21-19=2'] Exploring Operation: 3*2=6, Resulting Numbers: [13, 6] Generated Node #0,1,0: 12:[13, 6] Operation: 3*2=6 Exploring Operation: 13-2=11, Resulting Numbers: [3, 11] Generated Node #0,1,1: 12:[3, 11] Operation: 13-2=11 Moving to Node #0,0 Current State: 12:[19, 3, 8], Operations: ['21-13=8'] Exploring Operation: 19-8=11, Resulting Numbers: [3, 11] Generated Node #0,0,0: 12:[3, 11] Operation: 19-8=11 Exploring Operation: 19-3=16, Resulting Numbers: [8, 16] Generated Node #0,0,1: 12:[8, 16] Operation: 19-3=16 Moving to Node #0,1,0 Current State: 12:[13, 6], Operations: ['21-19=2', '3*2=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,12 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[3, 11], Operations: ['21-13=8', '19-8=11'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[3, 11], Operations: ['21-19=2', '13-2=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[8, 16], Operations: ['21-13=8', '19-3=16'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,12 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 53, 13, 91, 37 ]
97
[ "53+37=90", "91/13=7", "90+7=97" ]
Current State: 97:[53, 13, 91, 37], Operations: [] Exploring Operation: 53+37=90, Resulting Numbers: [13, 91, 90] Generated Node #2: [13, 91, 90] from Operation: 53+37=90 Current State: 97:[13, 91, 90], Operations: ['53+37=90'] Exploring Operation: 91/13=7, Resulting Numbers: [90, 7] Generated Node #3: [90, 7] from Operation: 91/13=7 Current State: 97:[90, 7], Operations: ['53+37=90', '91/13=7'] Exploring Operation: 90+7=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[53, 13, 91, 37], Operations: [] Exploring Operation: 53+37=90, Resulting Numbers: [13, 91, 90] Generated Node #0,0: 97:[13, 91, 90] Operation: 53+37=90 Exploring Operation: 13+37=50, Resulting Numbers: [53, 91, 50] Generated Node #0,1: 97:[53, 91, 50] Operation: 13+37=50 Exploring Operation: 53+13=66, Resulting Numbers: [91, 37, 66] Generated Node #0,2: 97:[91, 37, 66] Operation: 53+13=66 Moving to Node #0,0 Current State: 97:[13, 91, 90], Operations: ['53+37=90'] Exploring Operation: 13+90=103, Resulting Numbers: [91, 103] Generated Node #0,0,0: 97:[91, 103] Operation: 13+90=103 Exploring Operation: 91-13=78, Resulting Numbers: [90, 78] Generated Node #0,0,1: 97:[90, 78] Operation: 91-13=78 Exploring Operation: 13+91=104, Resulting Numbers: [90, 104] Generated Node #0,0,2: 97:[90, 104] Operation: 13+91=104 Moving to Node #0,1 Current State: 97:[53, 91, 50], Operations: ['13+37=50'] Exploring Operation: 53+50=103, Resulting Numbers: [91, 103] Generated Node #0,1,0: 97:[91, 103] Operation: 53+50=103 Exploring Operation: 53+91=144, Resulting Numbers: [50, 144] Generated Node #0,1,1: 97:[50, 144] Operation: 53+91=144 Exploring Operation: 91+50=141, Resulting Numbers: [53, 141] Generated Node #0,1,2: 97:[53, 141] Operation: 91+50=141 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[91, 103], Operations: ['13+37=50', '53+50=103'] Exploring Operation: 91*103=9373, Resulting Numbers: [9373] 9373,97 unequal: No Solution Exploring Operation: 91+103=194, Resulting Numbers: [194] 194,97 unequal: No Solution Exploring Operation: 103-91=12, Resulting Numbers: [12] 12,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[53, 141], Operations: ['13+37=50', '91+50=141'] Exploring Operation: 141-53=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 53+141=194, Resulting Numbers: [194] 194,97 unequal: No Solution Exploring Operation: 53*141=7473, Resulting Numbers: [7473] 7473,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[50, 144], Operations: ['13+37=50', '53+91=144'] Exploring Operation: 144-50=94, Resulting Numbers: [94] 94,97 unequal: No Solution Exploring Operation: 50*144=7200, Resulting Numbers: [7200] 7200,97 unequal: No Solution Exploring Operation: 50+144=194, Resulting Numbers: [194] 194,97 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: 97:[91, 37, 66], Operations: ['53+13=66'] Exploring Operation: 37+66=103, Resulting Numbers: [91, 103] Generated Node #0,2,0: 97:[91, 103] Operation: 37+66=103 Exploring Operation: 91+37=128, Resulting Numbers: [66, 128] Generated Node #0,2,1: 97:[66, 128] Operation: 91+37=128 Exploring Operation: 91-37=54, Resulting Numbers: [66, 54] Generated Node #0,2,2: 97:[66, 54] Operation: 91-37=54 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[91, 103], Operations: ['53+13=66', '37+66=103'] Exploring Operation: 91*103=9373, Resulting Numbers: [9373] 9373,97 unequal: No Solution Exploring Operation: 91+103=194, Resulting Numbers: [194] 194,97 unequal: No Solution Exploring Operation: 103-91=12, Resulting Numbers: [12] 12,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[66, 128], Operations: ['53+13=66', '91+37=128'] Exploring Operation: 66*128=8448, Resulting Numbers: [8448] 8448,97 unequal: No Solution Exploring Operation: 66+128=194, Resulting Numbers: [194] 194,97 unequal: No Solution Exploring Operation: 128-66=62, Resulting Numbers: [62] 62,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[66, 54], Operations: ['53+13=66', '91-37=54'] Exploring Operation: 66*54=3564, Resulting Numbers: [3564] 3564,97 unequal: No Solution Exploring Operation: 66+54=120, Resulting Numbers: [120] 120,97 unequal: No Solution Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,97 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: 97:[91, 103], Operations: ['53+37=90', '13+90=103'] Exploring Operation: 91*103=9373, Resulting Numbers: [9373] 9373,97 unequal: No Solution Exploring Operation: 103-91=12, Resulting Numbers: [12] 12,97 unequal: No Solution Exploring Operation: 91+103=194, Resulting Numbers: [194] 194,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[90, 104], Operations: ['53+37=90', '13+91=104'] Exploring Operation: 90*104=9360, Resulting Numbers: [9360] 9360,97 unequal: No Solution Exploring Operation: 104-90=14, Resulting Numbers: [14] 14,97 unequal: No Solution Exploring Operation: 90+104=194, Resulting Numbers: [194] 194,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[90, 78], Operations: ['53+37=90', '91-13=78'] Exploring Operation: 90+78=168, Resulting Numbers: [168] 168,97 unequal: No Solution Exploring Operation: 90-78=12, Resulting Numbers: [12] 12,97 unequal: No Solution Exploring Operation: 90*78=7020, Resulting Numbers: [7020] 7020,97 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 95, 39, 83, 39 ]
100
[ "95-39=56", "83-39=44", "56+44=100" ]
Current State: 100:[95, 39, 83, 39], Operations: [] Exploring Operation: 95-39=56, Resulting Numbers: [83, 56] Generated Node #2: [83, 56] from Operation: 95-39=56 Current State: 100:[83, 56], Operations: ['95-39=56'] Exploring Operation: 83-39=44, Resulting Numbers: [56, 44] Generated Node #3: [56, 44] from Operation: 83-39=44 Current State: 100:[56, 44], Operations: ['95-39=56', '83-39=44'] Exploring Operation: 56+44=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[95, 39, 83, 39], Operations: [] Exploring Operation: 83-39=44, Resulting Numbers: [95, 39, 44] Generated Node #0,0: 100:[95, 39, 44] Operation: 83-39=44 Exploring Operation: 83-39=44, Resulting Numbers: [95, 39, 44] Generated Node #0,1: 100:[95, 39, 44] Operation: 83-39=44 Moving to Node #0,0 Current State: 100:[95, 39, 44], Operations: ['83-39=44'] Exploring Operation: 95-39=56, Resulting Numbers: [44, 56] Generated Node #0,0,0: 100:[44, 56] Operation: 95-39=56 Exploring Operation: 44-39=5, Resulting Numbers: [95, 5] Generated Node #0,0,1: 100:[95, 5] Operation: 44-39=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[95, 5], Operations: ['83-39=44', '44-39=5'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 95+5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[95, 39, 83, 39], Operations: [] Exploring Operation: 83-39=44, Resulting Numbers: [95, 39, 44] Generated Node #0,0: 100:[95, 39, 44] Operation: 83-39=44 Moving to Node #0,0 Current State: 100:[95, 39, 44], Operations: ['83-39=44'] Exploring Operation: 44-39=5, Resulting Numbers: [95, 5] Generated Node #0,0,1: 100:[95, 5] Operation: 44-39=5 Moving to Node #0,0,1 Current State: 100:[95, 5], Operations: ['83-39=44', '44-39=5'] Exploring Operation: 95+5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 70, 4, 82, 44 ]
60
[ "70-4=66", "82+44=126", "126-66=60" ]
Current State: 60:[70, 4, 82, 44], Operations: [] Exploring Operation: 70-4=66, Resulting Numbers: [82, 44, 66] Generated Node #2: [82, 44, 66] from Operation: 70-4=66 Current State: 60:[82, 44, 66], Operations: ['70-4=66'] Exploring Operation: 82+44=126, Resulting Numbers: [66, 126] Generated Node #3: [66, 126] from Operation: 82+44=126 Current State: 60:[66, 126], Operations: ['70-4=66', '82+44=126'] Exploring Operation: 126-66=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[70, 4, 82, 44], Operations: [] Exploring Operation: 82-70=12, Resulting Numbers: [4, 44, 12] Generated Node #0,0: 60:[4, 44, 12] Operation: 82-70=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[4, 44, 12], Operations: ['82-70=12'] Exploring Operation: 44/4=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 60:[12, 11] Operation: 44/4=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[12, 11], Operations: ['82-70=12', '44/4=11'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,60 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
[ 36, 63, 50, 38 ]
66
[ "50-38=12", "36/12=3", "63+3=66" ]
Current State: 66:[36, 63, 50, 38], Operations: [] Exploring Operation: 50-38=12, Resulting Numbers: [36, 63, 12] Generated Node #2: [36, 63, 12] from Operation: 50-38=12 Current State: 66:[36, 63, 12], Operations: ['50-38=12'] Exploring Operation: 36/12=3, Resulting Numbers: [63, 3] Generated Node #3: [63, 3] from Operation: 36/12=3 Current State: 66:[63, 3], Operations: ['50-38=12', '36/12=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[36, 63, 50, 38], Operations: [] Exploring Operation: 50-38=12, Resulting Numbers: [36, 63, 12] Generated Node #0,0: 66:[36, 63, 12] Operation: 50-38=12 Exploring Operation: 63-50=13, Resulting Numbers: [36, 38, 13] Generated Node #0,1: 66:[36, 38, 13] Operation: 63-50=13 Exploring Operation: 50-36=14, Resulting Numbers: [63, 38, 14] Generated Node #0,2: 66:[63, 38, 14] Operation: 50-36=14 Exploring Operation: 38-36=2, Resulting Numbers: [63, 50, 2] Generated Node #0,3: 66:[63, 50, 2] Operation: 38-36=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[36, 63, 12], Operations: ['50-38=12'] Exploring Operation: 63-36=27, Resulting Numbers: [12, 27] Generated Node #0,0,0: 66:[12, 27] Operation: 63-36=27 Exploring Operation: 63+12=75, Resulting Numbers: [36, 75] Generated Node #0,0,1: 66:[36, 75] Operation: 63+12=75 Exploring Operation: 36-12=24, Resulting Numbers: [63, 24] Generated Node #0,0,2: 66:[63, 24] Operation: 36-12=24 Exploring Operation: 36/12=3, Resulting Numbers: [63, 3] Generated Node #0,0,3: 66:[63, 3] Operation: 36/12=3 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 66:[63, 3], Operations: ['50-38=12', '36/12=3'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,66 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,66 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[36, 63, 50, 38], Operations: [] Exploring Operation: 50-38=12, Resulting Numbers: [36, 63, 12] Generated Node #0,0: 66:[36, 63, 12] Operation: 50-38=12 Moving to Node #0,0 Current State: 66:[36, 63, 12], Operations: ['50-38=12'] Exploring Operation: 36/12=3, Resulting Numbers: [63, 3] Generated Node #0,0,3: 66:[63, 3] Operation: 36/12=3 Moving to Node #0,0,3 Current State: 66:[63, 3], Operations: ['50-38=12', '36/12=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 62, 71, 72, 16 ]
72
[ "71-62=9", "16*9=144", "144-72=72" ]
Current State: 72:[62, 71, 72, 16], Operations: [] Exploring Operation: 71-62=9, Resulting Numbers: [72, 16, 9] Generated Node #2: [72, 16, 9] from Operation: 71-62=9 Current State: 72:[72, 16, 9], Operations: ['71-62=9'] Exploring Operation: 16*9=144, Resulting Numbers: [72, 144] Generated Node #3: [72, 144] from Operation: 16*9=144 Current State: 72:[72, 144], Operations: ['71-62=9', '16*9=144'] Exploring Operation: 144-72=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[62, 71, 72, 16], Operations: [] Exploring Operation: 72-62=10, Resulting Numbers: [71, 16, 10] Generated Node #0,0: 72:[71, 16, 10] Operation: 72-62=10 Exploring Operation: 71-62=9, Resulting Numbers: [72, 16, 9] Generated Node #0,1: 72:[72, 16, 9] Operation: 71-62=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[72, 16, 9], Operations: ['71-62=9'] Exploring Operation: 16-9=7, Resulting Numbers: [72, 7] Generated Node #0,1,0: 72:[72, 7] Operation: 16-9=7 Exploring Operation: 16+9=25, Resulting Numbers: [72, 25] Generated Node #0,1,1: 72:[72, 25] Operation: 16+9=25 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[72, 7], Operations: ['71-62=9', '16-9=7'] Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[72, 25], Operations: ['71-62=9', '16+9=25'] Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[71, 16, 10], Operations: ['72-62=10'] Exploring Operation: 16-10=6, Resulting Numbers: [71, 6] Generated Node #0,0,0: 72:[71, 6] Operation: 16-10=6 Exploring Operation: 16+10=26, Resulting Numbers: [71, 26] Generated Node #0,0,1: 72:[71, 26] Operation: 16+10=26 Moving to Node #0,0,0 Current State: 72:[71, 6], Operations: ['72-62=10', '16-10=6'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,72 unequal: No Solution Exploring Operation: 71+6=77, Resulting Numbers: [77] 77,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[71, 26], Operations: ['72-62=10', '16+10=26'] Exploring Operation: 71-26=45, Resulting Numbers: [45] 45,72 unequal: No Solution Exploring Operation: 71+26=97, Resulting Numbers: [97] 97,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 25, 73, 12, 65 ]
78
[ "25-12=13", "65/13=5", "73+5=78" ]
Current State: 78:[25, 73, 12, 65], Operations: [] Exploring Operation: 25-12=13, Resulting Numbers: [73, 65, 13] Generated Node #2: [73, 65, 13] from Operation: 25-12=13 Current State: 78:[73, 65, 13], Operations: ['25-12=13'] Exploring Operation: 65/13=5, Resulting Numbers: [73, 5] Generated Node #3: [73, 5] from Operation: 65/13=5 Current State: 78:[73, 5], Operations: ['25-12=13', '65/13=5'] Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[25, 73, 12, 65], Operations: [] Exploring Operation: 73-65=8, Resulting Numbers: [25, 12, 8] Generated Node #0,0: 78:[25, 12, 8] Operation: 73-65=8 Exploring Operation: 65-25=40, Resulting Numbers: [73, 12, 40] Generated Node #0,1: 78:[73, 12, 40] Operation: 65-25=40 Moving to Node #0,0 Current State: 78:[25, 12, 8], Operations: ['73-65=8'] Exploring Operation: 12-8=4, Resulting Numbers: [25, 4] Generated Node #0,0,0: 78:[25, 4] Operation: 12-8=4 Exploring Operation: 25-12=13, Resulting Numbers: [8, 13] Generated Node #0,0,1: 78:[8, 13] Operation: 25-12=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[25, 4], Operations: ['73-65=8', '12-8=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,78 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[8, 13], Operations: ['73-65=8', '25-12=13'] Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,78 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,78 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: 78:[73, 12, 40], Operations: ['65-25=40'] Exploring Operation: 40-12=28, Resulting Numbers: [73, 28] Generated Node #0,1,0: 78:[73, 28] Operation: 40-12=28 Exploring Operation: 73-40=33, Resulting Numbers: [12, 33] Generated Node #0,1,1: 78:[12, 33] Operation: 73-40=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[73, 28], Operations: ['65-25=40', '40-12=28'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[12, 33], Operations: ['65-25=40', '73-40=33'] Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,78 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,78 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
[ 74, 97, 41, 15 ]
49
[ "97-74=23", "41-15=26", "23+26=49" ]
Current State: 49:[74, 97, 41, 15], Operations: [] Exploring Operation: 97-74=23, Resulting Numbers: [41, 15, 23] Generated Node #2: [41, 15, 23] from Operation: 97-74=23 Current State: 49:[41, 15, 23], Operations: ['97-74=23'] Exploring Operation: 41-15=26, Resulting Numbers: [23, 26] Generated Node #3: [23, 26] from Operation: 41-15=26 Current State: 49:[23, 26], Operations: ['97-74=23', '41-15=26'] Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[74, 97, 41, 15], Operations: [] Exploring Operation: 74-41=33, Resulting Numbers: [97, 15, 33] Generated Node #0,0: 49:[97, 15, 33] Operation: 74-41=33 Exploring Operation: 74-15=59, Resulting Numbers: [97, 41, 59] Generated Node #0,1: 49:[97, 41, 59] Operation: 74-15=59 Exploring Operation: 97-74=23, Resulting Numbers: [41, 15, 23] Generated Node #0,2: 49:[41, 15, 23] Operation: 97-74=23 Exploring Operation: 97-15=82, Resulting Numbers: [74, 41, 82] Generated Node #0,3: 49:[74, 41, 82] Operation: 97-15=82 Exploring Operation: 97-41=56, Resulting Numbers: [74, 15, 56] Generated Node #0,4: 49:[74, 15, 56] Operation: 97-41=56 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[41, 15, 23], Operations: ['97-74=23'] Exploring Operation: 23-15=8, Resulting Numbers: [41, 8] Generated Node #0,2,0: 49:[41, 8] Operation: 23-15=8 Exploring Operation: 15+23=38, Resulting Numbers: [41, 38] Generated Node #0,2,1: 49:[41, 38] Operation: 15+23=38 Exploring Operation: 41+23=64, Resulting Numbers: [15, 64] Generated Node #0,2,2: 49:[15, 64] Operation: 41+23=64 Exploring Operation: 41+15=56, Resulting Numbers: [23, 56] Generated Node #0,2,3: 49:[23, 56] Operation: 41+15=56 Exploring Operation: 41-23=18, Resulting Numbers: [15, 18] Generated Node #0,2,4: 49:[15, 18] Operation: 41-23=18 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 49:[41, 8], Operations: ['97-74=23', '23-15=8'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,49 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[74, 97, 41, 15], Operations: [] Exploring Operation: 97-74=23, Resulting Numbers: [41, 15, 23] Generated Node #0,2: 49:[41, 15, 23] Operation: 97-74=23 Moving to Node #0,2 Current State: 49:[41, 15, 23], Operations: ['97-74=23'] Exploring Operation: 23-15=8, Resulting Numbers: [41, 8] Generated Node #0,2,0: 49:[41, 8] Operation: 23-15=8 Moving to Node #0,2,0 Current State: 49:[41, 8], Operations: ['97-74=23', '23-15=8'] Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 82, 13, 64, 56 ]
61
[ "82-13=69", "64-56=8", "69-8=61" ]
Current State: 61:[82, 13, 64, 56], Operations: [] Exploring Operation: 82-13=69, Resulting Numbers: [64, 56, 69] Generated Node #2: [64, 56, 69] from Operation: 82-13=69 Current State: 61:[64, 56, 69], Operations: ['82-13=69'] Exploring Operation: 64-56=8, Resulting Numbers: [69, 8] Generated Node #3: [69, 8] from Operation: 64-56=8 Current State: 61:[69, 8], Operations: ['82-13=69', '64-56=8'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[82, 13, 64, 56], Operations: [] Exploring Operation: 82-13=69, Resulting Numbers: [64, 56, 69] Generated Node #0,0: 61:[64, 56, 69] Operation: 82-13=69 Exploring Operation: 13+56=69, Resulting Numbers: [82, 64, 69] Generated Node #0,1: 61:[82, 64, 69] Operation: 13+56=69 Moving to Node #0,0 Current State: 61:[64, 56, 69], Operations: ['82-13=69'] Exploring Operation: 69-56=13, Resulting Numbers: [64, 13] Generated Node #0,0,0: 61:[64, 13] Operation: 69-56=13 Exploring Operation: 64-56=8, Resulting Numbers: [69, 8] Generated Node #0,0,1: 61:[69, 8] Operation: 64-56=8 Moving to Node #0,1 Current State: 61:[82, 64, 69], Operations: ['13+56=69'] Exploring Operation: 82-69=13, Resulting Numbers: [64, 13] Generated Node #0,1,0: 61:[64, 13] Operation: 82-69=13 Exploring Operation: 82-64=18, Resulting Numbers: [69, 18] Generated Node #0,1,1: 61:[69, 18] Operation: 82-64=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[64, 13], Operations: ['13+56=69', '82-69=13'] Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,61 unequal: No Solution Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,61 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 #0,1,1 Current State: 61:[69, 18], Operations: ['13+56=69', '82-64=18'] Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,61 unequal: No Solution Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,61 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: 61:[64, 13], Operations: ['82-13=69', '69-56=13'] Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,61 unequal: No Solution Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[69, 8], Operations: ['82-13=69', '64-56=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,61 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[82, 13, 64, 56], Operations: [] Exploring Operation: 82-13=69, Resulting Numbers: [64, 56, 69] Generated Node #0,0: 61:[64, 56, 69] Operation: 82-13=69 Moving to Node #0,0 Current State: 61:[64, 56, 69], Operations: ['82-13=69'] Exploring Operation: 64-56=8, Resulting Numbers: [69, 8] Generated Node #0,0,1: 61:[69, 8] Operation: 64-56=8 Moving to Node #0,0,1 Current State: 61:[69, 8], Operations: ['82-13=69', '64-56=8'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 5, 88, 63, 45 ]
74
[ "5*45=225", "88+63=151", "225-151=74" ]
Current State: 74:[5, 88, 63, 45], Operations: [] Exploring Operation: 5*45=225, Resulting Numbers: [88, 63, 225] Generated Node #2: [88, 63, 225] from Operation: 5*45=225 Current State: 74:[88, 63, 225], Operations: ['5*45=225'] Exploring Operation: 88+63=151, Resulting Numbers: [225, 151] Generated Node #3: [225, 151] from Operation: 88+63=151 Current State: 74:[225, 151], Operations: ['5*45=225', '88+63=151'] Exploring Operation: 225-151=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[5, 88, 63, 45], Operations: [] Exploring Operation: 88-45=43, Resulting Numbers: [5, 63, 43] Generated Node #0,0: 74:[5, 63, 43] Operation: 88-45=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[5, 63, 43], Operations: ['88-45=43'] Exploring Operation: 5+63=68, Resulting Numbers: [43, 68] Generated Node #0,0,0: 74:[43, 68] Operation: 5+63=68 Moving to Node #0,0,0 Current State: 74:[43, 68], Operations: ['88-45=43', '5+63=68'] Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,74 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
[ 67, 61, 2, 84 ]
80
[ "67-61=6", "2+84=86", "86-6=80" ]
Current State: 80:[67, 61, 2, 84], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [2, 84, 6] Generated Node #2: [2, 84, 6] from Operation: 67-61=6 Current State: 80:[2, 84, 6], Operations: ['67-61=6'] Exploring Operation: 2+84=86, Resulting Numbers: [6, 86] Generated Node #3: [6, 86] from Operation: 2+84=86 Current State: 80:[6, 86], Operations: ['67-61=6', '2+84=86'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[67, 61, 2, 84], Operations: [] Exploring Operation: 61+2=63, Resulting Numbers: [67, 84, 63] Generated Node #0,0: 80:[67, 84, 63] Operation: 61+2=63 Exploring Operation: 84-67=17, Resulting Numbers: [61, 2, 17] Generated Node #0,1: 80:[61, 2, 17] Operation: 84-67=17 Exploring Operation: 84-61=23, Resulting Numbers: [67, 2, 23] Generated Node #0,2: 80:[67, 2, 23] Operation: 84-61=23 Exploring Operation: 67-61=6, Resulting Numbers: [2, 84, 6] Generated Node #0,3: 80:[2, 84, 6] Operation: 67-61=6 Exploring Operation: 67+2=69, Resulting Numbers: [61, 84, 69] Generated Node #0,4: 80:[61, 84, 69] Operation: 67+2=69 Moving to Node #0,3 Current State: 80:[2, 84, 6], Operations: ['67-61=6'] Exploring Operation: 2+6=8, Resulting Numbers: [84, 8] Generated Node #0,3,0: 80:[84, 8] Operation: 2+6=8 Exploring Operation: 84/2=42, Resulting Numbers: [6, 42] Generated Node #0,3,1: 80:[6, 42] Operation: 84/2=42 Exploring Operation: 84-6=78, Resulting Numbers: [2, 78] Generated Node #0,3,2: 80:[2, 78] Operation: 84-6=78 Exploring Operation: 84-2=82, Resulting Numbers: [6, 82] Generated Node #0,3,3: 80:[6, 82] Operation: 84-2=82 Exploring Operation: 84/6=14, Resulting Numbers: [2, 14] Generated Node #0,3,4: 80:[2, 14] Operation: 84/6=14 Moving to Node #0,2 Current State: 80:[67, 2, 23], Operations: ['84-61=23'] Exploring Operation: 67-23=44, Resulting Numbers: [2, 44] Generated Node #0,2,0: 80:[2, 44] Operation: 67-23=44 Exploring Operation: 67+23=90, Resulting Numbers: [2, 90] Generated Node #0,2,1: 80:[2, 90] Operation: 67+23=90 Exploring Operation: 67+2=69, Resulting Numbers: [23, 69] Generated Node #0,2,2: 80:[23, 69] Operation: 67+2=69 Exploring Operation: 67-2=65, Resulting Numbers: [23, 65] Generated Node #0,2,3: 80:[23, 65] Operation: 67-2=65 Exploring Operation: 23-2=21, Resulting Numbers: [67, 21] Generated Node #0,2,4: 80:[67, 21] Operation: 23-2=21 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[2, 44], Operations: ['84-61=23', '67-23=44'] Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,80 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,80 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[2, 90], Operations: ['84-61=23', '67+23=90'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,80 unequal: No Solution Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,80 unequal: No Solution Exploring Operation: 2*90=180, Resulting Numbers: [180] 180,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[23, 69], Operations: ['84-61=23', '67+2=69'] Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,80 unequal: No Solution Exploring Operation: 23*69=1587, Resulting Numbers: [1587] 1587,80 unequal: No Solution Exploring Operation: 23+69=92, Resulting Numbers: [92] 92,80 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 80:[67, 21], Operations: ['84-61=23', '23-2=21'] Exploring Operation: 67+21=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 67*21=1407, Resulting Numbers: [1407] 1407,80 unequal: No Solution Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[23, 65], Operations: ['84-61=23', '67-2=65'] Exploring Operation: 23*65=1495, Resulting Numbers: [1495] 1495,80 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,80 unequal: No Solution Exploring Operation: 23+65=88, Resulting Numbers: [88] 88,80 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: 80:[61, 2, 17], Operations: ['84-67=17'] Exploring Operation: 2+17=19, Resulting Numbers: [61, 19] Generated Node #0,1,0: 80:[61, 19] Operation: 2+17=19 Exploring Operation: 61-2=59, Resulting Numbers: [17, 59] Generated Node #0,1,1: 80:[17, 59] Operation: 61-2=59 Exploring Operation: 61-17=44, Resulting Numbers: [2, 44] Generated Node #0,1,2: 80:[2, 44] Operation: 61-17=44 Exploring Operation: 61+2=63, Resulting Numbers: [17, 63] Generated Node #0,1,3: 80:[17, 63] Operation: 61+2=63 Exploring Operation: 61+17=78, Resulting Numbers: [2, 78] Generated Node #0,1,4: 80:[2, 78] Operation: 61+17=78 Moving to Node #0,0 Current State: 80:[67, 84, 63], Operations: ['61+2=63'] Exploring Operation: 67+63=130, Resulting Numbers: [84, 130] Generated Node #0,0,0: 80:[84, 130] Operation: 67+63=130 Exploring Operation: 84-67=17, Resulting Numbers: [63, 17] Generated Node #0,0,1: 80:[63, 17] Operation: 84-67=17 Exploring Operation: 84+63=147, Resulting Numbers: [67, 147] Generated Node #0,0,2: 80:[67, 147] Operation: 84+63=147 Exploring Operation: 67-63=4, Resulting Numbers: [84, 4] Generated Node #0,0,3: 80:[84, 4] Operation: 67-63=4 Exploring Operation: 84-63=21, Resulting Numbers: [67, 21] Generated Node #0,0,4: 80:[67, 21] Operation: 84-63=21 Moving to Node #0,4 Current State: 80:[61, 84, 69], Operations: ['67+2=69'] Exploring Operation: 61+69=130, Resulting Numbers: [84, 130] Generated Node #0,4,0: 80:[84, 130] Operation: 61+69=130 Exploring Operation: 84-61=23, Resulting Numbers: [69, 23] Generated Node #0,4,1: 80:[69, 23] Operation: 84-61=23 Exploring Operation: 84-69=15, Resulting Numbers: [61, 15] Generated Node #0,4,2: 80:[61, 15] Operation: 84-69=15 Exploring Operation: 69-61=8, Resulting Numbers: [84, 8] Generated Node #0,4,3: 80:[84, 8] Operation: 69-61=8 Exploring Operation: 61+84=145, Resulting Numbers: [69, 145] Generated Node #0,4,4: 80:[69, 145] Operation: 61+84=145 Moving to Node #0,3,2 Current State: 80:[2, 78], Operations: ['67-61=6', '84-6=78'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,80 unequal: No Solution Exploring Operation: 2*78=156, Resulting Numbers: [156] 156,80 unequal: No Solution Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[67, 61, 2, 84], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [2, 84, 6] Generated Node #0,3: 80:[2, 84, 6] Operation: 67-61=6 Moving to Node #0,3 Current State: 80:[2, 84, 6], Operations: ['67-61=6'] Exploring Operation: 84-6=78, Resulting Numbers: [2, 78] Generated Node #0,3,2: 80:[2, 78] Operation: 84-6=78 Moving to Node #0,3,2 Current State: 80:[2, 78], Operations: ['67-61=6', '84-6=78'] Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
0.952257
hs_5
sum_heuristic
[ 20, 9, 81, 63 ]
54
[ "81-20=61", "63/9=7", "61-7=54" ]
Current State: 54:[20, 9, 81, 63], Operations: [] Exploring Operation: 81-20=61, Resulting Numbers: [9, 63, 61] Generated Node #2: [9, 63, 61] from Operation: 81-20=61 Current State: 54:[9, 63, 61], Operations: ['81-20=61'] Exploring Operation: 63/9=7, Resulting Numbers: [61, 7] Generated Node #3: [61, 7] from Operation: 63/9=7 Current State: 54:[61, 7], Operations: ['81-20=61', '63/9=7'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[20, 9, 81, 63], Operations: [] Exploring Operation: 81-63=18, Resulting Numbers: [20, 9, 18] Generated Node #0,0: 54:[20, 9, 18] Operation: 81-63=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[20, 9, 18], Operations: ['81-63=18'] Exploring Operation: 20-18=2, Resulting Numbers: [9, 2] Generated Node #0,0,0: 54:[9, 2] Operation: 20-18=2 Moving to Node #0,0,0 Current State: 54:[9, 2], Operations: ['81-63=18', '20-18=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,54 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
[ 64, 14, 46, 61 ]
96
[ "64-61=3", "46-14=32", "3*32=96" ]
Current State: 96:[64, 14, 46, 61], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [14, 46, 3] Generated Node #2: [14, 46, 3] from Operation: 64-61=3 Current State: 96:[14, 46, 3], Operations: ['64-61=3'] Exploring Operation: 46-14=32, Resulting Numbers: [3, 32] Generated Node #3: [3, 32] from Operation: 46-14=32 Current State: 96:[3, 32], Operations: ['64-61=3', '46-14=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[64, 14, 46, 61], Operations: [] Exploring Operation: 64-46=18, Resulting Numbers: [14, 61, 18] Generated Node #0,0: 96:[14, 61, 18] Operation: 64-46=18 Exploring Operation: 64-61=3, Resulting Numbers: [14, 46, 3] Generated Node #0,1: 96:[14, 46, 3] Operation: 64-61=3 Exploring Operation: 64-14=50, Resulting Numbers: [46, 61, 50] Generated Node #0,2: 96:[46, 61, 50] Operation: 64-14=50 Moving to Node #0,1 Current State: 96:[14, 46, 3], Operations: ['64-61=3'] Exploring Operation: 14-3=11, Resulting Numbers: [46, 11] Generated Node #0,1,0: 96:[46, 11] Operation: 14-3=11 Exploring Operation: 46-14=32, Resulting Numbers: [3, 32] Generated Node #0,1,1: 96:[3, 32] Operation: 46-14=32 Exploring Operation: 14+3=17, Resulting Numbers: [46, 17] Generated Node #0,1,2: 96:[46, 17] Operation: 14+3=17 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[3, 32], Operations: ['64-61=3', '46-14=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[64, 14, 46, 61], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [14, 46, 3] Generated Node #0,1: 96:[14, 46, 3] Operation: 64-61=3 Moving to Node #0,1 Current State: 96:[14, 46, 3], Operations: ['64-61=3'] Exploring Operation: 46-14=32, Resulting Numbers: [3, 32] Generated Node #0,1,1: 96:[3, 32] Operation: 46-14=32 Moving to Node #0,1,1 Current State: 96:[3, 32], Operations: ['64-61=3', '46-14=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 92, 77, 31, 94 ]
92
[ "94-92=2", "77-31=46", "2*46=92" ]
Current State: 92:[92, 77, 31, 94], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [77, 31, 2] Generated Node #2: [77, 31, 2] from Operation: 94-92=2 Current State: 92:[77, 31, 2], Operations: ['94-92=2'] Exploring Operation: 77-31=46, Resulting Numbers: [2, 46] Generated Node #3: [2, 46] from Operation: 77-31=46 Current State: 92:[2, 46], Operations: ['94-92=2', '77-31=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[92, 77, 31, 94], Operations: [] Exploring Operation: 77-31=46, Resulting Numbers: [92, 94, 46] Generated Node #0,0: 92:[92, 94, 46] Operation: 77-31=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[92, 94, 46], Operations: ['77-31=46'] Exploring Operation: 94-92=2, Resulting Numbers: [46, 2] Generated Node #0,0,0: 92:[46, 2] Operation: 94-92=2 Moving to Node #0,0,0 Current State: 92:[46, 2], Operations: ['77-31=46', '94-92=2'] Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[92, 77, 31, 94], Operations: [] Exploring Operation: 77-31=46, Resulting Numbers: [92, 94, 46] Generated Node #0,0: 92:[92, 94, 46] Operation: 77-31=46 Moving to Node #0,0 Current State: 92:[92, 94, 46], Operations: ['77-31=46'] Exploring Operation: 94-92=2, Resulting Numbers: [46, 2] Generated Node #0,0,0: 92:[46, 2] Operation: 94-92=2 Moving to Node #0,0,0 Current State: 92:[46, 2], Operations: ['77-31=46', '94-92=2'] Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 39, 7, 2, 91 ]
47
[ "39+7=46", "2+91=93", "93-46=47" ]
Current State: 47:[39, 7, 2, 91], Operations: [] Exploring Operation: 39+7=46, Resulting Numbers: [2, 91, 46] Generated Node #2: [2, 91, 46] from Operation: 39+7=46 Current State: 47:[2, 91, 46], Operations: ['39+7=46'] Exploring Operation: 2+91=93, Resulting Numbers: [46, 93] Generated Node #3: [46, 93] from Operation: 2+91=93 Current State: 47:[46, 93], Operations: ['39+7=46', '2+91=93'] Exploring Operation: 93-46=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[39, 7, 2, 91], Operations: [] Exploring Operation: 91/7=13, Resulting Numbers: [39, 2, 13] Generated Node #0,0: 47:[39, 2, 13] Operation: 91/7=13 Exploring Operation: 39+2=41, Resulting Numbers: [7, 91, 41] Generated Node #0,1: 47:[7, 91, 41] Operation: 39+2=41 Exploring Operation: 7*2=14, Resulting Numbers: [39, 91, 14] Generated Node #0,2: 47:[39, 91, 14] Operation: 7*2=14 Exploring Operation: 39+7=46, Resulting Numbers: [2, 91, 46] Generated Node #0,3: 47:[2, 91, 46] Operation: 39+7=46 Moving to Node #0,2 Current State: 47:[39, 91, 14], Operations: ['7*2=14'] Exploring Operation: 39-14=25, Resulting Numbers: [91, 25] Generated Node #0,2,0: 47:[91, 25] Operation: 39-14=25 Exploring Operation: 39+14=53, Resulting Numbers: [91, 53] Generated Node #0,2,1: 47:[91, 53] Operation: 39+14=53 Exploring Operation: 91-39=52, Resulting Numbers: [14, 52] Generated Node #0,2,2: 47:[14, 52] Operation: 91-39=52 Exploring Operation: 91-14=77, Resulting Numbers: [39, 77] Generated Node #0,2,3: 47:[39, 77] Operation: 91-14=77 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[14, 52], Operations: ['7*2=14', '91-39=52'] Exploring Operation: 14*52=728, Resulting Numbers: [728] 728,47 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,47 unequal: No Solution Exploring Operation: 14+52=66, Resulting Numbers: [66] 66,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 47:[39, 77], Operations: ['7*2=14', '91-14=77'] Exploring Operation: 39*77=3003, Resulting Numbers: [3003] 3003,47 unequal: No Solution Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,47 unequal: No Solution Exploring Operation: 39+77=116, Resulting Numbers: [116] 116,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[91, 53], Operations: ['7*2=14', '39+14=53'] Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,47 unequal: No Solution Exploring Operation: 91+53=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 91*53=4823, Resulting Numbers: [4823] 4823,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[91, 25], Operations: ['7*2=14', '39-14=25'] Exploring Operation: 91+25=116, Resulting Numbers: [116] 116,47 unequal: No Solution Exploring Operation: 91-25=66, Resulting Numbers: [66] 66,47 unequal: No Solution Exploring Operation: 91*25=2275, Resulting Numbers: [2275] 2275,47 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: 47:[39, 2, 13], Operations: ['91/7=13'] Exploring Operation: 2+13=15, Resulting Numbers: [39, 15] Generated Node #0,0,0: 47:[39, 15] Operation: 2+13=15 Exploring Operation: 39-2=37, Resulting Numbers: [13, 37] Generated Node #0,0,1: 47:[13, 37] Operation: 39-2=37 Exploring Operation: 39+2=41, Resulting Numbers: [13, 41] Generated Node #0,0,2: 47:[13, 41] Operation: 39+2=41 Exploring Operation: 2*13=26, Resulting Numbers: [39, 26] Generated Node #0,0,3: 47:[39, 26] Operation: 2*13=26 Moving to Node #0,3 Current State: 47:[2, 91, 46], Operations: ['39+7=46'] Exploring Operation: 46-2=44, Resulting Numbers: [91, 44] Generated Node #0,3,0: 47:[91, 44] Operation: 46-2=44 Exploring Operation: 2+46=48, Resulting Numbers: [91, 48] Generated Node #0,3,1: 47:[91, 48] Operation: 2+46=48 Exploring Operation: 2+91=93, Resulting Numbers: [46, 93] Generated Node #0,3,2: 47:[46, 93] Operation: 2+91=93 Exploring Operation: 91-2=89, Resulting Numbers: [46, 89] Generated Node #0,3,3: 47:[46, 89] Operation: 91-2=89 Moving to Node #0,1 Current State: 47:[7, 91, 41], Operations: ['39+2=41'] Exploring Operation: 91/7=13, Resulting Numbers: [41, 13] Generated Node #0,1,0: 47:[41, 13] Operation: 91/7=13 Exploring Operation: 91-7=84, Resulting Numbers: [41, 84] Generated Node #0,1,1: 47:[41, 84] Operation: 91-7=84 Exploring Operation: 7+41=48, Resulting Numbers: [91, 48] Generated Node #0,1,2: 47:[91, 48] Operation: 7+41=48 Exploring Operation: 91-41=50, Resulting Numbers: [7, 50] Generated Node #0,1,3: 47:[7, 50] Operation: 91-41=50 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[41, 13], Operations: ['39+2=41', '91/7=13'] Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,47 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[41, 84], Operations: ['39+2=41', '91-7=84'] Exploring Operation: 41*84=3444, Resulting Numbers: [3444] 3444,47 unequal: No Solution Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 41+84=125, Resulting Numbers: [125] 125,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 47:[7, 50], Operations: ['39+2=41', '91-41=50'] Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,47 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[91, 48], Operations: ['39+2=41', '7+41=48'] Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 91+48=139, Resulting Numbers: [139] 139,47 unequal: No Solution Exploring Operation: 91*48=4368, Resulting Numbers: [4368] 4368,47 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: 47:[39, 26], Operations: ['91/7=13', '2*13=26'] Exploring Operation: 39+26=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 39*26=1014, Resulting Numbers: [1014] 1014,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[13, 41], Operations: ['91/7=13', '39+2=41'] Exploring Operation: 13*41=533, Resulting Numbers: [533] 533,47 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 13+41=54, Resulting Numbers: [54] 54,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[39, 15], Operations: ['91/7=13', '2+13=15'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,47 unequal: No Solution Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[46, 89], Operations: ['39+7=46', '91-2=89'] Exploring Operation: 46*89=4094, Resulting Numbers: [4094] 4094,47 unequal: No Solution Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 46+89=135, Resulting Numbers: [135] 135,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[13, 37], Operations: ['91/7=13', '39-2=37'] Exploring Operation: 13+37=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 13*37=481, Resulting Numbers: [481] 481,47 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,47 unequal: No Solution Moving to Node #0,3,1 Current State: 47:[91, 48], Operations: ['39+7=46', '2+46=48'] Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 91+48=139, Resulting Numbers: [139] 139,47 unequal: No Solution Exploring Operation: 91*48=4368, Resulting Numbers: [4368] 4368,47 unequal: No Solution Moving to Node #0,3,2 Current State: 47:[46, 93], Operations: ['39+7=46', '2+91=93'] Exploring Operation: 46+93=139, Resulting Numbers: [139] 139,47 unequal: No Solution Exploring Operation: 93-46=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[39, 7, 2, 91], Operations: [] Exploring Operation: 39+7=46, Resulting Numbers: [2, 91, 46] Generated Node #0,3: 47:[2, 91, 46] Operation: 39+7=46 Moving to Node #0,3 Current State: 47:[2, 91, 46], Operations: ['39+7=46'] Exploring Operation: 2+91=93, Resulting Numbers: [46, 93] Generated Node #0,3,2: 47:[46, 93] Operation: 2+91=93 Moving to Node #0,3,2 Current State: 47:[46, 93], Operations: ['39+7=46', '2+91=93'] Exploring Operation: 93-46=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
0.940972
hs_4
mult_heuristic
[ 45, 14, 43, 47 ]
15
[ "47-45=2", "14*2=28", "43-28=15" ]
Current State: 15:[45, 14, 43, 47], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [14, 43, 2] Generated Node #2: [14, 43, 2] from Operation: 47-45=2 Current State: 15:[14, 43, 2], Operations: ['47-45=2'] Exploring Operation: 14*2=28, Resulting Numbers: [43, 28] Generated Node #3: [43, 28] from Operation: 14*2=28 Current State: 15:[43, 28], Operations: ['47-45=2', '14*2=28'] Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[45, 14, 43, 47], Operations: [] Exploring Operation: 45-43=2, Resulting Numbers: [14, 47, 2] Generated Node #0,0: 15:[14, 47, 2] Operation: 45-43=2 Exploring Operation: 47-45=2, Resulting Numbers: [14, 43, 2] Generated Node #0,1: 15:[14, 43, 2] Operation: 47-45=2 Exploring Operation: 45-14=31, Resulting Numbers: [43, 47, 31] Generated Node #0,2: 15:[43, 47, 31] Operation: 45-14=31 Exploring Operation: 47-43=4, Resulting Numbers: [45, 14, 4] Generated Node #0,3: 15:[45, 14, 4] Operation: 47-43=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[14, 43, 2], Operations: ['47-45=2'] Exploring Operation: 43-2=41, Resulting Numbers: [14, 41] Generated Node #0,1,0: 15:[14, 41] Operation: 43-2=41 Exploring Operation: 43-14=29, Resulting Numbers: [2, 29] Generated Node #0,1,1: 15:[2, 29] Operation: 43-14=29 Exploring Operation: 14/2=7, Resulting Numbers: [43, 7] Generated Node #0,1,2: 15:[43, 7] Operation: 14/2=7 Exploring Operation: 14+2=16, Resulting Numbers: [43, 16] Generated Node #0,1,3: 15:[43, 16] Operation: 14+2=16 Moving to Node #0,1,1 Current State: 15:[2, 29], Operations: ['47-45=2', '43-14=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,15 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[14, 41], Operations: ['47-45=2', '43-2=41'] Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,15 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[43, 16], Operations: ['47-45=2', '14+2=16'] Exploring Operation: 43*16=688, Resulting Numbers: [688] 688,15 unequal: No Solution Exploring Operation: 43+16=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[43, 7], Operations: ['47-45=2', '14/2=7'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,15 unequal: No Solution Exploring Operation: 43*7=301, Resulting Numbers: [301] 301,15 unequal: No Solution Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,15 unequal: No Solution No 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: 15:[45, 14, 4], Operations: ['47-43=4'] Exploring Operation: 45+4=49, Resulting Numbers: [14, 49] Generated Node #0,3,0: 15:[14, 49] Operation: 45+4=49 Exploring Operation: 14+4=18, Resulting Numbers: [45, 18] Generated Node #0,3,1: 15:[45, 18] Operation: 14+4=18 Exploring Operation: 45-4=41, Resulting Numbers: [14, 41] Generated Node #0,3,2: 15:[14, 41] Operation: 45-4=41 Exploring Operation: 45-14=31, Resulting Numbers: [4, 31] Generated Node #0,3,3: 15:[4, 31] Operation: 45-14=31 Moving to Node #0,3,3 Current State: 15:[4, 31], Operations: ['47-43=4', '45-14=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,15 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,15 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,15 unequal: No Solution Moving to Node #0,3,2 Current State: 15:[14, 41], Operations: ['47-43=4', '45-4=41'] Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,15 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[45, 18], Operations: ['47-43=4', '14+4=18'] Exploring Operation: 45*18=810, Resulting Numbers: [810] 810,15 unequal: No Solution Exploring Operation: 45+18=63, Resulting Numbers: [63] 63,15 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[14, 49], Operations: ['47-43=4', '45+4=49'] Exploring Operation: 14+49=63, Resulting Numbers: [63] 63,15 unequal: No Solution Exploring Operation: 14*49=686, Resulting Numbers: [686] 686,15 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[14, 47, 2], Operations: ['45-43=2'] Exploring Operation: 47-2=45, Resulting Numbers: [14, 45] Generated Node #0,0,0: 15:[14, 45] Operation: 47-2=45 Exploring Operation: 14/2=7, Resulting Numbers: [47, 7] Generated Node #0,0,1: 15:[47, 7] Operation: 14/2=7 Exploring Operation: 47-14=33, Resulting Numbers: [2, 33] Generated Node #0,0,2: 15:[2, 33] Operation: 47-14=33 Exploring Operation: 14+2=16, Resulting Numbers: [47, 16] Generated Node #0,0,3: 15:[47, 16] Operation: 14+2=16 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 15:[2, 33], Operations: ['45-43=2', '47-14=33'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,15 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[14, 45], Operations: ['45-43=2', '47-2=45'] Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,15 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,15 unequal: No Solution Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 15:[47, 16], Operations: ['45-43=2', '14+2=16'] Exploring Operation: 47*16=752, Resulting Numbers: [752] 752,15 unequal: No Solution Exploring Operation: 47+16=63, Resulting Numbers: [63] 63,15 unequal: No Solution Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[47, 7], Operations: ['45-43=2', '14/2=7'] Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,15 unequal: No Solution Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,15 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[43, 47, 31], Operations: ['45-14=31'] Exploring Operation: 47-43=4, Resulting Numbers: [31, 4] Generated Node #0,2,0: 15:[31, 4] Operation: 47-43=4 Exploring Operation: 47-31=16, Resulting Numbers: [43, 16] Generated Node #0,2,1: 15:[43, 16] Operation: 47-31=16 Exploring Operation: 43-31=12, Resulting Numbers: [47, 12] Generated Node #0,2,2: 15:[47, 12] Operation: 43-31=12 Exploring Operation: 43+47=90, Resulting Numbers: [31, 90] Generated Node #0,2,3: 15:[31, 90] Operation: 43+47=90 Moving to Node #0,2,0 Current State: 15:[31, 4], Operations: ['45-14=31', '47-43=4'] Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,15 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,15 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[43, 16], Operations: ['45-14=31', '47-31=16'] Exploring Operation: 43*16=688, Resulting Numbers: [688] 688,15 unequal: No Solution Exploring Operation: 43+16=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[47, 12], Operations: ['45-14=31', '43-31=12'] Exploring Operation: 47*12=564, Resulting Numbers: [564] 564,15 unequal: No Solution Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[31, 90], Operations: ['45-14=31', '43+47=90'] Exploring Operation: 31+90=121, Resulting Numbers: [121] 121,15 unequal: No Solution Exploring Operation: 31*90=2790, Resulting Numbers: [2790] 2790,15 unequal: No Solution Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,15 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
[ 7, 4, 82, 2 ]
44
[ "7-4=3", "82/2=41", "3+41=44" ]
Current State: 44:[7, 4, 82, 2], Operations: [] Exploring Operation: 7-4=3, Resulting Numbers: [82, 2, 3] Generated Node #2: [82, 2, 3] from Operation: 7-4=3 Current State: 44:[82, 2, 3], Operations: ['7-4=3'] Exploring Operation: 82/2=41, Resulting Numbers: [3, 41] Generated Node #3: [3, 41] from Operation: 82/2=41 Current State: 44:[3, 41], Operations: ['7-4=3', '82/2=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[7, 4, 82, 2], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [7, 4, 41] Generated Node #0,0: 44:[7, 4, 41] Operation: 82/2=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[7, 4, 41], Operations: ['82/2=41'] Exploring Operation: 7+4=11, Resulting Numbers: [41, 11] Generated Node #0,0,0: 44:[41, 11] Operation: 7+4=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[41, 11], Operations: ['82/2=41', '7+4=11'] Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,44 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
[ 20, 4, 54, 68 ]
32
[ "20+68=88", "88/4=22", "54-22=32" ]
Current State: 32:[20, 4, 54, 68], Operations: [] Exploring Operation: 20+68=88, Resulting Numbers: [4, 54, 88] Generated Node #2: [4, 54, 88] from Operation: 20+68=88 Current State: 32:[4, 54, 88], Operations: ['20+68=88'] Exploring Operation: 88/4=22, Resulting Numbers: [54, 22] Generated Node #3: [54, 22] from Operation: 88/4=22 Current State: 32:[54, 22], Operations: ['20+68=88', '88/4=22'] Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[20, 4, 54, 68], Operations: [] Exploring Operation: 68/4=17, Resulting Numbers: [20, 54, 17] Generated Node #0,0: 32:[20, 54, 17] Operation: 68/4=17 Exploring Operation: 68-54=14, Resulting Numbers: [20, 4, 14] Generated Node #0,1: 32:[20, 4, 14] Operation: 68-54=14 Exploring Operation: 54-20=34, Resulting Numbers: [4, 68, 34] Generated Node #0,2: 32:[4, 68, 34] Operation: 54-20=34 Exploring Operation: 68-20=48, Resulting Numbers: [4, 54, 48] Generated Node #0,3: 32:[4, 54, 48] Operation: 68-20=48 Exploring Operation: 20-4=16, Resulting Numbers: [54, 68, 16] Generated Node #0,4: 32:[54, 68, 16] Operation: 20-4=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[20, 4, 14], Operations: ['68-54=14'] Exploring Operation: 20+14=34, Resulting Numbers: [4, 34] Generated Node #0,1,0: 32:[4, 34] Operation: 20+14=34 Exploring Operation: 20-4=16, Resulting Numbers: [14, 16] Generated Node #0,1,1: 32:[14, 16] Operation: 20-4=16 Exploring Operation: 20-14=6, Resulting Numbers: [4, 6] Generated Node #0,1,2: 32:[4, 6] Operation: 20-14=6 Exploring Operation: 20/4=5, Resulting Numbers: [14, 5] Generated Node #0,1,3: 32:[14, 5] Operation: 20/4=5 Exploring Operation: 4+14=18, Resulting Numbers: [20, 18] Generated Node #0,1,4: 32:[20, 18] Operation: 4+14=18 Moving to Node #0,1,0 Current State: 32:[4, 34], Operations: ['68-54=14', '20+14=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,32 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,32 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,32 unequal: No Solution Moving to Node #0,1,2 Current State: 32:[4, 6], Operations: ['68-54=14', '20-14=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[14, 16], Operations: ['68-54=14', '20-4=16'] Exploring Operation: 14*16=224, Resulting Numbers: [224] 224,32 unequal: No Solution Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,32 unequal: No Solution Moving to Node #0,1,3 Current State: 32:[14, 5], Operations: ['68-54=14', '20/4=5'] Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,32 unequal: No Solution Moving to Node #0,1,4 Current State: 32:[20, 18], Operations: ['68-54=14', '4+14=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,32 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,32 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[20, 54, 17], Operations: ['68/4=17'] Exploring Operation: 20-17=3, Resulting Numbers: [54, 3] Generated Node #0,0,0: 32:[54, 3] Operation: 20-17=3 Exploring Operation: 20+17=37, Resulting Numbers: [54, 37] Generated Node #0,0,1: 32:[54, 37] Operation: 20+17=37 Exploring Operation: 54-20=34, Resulting Numbers: [17, 34] Generated Node #0,0,2: 32:[17, 34] Operation: 54-20=34 Exploring Operation: 20+54=74, Resulting Numbers: [17, 74] Generated Node #0,0,3: 32:[17, 74] Operation: 20+54=74 Exploring Operation: 54-17=37, Resulting Numbers: [20, 37] Generated Node #0,0,4: 32:[20, 37] Operation: 54-17=37 Moving to Node #0,0,2 Current State: 32:[17, 34], Operations: ['68/4=17', '54-20=34'] Exploring Operation: 17*34=578, Resulting Numbers: [578] 578,32 unequal: No Solution Exploring Operation: 17+34=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,32 unequal: No Solution Moving to Node #0,0,4 Current State: 32:[20, 37], Operations: ['68/4=17', '54-17=37'] Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,32 unequal: No Solution Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[54, 3], Operations: ['68/4=17', '20-17=3'] Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,32 unequal: No Solution Exploring Operation: 54*3=162, Resulting Numbers: [162] 162,32 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[54, 37], Operations: ['68/4=17', '20+17=37'] Exploring Operation: 54+37=91, Resulting Numbers: [91] 91,32 unequal: No Solution Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 54*37=1998, Resulting Numbers: [1998] 1998,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[17, 74], Operations: ['68/4=17', '20+54=74'] Exploring Operation: 17*74=1258, Resulting Numbers: [1258] 1258,32 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,32 unequal: No Solution Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,32 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 Current State: 32:[4, 68, 34], Operations: ['54-20=34'] Exploring Operation: 34-4=30, Resulting Numbers: [68, 30] Generated Node #0,2,0: 32:[68, 30] Operation: 34-4=30 Exploring Operation: 68/4=17, Resulting Numbers: [34, 17] Generated Node #0,2,1: 32:[34, 17] Operation: 68/4=17 Exploring Operation: 68/34=2, Resulting Numbers: [4, 2] Generated Node #0,2,2: 32:[4, 2] Operation: 68/34=2 Exploring Operation: 68-4=64, Resulting Numbers: [34, 64] Generated Node #0,2,3: 32:[34, 64] Operation: 68-4=64 Exploring Operation: 68-34=34, Resulting Numbers: [4, 34] Generated Node #0,2,4: 32:[4, 34] Operation: 68-34=34 Moving to Node #0,2,2 Current State: 32:[4, 2], Operations: ['54-20=34', '68/34=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,32 unequal: No Solution Moving to Node #0,2,4 Current State: 32:[4, 34], Operations: ['54-20=34', '68-34=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,32 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[34, 17], Operations: ['54-20=34', '68/4=17'] Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,32 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[34, 64], Operations: ['54-20=34', '68-4=64'] Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 34+64=98, Resulting Numbers: [98] 98,32 unequal: No Solution Exploring Operation: 34*64=2176, Resulting Numbers: [2176] 2176,32 unequal: No Solution Moving to Node #0,2,0 Current State: 32:[68, 30], Operations: ['54-20=34', '34-4=30'] Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,32 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,32 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,32 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 #0,3 Current State: 32:[4, 54, 48], Operations: ['68-20=48'] Exploring Operation: 4+54=58, Resulting Numbers: [48, 58] Generated Node #0,3,0: 32:[48, 58] Operation: 4+54=58 Exploring Operation: 48-4=44, Resulting Numbers: [54, 44] Generated Node #0,3,1: 32:[54, 44] Operation: 48-4=44 Exploring Operation: 48/4=12, Resulting Numbers: [54, 12] Generated Node #0,3,2: 32:[54, 12] Operation: 48/4=12 Exploring Operation: 54-48=6, Resulting Numbers: [4, 6] Generated Node #0,3,3: 32:[4, 6] Operation: 54-48=6 Exploring Operation: 54-4=50, Resulting Numbers: [48, 50] Generated Node #0,3,4: 32:[48, 50] Operation: 54-4=50 Moving to Node #0,3,3 Current State: 32:[4, 6], Operations: ['68-20=48', '54-48=6'] Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,32 unequal: No Solution Moving to Node #0,3,2 Current State: 32:[54, 12], Operations: ['68-20=48', '48/4=12'] Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,32 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,32 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,32 unequal: No Solution Moving to Node #0,3,1 Current State: 32:[54, 44], Operations: ['68-20=48', '48-4=44'] Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,32 unequal: No Solution Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,32 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,32 unequal: No Solution Moving to Node #0,3,4 Current State: 32:[48, 50], Operations: ['68-20=48', '54-4=50'] Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,32 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[48, 58], Operations: ['68-20=48', '4+54=58'] Exploring Operation: 48*58=2784, Resulting Numbers: [2784] 2784,32 unequal: No Solution Exploring Operation: 48+58=106, Resulting Numbers: [106] 106,32 unequal: No Solution Exploring Operation: 58-48=10, Resulting Numbers: [10] 10,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 32:[54, 68, 16], Operations: ['20-4=16'] Exploring Operation: 54-16=38, Resulting Numbers: [68, 38] Generated Node #0,4,0: 32:[68, 38] Operation: 54-16=38 Exploring Operation: 68-54=14, Resulting Numbers: [16, 14] Generated Node #0,4,1: 32:[16, 14] Operation: 68-54=14 Exploring Operation: 68-16=52, Resulting Numbers: [54, 52] Generated Node #0,4,2: 32:[54, 52] Operation: 68-16=52 Exploring Operation: 68+16=84, Resulting Numbers: [54, 84] Generated Node #0,4,3: 32:[54, 84] Operation: 68+16=84 Exploring Operation: 54+16=70, Resulting Numbers: [68, 70] Generated Node #0,4,4: 32:[68, 70] Operation: 54+16=70 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 32:[16, 14], Operations: ['20-4=16', '68-54=14'] Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,32 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 32:[68, 38], Operations: ['20-4=16', '54-16=38'] Exploring Operation: 68*38=2584, Resulting Numbers: [2584] 2584,32 unequal: No Solution Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 68+38=106, Resulting Numbers: [106] 106,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 32:[54, 52], Operations: ['20-4=16', '68-16=52'] Exploring Operation: 54+52=106, Resulting Numbers: [106] 106,32 unequal: No Solution Exploring Operation: 54*52=2808, Resulting Numbers: [2808] 2808,32 unequal: No Solution Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 32:[54, 84], Operations: ['20-4=16', '68+16=84'] Exploring Operation: 54*84=4536, Resulting Numbers: [4536] 4536,32 unequal: No Solution Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 54+84=138, Resulting Numbers: [138] 138,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 32:[68, 70], Operations: ['20-4=16', '54+16=70'] Exploring Operation: 70-68=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 68+70=138, Resulting Numbers: [138] 138,32 unequal: No Solution Exploring Operation: 68*70=4760, Resulting Numbers: [4760] 4760,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 47, 14, 72, 68 ]
79
[ "47+14=61", "72+68=140", "140-61=79" ]
Current State: 79:[47, 14, 72, 68], Operations: [] Exploring Operation: 47+14=61, Resulting Numbers: [72, 68, 61] Generated Node #2: [72, 68, 61] from Operation: 47+14=61 Current State: 79:[72, 68, 61], Operations: ['47+14=61'] Exploring Operation: 72+68=140, Resulting Numbers: [61, 140] Generated Node #3: [61, 140] from Operation: 72+68=140 Current State: 79:[61, 140], Operations: ['47+14=61', '72+68=140'] Exploring Operation: 140-61=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[47, 14, 72, 68], Operations: [] Exploring Operation: 47+14=61, Resulting Numbers: [72, 68, 61] Generated Node #0,0: 79:[72, 68, 61] Operation: 47+14=61 Exploring Operation: 14+68=82, Resulting Numbers: [47, 72, 82] Generated Node #0,1: 79:[47, 72, 82] Operation: 14+68=82 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[72, 68, 61], Operations: ['47+14=61'] Exploring Operation: 68+61=129, Resulting Numbers: [72, 129] Generated Node #0,0,0: 79:[72, 129] Operation: 68+61=129 Exploring Operation: 72+61=133, Resulting Numbers: [68, 133] Generated Node #0,0,1: 79:[68, 133] Operation: 72+61=133 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[72, 129], Operations: ['47+14=61', '68+61=129'] Exploring Operation: 129-72=57, Resulting Numbers: [57] 57,79 unequal: No Solution Exploring Operation: 72+129=201, Resulting Numbers: [201] 201,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[68, 133], Operations: ['47+14=61', '72+61=133'] Exploring Operation: 133-68=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 68+133=201, Resulting Numbers: [201] 201,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[47, 72, 82], Operations: ['14+68=82'] Exploring Operation: 47+72=119, Resulting Numbers: [82, 119] Generated Node #0,1,0: 79:[82, 119] Operation: 47+72=119 Exploring Operation: 82-47=35, Resulting Numbers: [72, 35] Generated Node #0,1,1: 79:[72, 35] Operation: 82-47=35 Moving to Node #0,1,0 Current State: 79:[82, 119], Operations: ['14+68=82', '47+72=119'] Exploring Operation: 119-82=37, Resulting Numbers: [37] 37,79 unequal: No Solution Exploring Operation: 82+119=201, Resulting Numbers: [201] 201,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[72, 35], Operations: ['14+68=82', '82-47=35'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,79 unequal: No Solution Exploring Operation: 72+35=107, Resulting Numbers: [107] 107,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 62, 7, 65, 58 ]
18
[ "62-58=4", "7+65=72", "72/4=18" ]
Current State: 18:[62, 7, 65, 58], Operations: [] Exploring Operation: 62-58=4, Resulting Numbers: [7, 65, 4] Generated Node #2: [7, 65, 4] from Operation: 62-58=4 Current State: 18:[7, 65, 4], Operations: ['62-58=4'] Exploring Operation: 7+65=72, Resulting Numbers: [4, 72] Generated Node #3: [4, 72] from Operation: 7+65=72 Current State: 18:[4, 72], Operations: ['62-58=4', '7+65=72'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[62, 7, 65, 58], Operations: [] Exploring Operation: 65-58=7, Resulting Numbers: [62, 7, 7] Generated Node #0,0: 18:[62, 7, 7] Operation: 65-58=7 Exploring Operation: 62-7=55, Resulting Numbers: [65, 58, 55] Generated Node #0,1: 18:[65, 58, 55] Operation: 62-7=55 Exploring Operation: 65-62=3, Resulting Numbers: [7, 58, 3] Generated Node #0,2: 18:[7, 58, 3] Operation: 65-62=3 Exploring Operation: 62-58=4, Resulting Numbers: [7, 65, 4] Generated Node #0,3: 18:[7, 65, 4] Operation: 62-58=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[7, 58, 3], Operations: ['65-62=3'] Exploring Operation: 7+3=10, Resulting Numbers: [58, 10] Generated Node #0,2,0: 18:[58, 10] Operation: 7+3=10 Exploring Operation: 58-7=51, Resulting Numbers: [3, 51] Generated Node #0,2,1: 18:[3, 51] Operation: 58-7=51 Exploring Operation: 58-3=55, Resulting Numbers: [7, 55] Generated Node #0,2,2: 18:[7, 55] Operation: 58-3=55 Exploring Operation: 7-3=4, Resulting Numbers: [58, 4] Generated Node #0,2,3: 18:[58, 4] Operation: 7-3=4 Moving to Node #0,2,1 Current State: 18:[3, 51], Operations: ['65-62=3', '58-7=51'] Exploring Operation: 3*51=153, Resulting Numbers: [153] 153,18 unequal: No Solution Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,18 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[7, 55], Operations: ['65-62=3', '58-3=55'] Exploring Operation: 7+55=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 7*55=385, Resulting Numbers: [385] 385,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[58, 4], Operations: ['65-62=3', '7-3=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,18 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[58, 10], Operations: ['65-62=3', '7+3=10'] Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,18 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[62, 7, 7], Operations: ['65-58=7'] Exploring Operation: 62-7=55, Resulting Numbers: [7, 55] Generated Node #0,0,0: 18:[7, 55] Operation: 62-7=55 Exploring Operation: 7/7=1, Resulting Numbers: [62, 1] Generated Node #0,0,1: 18:[62, 1] Operation: 7/7=1 Exploring Operation: 62-7=55, Resulting Numbers: [7, 55] Generated Node #0,0,2: 18:[7, 55] Operation: 62-7=55 Exploring Operation: 7-7=0, Resulting Numbers: [62, 0] Generated Node #0,0,3: 18:[62, 0] Operation: 7-7=0 Moving to Node #0,0,0 Current State: 18:[7, 55], Operations: ['65-58=7', '62-7=55'] Exploring Operation: 7+55=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 7*55=385, Resulting Numbers: [385] 385,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[7, 55], Operations: ['65-58=7', '62-7=55'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 7+55=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 7*55=385, Resulting Numbers: [385] 385,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[62, 1], Operations: ['65-58=7', '7/7=1'] Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,18 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,18 unequal: No Solution Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[62, 0], Operations: ['65-58=7', '7-7=0'] Exploring Operation: 62*0=0, Resulting Numbers: [0] 0,18 unequal: No Solution Exploring Operation: 62-0=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 62+0=62, Resulting Numbers: [62] 62,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 18:[7, 65, 4], Operations: ['62-58=4'] Exploring Operation: 65-7=58, Resulting Numbers: [4, 58] Generated Node #0,3,0: 18:[4, 58] Operation: 65-7=58 Exploring Operation: 7-4=3, Resulting Numbers: [65, 3] Generated Node #0,3,1: 18:[65, 3] Operation: 7-4=3 Exploring Operation: 7+4=11, Resulting Numbers: [65, 11] Generated Node #0,3,2: 18:[65, 11] Operation: 7+4=11 Exploring Operation: 65-4=61, Resulting Numbers: [7, 61] Generated Node #0,3,3: 18:[7, 61] Operation: 65-4=61 Moving to Node #0,3,0 Current State: 18:[4, 58], Operations: ['62-58=4', '65-7=58'] Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,18 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,18 unequal: No Solution Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[7, 61], Operations: ['62-58=4', '65-4=61'] Exploring Operation: 7+61=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 7*61=427, Resulting Numbers: [427] 427,18 unequal: No Solution Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[65, 3], Operations: ['62-58=4', '7-4=3'] Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,18 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[65, 11], Operations: ['62-58=4', '7+4=11'] Exploring Operation: 65+11=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 65*11=715, Resulting Numbers: [715] 715,18 unequal: No Solution Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[65, 58, 55], Operations: ['62-7=55'] Exploring Operation: 65-55=10, Resulting Numbers: [58, 10] Generated Node #0,1,0: 18:[58, 10] Operation: 65-55=10 Exploring Operation: 65+58=123, Resulting Numbers: [55, 123] Generated Node #0,1,1: 18:[55, 123] Operation: 65+58=123 Exploring Operation: 65-58=7, Resulting Numbers: [55, 7] Generated Node #0,1,2: 18:[55, 7] Operation: 65-58=7 Exploring Operation: 58-55=3, Resulting Numbers: [65, 3] Generated Node #0,1,3: 18:[65, 3] Operation: 58-55=3 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 18:[55, 7], Operations: ['62-7=55', '65-58=7'] Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,18 unequal: No Solution Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,18 unequal: No Solution No 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: 18:[58, 10], Operations: ['62-7=55', '65-55=10'] Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,18 unequal: No Solution No 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: 18:[65, 3], Operations: ['62-7=55', '58-55=3'] Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,18 unequal: No Solution Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,18 unequal: No Solution No 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: 18:[55, 123], Operations: ['62-7=55', '65+58=123'] Exploring Operation: 55*123=6765, Resulting Numbers: [6765] 6765,18 unequal: No Solution Exploring Operation: 123-55=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 55+123=178, Resulting Numbers: [178] 178,18 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_4
mult_heuristic
[ 7, 43, 18, 16 ]
18
[ "43-7=36", "18-16=2", "36/2=18" ]
Current State: 18:[7, 43, 18, 16], Operations: [] Exploring Operation: 43-7=36, Resulting Numbers: [18, 16, 36] Generated Node #2: [18, 16, 36] from Operation: 43-7=36 Current State: 18:[18, 16, 36], Operations: ['43-7=36'] Exploring Operation: 18-16=2, Resulting Numbers: [36, 2] Generated Node #3: [36, 2] from Operation: 18-16=2 Current State: 18:[36, 2], Operations: ['43-7=36', '18-16=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[7, 43, 18, 16], Operations: [] Exploring Operation: 43-18=25, Resulting Numbers: [7, 16, 25] Generated Node #0,0: 18:[7, 16, 25] Operation: 43-18=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[7, 16, 25], Operations: ['43-18=25'] Exploring Operation: 25-16=9, Resulting Numbers: [7, 9] Generated Node #0,0,0: 18:[7, 9] Operation: 25-16=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[7, 9], Operations: ['43-18=25', '25-16=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,18 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
sum_heuristic
[ 36, 3, 76, 19 ]
29
[ "36-3=33", "76/19=4", "33-4=29" ]
Current State: 29:[36, 3, 76, 19], Operations: [] Exploring Operation: 36-3=33, Resulting Numbers: [76, 19, 33] Generated Node #2: [76, 19, 33] from Operation: 36-3=33 Current State: 29:[76, 19, 33], Operations: ['36-3=33'] Exploring Operation: 76/19=4, Resulting Numbers: [33, 4] Generated Node #3: [33, 4] from Operation: 76/19=4 Current State: 29:[33, 4], Operations: ['36-3=33', '76/19=4'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[36, 3, 76, 19], Operations: [] Exploring Operation: 36-3=33, Resulting Numbers: [76, 19, 33] Generated Node #0,0: 29:[76, 19, 33] Operation: 36-3=33 Exploring Operation: 3+19=22, Resulting Numbers: [36, 76, 22] Generated Node #0,1: 29:[36, 76, 22] Operation: 3+19=22 Exploring Operation: 76-3=73, Resulting Numbers: [36, 19, 73] Generated Node #0,2: 29:[36, 19, 73] Operation: 76-3=73 Exploring Operation: 76/19=4, Resulting Numbers: [36, 3, 4] Generated Node #0,3: 29:[36, 3, 4] Operation: 76/19=4 Exploring Operation: 76-36=40, Resulting Numbers: [3, 19, 40] Generated Node #0,4: 29:[3, 19, 40] Operation: 76-36=40 Start Sub Search at level 1: Moving to Node #0,4 Current State: 29:[3, 19, 40], Operations: ['76-36=40'] Exploring Operation: 3+40=43, Resulting Numbers: [19, 43] Generated Node #0,4,0: 29:[19, 43] Operation: 3+40=43 Exploring Operation: 3+19=22, Resulting Numbers: [40, 22] Generated Node #0,4,1: 29:[40, 22] Operation: 3+19=22 Exploring Operation: 19-3=16, Resulting Numbers: [40, 16] Generated Node #0,4,2: 29:[40, 16] Operation: 19-3=16 Exploring Operation: 40-19=21, Resulting Numbers: [3, 21] Generated Node #0,4,3: 29:[3, 21] Operation: 40-19=21 Exploring Operation: 40-3=37, Resulting Numbers: [19, 37] Generated Node #0,4,4: 29:[19, 37] Operation: 40-3=37 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 29:[40, 22], Operations: ['76-36=40', '3+19=22'] Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 40*22=880, Resulting Numbers: [880] 880,29 unequal: No Solution Exploring Operation: 40+22=62, Resulting Numbers: [62] 62,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 29:[19, 37], Operations: ['76-36=40', '40-3=37'] Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,29 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 29:[19, 43], Operations: ['76-36=40', '3+40=43'] Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,29 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,29 unequal: No Solution Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 29:[40, 16], Operations: ['76-36=40', '19-3=16'] Exploring Operation: 40+16=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 40*16=640, Resulting Numbers: [640] 640,29 unequal: No Solution Exploring Operation: 40-16=24, Resulting Numbers: [24] 24,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 29:[3, 21], Operations: ['76-36=40', '40-19=21'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,29 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,29 unequal: No Solution Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 29:[36, 3, 4], Operations: ['76/19=4'] Exploring Operation: 3*4=12, Resulting Numbers: [36, 12] Generated Node #0,3,0: 29:[36, 12] Operation: 3*4=12 Exploring Operation: 36-4=32, Resulting Numbers: [3, 32] Generated Node #0,3,1: 29:[3, 32] Operation: 36-4=32 Exploring Operation: 3+4=7, Resulting Numbers: [36, 7] Generated Node #0,3,2: 29:[36, 7] Operation: 3+4=7 Exploring Operation: 36-3=33, Resulting Numbers: [4, 33] Generated Node #0,3,3: 29:[4, 33] Operation: 36-3=33 Exploring Operation: 36+3=39, Resulting Numbers: [4, 39] Generated Node #0,3,4: 29:[4, 39] Operation: 36+3=39 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 29:[36, 12], Operations: ['76/19=4', '3*4=12'] Exploring Operation: 36+12=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,29 unequal: No Solution Exploring Operation: 36*12=432, Resulting Numbers: [432] 432,29 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 29:[3, 32], Operations: ['76/19=4', '36-4=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,29 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[36, 3, 76, 19], Operations: [] Exploring Operation: 76/19=4, Resulting Numbers: [36, 3, 4] Generated Node #0,3: 29:[36, 3, 4] Operation: 76/19=4 Moving to Node #0,3 Current State: 29:[36, 3, 4], Operations: ['76/19=4'] Exploring Operation: 36-4=32, Resulting Numbers: [3, 32] Generated Node #0,3,1: 29:[3, 32] Operation: 36-4=32 Moving to Node #0,3,1 Current State: 29:[3, 32], Operations: ['76/19=4', '36-4=32'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.963542
hs_5
mult_heuristic
[ 40, 10, 72, 37 ]
85
[ "40+10=50", "72-37=35", "50+35=85" ]
Current State: 85:[40, 10, 72, 37], Operations: [] Exploring Operation: 40+10=50, Resulting Numbers: [72, 37, 50] Generated Node #2: [72, 37, 50] from Operation: 40+10=50 Current State: 85:[72, 37, 50], Operations: ['40+10=50'] Exploring Operation: 72-37=35, Resulting Numbers: [50, 35] Generated Node #3: [50, 35] from Operation: 72-37=35 Current State: 85:[50, 35], Operations: ['40+10=50', '72-37=35'] Exploring Operation: 50+35=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[40, 10, 72, 37], Operations: [] Exploring Operation: 40+37=77, Resulting Numbers: [10, 72, 77] Generated Node #0,0: 85:[10, 72, 77] Operation: 40+37=77 Exploring Operation: 40/10=4, Resulting Numbers: [72, 37, 4] Generated Node #0,1: 85:[72, 37, 4] Operation: 40/10=4 Exploring Operation: 40-37=3, Resulting Numbers: [10, 72, 3] Generated Node #0,2: 85:[10, 72, 3] Operation: 40-37=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[10, 72, 3], Operations: ['40-37=3'] Exploring Operation: 10-3=7, Resulting Numbers: [72, 7] Generated Node #0,2,0: 85:[72, 7] Operation: 10-3=7 Exploring Operation: 10+72=82, Resulting Numbers: [3, 82] Generated Node #0,2,1: 85:[3, 82] Operation: 10+72=82 Exploring Operation: 72/3=24, Resulting Numbers: [10, 24] Generated Node #0,2,2: 85:[10, 24] Operation: 72/3=24 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 85:[3, 82], Operations: ['40-37=3', '10+72=82'] Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,85 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,85 unequal: No Solution Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[40, 10, 72, 37], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [10, 72, 3] Generated Node #0,2: 85:[10, 72, 3] Operation: 40-37=3 Moving to Node #0,2 Current State: 85:[10, 72, 3], Operations: ['40-37=3'] Exploring Operation: 10+72=82, Resulting Numbers: [3, 82] Generated Node #0,2,1: 85:[3, 82] Operation: 10+72=82 Moving to Node #0,2,1 Current State: 85:[3, 82], Operations: ['40-37=3', '10+72=82'] Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 57, 64, 28, 20 ]
19
[ "57*28=1596", "64+20=84", "1596/84=19" ]
Current State: 19:[57, 64, 28, 20], Operations: [] Exploring Operation: 57*28=1596, Resulting Numbers: [64, 20, 1596] Generated Node #2: [64, 20, 1596] from Operation: 57*28=1596 Current State: 19:[64, 20, 1596], Operations: ['57*28=1596'] Exploring Operation: 64+20=84, Resulting Numbers: [1596, 84] Generated Node #3: [1596, 84] from Operation: 64+20=84 Current State: 19:[1596, 84], Operations: ['57*28=1596', '64+20=84'] Exploring Operation: 1596/84=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[57, 64, 28, 20], Operations: [] Exploring Operation: 64-57=7, Resulting Numbers: [28, 20, 7] Generated Node #0,0: 19:[28, 20, 7] Operation: 64-57=7 Moving to Node #0,0 Current State: 19:[28, 20, 7], Operations: ['64-57=7'] Exploring Operation: 28-7=21, Resulting Numbers: [20, 21] Generated Node #0,0,0: 19:[20, 21] Operation: 28-7=21 Moving to Node #0,0,0 Current State: 19:[20, 21], Operations: ['64-57=7', '28-7=21'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,19 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 10, 69, 34, 80 ]
43
[ "80/10=8", "69-34=35", "8+35=43" ]
Current State: 43:[10, 69, 34, 80], Operations: [] Exploring Operation: 80/10=8, Resulting Numbers: [69, 34, 8] Generated Node #2: [69, 34, 8] from Operation: 80/10=8 Current State: 43:[69, 34, 8], Operations: ['80/10=8'] Exploring Operation: 69-34=35, Resulting Numbers: [8, 35] Generated Node #3: [8, 35] from Operation: 69-34=35 Current State: 43:[8, 35], Operations: ['80/10=8', '69-34=35'] Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[10, 69, 34, 80], Operations: [] Exploring Operation: 80-34=46, Resulting Numbers: [10, 69, 46] Generated Node #0,0: 43:[10, 69, 46] Operation: 80-34=46 Exploring Operation: 10+34=44, Resulting Numbers: [69, 80, 44] Generated Node #0,1: 43:[69, 80, 44] Operation: 10+34=44 Exploring Operation: 69-10=59, Resulting Numbers: [34, 80, 59] Generated Node #0,2: 43:[34, 80, 59] Operation: 69-10=59 Exploring Operation: 80-10=70, Resulting Numbers: [69, 34, 70] Generated Node #0,3: 43:[69, 34, 70] Operation: 80-10=70 Moving to Node #0,0 Current State: 43:[10, 69, 46], Operations: ['80-34=46'] Exploring Operation: 69-10=59, Resulting Numbers: [46, 59] Generated Node #0,0,0: 43:[46, 59] Operation: 69-10=59 Exploring Operation: 10+69=79, Resulting Numbers: [46, 79] Generated Node #0,0,1: 43:[46, 79] Operation: 10+69=79 Exploring Operation: 46-10=36, Resulting Numbers: [69, 36] Generated Node #0,0,2: 43:[69, 36] Operation: 46-10=36 Exploring Operation: 10+46=56, Resulting Numbers: [69, 56] Generated Node #0,0,3: 43:[69, 56] Operation: 10+46=56 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[46, 59], Operations: ['80-34=46', '69-10=59'] Exploring Operation: 46+59=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 46*59=2714, Resulting Numbers: [2714] 2714,43 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 #0,0,2 Current State: 43:[69, 36], Operations: ['80-34=46', '46-10=36'] Exploring Operation: 69*36=2484, Resulting Numbers: [2484] 2484,43 unequal: No Solution Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 69+36=105, Resulting Numbers: [105] 105,43 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:[46, 79], Operations: ['80-34=46', '10+69=79'] Exploring Operation: 46+79=125, Resulting Numbers: [125] 125,43 unequal: No Solution Exploring Operation: 46*79=3634, Resulting Numbers: [3634] 3634,43 unequal: No Solution Exploring Operation: 79-46=33, Resulting Numbers: [33] 33,43 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 #0,0,3 Current State: 43:[69, 56], Operations: ['80-34=46', '10+46=56'] Exploring Operation: 69*56=3864, Resulting Numbers: [3864] 3864,43 unequal: No Solution Exploring Operation: 69-56=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 69+56=125, Resulting Numbers: [125] 125,43 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: 43:[69, 34, 70], Operations: ['80-10=70'] Exploring Operation: 70-69=1, Resulting Numbers: [34, 1] Generated Node #0,3,0: 43:[34, 1] Operation: 70-69=1 Exploring Operation: 69-34=35, Resulting Numbers: [70, 35] Generated Node #0,3,1: 43:[70, 35] Operation: 69-34=35 Exploring Operation: 70-34=36, Resulting Numbers: [69, 36] Generated Node #0,3,2: 43:[69, 36] Operation: 70-34=36 Exploring Operation: 69+34=103, Resulting Numbers: [70, 103] Generated Node #0,3,3: 43:[70, 103] Operation: 69+34=103 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 43:[69, 36], Operations: ['80-10=70', '70-34=36'] Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 69+36=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 69*36=2484, Resulting Numbers: [2484] 2484,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 43:[70, 35], Operations: ['80-10=70', '69-34=35'] Exploring Operation: 70/35=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,43 unequal: No Solution Exploring Operation: 70*35=2450, Resulting Numbers: [2450] 2450,43 unequal: No Solution Exploring Operation: 70+35=105, Resulting Numbers: [105] 105,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 43:[34, 1], Operations: ['80-10=70', '70-69=1'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,43 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,43 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 43:[70, 103], Operations: ['80-10=70', '69+34=103'] Exploring Operation: 70*103=7210, Resulting Numbers: [7210] 7210,43 unequal: No Solution Exploring Operation: 70+103=173, Resulting Numbers: [173] 173,43 unequal: No Solution Exploring Operation: 103-70=33, Resulting Numbers: [33] 33,43 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: 43:[34, 80, 59], Operations: ['69-10=59'] Exploring Operation: 59-34=25, Resulting Numbers: [80, 25] Generated Node #0,2,0: 43:[80, 25] Operation: 59-34=25 Exploring Operation: 80-34=46, Resulting Numbers: [59, 46] Generated Node #0,2,1: 43:[59, 46] Operation: 80-34=46 Exploring Operation: 34+80=114, Resulting Numbers: [59, 114] Generated Node #0,2,2: 43:[59, 114] Operation: 34+80=114 Exploring Operation: 80-59=21, Resulting Numbers: [34, 21] Generated Node #0,2,3: 43:[34, 21] Operation: 80-59=21 Moving to Node #0,1 Current State: 43:[69, 80, 44], Operations: ['10+34=44'] Exploring Operation: 69+80=149, Resulting Numbers: [44, 149] Generated Node #0,1,0: 43:[44, 149] Operation: 69+80=149 Exploring Operation: 80-44=36, Resulting Numbers: [69, 36] Generated Node #0,1,1: 43:[69, 36] Operation: 80-44=36 Exploring Operation: 80-69=11, Resulting Numbers: [44, 11] Generated Node #0,1,2: 43:[44, 11] Operation: 80-69=11 Exploring Operation: 69-44=25, Resulting Numbers: [80, 25] Generated Node #0,1,3: 43:[80, 25] Operation: 69-44=25 Moving to Node #0,2,1 Current State: 43:[59, 46], Operations: ['69-10=59', '80-34=46'] Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,43 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[34, 21], Operations: ['69-10=59', '80-59=21'] Exploring Operation: 34-21=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 34+21=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 34*21=714, Resulting Numbers: [714] 714,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[44, 11], Operations: ['10+34=44', '80-69=11'] Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 44*11=484, Resulting Numbers: [484] 484,43 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,43 unequal: No Solution Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[69, 36], Operations: ['10+34=44', '80-44=36'] Exploring Operation: 69+36=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 69*36=2484, Resulting Numbers: [2484] 2484,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[80, 25], Operations: ['69-10=59', '59-34=25'] Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[80, 25], Operations: ['10+34=44', '69-44=25'] Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,43 unequal: No Solution Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[59, 114], Operations: ['69-10=59', '34+80=114'] Exploring Operation: 59*114=6726, Resulting Numbers: [6726] 6726,43 unequal: No Solution Exploring Operation: 114-59=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 59+114=173, Resulting Numbers: [173] 173,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[44, 149], Operations: ['10+34=44', '69+80=149'] Exploring Operation: 44*149=6556, Resulting Numbers: [6556] 6556,43 unequal: No Solution Exploring Operation: 149-44=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 44+149=193, Resulting Numbers: [193] 193,43 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 84, 35, 56, 77 ]
98
[ "84+35=119", "77-56=21", "119-21=98" ]
Current State: 98:[84, 35, 56, 77], Operations: [] Exploring Operation: 84+35=119, Resulting Numbers: [56, 77, 119] Generated Node #2: [56, 77, 119] from Operation: 84+35=119 Current State: 98:[56, 77, 119], Operations: ['84+35=119'] Exploring Operation: 77-56=21, Resulting Numbers: [119, 21] Generated Node #3: [119, 21] from Operation: 77-56=21 Current State: 98:[119, 21], Operations: ['84+35=119', '77-56=21'] Exploring Operation: 119-21=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[84, 35, 56, 77], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [35, 56, 7] Generated Node #0,0: 98:[35, 56, 7] Operation: 84-77=7 Exploring Operation: 84-35=49, Resulting Numbers: [56, 77, 49] Generated Node #0,1: 98:[56, 77, 49] Operation: 84-35=49 Exploring Operation: 77-35=42, Resulting Numbers: [84, 56, 42] Generated Node #0,2: 98:[84, 56, 42] Operation: 77-35=42 Exploring Operation: 35+77=112, Resulting Numbers: [84, 56, 112] Generated Node #0,3: 98:[84, 56, 112] Operation: 35+77=112 Moving to Node #0,0 Current State: 98:[35, 56, 7], Operations: ['84-77=7'] Exploring Operation: 56-35=21, Resulting Numbers: [7, 21] Generated Node #0,0,0: 98:[7, 21] Operation: 56-35=21 Exploring Operation: 35+7=42, Resulting Numbers: [56, 42] Generated Node #0,0,1: 98:[56, 42] Operation: 35+7=42 Exploring Operation: 35+56=91, Resulting Numbers: [7, 91] Generated Node #0,0,2: 98:[7, 91] Operation: 35+56=91 Exploring Operation: 35/7=5, Resulting Numbers: [56, 5] Generated Node #0,0,3: 98:[56, 5] Operation: 35/7=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[7, 21], Operations: ['84-77=7', '56-35=21'] Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,98 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,98 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 7*21=147, Resulting Numbers: [147] 147,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[7, 91], Operations: ['84-77=7', '35+56=91'] Exploring Operation: 7+91=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[84, 35, 56, 77], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [35, 56, 7] Generated Node #0,0: 98:[35, 56, 7] Operation: 84-77=7 Moving to Node #0,0 Current State: 98:[35, 56, 7], Operations: ['84-77=7'] Exploring Operation: 35+56=91, Resulting Numbers: [7, 91] Generated Node #0,0,2: 98:[7, 91] Operation: 35+56=91 Moving to Node #0,0,2 Current State: 98:[7, 91], Operations: ['84-77=7', '35+56=91'] Exploring Operation: 7+91=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 31, 38, 2, 58 ]
71
[ "58-38=20", "2*20=40", "31+40=71" ]
Current State: 71:[31, 38, 2, 58], Operations: [] Exploring Operation: 58-38=20, Resulting Numbers: [31, 2, 20] Generated Node #2: [31, 2, 20] from Operation: 58-38=20 Current State: 71:[31, 2, 20], Operations: ['58-38=20'] Exploring Operation: 2*20=40, Resulting Numbers: [31, 40] Generated Node #3: [31, 40] from Operation: 2*20=40 Current State: 71:[31, 40], Operations: ['58-38=20', '2*20=40'] Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[31, 38, 2, 58], Operations: [] Exploring Operation: 31+38=69, Resulting Numbers: [2, 58, 69] Generated Node #0,0: 71:[2, 58, 69] Operation: 31+38=69 Exploring Operation: 38*2=76, Resulting Numbers: [31, 58, 76] Generated Node #0,1: 71:[31, 58, 76] Operation: 38*2=76 Exploring Operation: 31+2=33, Resulting Numbers: [38, 58, 33] Generated Node #0,2: 71:[38, 58, 33] Operation: 31+2=33 Exploring Operation: 31*2=62, Resulting Numbers: [38, 58, 62] Generated Node #0,3: 71:[38, 58, 62] Operation: 31*2=62 Moving to Node #0,3 Current State: 71:[38, 58, 62], Operations: ['31*2=62'] Exploring Operation: 58-38=20, Resulting Numbers: [62, 20] Generated Node #0,3,0: 71:[62, 20] Operation: 58-38=20 Exploring Operation: 62-38=24, Resulting Numbers: [58, 24] Generated Node #0,3,1: 71:[58, 24] Operation: 62-38=24 Exploring Operation: 38+58=96, Resulting Numbers: [62, 96] Generated Node #0,3,2: 71:[62, 96] Operation: 38+58=96 Exploring Operation: 38+62=100, Resulting Numbers: [58, 100] Generated Node #0,3,3: 71:[58, 100] Operation: 38+62=100 Moving to Node #0,1 Current State: 71:[31, 58, 76], Operations: ['38*2=76'] Exploring Operation: 31+58=89, Resulting Numbers: [76, 89] Generated Node #0,1,0: 71:[76, 89] Operation: 31+58=89 Exploring Operation: 58-31=27, Resulting Numbers: [76, 27] Generated Node #0,1,1: 71:[76, 27] Operation: 58-31=27 Exploring Operation: 76-31=45, Resulting Numbers: [58, 45] Generated Node #0,1,2: 71:[58, 45] Operation: 76-31=45 Exploring Operation: 31+76=107, Resulting Numbers: [58, 107] Generated Node #0,1,3: 71:[58, 107] Operation: 31+76=107 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[76, 89], Operations: ['38*2=76', '31+58=89'] Exploring Operation: 76*89=6764, Resulting Numbers: [6764] 6764,71 unequal: No Solution Exploring Operation: 76+89=165, Resulting Numbers: [165] 165,71 unequal: No Solution Exploring Operation: 89-76=13, Resulting Numbers: [13] 13,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 71:[58, 45], Operations: ['38*2=76', '76-31=45'] Exploring Operation: 58+45=103, Resulting Numbers: [103] 103,71 unequal: No Solution Exploring Operation: 58*45=2610, Resulting Numbers: [2610] 2610,71 unequal: No Solution Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[76, 27], Operations: ['38*2=76', '58-31=27'] Exploring Operation: 76+27=103, Resulting Numbers: [103] 103,71 unequal: No Solution Exploring Operation: 76-27=49, Resulting Numbers: [49] 49,71 unequal: No Solution Exploring Operation: 76*27=2052, Resulting Numbers: [2052] 2052,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 71:[58, 107], Operations: ['38*2=76', '31+76=107'] Exploring Operation: 107-58=49, Resulting Numbers: [49] 49,71 unequal: No Solution Exploring Operation: 58+107=165, Resulting Numbers: [165] 165,71 unequal: No Solution Exploring Operation: 58*107=6206, Resulting Numbers: [6206] 6206,71 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: 71:[38, 58, 33], Operations: ['31+2=33'] Exploring Operation: 38+58=96, Resulting Numbers: [33, 96] Generated Node #0,2,0: 71:[33, 96] Operation: 38+58=96 Exploring Operation: 58+33=91, Resulting Numbers: [38, 91] Generated Node #0,2,1: 71:[38, 91] Operation: 58+33=91 Exploring Operation: 38-33=5, Resulting Numbers: [58, 5] Generated Node #0,2,2: 71:[58, 5] Operation: 38-33=5 Exploring Operation: 38+33=71, Resulting Numbers: [58, 71] Generated Node #0,2,3: 71:[58, 71] Operation: 38+33=71 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 71:[58, 71], Operations: ['31+2=33', '38+33=71'] Exploring Operation: 71-58=13, Resulting Numbers: [13] 13,71 unequal: No Solution Exploring Operation: 58*71=4118, Resulting Numbers: [4118] 4118,71 unequal: No Solution Exploring Operation: 58+71=129, Resulting Numbers: [129] 129,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[38, 91], Operations: ['31+2=33', '58+33=91'] Exploring Operation: 38*91=3458, Resulting Numbers: [3458] 3458,71 unequal: No Solution Exploring Operation: 38+91=129, Resulting Numbers: [129] 129,71 unequal: No Solution Exploring Operation: 91-38=53, Resulting Numbers: [53] 53,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[33, 96], Operations: ['31+2=33', '38+58=96'] Exploring Operation: 33*96=3168, Resulting Numbers: [3168] 3168,71 unequal: No Solution Exploring Operation: 96-33=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 33+96=129, Resulting Numbers: [129] 129,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[58, 5], Operations: ['31+2=33', '38-33=5'] Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,71 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 71:[2, 58, 69], Operations: ['31+38=69'] Exploring Operation: 69-2=67, Resulting Numbers: [58, 67] Generated Node #0,0,0: 71:[58, 67] Operation: 69-2=67 Exploring Operation: 2+69=71, Resulting Numbers: [58, 71] Generated Node #0,0,1: 71:[58, 71] Operation: 2+69=71 Exploring Operation: 2+58=60, Resulting Numbers: [69, 60] Generated Node #0,0,2: 71:[69, 60] Operation: 2+58=60 Exploring Operation: 58-2=56, Resulting Numbers: [69, 56] Generated Node #0,0,3: 71:[69, 56] Operation: 58-2=56 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[58, 71], Operations: ['31+38=69', '2+69=71'] Exploring Operation: 58+71=129, Resulting Numbers: [129] 129,71 unequal: No Solution Exploring Operation: 58*71=4118, Resulting Numbers: [4118] 4118,71 unequal: No Solution Exploring Operation: 71-58=13, Resulting Numbers: [13] 13,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[69, 60], Operations: ['31+38=69', '2+58=60'] Exploring Operation: 69+60=129, Resulting Numbers: [129] 129,71 unequal: No Solution Exploring Operation: 69-60=9, Resulting Numbers: [9] 9,71 unequal: No Solution Exploring Operation: 69*60=4140, Resulting Numbers: [4140] 4140,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[58, 67], Operations: ['31+38=69', '69-2=67'] Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,71 unequal: No Solution Exploring Operation: 58*67=3886, Resulting Numbers: [3886] 3886,71 unequal: No Solution Exploring Operation: 58+67=125, Resulting Numbers: [125] 125,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 71:[69, 56], Operations: ['31+38=69', '58-2=56'] Exploring Operation: 69-56=13, Resulting Numbers: [13] 13,71 unequal: No Solution Exploring Operation: 69*56=3864, Resulting Numbers: [3864] 3864,71 unequal: No Solution Exploring Operation: 69+56=125, Resulting Numbers: [125] 125,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 71:[62, 96], Operations: ['31*2=62', '38+58=96'] Exploring Operation: 62*96=5952, Resulting Numbers: [5952] 5952,71 unequal: No Solution Exploring Operation: 96-62=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 62+96=158, Resulting Numbers: [158] 158,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[58, 100], Operations: ['31*2=62', '38+62=100'] Exploring Operation: 100-58=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 58+100=158, Resulting Numbers: [158] 158,71 unequal: No Solution Exploring Operation: 58*100=5800, Resulting Numbers: [5800] 5800,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[58, 24], Operations: ['31*2=62', '62-38=24'] Exploring Operation: 58+24=82, Resulting Numbers: [82] 82,71 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 58*24=1392, Resulting Numbers: [1392] 1392,71 unequal: No Solution Moving to Node #0,3,0 Current State: 71:[62, 20], Operations: ['31*2=62', '58-38=20'] Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,71 unequal: No Solution Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,71 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,71 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 16, 59, 24, 13 ]
67
[ "16-13=3", "24/3=8", "59+8=67" ]
Current State: 67:[16, 59, 24, 13], Operations: [] Exploring Operation: 16-13=3, Resulting Numbers: [59, 24, 3] Generated Node #2: [59, 24, 3] from Operation: 16-13=3 Current State: 67:[59, 24, 3], Operations: ['16-13=3'] Exploring Operation: 24/3=8, Resulting Numbers: [59, 8] Generated Node #3: [59, 8] from Operation: 24/3=8 Current State: 67:[59, 8], Operations: ['16-13=3', '24/3=8'] Exploring Operation: 59+8=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[16, 59, 24, 13], Operations: [] Exploring Operation: 24+13=37, Resulting Numbers: [16, 59, 37] Generated Node #0,0: 67:[16, 59, 37] Operation: 24+13=37 Exploring Operation: 16+13=29, Resulting Numbers: [59, 24, 29] Generated Node #0,1: 67:[59, 24, 29] Operation: 16+13=29 Exploring Operation: 59+13=72, Resulting Numbers: [16, 24, 72] Generated Node #0,2: 67:[16, 24, 72] Operation: 59+13=72 Exploring Operation: 16+24=40, Resulting Numbers: [59, 13, 40] Generated Node #0,3: 67:[59, 13, 40] Operation: 16+24=40 Moving to Node #0,0 Current State: 67:[16, 59, 37], Operations: ['24+13=37'] Exploring Operation: 16+37=53, Resulting Numbers: [59, 53] Generated Node #0,0,0: 67:[59, 53] Operation: 16+37=53 Exploring Operation: 59-16=43, Resulting Numbers: [37, 43] Generated Node #0,0,1: 67:[37, 43] Operation: 59-16=43 Exploring Operation: 16+59=75, Resulting Numbers: [37, 75] Generated Node #0,0,2: 67:[37, 75] Operation: 16+59=75 Exploring Operation: 37-16=21, Resulting Numbers: [59, 21] Generated Node #0,0,3: 67:[59, 21] Operation: 37-16=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[59, 53], Operations: ['24+13=37', '16+37=53'] Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 59+53=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 59*53=3127, Resulting Numbers: [3127] 3127,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[37, 75], Operations: ['24+13=37', '16+59=75'] Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 37*75=2775, Resulting Numbers: [2775] 2775,67 unequal: No Solution Exploring Operation: 37+75=112, Resulting Numbers: [112] 112,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[37, 43], Operations: ['24+13=37', '59-16=43'] Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 37+43=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 37*43=1591, Resulting Numbers: [1591] 1591,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 67:[59, 21], Operations: ['24+13=37', '37-16=21'] Exploring Operation: 59*21=1239, Resulting Numbers: [1239] 1239,67 unequal: No Solution Exploring Operation: 59+21=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,67 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: 67:[59, 13, 40], Operations: ['16+24=40'] Exploring Operation: 13+40=53, Resulting Numbers: [59, 53] Generated Node #0,3,0: 67:[59, 53] Operation: 13+40=53 Exploring Operation: 59+13=72, Resulting Numbers: [40, 72] Generated Node #0,3,1: 67:[40, 72] Operation: 59+13=72 Exploring Operation: 40-13=27, Resulting Numbers: [59, 27] Generated Node #0,3,2: 67:[59, 27] Operation: 40-13=27 Exploring Operation: 59-13=46, Resulting Numbers: [40, 46] Generated Node #0,3,3: 67:[40, 46] Operation: 59-13=46 Moving to Node #0,1 Current State: 67:[59, 24, 29], Operations: ['16+13=29'] Exploring Operation: 59+29=88, Resulting Numbers: [24, 88] Generated Node #0,1,0: 67:[24, 88] Operation: 59+29=88 Exploring Operation: 24+29=53, Resulting Numbers: [59, 53] Generated Node #0,1,1: 67:[59, 53] Operation: 24+29=53 Exploring Operation: 59+24=83, Resulting Numbers: [29, 83] Generated Node #0,1,2: 67:[29, 83] Operation: 59+24=83 Exploring Operation: 59-24=35, Resulting Numbers: [29, 35] Generated Node #0,1,3: 67:[29, 35] Operation: 59-24=35 Moving to Node #0,2 Current State: 67:[16, 24, 72], Operations: ['59+13=72'] Exploring Operation: 72-16=56, Resulting Numbers: [24, 56] Generated Node #0,2,0: 67:[24, 56] Operation: 72-16=56 Exploring Operation: 24-16=8, Resulting Numbers: [72, 8] Generated Node #0,2,1: 67:[72, 8] Operation: 24-16=8 Exploring Operation: 16+24=40, Resulting Numbers: [72, 40] Generated Node #0,2,2: 67:[72, 40] Operation: 16+24=40 Exploring Operation: 16+72=88, Resulting Numbers: [24, 88] Generated Node #0,2,3: 67:[24, 88] Operation: 16+72=88 Moving to Node #0,3,0 Current State: 67:[59, 53], Operations: ['16+24=40', '13+40=53'] Exploring Operation: 59+53=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 59*53=3127, Resulting Numbers: [3127] 3127,67 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[59, 53], Operations: ['16+13=29', '24+29=53'] Exploring Operation: 59*53=3127, Resulting Numbers: [3127] 3127,67 unequal: No Solution Exploring Operation: 59+53=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[40, 72], Operations: ['16+24=40', '59+13=72'] Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 40*72=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 40+72=112, Resulting Numbers: [112] 112,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[72, 40], Operations: ['59+13=72', '16+24=40'] Exploring Operation: 72*40=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[59, 27], Operations: ['16+24=40', '40-13=27'] Exploring Operation: 59*27=1593, Resulting Numbers: [1593] 1593,67 unequal: No Solution Exploring Operation: 59+27=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[40, 46], Operations: ['16+24=40', '59-13=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 40*46=1840, Resulting Numbers: [1840] 1840,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[29, 83], Operations: ['16+13=29', '59+24=83'] Exploring Operation: 29+83=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 29*83=2407, Resulting Numbers: [2407] 2407,67 unequal: No Solution Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[24, 56], Operations: ['59+13=72', '72-16=56'] Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 24+56=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 24*56=1344, Resulting Numbers: [1344] 1344,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[24, 88], Operations: ['59+13=72', '16+72=88'] Exploring Operation: 24+88=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 24*88=2112, Resulting Numbers: [2112] 2112,67 unequal: No Solution Exploring Operation: 88-24=64, Resulting Numbers: [64] 64,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[72, 8], Operations: ['59+13=72', '24-16=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 72*8=576, Resulting Numbers: [576] 576,67 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[24, 88], Operations: ['16+13=29', '59+29=88'] Exploring Operation: 24*88=2112, Resulting Numbers: [2112] 2112,67 unequal: No Solution Exploring Operation: 24+88=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 88-24=64, Resulting Numbers: [64] 64,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[29, 35], Operations: ['16+13=29', '59-24=35'] Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 29*35=1015, Resulting Numbers: [1015] 1015,67 unequal: No Solution Exploring Operation: 29+35=64, Resulting Numbers: [64] 64,67 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 81, 42, 75, 41 ]
34
[ "81-75=6", "42/6=7", "41-7=34" ]
Current State: 34:[81, 42, 75, 41], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [42, 41, 6] Generated Node #2: [42, 41, 6] from Operation: 81-75=6 Current State: 34:[42, 41, 6], Operations: ['81-75=6'] Exploring Operation: 42/6=7, Resulting Numbers: [41, 7] Generated Node #3: [41, 7] from Operation: 42/6=7 Current State: 34:[41, 7], Operations: ['81-75=6', '42/6=7'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[81, 42, 75, 41], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [42, 41, 6] Generated Node #0,0: 34:[42, 41, 6] Operation: 81-75=6 Exploring Operation: 75-41=34, Resulting Numbers: [81, 42, 34] Generated Node #0,1: 34:[81, 42, 34] Operation: 75-41=34 Exploring Operation: 81-41=40, Resulting Numbers: [42, 75, 40] Generated Node #0,2: 34:[42, 75, 40] Operation: 81-41=40 Exploring Operation: 75-42=33, Resulting Numbers: [81, 41, 33] Generated Node #0,3: 34:[81, 41, 33] Operation: 75-42=33 Exploring Operation: 81-42=39, Resulting Numbers: [75, 41, 39] Generated Node #0,4: 34:[75, 41, 39] Operation: 81-42=39 Moving to Node #0,0 Current State: 34:[42, 41, 6], Operations: ['81-75=6'] Exploring Operation: 41-6=35, Resulting Numbers: [42, 35] Generated Node #0,0,0: 34:[42, 35] Operation: 41-6=35 Exploring Operation: 42+6=48, Resulting Numbers: [41, 48] Generated Node #0,0,1: 34:[41, 48] Operation: 42+6=48 Exploring Operation: 42/6=7, Resulting Numbers: [41, 7] Generated Node #0,0,2: 34:[41, 7] Operation: 42/6=7 Exploring Operation: 42-6=36, Resulting Numbers: [41, 36] Generated Node #0,0,3: 34:[41, 36] Operation: 42-6=36 Exploring Operation: 42-41=1, Resulting Numbers: [6, 1] Generated Node #0,0,4: 34:[6, 1] Operation: 42-41=1 Moving to Node #0,4 Current State: 34:[75, 41, 39], Operations: ['81-42=39'] Exploring Operation: 75-41=34, Resulting Numbers: [39, 34] Generated Node #0,4,0: 34:[39, 34] Operation: 75-41=34 Exploring Operation: 75+39=114, Resulting Numbers: [41, 114] Generated Node #0,4,1: 34:[41, 114] Operation: 75+39=114 Exploring Operation: 75-39=36, Resulting Numbers: [41, 36] Generated Node #0,4,2: 34:[41, 36] Operation: 75-39=36 Exploring Operation: 41-39=2, Resulting Numbers: [75, 2] Generated Node #0,4,3: 34:[75, 2] Operation: 41-39=2 Exploring Operation: 75+41=116, Resulting Numbers: [39, 116] Generated Node #0,4,4: 34:[39, 116] Operation: 75+41=116 Moving to Node #0,1 Current State: 34:[81, 42, 34], Operations: ['75-41=34'] Exploring Operation: 81-34=47, Resulting Numbers: [42, 47] Generated Node #0,1,0: 34:[42, 47] Operation: 81-34=47 Exploring Operation: 81-42=39, Resulting Numbers: [34, 39] Generated Node #0,1,1: 34:[34, 39] Operation: 81-42=39 Exploring Operation: 42-34=8, Resulting Numbers: [81, 8] Generated Node #0,1,2: 34:[81, 8] Operation: 42-34=8 Exploring Operation: 81+34=115, Resulting Numbers: [42, 115] Generated Node #0,1,3: 34:[42, 115] Operation: 81+34=115 Exploring Operation: 81+42=123, Resulting Numbers: [34, 123] Generated Node #0,1,4: 34:[34, 123] Operation: 81+42=123 Moving to Node #0,2 Current State: 34:[42, 75, 40], Operations: ['81-41=40'] Exploring Operation: 75-40=35, Resulting Numbers: [42, 35] Generated Node #0,2,0: 34:[42, 35] Operation: 75-40=35 Exploring Operation: 42-40=2, Resulting Numbers: [75, 2] Generated Node #0,2,1: 34:[75, 2] Operation: 42-40=2 Exploring Operation: 75-42=33, Resulting Numbers: [40, 33] Generated Node #0,2,2: 34:[40, 33] Operation: 75-42=33 Exploring Operation: 42+75=117, Resulting Numbers: [40, 117] Generated Node #0,2,3: 34:[40, 117] Operation: 42+75=117 Exploring Operation: 42+40=82, Resulting Numbers: [75, 82] Generated Node #0,2,4: 34:[75, 82] Operation: 42+40=82 Moving to Node #0,3 Current State: 34:[81, 41, 33], Operations: ['75-42=33'] Exploring Operation: 41-33=8, Resulting Numbers: [81, 8] Generated Node #0,3,0: 34:[81, 8] Operation: 41-33=8 Exploring Operation: 81+33=114, Resulting Numbers: [41, 114] Generated Node #0,3,1: 34:[41, 114] Operation: 81+33=114 Exploring Operation: 41+33=74, Resulting Numbers: [81, 74] Generated Node #0,3,2: 34:[81, 74] Operation: 41+33=74 Exploring Operation: 81-33=48, Resulting Numbers: [41, 48] Generated Node #0,3,3: 34:[41, 48] Operation: 81-33=48 Exploring Operation: 81-41=40, Resulting Numbers: [33, 40] Generated Node #0,3,4: 34:[33, 40] Operation: 81-41=40 Moving to Node #0,0,4 Current State: 34:[6, 1], Operations: ['81-75=6', '42-41=1'] Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,34 unequal: No Solution Moving to Node #0,4,0 Current State: 34:[39, 34], Operations: ['81-42=39', '75-41=34'] Exploring Operation: 39*34=1326, Resulting Numbers: [1326] 1326,34 unequal: No Solution Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 39+34=73, Resulting Numbers: [73] 73,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[34, 39], Operations: ['75-41=34', '81-42=39'] Exploring Operation: 34+39=73, Resulting Numbers: [73] 73,34 unequal: No Solution Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 34*39=1326, Resulting Numbers: [1326] 1326,34 unequal: No Solution Moving to Node #0,3,4 Current State: 34:[33, 40], Operations: ['75-42=33', '81-41=40'] Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,34 unequal: No Solution Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,34 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[40, 33], Operations: ['81-41=40', '75-42=33'] Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 40*33=1320, Resulting Numbers: [1320] 1320,34 unequal: No Solution Exploring Operation: 40+33=73, Resulting Numbers: [73] 73,34 unequal: No Solution Moving to Node #0,4,2 Current State: 34:[41, 36], Operations: ['81-42=39', '75-39=36'] Exploring Operation: 41*36=1476, Resulting Numbers: [1476] 1476,34 unequal: No Solution Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,34 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,34 unequal: No Solution Moving to Node #0,0,3 Current State: 34:[41, 36], Operations: ['81-75=6', '42-6=36'] Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,34 unequal: No Solution Exploring Operation: 41*36=1476, Resulting Numbers: [1476] 1476,34 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[42, 35], Operations: ['81-75=6', '41-6=35'] Exploring Operation: 42+35=77, Resulting Numbers: [77] 77,34 unequal: No Solution Exploring Operation: 42*35=1470, Resulting Numbers: [1470] 1470,34 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[42, 35], Operations: ['81-41=40', '75-40=35'] Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 42*35=1470, Resulting Numbers: [1470] 1470,34 unequal: No Solution Exploring Operation: 42+35=77, Resulting Numbers: [77] 77,34 unequal: No Solution Moving to Node #0,0,2 Current State: 34:[41, 7], Operations: ['81-75=6', '42/6=7'] Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,34 unequal: No Solution Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,34 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[81, 42, 75, 41], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [42, 41, 6] Generated Node #0,0: 34:[42, 41, 6] Operation: 81-75=6 Moving to Node #0,0 Current State: 34:[42, 41, 6], Operations: ['81-75=6'] Exploring Operation: 42/6=7, Resulting Numbers: [41, 7] Generated Node #0,0,2: 34:[41, 7] Operation: 42/6=7 Moving to Node #0,0,2 Current State: 34:[41, 7], Operations: ['81-75=6', '42/6=7'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.943576
hs_5
mult_heuristic
[ 10, 33, 11, 3 ]
56
[ "33-10=23", "11*3=33", "23+33=56" ]
Current State: 56:[10, 33, 11, 3], Operations: [] Exploring Operation: 33-10=23, Resulting Numbers: [11, 3, 23] Generated Node #2: [11, 3, 23] from Operation: 33-10=23 Current State: 56:[11, 3, 23], Operations: ['33-10=23'] Exploring Operation: 11*3=33, Resulting Numbers: [23, 33] Generated Node #3: [23, 33] from Operation: 11*3=33 Current State: 56:[23, 33], Operations: ['33-10=23', '11*3=33'] Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[10, 33, 11, 3], Operations: [] Exploring Operation: 11-10=1, Resulting Numbers: [33, 3, 1] Generated Node #0,0: 56:[33, 3, 1] Operation: 11-10=1 Exploring Operation: 33/11=3, Resulting Numbers: [10, 3, 3] Generated Node #0,1: 56:[10, 3, 3] Operation: 33/11=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[10, 3, 3], Operations: ['33/11=3'] Exploring Operation: 10-3=7, Resulting Numbers: [3, 7] Generated Node #0,1,0: 56:[3, 7] Operation: 10-3=7 Exploring Operation: 10-3=7, Resulting Numbers: [3, 7] Generated Node #0,1,1: 56:[3, 7] Operation: 10-3=7 Moving to Node #0,1,0 Current State: 56:[3, 7], Operations: ['33/11=3', '10-3=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[3, 7], Operations: ['33/11=3', '10-3=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[33, 3, 1], Operations: ['11-10=1'] Exploring Operation: 33-3=30, Resulting Numbers: [1, 30] Generated Node #0,0,0: 56:[1, 30] Operation: 33-3=30 Exploring Operation: 33/3=11, Resulting Numbers: [1, 11] Generated Node #0,0,1: 56:[1, 11] Operation: 33/3=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[1, 30], Operations: ['11-10=1', '33-3=30'] Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,56 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,56 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 #0,0,1 Current State: 56:[1, 11], Operations: ['11-10=1', '33/3=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 53, 12, 79, 2 ]
20
[ "79-53=26", "12/2=6", "26-6=20" ]
Current State: 20:[53, 12, 79, 2], Operations: [] Exploring Operation: 79-53=26, Resulting Numbers: [12, 2, 26] Generated Node #2: [12, 2, 26] from Operation: 79-53=26 Current State: 20:[12, 2, 26], Operations: ['79-53=26'] Exploring Operation: 12/2=6, Resulting Numbers: [26, 6] Generated Node #3: [26, 6] from Operation: 12/2=6 Current State: 20:[26, 6], Operations: ['79-53=26', '12/2=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[53, 12, 79, 2], Operations: [] Exploring Operation: 79-12=67, Resulting Numbers: [53, 2, 67] Generated Node #0,0: 20:[53, 2, 67] Operation: 79-12=67 Exploring Operation: 53-12=41, Resulting Numbers: [79, 2, 41] Generated Node #0,1: 20:[79, 2, 41] Operation: 53-12=41 Exploring Operation: 79-53=26, Resulting Numbers: [12, 2, 26] Generated Node #0,2: 20:[12, 2, 26] Operation: 79-53=26 Moving to Node #0,2 Current State: 20:[12, 2, 26], Operations: ['79-53=26'] Exploring Operation: 26/2=13, Resulting Numbers: [12, 13] Generated Node #0,2,0: 20:[12, 13] Operation: 26/2=13 Exploring Operation: 12-2=10, Resulting Numbers: [26, 10] Generated Node #0,2,1: 20:[26, 10] Operation: 12-2=10 Exploring Operation: 26-12=14, Resulting Numbers: [2, 14] Generated Node #0,2,2: 20:[2, 14] Operation: 26-12=14 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 20:[2, 14], Operations: ['79-53=26', '26-12=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 20:[12, 13], Operations: ['79-53=26', '26/2=13'] Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,20 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,20 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 20:[26, 10], Operations: ['79-53=26', '12-2=10'] Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,20 unequal: No Solution Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,20 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: 20:[53, 2, 67], Operations: ['79-12=67'] Exploring Operation: 67-2=65, Resulting Numbers: [53, 65] Generated Node #0,0,0: 20:[53, 65] Operation: 67-2=65 Exploring Operation: 53-2=51, Resulting Numbers: [67, 51] Generated Node #0,0,1: 20:[67, 51] Operation: 53-2=51 Exploring Operation: 67-53=14, Resulting Numbers: [2, 14] Generated Node #0,0,2: 20:[2, 14] Operation: 67-53=14 Moving to Node #0,1 Current State: 20:[79, 2, 41], Operations: ['53-12=41'] Exploring Operation: 79-41=38, Resulting Numbers: [2, 38] Generated Node #0,1,0: 20:[2, 38] Operation: 79-41=38 Exploring Operation: 79-2=77, Resulting Numbers: [41, 77] Generated Node #0,1,1: 20:[41, 77] Operation: 79-2=77 Exploring Operation: 41-2=39, Resulting Numbers: [79, 39] Generated Node #0,1,2: 20:[79, 39] Operation: 41-2=39 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[2, 38], Operations: ['53-12=41', '79-41=38'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,20 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,20 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 20:[41, 77], Operations: ['53-12=41', '79-2=77'] Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,20 unequal: No Solution Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,20 unequal: No Solution Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 20:[79, 39], Operations: ['53-12=41', '41-2=39'] Exploring Operation: 79*39=3081, Resulting Numbers: [3081] 3081,20 unequal: No Solution Exploring Operation: 79+39=118, Resulting Numbers: [118] 118,20 unequal: No Solution Exploring Operation: 79-39=40, Resulting Numbers: [40] 40,20 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: 20:[2, 14], Operations: ['79-12=67', '67-53=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[53, 65], Operations: ['79-12=67', '67-2=65'] Exploring Operation: 65-53=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 53*65=3445, Resulting Numbers: [3445] 3445,20 unequal: No Solution Exploring Operation: 53+65=118, Resulting Numbers: [118] 118,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[67, 51], Operations: ['79-12=67', '53-2=51'] Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 67+51=118, Resulting Numbers: [118] 118,20 unequal: No Solution Exploring Operation: 67*51=3417, Resulting Numbers: [3417] 3417,20 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 61, 7, 71, 63 ]
66
[ "61+7=68", "71+63=134", "134-68=66" ]
Current State: 66:[61, 7, 71, 63], Operations: [] Exploring Operation: 61+7=68, Resulting Numbers: [71, 63, 68] Generated Node #2: [71, 63, 68] from Operation: 61+7=68 Current State: 66:[71, 63, 68], Operations: ['61+7=68'] Exploring Operation: 71+63=134, Resulting Numbers: [68, 134] Generated Node #3: [68, 134] from Operation: 71+63=134 Current State: 66:[68, 134], Operations: ['61+7=68', '71+63=134'] Exploring Operation: 134-68=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[61, 7, 71, 63], Operations: [] Exploring Operation: 71-63=8, Resulting Numbers: [61, 7, 8] Generated Node #0,0: 66:[61, 7, 8] Operation: 71-63=8 Exploring Operation: 61+7=68, Resulting Numbers: [71, 63, 68] Generated Node #0,1: 66:[71, 63, 68] Operation: 61+7=68 Exploring Operation: 63-61=2, Resulting Numbers: [7, 71, 2] Generated Node #0,2: 66:[7, 71, 2] Operation: 63-61=2 Exploring Operation: 71-61=10, Resulting Numbers: [7, 63, 10] Generated Node #0,3: 66:[7, 63, 10] Operation: 71-61=10 Start Sub Search at level 1: Moving to Node #0,3 Current State: 66:[7, 63, 10], Operations: ['71-61=10'] Exploring Operation: 7+63=70, Resulting Numbers: [10, 70] Generated Node #0,3,0: 66:[10, 70] Operation: 7+63=70 Exploring Operation: 7*10=70, Resulting Numbers: [63, 70] Generated Node #0,3,1: 66:[63, 70] Operation: 7*10=70 Exploring Operation: 10-7=3, Resulting Numbers: [63, 3] Generated Node #0,3,2: 66:[63, 3] Operation: 10-7=3 Exploring Operation: 63/7=9, Resulting Numbers: [10, 9] Generated Node #0,3,3: 66:[10, 9] Operation: 63/7=9 Moving to Node #0,3,2 Current State: 66:[63, 3], Operations: ['71-61=10', '10-7=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[61, 7, 71, 63], Operations: [] Exploring Operation: 71-61=10, Resulting Numbers: [7, 63, 10] Generated Node #0,3: 66:[7, 63, 10] Operation: 71-61=10 Moving to Node #0,3 Current State: 66:[7, 63, 10], Operations: ['71-61=10'] Exploring Operation: 10-7=3, Resulting Numbers: [63, 3] Generated Node #0,3,2: 66:[63, 3] Operation: 10-7=3 Moving to Node #0,3,2 Current State: 66:[63, 3], Operations: ['71-61=10', '10-7=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 32, 9, 55, 2 ]
30
[ "32-9=23", "55-2=53", "53-23=30" ]
Current State: 30:[32, 9, 55, 2], Operations: [] Exploring Operation: 32-9=23, Resulting Numbers: [55, 2, 23] Generated Node #2: [55, 2, 23] from Operation: 32-9=23 Current State: 30:[55, 2, 23], Operations: ['32-9=23'] Exploring Operation: 55-2=53, Resulting Numbers: [23, 53] Generated Node #3: [23, 53] from Operation: 55-2=53 Current State: 30:[23, 53], Operations: ['32-9=23', '55-2=53'] Exploring Operation: 53-23=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[32, 9, 55, 2], Operations: [] Exploring Operation: 32/2=16, Resulting Numbers: [9, 55, 16] Generated Node #0,0: 30:[9, 55, 16] Operation: 32/2=16 Exploring Operation: 55-32=23, Resulting Numbers: [9, 2, 23] Generated Node #0,1: 30:[9, 2, 23] Operation: 55-32=23 Exploring Operation: 55-2=53, Resulting Numbers: [32, 9, 53] Generated Node #0,2: 30:[32, 9, 53] Operation: 55-2=53 Exploring Operation: 32-2=30, Resulting Numbers: [9, 55, 30] Generated Node #0,3: 30:[9, 55, 30] Operation: 32-2=30 Exploring Operation: 55-9=46, Resulting Numbers: [32, 2, 46] Generated Node #0,4: 30:[32, 2, 46] Operation: 55-9=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[9, 2, 23], Operations: ['55-32=23'] Exploring Operation: 9+2=11, Resulting Numbers: [23, 11] Generated Node #0,1,0: 30:[23, 11] Operation: 9+2=11 Exploring Operation: 9+23=32, Resulting Numbers: [2, 32] Generated Node #0,1,1: 30:[2, 32] Operation: 9+23=32 Exploring Operation: 2+23=25, Resulting Numbers: [9, 25] Generated Node #0,1,2: 30:[9, 25] Operation: 2+23=25 Exploring Operation: 23-2=21, Resulting Numbers: [9, 21] Generated Node #0,1,3: 30:[9, 21] Operation: 23-2=21 Exploring Operation: 23-9=14, Resulting Numbers: [2, 14] Generated Node #0,1,4: 30:[2, 14] Operation: 23-9=14 Moving to Node #0,1,4 Current State: 30:[2, 14], Operations: ['55-32=23', '23-9=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[2, 32], Operations: ['55-32=23', '9+23=32'] Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[32, 9, 55, 2], Operations: [] Exploring Operation: 55-32=23, Resulting Numbers: [9, 2, 23] Generated Node #0,1: 30:[9, 2, 23] Operation: 55-32=23 Moving to Node #0,1 Current State: 30:[9, 2, 23], Operations: ['55-32=23'] Exploring Operation: 9+23=32, Resulting Numbers: [2, 32] Generated Node #0,1,1: 30:[2, 32] Operation: 9+23=32 Moving to Node #0,1,1 Current State: 30:[2, 32], Operations: ['55-32=23', '9+23=32'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 76, 75, 96, 70 ]
26
[ "76-75=1", "96-70=26", "1*26=26" ]
Current State: 26:[76, 75, 96, 70], Operations: [] Exploring Operation: 76-75=1, Resulting Numbers: [96, 70, 1] Generated Node #2: [96, 70, 1] from Operation: 76-75=1 Current State: 26:[96, 70, 1], Operations: ['76-75=1'] Exploring Operation: 96-70=26, Resulting Numbers: [1, 26] Generated Node #3: [1, 26] from Operation: 96-70=26 Current State: 26:[1, 26], Operations: ['76-75=1', '96-70=26'] Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[76, 75, 96, 70], Operations: [] Exploring Operation: 96-76=20, Resulting Numbers: [75, 70, 20] Generated Node #0,0: 26:[75, 70, 20] Operation: 96-76=20 Exploring Operation: 96-70=26, Resulting Numbers: [76, 75, 26] Generated Node #0,1: 26:[76, 75, 26] Operation: 96-70=26 Exploring Operation: 96-75=21, Resulting Numbers: [76, 70, 21] Generated Node #0,2: 26:[76, 70, 21] Operation: 96-75=21 Moving to Node #0,0 Current State: 26:[75, 70, 20], Operations: ['96-76=20'] Exploring Operation: 75-20=55, Resulting Numbers: [70, 55] Generated Node #0,0,0: 26:[70, 55] Operation: 75-20=55 Exploring Operation: 75-70=5, Resulting Numbers: [20, 5] Generated Node #0,0,1: 26:[20, 5] Operation: 75-70=5 Exploring Operation: 70-20=50, Resulting Numbers: [75, 50] Generated Node #0,0,2: 26:[75, 50] Operation: 70-20=50 Moving to Node #0,1 Current State: 26:[76, 75, 26], Operations: ['96-70=26'] Exploring Operation: 75-26=49, Resulting Numbers: [76, 49] Generated Node #0,1,0: 26:[76, 49] Operation: 75-26=49 Exploring Operation: 76-26=50, Resulting Numbers: [75, 50] Generated Node #0,1,1: 26:[75, 50] Operation: 76-26=50 Exploring Operation: 76-75=1, Resulting Numbers: [26, 1] Generated Node #0,1,2: 26:[26, 1] Operation: 76-75=1 Moving to Node #0,2 Current State: 26:[76, 70, 21], Operations: ['96-75=21'] Exploring Operation: 70-21=49, Resulting Numbers: [76, 49] Generated Node #0,2,0: 26:[76, 49] Operation: 70-21=49 Exploring Operation: 76-70=6, Resulting Numbers: [21, 6] Generated Node #0,2,1: 26:[21, 6] Operation: 76-70=6 Exploring Operation: 76-21=55, Resulting Numbers: [70, 55] Generated Node #0,2,2: 26:[70, 55] Operation: 76-21=55 Moving to Node #0,1,2 Current State: 26:[26, 1], Operations: ['96-70=26', '76-75=1'] Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[76, 75, 96, 70], Operations: [] Exploring Operation: 96-70=26, Resulting Numbers: [76, 75, 26] Generated Node #0,1: 26:[76, 75, 26] Operation: 96-70=26 Moving to Node #0,1 Current State: 26:[76, 75, 26], Operations: ['96-70=26'] Exploring Operation: 76-75=1, Resulting Numbers: [26, 1] Generated Node #0,1,2: 26:[26, 1] Operation: 76-75=1 Moving to Node #0,1,2 Current State: 26:[26, 1], Operations: ['96-70=26', '76-75=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.984375
hs_3
mult_heuristic
[ 25, 15, 23, 60 ]
29
[ "25-15=10", "60/10=6", "23+6=29" ]
Current State: 29:[25, 15, 23, 60], Operations: [] Exploring Operation: 25-15=10, Resulting Numbers: [23, 60, 10] Generated Node #2: [23, 60, 10] from Operation: 25-15=10 Current State: 29:[23, 60, 10], Operations: ['25-15=10'] Exploring Operation: 60/10=6, Resulting Numbers: [23, 6] Generated Node #3: [23, 6] from Operation: 60/10=6 Current State: 29:[23, 6], Operations: ['25-15=10', '60/10=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[25, 15, 23, 60], Operations: [] Exploring Operation: 60-25=35, Resulting Numbers: [15, 23, 35] Generated Node #0,0: 29:[15, 23, 35] Operation: 60-25=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[15, 23, 35], Operations: ['60-25=35'] Exploring Operation: 15+23=38, Resulting Numbers: [35, 38] Generated Node #0,0,0: 29:[35, 38] Operation: 15+23=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[35, 38], Operations: ['60-25=35', '15+23=38'] Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 53, 63, 34, 46 ]
22
[ "63-53=10", "46-34=12", "10+12=22" ]
Current State: 22:[53, 63, 34, 46], Operations: [] Exploring Operation: 63-53=10, Resulting Numbers: [34, 46, 10] Generated Node #2: [34, 46, 10] from Operation: 63-53=10 Current State: 22:[34, 46, 10], Operations: ['63-53=10'] Exploring Operation: 46-34=12, Resulting Numbers: [10, 12] Generated Node #3: [10, 12] from Operation: 46-34=12 Current State: 22:[10, 12], Operations: ['63-53=10', '46-34=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[53, 63, 34, 46], Operations: [] Exploring Operation: 63-46=17, Resulting Numbers: [53, 34, 17] Generated Node #0,0: 22:[53, 34, 17] Operation: 63-46=17 Exploring Operation: 63-53=10, Resulting Numbers: [34, 46, 10] Generated Node #0,1: 22:[34, 46, 10] Operation: 63-53=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[34, 46, 10], Operations: ['63-53=10'] Exploring Operation: 46-34=12, Resulting Numbers: [10, 12] Generated Node #0,1,0: 22:[10, 12] Operation: 46-34=12 Exploring Operation: 34-10=24, Resulting Numbers: [46, 24] Generated Node #0,1,1: 22:[46, 24] Operation: 34-10=24 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[10, 12], Operations: ['63-53=10', '46-34=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[53, 63, 34, 46], Operations: [] Exploring Operation: 63-53=10, Resulting Numbers: [34, 46, 10] Generated Node #0,1: 22:[34, 46, 10] Operation: 63-53=10 Moving to Node #0,1 Current State: 22:[34, 46, 10], Operations: ['63-53=10'] Exploring Operation: 46-34=12, Resulting Numbers: [10, 12] Generated Node #0,1,0: 22:[10, 12] Operation: 46-34=12 Moving to Node #0,1,0 Current State: 22:[10, 12], Operations: ['63-53=10', '46-34=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 11, 48, 96, 49 ]
76
[ "49-11=38", "96/48=2", "38*2=76" ]
Current State: 76:[11, 48, 96, 49], Operations: [] Exploring Operation: 49-11=38, Resulting Numbers: [48, 96, 38] Generated Node #2: [48, 96, 38] from Operation: 49-11=38 Current State: 76:[48, 96, 38], Operations: ['49-11=38'] Exploring Operation: 96/48=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 96/48=2 Current State: 76:[38, 2], Operations: ['49-11=38', '96/48=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[11, 48, 96, 49], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [11, 49, 2] Generated Node #0,0: 76:[11, 49, 2] Operation: 96/48=2 Moving to Node #0,0 Current State: 76:[11, 49, 2], Operations: ['96/48=2'] Exploring Operation: 49-11=38, Resulting Numbers: [2, 38] Generated Node #0,0,0: 76:[2, 38] Operation: 49-11=38 Moving to Node #0,0,0 Current State: 76:[2, 38], Operations: ['96/48=2', '49-11=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[11, 48, 96, 49], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [11, 49, 2] Generated Node #0,0: 76:[11, 49, 2] Operation: 96/48=2 Moving to Node #0,0 Current State: 76:[11, 49, 2], Operations: ['96/48=2'] Exploring Operation: 49-11=38, Resulting Numbers: [2, 38] Generated Node #0,0,0: 76:[2, 38] Operation: 49-11=38 Moving to Node #0,0,0 Current State: 76:[2, 38], Operations: ['96/48=2', '49-11=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 33, 62, 8, 26 ]
24
[ "62-33=29", "29-26=3", "8*3=24" ]
Current State: 24:[33, 62, 8, 26], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [8, 26, 29] Generated Node #2: [8, 26, 29] from Operation: 62-33=29 Current State: 24:[8, 26, 29], Operations: ['62-33=29'] Exploring Operation: 29-26=3, Resulting Numbers: [8, 3] Generated Node #3: [8, 3] from Operation: 29-26=3 Current State: 24:[8, 3], Operations: ['62-33=29', '29-26=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[33, 62, 8, 26], Operations: [] Exploring Operation: 33-26=7, Resulting Numbers: [62, 8, 7] Generated Node #0,0: 24:[62, 8, 7] Operation: 33-26=7 Exploring Operation: 33-8=25, Resulting Numbers: [62, 26, 25] Generated Node #0,1: 24:[62, 26, 25] Operation: 33-8=25 Exploring Operation: 62-33=29, Resulting Numbers: [8, 26, 29] Generated Node #0,2: 24:[8, 26, 29] Operation: 62-33=29 Exploring Operation: 62-26=36, Resulting Numbers: [33, 8, 36] Generated Node #0,3: 24:[33, 8, 36] Operation: 62-26=36 Moving to Node #0,2 Current State: 24:[8, 26, 29], Operations: ['62-33=29'] Exploring Operation: 26-8=18, Resulting Numbers: [29, 18] Generated Node #0,2,0: 24:[29, 18] Operation: 26-8=18 Exploring Operation: 8+26=34, Resulting Numbers: [29, 34] Generated Node #0,2,1: 24:[29, 34] Operation: 8+26=34 Exploring Operation: 29-8=21, Resulting Numbers: [26, 21] Generated Node #0,2,2: 24:[26, 21] Operation: 29-8=21 Exploring Operation: 29-26=3, Resulting Numbers: [8, 3] Generated Node #0,2,3: 24:[8, 3] Operation: 29-26=3 Moving to Node #0,3 Current State: 24:[33, 8, 36], Operations: ['62-26=36'] Exploring Operation: 33-8=25, Resulting Numbers: [36, 25] Generated Node #0,3,0: 24:[36, 25] Operation: 33-8=25 Exploring Operation: 36-8=28, Resulting Numbers: [33, 28] Generated Node #0,3,1: 24:[33, 28] Operation: 36-8=28 Exploring Operation: 36-33=3, Resulting Numbers: [8, 3] Generated Node #0,3,2: 24:[8, 3] Operation: 36-33=3 Exploring Operation: 33+8=41, Resulting Numbers: [36, 41] Generated Node #0,3,3: 24:[36, 41] Operation: 33+8=41 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 24:[8, 3], Operations: ['62-26=36', '36-33=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[33, 62, 8, 26], Operations: [] Exploring Operation: 62-26=36, Resulting Numbers: [33, 8, 36] Generated Node #0,3: 24:[33, 8, 36] Operation: 62-26=36 Moving to Node #0,3 Current State: 24:[33, 8, 36], Operations: ['62-26=36'] Exploring Operation: 36-33=3, Resulting Numbers: [8, 3] Generated Node #0,3,2: 24:[8, 3] Operation: 36-33=3 Moving to Node #0,3,2 Current State: 24:[8, 3], Operations: ['62-26=36', '36-33=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 87, 58, 89, 42 ]
98
[ "87+58=145", "89-42=47", "145-47=98" ]
Current State: 98:[87, 58, 89, 42], Operations: [] Exploring Operation: 87+58=145, Resulting Numbers: [89, 42, 145] Generated Node #2: [89, 42, 145] from Operation: 87+58=145 Current State: 98:[89, 42, 145], Operations: ['87+58=145'] Exploring Operation: 89-42=47, Resulting Numbers: [145, 47] Generated Node #3: [145, 47] from Operation: 89-42=47 Current State: 98:[145, 47], Operations: ['87+58=145', '89-42=47'] Exploring Operation: 145-47=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[87, 58, 89, 42], Operations: [] Exploring Operation: 87-42=45, Resulting Numbers: [58, 89, 45] Generated Node #0,0: 98:[58, 89, 45] Operation: 87-42=45 Exploring Operation: 58+42=100, Resulting Numbers: [87, 89, 100] Generated Node #0,1: 98:[87, 89, 100] Operation: 58+42=100 Exploring Operation: 58-42=16, Resulting Numbers: [87, 89, 16] Generated Node #0,2: 98:[87, 89, 16] Operation: 58-42=16 Exploring Operation: 89-87=2, Resulting Numbers: [58, 42, 2] Generated Node #0,3: 98:[58, 42, 2] Operation: 89-87=2 Exploring Operation: 89-42=47, Resulting Numbers: [87, 58, 47] Generated Node #0,4: 98:[87, 58, 47] Operation: 89-42=47 Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[58, 42, 2], Operations: ['89-87=2'] Exploring Operation: 58+42=100, Resulting Numbers: [2, 100] Generated Node #0,3,0: 98:[2, 100] Operation: 58+42=100 Exploring Operation: 42/2=21, Resulting Numbers: [58, 21] Generated Node #0,3,1: 98:[58, 21] Operation: 42/2=21 Exploring Operation: 42+2=44, Resulting Numbers: [58, 44] Generated Node #0,3,2: 98:[58, 44] Operation: 42+2=44 Exploring Operation: 58-2=56, Resulting Numbers: [42, 56] Generated Node #0,3,3: 98:[42, 56] Operation: 58-2=56 Exploring Operation: 58-42=16, Resulting Numbers: [2, 16] Generated Node #0,3,4: 98:[2, 16] Operation: 58-42=16 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 98:[2, 100], Operations: ['89-87=2', '58+42=100'] Exploring Operation: 2*100=200, Resulting Numbers: [200] 200,98 unequal: No Solution Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[87, 58, 89, 42], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [58, 42, 2] Generated Node #0,3: 98:[58, 42, 2] Operation: 89-87=2 Moving to Node #0,3 Current State: 98:[58, 42, 2], Operations: ['89-87=2'] Exploring Operation: 58+42=100, Resulting Numbers: [2, 100] Generated Node #0,3,0: 98:[2, 100] Operation: 58+42=100 Moving to Node #0,3,0 Current State: 98:[2, 100], Operations: ['89-87=2', '58+42=100'] Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 20, 81, 85, 15 ]
74
[ "20+85=105", "105/15=7", "81-7=74" ]
Current State: 74:[20, 81, 85, 15], Operations: [] Exploring Operation: 20+85=105, Resulting Numbers: [81, 15, 105] Generated Node #2: [81, 15, 105] from Operation: 20+85=105 Current State: 74:[81, 15, 105], Operations: ['20+85=105'] Exploring Operation: 105/15=7, Resulting Numbers: [81, 7] Generated Node #3: [81, 7] from Operation: 105/15=7 Current State: 74:[81, 7], Operations: ['20+85=105', '105/15=7'] Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[20, 81, 85, 15], Operations: [] Exploring Operation: 20-15=5, Resulting Numbers: [81, 85, 5] Generated Node #0,0: 74:[81, 85, 5] Operation: 20-15=5 Exploring Operation: 20+15=35, Resulting Numbers: [81, 85, 35] Generated Node #0,1: 74:[81, 85, 35] Operation: 20+15=35 Exploring Operation: 85-15=70, Resulting Numbers: [20, 81, 70] Generated Node #0,2: 74:[20, 81, 70] Operation: 85-15=70 Moving to Node #0,1 Current State: 74:[81, 85, 35], Operations: ['20+15=35'] Exploring Operation: 85-81=4, Resulting Numbers: [35, 4] Generated Node #0,1,0: 74:[35, 4] Operation: 85-81=4 Exploring Operation: 85-35=50, Resulting Numbers: [81, 50] Generated Node #0,1,1: 74:[81, 50] Operation: 85-35=50 Exploring Operation: 81-35=46, Resulting Numbers: [85, 46] Generated Node #0,1,2: 74:[85, 46] Operation: 81-35=46 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[35, 4], Operations: ['20+15=35', '85-81=4'] Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,74 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,74 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,74 unequal: No Solution No 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: 74:[81, 50], Operations: ['20+15=35', '85-35=50'] Exploring Operation: 81+50=131, Resulting Numbers: [131] 131,74 unequal: No Solution Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,74 unequal: No Solution Exploring Operation: 81*50=4050, Resulting Numbers: [4050] 4050,74 unequal: No Solution No 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: 74:[85, 46], Operations: ['20+15=35', '81-35=46'] Exploring Operation: 85+46=131, Resulting Numbers: [131] 131,74 unequal: No Solution Exploring Operation: 85-46=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 85*46=3910, Resulting Numbers: [3910] 3910,74 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: 74:[81, 85, 5], Operations: ['20-15=5'] Exploring Operation: 85-81=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 74:[5, 4] Operation: 85-81=4 Exploring Operation: 85-5=80, Resulting Numbers: [81, 80] Generated Node #0,0,1: 74:[81, 80] Operation: 85-5=80 Exploring Operation: 81-5=76, Resulting Numbers: [85, 76] Generated Node #0,0,2: 74:[85, 76] Operation: 81-5=76 Moving to Node #0,2 Current State: 74:[20, 81, 70], Operations: ['85-15=70'] Exploring Operation: 70-20=50, Resulting Numbers: [81, 50] Generated Node #0,2,0: 74:[81, 50] Operation: 70-20=50 Exploring Operation: 20+70=90, Resulting Numbers: [81, 90] Generated Node #0,2,1: 74:[81, 90] Operation: 20+70=90 Exploring Operation: 81-20=61, Resulting Numbers: [70, 61] Generated Node #0,2,2: 74:[70, 61] Operation: 81-20=61 Moving to Node #0,0,0 Current State: 74:[5, 4], Operations: ['20-15=5', '85-81=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,74 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,74 unequal: No Solution Moving to Node #0,0,2 Current State: 74:[85, 76], Operations: ['20-15=5', '81-5=76'] Exploring Operation: 85+76=161, Resulting Numbers: [161] 161,74 unequal: No Solution Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 85*76=6460, Resulting Numbers: [6460] 6460,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[81, 80], Operations: ['20-15=5', '85-5=80'] Exploring Operation: 81*80=6480, Resulting Numbers: [6480] 6480,74 unequal: No Solution Exploring Operation: 81+80=161, Resulting Numbers: [161] 161,74 unequal: No Solution Exploring Operation: 81-80=1, Resulting Numbers: [1] 1,74 unequal: No Solution Moving to Node #0,2,2 Current State: 74:[70, 61], Operations: ['85-15=70', '81-20=61'] Exploring Operation: 70-61=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 70*61=4270, Resulting Numbers: [4270] 4270,74 unequal: No Solution Exploring Operation: 70+61=131, Resulting Numbers: [131] 131,74 unequal: No Solution Moving to Node #0,2,0 Current State: 74:[81, 50], Operations: ['85-15=70', '70-20=50'] Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,74 unequal: No Solution Exploring Operation: 81+50=131, Resulting Numbers: [131] 131,74 unequal: No Solution Exploring Operation: 81*50=4050, Resulting Numbers: [4050] 4050,74 unequal: No Solution Moving to Node #0,2,1 Current State: 74:[81, 90], Operations: ['85-15=70', '20+70=90'] Exploring Operation: 90-81=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 81+90=171, Resulting Numbers: [171] 171,74 unequal: No Solution Exploring Operation: 81*90=7290, Resulting Numbers: [7290] 7290,74 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 75, 16, 8, 14 ]
67
[ "75-14=61", "16*8=128", "128-61=67" ]
Current State: 67:[75, 16, 8, 14], Operations: [] Exploring Operation: 75-14=61, Resulting Numbers: [16, 8, 61] Generated Node #2: [16, 8, 61] from Operation: 75-14=61 Current State: 67:[16, 8, 61], Operations: ['75-14=61'] Exploring Operation: 16*8=128, Resulting Numbers: [61, 128] Generated Node #3: [61, 128] from Operation: 16*8=128 Current State: 67:[61, 128], Operations: ['75-14=61', '16*8=128'] Exploring Operation: 128-61=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[75, 16, 8, 14], Operations: [] Exploring Operation: 16+8=24, Resulting Numbers: [75, 14, 24] Generated Node #0,0: 67:[75, 14, 24] Operation: 16+8=24 Exploring Operation: 8*14=112, Resulting Numbers: [75, 16, 112] Generated Node #0,1: 67:[75, 16, 112] Operation: 8*14=112 Exploring Operation: 16+14=30, Resulting Numbers: [75, 8, 30] Generated Node #0,2: 67:[75, 8, 30] Operation: 16+14=30 Exploring Operation: 8+14=22, Resulting Numbers: [75, 16, 22] Generated Node #0,3: 67:[75, 16, 22] Operation: 8+14=22 Exploring Operation: 75-8=67, Resulting Numbers: [16, 14, 67] Generated Node #0,4: 67:[16, 14, 67] Operation: 75-8=67 Moving to Node #0,0 Current State: 67:[75, 14, 24], Operations: ['16+8=24'] Exploring Operation: 75+14=89, Resulting Numbers: [24, 89] Generated Node #0,0,0: 67:[24, 89] Operation: 75+14=89 Exploring Operation: 75-24=51, Resulting Numbers: [14, 51] Generated Node #0,0,1: 67:[14, 51] Operation: 75-24=51 Exploring Operation: 24-14=10, Resulting Numbers: [75, 10] Generated Node #0,0,2: 67:[75, 10] Operation: 24-14=10 Exploring Operation: 75-14=61, Resulting Numbers: [24, 61] Generated Node #0,0,3: 67:[24, 61] Operation: 75-14=61 Exploring Operation: 14+24=38, Resulting Numbers: [75, 38] Generated Node #0,0,4: 67:[75, 38] Operation: 14+24=38 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 67:[75, 38], Operations: ['16+8=24', '14+24=38'] Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,67 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,67 unequal: No Solution Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 67:[24, 61], Operations: ['16+8=24', '75-14=61'] Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,67 unequal: No Solution Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,67 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[24, 89], Operations: ['16+8=24', '75+14=89'] Exploring Operation: 89-24=65, Resulting Numbers: [65] 65,67 unequal: No Solution Exploring Operation: 24*89=2136, Resulting Numbers: [2136] 2136,67 unequal: No Solution Exploring Operation: 24+89=113, Resulting Numbers: [113] 113,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[75, 10], Operations: ['16+8=24', '24-14=10'] Exploring Operation: 75+10=85, Resulting Numbers: [85] 85,67 unequal: No Solution Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,67 unequal: No Solution Exploring Operation: 75*10=750, Resulting Numbers: [750] 750,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[14, 51], Operations: ['16+8=24', '75-24=51'] Exploring Operation: 14*51=714, Resulting Numbers: [714] 714,67 unequal: No Solution Exploring Operation: 14+51=65, Resulting Numbers: [65] 65,67 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 67:[75, 8, 30], Operations: ['16+14=30'] Exploring Operation: 75-8=67, Resulting Numbers: [30, 67] Generated Node #0,2,0: 67:[30, 67] Operation: 75-8=67 Exploring Operation: 8+30=38, Resulting Numbers: [75, 38] Generated Node #0,2,1: 67:[75, 38] Operation: 8+30=38 Exploring Operation: 75-30=45, Resulting Numbers: [8, 45] Generated Node #0,2,2: 67:[8, 45] Operation: 75-30=45 Exploring Operation: 75+8=83, Resulting Numbers: [30, 83] Generated Node #0,2,3: 67:[30, 83] Operation: 75+8=83 Exploring Operation: 30-8=22, Resulting Numbers: [75, 22] Generated Node #0,2,4: 67:[75, 22] Operation: 30-8=22 Moving to Node #0,4 Current State: 67:[16, 14, 67], Operations: ['75-8=67'] Exploring Operation: 16+14=30, Resulting Numbers: [67, 30] Generated Node #0,4,0: 67:[67, 30] Operation: 16+14=30 Exploring Operation: 67-14=53, Resulting Numbers: [16, 53] Generated Node #0,4,1: 67:[16, 53] Operation: 67-14=53 Exploring Operation: 16-14=2, Resulting Numbers: [67, 2] Generated Node #0,4,2: 67:[67, 2] Operation: 16-14=2 Exploring Operation: 16+67=83, Resulting Numbers: [14, 83] Generated Node #0,4,3: 67:[14, 83] Operation: 16+67=83 Exploring Operation: 14+67=81, Resulting Numbers: [16, 81] Generated Node #0,4,4: 67:[16, 81] Operation: 14+67=81 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 67:[67, 30], Operations: ['75-8=67', '16+14=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,67 unequal: No Solution Exploring Operation: 67*30=2010, Resulting Numbers: [2010] 2010,67 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,67 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 #0,4,1 Current State: 67:[16, 53], Operations: ['75-8=67', '67-14=53'] Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 16+53=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 16*53=848, Resulting Numbers: [848] 848,67 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 #0,4,2 Current State: 67:[67, 2], Operations: ['75-8=67', '16-14=2'] Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,67 unequal: No Solution Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,67 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 #0,4,4 Current State: 67:[16, 81], Operations: ['75-8=67', '14+67=81'] Exploring Operation: 16+81=97, Resulting Numbers: [97] 97,67 unequal: No Solution Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,67 unequal: No Solution Exploring Operation: 16*81=1296, Resulting Numbers: [1296] 1296,67 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 #0,4,3 Current State: 67:[14, 83], Operations: ['75-8=67', '16+67=83'] Exploring Operation: 14*83=1162, Resulting Numbers: [1162] 1162,67 unequal: No Solution Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 14+83=97, Resulting Numbers: [97] 97,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 67:[75, 16, 112], Operations: ['8*14=112'] Exploring Operation: 75-16=59, Resulting Numbers: [112, 59] Generated Node #0,1,0: 67:[112, 59] Operation: 75-16=59 Exploring Operation: 75+16=91, Resulting Numbers: [112, 91] Generated Node #0,1,1: 67:[112, 91] Operation: 75+16=91 Exploring Operation: 112-16=96, Resulting Numbers: [75, 96] Generated Node #0,1,2: 67:[75, 96] Operation: 112-16=96 Exploring Operation: 112/16=7, Resulting Numbers: [75, 7] Generated Node #0,1,3: 67:[75, 7] Operation: 112/16=7 Exploring Operation: 16+112=128, Resulting Numbers: [75, 128] Generated Node #0,1,4: 67:[75, 128] Operation: 16+112=128 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[75, 96], Operations: ['8*14=112', '112-16=96'] Exploring Operation: 75*96=7200, Resulting Numbers: [7200] 7200,67 unequal: No Solution Exploring Operation: 75+96=171, Resulting Numbers: [171] 171,67 unequal: No Solution Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[112, 59], Operations: ['8*14=112', '75-16=59'] Exploring Operation: 112-59=53, Resulting Numbers: [53] 53,67 unequal: No Solution Exploring Operation: 112+59=171, Resulting Numbers: [171] 171,67 unequal: No Solution Exploring Operation: 112*59=6608, Resulting Numbers: [6608] 6608,67 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 #0,1,3 Current State: 67:[75, 7], Operations: ['8*14=112', '112/16=7'] Exploring Operation: 75*7=525, Resulting Numbers: [525] 525,67 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,67 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:[112, 91], Operations: ['8*14=112', '75+16=91'] Exploring Operation: 112*91=10192, Resulting Numbers: [10192] 10192,67 unequal: No Solution Exploring Operation: 112+91=203, Resulting Numbers: [203] 203,67 unequal: No Solution Exploring Operation: 112-91=21, Resulting Numbers: [21] 21,67 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 #0,1,4 Current State: 67:[75, 128], Operations: ['8*14=112', '16+112=128'] Exploring Operation: 75*128=9600, Resulting Numbers: [9600] 9600,67 unequal: No Solution Exploring Operation: 75+128=203, Resulting Numbers: [203] 203,67 unequal: No Solution Exploring Operation: 128-75=53, Resulting Numbers: [53] 53,67 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: 67:[75, 16, 22], Operations: ['8+14=22'] Exploring Operation: 16+22=38, Resulting Numbers: [75, 38] Generated Node #0,3,0: 67:[75, 38] Operation: 16+22=38 Exploring Operation: 75-16=59, Resulting Numbers: [22, 59] Generated Node #0,3,1: 67:[22, 59] Operation: 75-16=59 Exploring Operation: 75-22=53, Resulting Numbers: [16, 53] Generated Node #0,3,2: 67:[16, 53] Operation: 75-22=53 Exploring Operation: 75+16=91, Resulting Numbers: [22, 91] Generated Node #0,3,3: 67:[22, 91] Operation: 75+16=91 Exploring Operation: 22-16=6, Resulting Numbers: [75, 6] Generated Node #0,3,4: 67:[75, 6] Operation: 22-16=6 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 67:[75, 38], Operations: ['8+14=22', '16+22=38'] Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,67 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,67 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 #0,3,1 Current State: 67:[22, 59], Operations: ['8+14=22', '75-16=59'] Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 22*59=1298, Resulting Numbers: [1298] 1298,67 unequal: No Solution Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,67 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 #0,3,2 Current State: 67:[16, 53], Operations: ['8+14=22', '75-22=53'] Exploring Operation: 16+53=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 16*53=848, Resulting Numbers: [848] 848,67 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 #0,3,3 Current State: 67:[22, 91], Operations: ['8+14=22', '75+16=91'] Exploring Operation: 22*91=2002, Resulting Numbers: [2002] 2002,67 unequal: No Solution Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 22+91=113, Resulting Numbers: [113] 113,67 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 #0,3,4 Current State: 67:[75, 6], Operations: ['8+14=22', '22-16=6'] Exploring Operation: 75*6=450, Resulting Numbers: [450] 450,67 unequal: No Solution Exploring Operation: 75+6=81, Resulting Numbers: [81] 81,67 unequal: No Solution Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 67:[30, 67], Operations: ['16+14=30', '75-8=67'] Exploring Operation: 30*67=2010, Resulting Numbers: [2010] 2010,67 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 30+67=97, Resulting Numbers: [97] 97,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[75, 38], Operations: ['16+14=30', '8+30=38'] Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,67 unequal: No Solution Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[30, 83], Operations: ['16+14=30', '75+8=83'] Exploring Operation: 30+83=113, Resulting Numbers: [113] 113,67 unequal: No Solution Exploring Operation: 30*83=2490, Resulting Numbers: [2490] 2490,67 unequal: No Solution Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,67 unequal: No Solution Moving to Node #0,2,4 Current State: 67:[75, 22], Operations: ['16+14=30', '30-8=22'] Exploring Operation: 75+22=97, Resulting Numbers: [97] 97,67 unequal: No Solution Exploring Operation: 75-22=53, Resulting Numbers: [53] 53,67 unequal: No Solution Exploring Operation: 75*22=1650, Resulting Numbers: [1650] 1650,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[8, 45], Operations: ['16+14=30', '75-30=45'] Exploring Operation: 8+45=53, Resulting Numbers: [53] 53,67 unequal: No Solution Exploring Operation: 8*45=360, Resulting Numbers: [360] 360,67 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,67 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 97, 2, 89, 32 ]
22
[ "97+2=99", "89+32=121", "121-99=22" ]
Current State: 22:[97, 2, 89, 32], Operations: [] Exploring Operation: 97+2=99, Resulting Numbers: [89, 32, 99] Generated Node #2: [89, 32, 99] from Operation: 97+2=99 Current State: 22:[89, 32, 99], Operations: ['97+2=99'] Exploring Operation: 89+32=121, Resulting Numbers: [99, 121] Generated Node #3: [99, 121] from Operation: 89+32=121 Current State: 22:[99, 121], Operations: ['97+2=99', '89+32=121'] Exploring Operation: 121-99=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[97, 2, 89, 32], Operations: [] Exploring Operation: 97-89=8, Resulting Numbers: [2, 32, 8] Generated Node #0,0: 22:[2, 32, 8] Operation: 97-89=8 Moving to Node #0,0 Current State: 22:[2, 32, 8], Operations: ['97-89=8'] Exploring Operation: 32-8=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 22:[2, 24] Operation: 32-8=24 Moving to Node #0,0,0 Current State: 22:[2, 24], Operations: ['97-89=8', '32-8=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[97, 2, 89, 32], Operations: [] Exploring Operation: 97-89=8, Resulting Numbers: [2, 32, 8] Generated Node #0,0: 22:[2, 32, 8] Operation: 97-89=8 Moving to Node #0,0 Current State: 22:[2, 32, 8], Operations: ['97-89=8'] Exploring Operation: 32-8=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 22:[2, 24] Operation: 32-8=24 Moving to Node #0,0,0 Current State: 22:[2, 24], Operations: ['97-89=8', '32-8=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 48, 21, 42, 10 ]
30
[ "48+42=90", "90/10=9", "21+9=30" ]
Current State: 30:[48, 21, 42, 10], Operations: [] Exploring Operation: 48+42=90, Resulting Numbers: [21, 10, 90] Generated Node #2: [21, 10, 90] from Operation: 48+42=90 Current State: 30:[21, 10, 90], Operations: ['48+42=90'] Exploring Operation: 90/10=9, Resulting Numbers: [21, 9] Generated Node #3: [21, 9] from Operation: 90/10=9 Current State: 30:[21, 9], Operations: ['48+42=90', '90/10=9'] Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[48, 21, 42, 10], Operations: [] Exploring Operation: 48-21=27, Resulting Numbers: [42, 10, 27] Generated Node #0,0: 30:[42, 10, 27] Operation: 48-21=27 Exploring Operation: 42-21=21, Resulting Numbers: [48, 10, 21] Generated Node #0,1: 30:[48, 10, 21] Operation: 42-21=21 Exploring Operation: 42/21=2, Resulting Numbers: [48, 10, 2] Generated Node #0,2: 30:[48, 10, 2] Operation: 42/21=2 Exploring Operation: 48-42=6, Resulting Numbers: [21, 10, 6] Generated Node #0,3: 30:[21, 10, 6] Operation: 48-42=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[21, 10, 6], Operations: ['48-42=6'] Exploring Operation: 21+6=27, Resulting Numbers: [10, 27] Generated Node #0,3,0: 30:[10, 27] Operation: 21+6=27 Exploring Operation: 21-10=11, Resulting Numbers: [6, 11] Generated Node #0,3,1: 30:[6, 11] Operation: 21-10=11 Exploring Operation: 21+10=31, Resulting Numbers: [6, 31] Generated Node #0,3,2: 30:[6, 31] Operation: 21+10=31 Exploring Operation: 21-6=15, Resulting Numbers: [10, 15] Generated Node #0,3,3: 30:[10, 15] Operation: 21-6=15 Moving to Node #0,3,3 Current State: 30:[10, 15], Operations: ['48-42=6', '21-6=15'] Exploring Operation: 10*15=150, Resulting Numbers: [150] 150,30 unequal: No Solution Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,30 unequal: No Solution Moving to Node #0,3,2 Current State: 30:[6, 31], Operations: ['48-42=6', '21+10=31'] Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,30 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,30 unequal: No Solution Moving to Node #0,3,1 Current State: 30:[6, 11], Operations: ['48-42=6', '21-10=11'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[10, 27], Operations: ['48-42=6', '21+6=27'] Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,30 unequal: No Solution Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,30 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 #0,0 Current State: 30:[42, 10, 27], Operations: ['48-21=27'] Exploring Operation: 42-27=15, Resulting Numbers: [10, 15] Generated Node #0,0,0: 30:[10, 15] Operation: 42-27=15 Exploring Operation: 42-10=32, Resulting Numbers: [27, 32] Generated Node #0,0,1: 30:[27, 32] Operation: 42-10=32 Exploring Operation: 10+27=37, Resulting Numbers: [42, 37] Generated Node #0,0,2: 30:[42, 37] Operation: 10+27=37 Exploring Operation: 27-10=17, Resulting Numbers: [42, 17] Generated Node #0,0,3: 30:[42, 17] Operation: 27-10=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[10, 15], Operations: ['48-21=27', '42-27=15'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 10*15=150, Resulting Numbers: [150] 150,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[27, 32], Operations: ['48-21=27', '42-10=32'] Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 27+32=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 27*32=864, Resulting Numbers: [864] 864,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 30:[42, 17], Operations: ['48-21=27', '27-10=17'] Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 30:[42, 37], Operations: ['48-21=27', '10+27=37'] Exploring Operation: 42*37=1554, Resulting Numbers: [1554] 1554,30 unequal: No Solution Exploring Operation: 42+37=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,30 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 #0,2 Current State: 30:[48, 10, 2], Operations: ['42/21=2'] Exploring Operation: 48-10=38, Resulting Numbers: [2, 38] Generated Node #0,2,0: 30:[2, 38] Operation: 48-10=38 Exploring Operation: 10/2=5, Resulting Numbers: [48, 5] Generated Node #0,2,1: 30:[48, 5] Operation: 10/2=5 Exploring Operation: 48/2=24, Resulting Numbers: [10, 24] Generated Node #0,2,2: 30:[10, 24] Operation: 48/2=24 Exploring Operation: 48-2=46, Resulting Numbers: [10, 46] Generated Node #0,2,3: 30:[10, 46] Operation: 48-2=46 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[10, 24], Operations: ['42/21=2', '48/2=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,30 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:[2, 38], Operations: ['42/21=2', '48-10=38'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,30 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,30 unequal: No Solution Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,30 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 #0,2,3 Current State: 30:[10, 46], Operations: ['42/21=2', '48-2=46'] Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,30 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,30 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 #0,2,1 Current State: 30:[48, 5], Operations: ['42/21=2', '10/2=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 48*5=240, Resulting Numbers: [240] 240,30 unequal: No Solution Exploring Operation: 48+5=53, Resulting Numbers: [53] 53,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[48, 10, 21], Operations: ['42-21=21'] Exploring Operation: 10+21=31, Resulting Numbers: [48, 31] Generated Node #0,1,0: 30:[48, 31] Operation: 10+21=31 Exploring Operation: 48-10=38, Resulting Numbers: [21, 38] Generated Node #0,1,1: 30:[21, 38] Operation: 48-10=38 Exploring Operation: 48-21=27, Resulting Numbers: [10, 27] Generated Node #0,1,2: 30:[10, 27] Operation: 48-21=27 Exploring Operation: 21-10=11, Resulting Numbers: [48, 11] Generated Node #0,1,3: 30:[48, 11] Operation: 21-10=11 Moving to Node #0,1,2 Current State: 30:[10, 27], Operations: ['42-21=21', '48-21=27'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,30 unequal: No Solution Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[21, 38], Operations: ['42-21=21', '48-10=38'] Exploring Operation: 21*38=798, Resulting Numbers: [798] 798,30 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[48, 11], Operations: ['42-21=21', '21-10=11'] Exploring Operation: 48*11=528, Resulting Numbers: [528] 528,30 unequal: No Solution Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[48, 31], Operations: ['42-21=21', '10+21=31'] Exploring Operation: 48+31=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 48*31=1488, Resulting Numbers: [1488] 1488,30 unequal: No Solution Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,30 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
[ 1, 4, 73, 61 ]
47
[ "73-61=12", "4*12=48", "48-1=47" ]
Current State: 47:[1, 4, 73, 61], Operations: [] Exploring Operation: 73-61=12, Resulting Numbers: [1, 4, 12] Generated Node #2: [1, 4, 12] from Operation: 73-61=12 Current State: 47:[1, 4, 12], Operations: ['73-61=12'] Exploring Operation: 4*12=48, Resulting Numbers: [1, 48] Generated Node #3: [1, 48] from Operation: 4*12=48 Current State: 47:[1, 48], Operations: ['73-61=12', '4*12=48'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[1, 4, 73, 61], Operations: [] Exploring Operation: 73-1=72, Resulting Numbers: [4, 61, 72] Generated Node #0,0: 47:[4, 61, 72] Operation: 73-1=72 Exploring Operation: 1+4=5, Resulting Numbers: [73, 61, 5] Generated Node #0,1: 47:[73, 61, 5] Operation: 1+4=5 Exploring Operation: 61-1=60, Resulting Numbers: [4, 73, 60] Generated Node #0,2: 47:[4, 73, 60] Operation: 61-1=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[4, 61, 72], Operations: ['73-1=72'] Exploring Operation: 4+61=65, Resulting Numbers: [72, 65] Generated Node #0,0,0: 47:[72, 65] Operation: 4+61=65 Exploring Operation: 61-4=57, Resulting Numbers: [72, 57] Generated Node #0,0,1: 47:[72, 57] Operation: 61-4=57 Exploring Operation: 72-4=68, Resulting Numbers: [61, 68] Generated Node #0,0,2: 47:[61, 68] Operation: 72-4=68 Moving to Node #0,0,1 Current State: 47:[72, 57], Operations: ['73-1=72', '61-4=57'] Exploring Operation: 72+57=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 72*57=4104, Resulting Numbers: [4104] 4104,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[61, 68], Operations: ['73-1=72', '72-4=68'] Exploring Operation: 68-61=7, Resulting Numbers: [7] 7,47 unequal: No Solution Exploring Operation: 61+68=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 61*68=4148, Resulting Numbers: [4148] 4148,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[72, 65], Operations: ['73-1=72', '4+61=65'] Exploring Operation: 72*65=4680, Resulting Numbers: [4680] 4680,47 unequal: No Solution Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,47 unequal: No Solution Exploring Operation: 72+65=137, Resulting Numbers: [137] 137,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[73, 61, 5], Operations: ['1+4=5'] Exploring Operation: 73+5=78, Resulting Numbers: [61, 78] Generated Node #0,1,0: 47:[61, 78] Operation: 73+5=78 Exploring Operation: 73-5=68, Resulting Numbers: [61, 68] Generated Node #0,1,1: 47:[61, 68] Operation: 73-5=68 Exploring Operation: 61-5=56, Resulting Numbers: [73, 56] Generated Node #0,1,2: 47:[73, 56] Operation: 61-5=56 Moving to Node #0,1,1 Current State: 47:[61, 68], Operations: ['1+4=5', '73-5=68'] Exploring Operation: 61+68=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 61*68=4148, Resulting Numbers: [4148] 4148,47 unequal: No Solution Exploring Operation: 68-61=7, Resulting Numbers: [7] 7,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[73, 56], Operations: ['1+4=5', '61-5=56'] Exploring Operation: 73-56=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 73+56=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 73*56=4088, Resulting Numbers: [4088] 4088,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[61, 78], Operations: ['1+4=5', '73+5=78'] Exploring Operation: 61*78=4758, Resulting Numbers: [4758] 4758,47 unequal: No Solution Exploring Operation: 61+78=139, Resulting Numbers: [139] 139,47 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[4, 73, 60], Operations: ['61-1=60'] Exploring Operation: 60-4=56, Resulting Numbers: [73, 56] Generated Node #0,2,0: 47:[73, 56] Operation: 60-4=56 Exploring Operation: 73-4=69, Resulting Numbers: [60, 69] Generated Node #0,2,1: 47:[60, 69] Operation: 73-4=69 Exploring Operation: 4+73=77, Resulting Numbers: [60, 77] Generated Node #0,2,2: 47:[60, 77] Operation: 4+73=77 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 47:[73, 56], Operations: ['61-1=60', '60-4=56'] Exploring Operation: 73+56=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 73-56=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 73*56=4088, Resulting Numbers: [4088] 4088,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 47:[60, 69], Operations: ['61-1=60', '73-4=69'] Exploring Operation: 60*69=4140, Resulting Numbers: [4140] 4140,47 unequal: No Solution Exploring Operation: 69-60=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 60+69=129, Resulting Numbers: [129] 129,47 unequal: No Solution No 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: 47:[60, 77], Operations: ['61-1=60', '4+73=77'] Exploring Operation: 77-60=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 60+77=137, Resulting Numbers: [137] 137,47 unequal: No Solution Exploring Operation: 60*77=4620, Resulting Numbers: [4620] 4620,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 17, 15, 19, 45 ]
96
[ "17+15=32", "19+45=64", "32+64=96" ]
Current State: 96:[17, 15, 19, 45], Operations: [] Exploring Operation: 17+15=32, Resulting Numbers: [19, 45, 32] Generated Node #2: [19, 45, 32] from Operation: 17+15=32 Current State: 96:[19, 45, 32], Operations: ['17+15=32'] Exploring Operation: 19+45=64, Resulting Numbers: [32, 64] Generated Node #3: [32, 64] from Operation: 19+45=64 Current State: 96:[32, 64], Operations: ['17+15=32', '19+45=64'] Exploring Operation: 32+64=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[17, 15, 19, 45], Operations: [] Exploring Operation: 19-15=4, Resulting Numbers: [17, 45, 4] Generated Node #0,0: 96:[17, 45, 4] Operation: 19-15=4 Exploring Operation: 19-17=2, Resulting Numbers: [15, 45, 2] Generated Node #0,1: 96:[15, 45, 2] Operation: 19-17=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[17, 45, 4], Operations: ['19-15=4'] Exploring Operation: 45-17=28, Resulting Numbers: [4, 28] Generated Node #0,0,0: 96:[4, 28] Operation: 45-17=28 Exploring Operation: 45+4=49, Resulting Numbers: [17, 49] Generated Node #0,0,1: 96:[17, 49] Operation: 45+4=49 Moving to Node #0,0,1 Current State: 96:[17, 49], Operations: ['19-15=4', '45+4=49'] Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 17+49=66, Resulting Numbers: [66] 66,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[4, 28], Operations: ['19-15=4', '45-17=28'] Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[15, 45, 2], Operations: ['19-17=2'] Exploring Operation: 45/15=3, Resulting Numbers: [2, 3] Generated Node #0,1,0: 96:[2, 3] Operation: 45/15=3 Exploring Operation: 45-15=30, Resulting Numbers: [2, 30] Generated Node #0,1,1: 96:[2, 30] Operation: 45-15=30 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[2, 3], Operations: ['19-17=2', '45/15=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[2, 30], Operations: ['19-17=2', '45-15=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 33, 62, 90, 85 ]
19
[ "33+62=95", "90-85=5", "95/5=19" ]
Current State: 19:[33, 62, 90, 85], Operations: [] Exploring Operation: 33+62=95, Resulting Numbers: [90, 85, 95] Generated Node #2: [90, 85, 95] from Operation: 33+62=95 Current State: 19:[90, 85, 95], Operations: ['33+62=95'] Exploring Operation: 90-85=5, Resulting Numbers: [95, 5] Generated Node #3: [95, 5] from Operation: 90-85=5 Current State: 19:[95, 5], Operations: ['33+62=95', '90-85=5'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[33, 62, 90, 85], Operations: [] Exploring Operation: 90-85=5, Resulting Numbers: [33, 62, 5] Generated Node #0,0: 19:[33, 62, 5] Operation: 90-85=5 Exploring Operation: 90-62=28, Resulting Numbers: [33, 85, 28] Generated Node #0,1: 19:[33, 85, 28] Operation: 90-62=28 Exploring Operation: 62-33=29, Resulting Numbers: [90, 85, 29] Generated Node #0,2: 19:[90, 85, 29] Operation: 62-33=29 Exploring Operation: 85-62=23, Resulting Numbers: [33, 90, 23] Generated Node #0,3: 19:[33, 90, 23] Operation: 85-62=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[33, 62, 5], Operations: ['90-85=5'] Exploring Operation: 62-33=29, Resulting Numbers: [5, 29] Generated Node #0,0,0: 19:[5, 29] Operation: 62-33=29 Exploring Operation: 33+5=38, Resulting Numbers: [62, 38] Generated Node #0,0,1: 19:[62, 38] Operation: 33+5=38 Exploring Operation: 33-5=28, Resulting Numbers: [62, 28] Generated Node #0,0,2: 19:[62, 28] Operation: 33-5=28 Exploring Operation: 62-5=57, Resulting Numbers: [33, 57] Generated Node #0,0,3: 19:[33, 57] Operation: 62-5=57 Moving to Node #0,0,0 Current State: 19:[5, 29], Operations: ['90-85=5', '62-33=29'] Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,19 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[33, 57], Operations: ['90-85=5', '62-5=57'] Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[62, 28], Operations: ['90-85=5', '33-5=28'] Exploring Operation: 62*28=1736, Resulting Numbers: [1736] 1736,19 unequal: No Solution Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[62, 38], Operations: ['90-85=5', '33+5=38'] Exploring Operation: 62-38=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 62*38=2356, Resulting Numbers: [2356] 2356,19 unequal: No Solution Exploring Operation: 62+38=100, Resulting Numbers: [100] 100,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[33, 85, 28], Operations: ['90-62=28'] Exploring Operation: 85-33=52, Resulting Numbers: [28, 52] Generated Node #0,1,0: 19:[28, 52] Operation: 85-33=52 Exploring Operation: 85-28=57, Resulting Numbers: [33, 57] Generated Node #0,1,1: 19:[33, 57] Operation: 85-28=57 Exploring Operation: 33+85=118, Resulting Numbers: [28, 118] Generated Node #0,1,2: 19:[28, 118] Operation: 33+85=118 Exploring Operation: 33-28=5, Resulting Numbers: [85, 5] Generated Node #0,1,3: 19:[85, 5] Operation: 33-28=5 Moving to Node #0,1,0 Current State: 19:[28, 52], Operations: ['90-62=28', '85-33=52'] Exploring Operation: 28+52=80, Resulting Numbers: [80] 80,19 unequal: No Solution Exploring Operation: 52-28=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 28*52=1456, Resulting Numbers: [1456] 1456,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[33, 57], Operations: ['90-62=28', '85-28=57'] Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,19 unequal: No Solution Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,19 unequal: No Solution Moving to Node #0,1,3 Current State: 19:[85, 5], Operations: ['90-62=28', '33-28=5'] Exploring Operation: 85*5=425, Resulting Numbers: [425] 425,19 unequal: No Solution Exploring Operation: 85+5=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,19 unequal: No Solution Exploring Operation: 85-5=80, Resulting Numbers: [80] 80,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[28, 118], Operations: ['90-62=28', '33+85=118'] Exploring Operation: 118-28=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 28*118=3304, Resulting Numbers: [3304] 3304,19 unequal: No Solution Exploring Operation: 28+118=146, Resulting Numbers: [146] 146,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[33, 90, 23], Operations: ['85-62=23'] Exploring Operation: 90-33=57, Resulting Numbers: [23, 57] Generated Node #0,3,0: 19:[23, 57] Operation: 90-33=57 Exploring Operation: 33-23=10, Resulting Numbers: [90, 10] Generated Node #0,3,1: 19:[90, 10] Operation: 33-23=10 Exploring Operation: 33+90=123, Resulting Numbers: [23, 123] Generated Node #0,3,2: 19:[23, 123] Operation: 33+90=123 Exploring Operation: 90-23=67, Resulting Numbers: [33, 67] Generated Node #0,3,3: 19:[33, 67] Operation: 90-23=67 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 19:[23, 57], Operations: ['85-62=23', '90-33=57'] Exploring Operation: 23+57=80, Resulting Numbers: [80] 80,19 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 23*57=1311, Resulting Numbers: [1311] 1311,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 19:[33, 67], Operations: ['85-62=23', '90-23=67'] Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 33+67=100, Resulting Numbers: [100] 100,19 unequal: No Solution Exploring Operation: 33*67=2211, Resulting Numbers: [2211] 2211,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 19:[90, 10], Operations: ['85-62=23', '33-23=10'] Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,19 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,19 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,19 unequal: No Solution Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 19:[23, 123], Operations: ['85-62=23', '33+90=123'] Exploring Operation: 23*123=2829, Resulting Numbers: [2829] 2829,19 unequal: No Solution Exploring Operation: 123-23=100, Resulting Numbers: [100] 100,19 unequal: No Solution Exploring Operation: 23+123=146, Resulting Numbers: [146] 146,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[90, 85, 29], Operations: ['62-33=29'] Exploring Operation: 90-29=61, Resulting Numbers: [85, 61] Generated Node #0,2,0: 19:[85, 61] Operation: 90-29=61 Exploring Operation: 90-85=5, Resulting Numbers: [29, 5] Generated Node #0,2,1: 19:[29, 5] Operation: 90-85=5 Exploring Operation: 90+85=175, Resulting Numbers: [29, 175] Generated Node #0,2,2: 19:[29, 175] Operation: 90+85=175 Exploring Operation: 85-29=56, Resulting Numbers: [90, 56] Generated Node #0,2,3: 19:[90, 56] Operation: 85-29=56 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 19:[29, 5], Operations: ['62-33=29', '90-85=5'] Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,19 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 19:[85, 61], Operations: ['62-33=29', '90-29=61'] Exploring Operation: 85+61=146, Resulting Numbers: [146] 146,19 unequal: No Solution Exploring Operation: 85-61=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 85*61=5185, Resulting Numbers: [5185] 5185,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 19:[90, 56], Operations: ['62-33=29', '85-29=56'] Exploring Operation: 90-56=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 90*56=5040, Resulting Numbers: [5040] 5040,19 unequal: No Solution Exploring Operation: 90+56=146, Resulting Numbers: [146] 146,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 19:[29, 175], Operations: ['62-33=29', '90+85=175'] Exploring Operation: 175-29=146, Resulting Numbers: [146] 146,19 unequal: No Solution Exploring Operation: 29*175=5075, Resulting Numbers: [5075] 5075,19 unequal: No Solution Exploring Operation: 29+175=204, Resulting Numbers: [204] 204,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 68, 56, 72, 40 ]
70
[ "68-40=28", "56/28=2", "72-2=70" ]
Current State: 70:[68, 56, 72, 40], Operations: [] Exploring Operation: 68-40=28, Resulting Numbers: [56, 72, 28] Generated Node #2: [56, 72, 28] from Operation: 68-40=28 Current State: 70:[56, 72, 28], Operations: ['68-40=28'] Exploring Operation: 56/28=2, Resulting Numbers: [72, 2] Generated Node #3: [72, 2] from Operation: 56/28=2 Current State: 70:[72, 2], Operations: ['68-40=28', '56/28=2'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[68, 56, 72, 40], Operations: [] Exploring Operation: 72-40=32, Resulting Numbers: [68, 56, 32] Generated Node #0,0: 70:[68, 56, 32] Operation: 72-40=32 Exploring Operation: 68-56=12, Resulting Numbers: [72, 40, 12] Generated Node #0,1: 70:[72, 40, 12] Operation: 68-56=12 Exploring Operation: 56-40=16, Resulting Numbers: [68, 72, 16] Generated Node #0,2: 70:[68, 72, 16] Operation: 56-40=16 Exploring Operation: 72-68=4, Resulting Numbers: [56, 40, 4] Generated Node #0,3: 70:[56, 40, 4] Operation: 72-68=4 Exploring Operation: 72-56=16, Resulting Numbers: [68, 40, 16] Generated Node #0,4: 70:[68, 40, 16] Operation: 72-56=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[68, 72, 16], Operations: ['56-40=16'] Exploring Operation: 72-68=4, Resulting Numbers: [16, 4] Generated Node #0,2,0: 70:[16, 4] Operation: 72-68=4 Exploring Operation: 72+16=88, Resulting Numbers: [68, 88] Generated Node #0,2,1: 70:[68, 88] Operation: 72+16=88 Exploring Operation: 72-16=56, Resulting Numbers: [68, 56] Generated Node #0,2,2: 70:[68, 56] Operation: 72-16=56 Exploring Operation: 68-16=52, Resulting Numbers: [72, 52] Generated Node #0,2,3: 70:[72, 52] Operation: 68-16=52 Exploring Operation: 68+16=84, Resulting Numbers: [72, 84] Generated Node #0,2,4: 70:[72, 84] Operation: 68+16=84 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[16, 4], Operations: ['56-40=16', '72-68=4'] Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,70 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 70:[68, 56], Operations: ['56-40=16', '72-16=56'] Exploring Operation: 68*56=3808, Resulting Numbers: [3808] 3808,70 unequal: No Solution Exploring Operation: 68+56=124, Resulting Numbers: [124] 124,70 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 70:[72, 84], Operations: ['56-40=16', '68+16=84'] Exploring Operation: 84-72=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 72*84=6048, Resulting Numbers: [6048] 6048,70 unequal: No Solution Exploring Operation: 72+84=156, Resulting Numbers: [156] 156,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 70:[72, 52], Operations: ['56-40=16', '68-16=52'] Exploring Operation: 72-52=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 72+52=124, Resulting Numbers: [124] 124,70 unequal: No Solution Exploring Operation: 72*52=3744, Resulting Numbers: [3744] 3744,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 70:[68, 88], Operations: ['56-40=16', '72+16=88'] Exploring Operation: 68+88=156, Resulting Numbers: [156] 156,70 unequal: No Solution Exploring Operation: 88-68=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 68*88=5984, Resulting Numbers: [5984] 5984,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[72, 40, 12], Operations: ['68-56=12'] Exploring Operation: 72/12=6, Resulting Numbers: [40, 6] Generated Node #0,1,0: 70:[40, 6] Operation: 72/12=6 Exploring Operation: 72-12=60, Resulting Numbers: [40, 60] Generated Node #0,1,1: 70:[40, 60] Operation: 72-12=60 Exploring Operation: 72+12=84, Resulting Numbers: [40, 84] Generated Node #0,1,2: 70:[40, 84] Operation: 72+12=84 Exploring Operation: 40-12=28, Resulting Numbers: [72, 28] Generated Node #0,1,3: 70:[72, 28] Operation: 40-12=28 Exploring Operation: 72-40=32, Resulting Numbers: [12, 32] Generated Node #0,1,4: 70:[12, 32] Operation: 72-40=32 Moving to Node #0,1,4 Current State: 70:[12, 32], Operations: ['68-56=12', '72-40=32'] Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[40, 6], Operations: ['68-56=12', '72/12=6'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,70 unequal: No Solution Exploring Operation: 40*6=240, Resulting Numbers: [240] 240,70 unequal: No Solution Exploring Operation: 40+6=46, Resulting Numbers: [46] 46,70 unequal: No Solution Moving to Node #0,1,3 Current State: 70:[72, 28], Operations: ['68-56=12', '40-12=28'] Exploring Operation: 72+28=100, Resulting Numbers: [100] 100,70 unequal: No Solution Exploring Operation: 72*28=2016, Resulting Numbers: [2016] 2016,70 unequal: No Solution Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[40, 60], Operations: ['68-56=12', '72-12=60'] Exploring Operation: 60-40=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 40+60=100, Resulting Numbers: [100] 100,70 unequal: No Solution Exploring Operation: 40*60=2400, Resulting Numbers: [2400] 2400,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[40, 84], Operations: ['68-56=12', '72+12=84'] Exploring Operation: 40*84=3360, Resulting Numbers: [3360] 3360,70 unequal: No Solution Exploring Operation: 40+84=124, Resulting Numbers: [124] 124,70 unequal: No Solution Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,70 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 #0,4 Current State: 70:[68, 40, 16], Operations: ['72-56=16'] Exploring Operation: 68+16=84, Resulting Numbers: [40, 84] Generated Node #0,4,0: 70:[40, 84] Operation: 68+16=84 Exploring Operation: 68-16=52, Resulting Numbers: [40, 52] Generated Node #0,4,1: 70:[40, 52] Operation: 68-16=52 Exploring Operation: 68-40=28, Resulting Numbers: [16, 28] Generated Node #0,4,2: 70:[16, 28] Operation: 68-40=28 Exploring Operation: 40-16=24, Resulting Numbers: [68, 24] Generated Node #0,4,3: 70:[68, 24] Operation: 40-16=24 Exploring Operation: 40+16=56, Resulting Numbers: [68, 56] Generated Node #0,4,4: 70:[68, 56] Operation: 40+16=56 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 70:[16, 28], Operations: ['72-56=16', '68-40=28'] Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 16*28=448, Resulting Numbers: [448] 448,70 unequal: No Solution Exploring Operation: 16+28=44, Resulting Numbers: [44] 44,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 70:[68, 24], Operations: ['72-56=16', '40-16=24'] Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,70 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 68*24=1632, Resulting Numbers: [1632] 1632,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 70:[68, 56], Operations: ['72-56=16', '40+16=56'] Exploring Operation: 68+56=124, Resulting Numbers: [124] 124,70 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 68*56=3808, Resulting Numbers: [3808] 3808,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 70:[40, 84], Operations: ['72-56=16', '68+16=84'] Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 40+84=124, Resulting Numbers: [124] 124,70 unequal: No Solution Exploring Operation: 40*84=3360, Resulting Numbers: [3360] 3360,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 70:[40, 52], Operations: ['72-56=16', '68-16=52'] Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,70 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[68, 56, 32], Operations: ['72-40=32'] Exploring Operation: 68+32=100, Resulting Numbers: [56, 100] Generated Node #0,0,0: 70:[56, 100] Operation: 68+32=100 Exploring Operation: 68-56=12, Resulting Numbers: [32, 12] Generated Node #0,0,1: 70:[32, 12] Operation: 68-56=12 Exploring Operation: 56-32=24, Resulting Numbers: [68, 24] Generated Node #0,0,2: 70:[68, 24] Operation: 56-32=24 Exploring Operation: 56+32=88, Resulting Numbers: [68, 88] Generated Node #0,0,3: 70:[68, 88] Operation: 56+32=88 Exploring Operation: 68-32=36, Resulting Numbers: [56, 36] Generated Node #0,0,4: 70:[56, 36] Operation: 68-32=36 Moving to Node #0,0,1 Current State: 70:[32, 12], Operations: ['72-40=32', '68-56=12'] Exploring Operation: 32+12=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 32*12=384, Resulting Numbers: [384] 384,70 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[68, 24], Operations: ['72-40=32', '56-32=24'] Exploring Operation: 68*24=1632, Resulting Numbers: [1632] 1632,70 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,70 unequal: No Solution Moving to Node #0,0,4 Current State: 70:[56, 36], Operations: ['72-40=32', '68-32=36'] Exploring Operation: 56*36=2016, Resulting Numbers: [2016] 2016,70 unequal: No Solution Exploring Operation: 56+36=92, Resulting Numbers: [92] 92,70 unequal: No Solution Exploring Operation: 56-36=20, Resulting Numbers: [20] 20,70 unequal: No Solution Moving to Node #0,0,3 Current State: 70:[68, 88], Operations: ['72-40=32', '56+32=88'] Exploring Operation: 68*88=5984, Resulting Numbers: [5984] 5984,70 unequal: No Solution Exploring Operation: 68+88=156, Resulting Numbers: [156] 156,70 unequal: No Solution Exploring Operation: 88-68=20, Resulting Numbers: [20] 20,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[56, 100], Operations: ['72-40=32', '68+32=100'] Exploring Operation: 56+100=156, Resulting Numbers: [156] 156,70 unequal: No Solution Exploring Operation: 56*100=5600, Resulting Numbers: [5600] 5600,70 unequal: No Solution Exploring Operation: 100-56=44, Resulting Numbers: [44] 44,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[56, 40, 4], Operations: ['72-68=4'] Exploring Operation: 40-4=36, Resulting Numbers: [56, 36] Generated Node #0,3,0: 70:[56, 36] Operation: 40-4=36 Exploring Operation: 40/4=10, Resulting Numbers: [56, 10] Generated Node #0,3,1: 70:[56, 10] Operation: 40/4=10 Exploring Operation: 56-40=16, Resulting Numbers: [4, 16] Generated Node #0,3,2: 70:[4, 16] Operation: 56-40=16 Exploring Operation: 56+4=60, Resulting Numbers: [40, 60] Generated Node #0,3,3: 70:[40, 60] Operation: 56+4=60 Exploring Operation: 56/4=14, Resulting Numbers: [40, 14] Generated Node #0,3,4: 70:[40, 14] Operation: 56/4=14 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 70:[4, 16], Operations: ['72-68=4', '56-40=16'] Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,70 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 70:[40, 14], Operations: ['72-68=4', '56/4=14'] Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,70 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,70 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 70:[56, 10], Operations: ['72-68=4', '40/4=10'] Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,70 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,70 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 70:[56, 36], Operations: ['72-68=4', '40-4=36'] Exploring Operation: 56-36=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 56*36=2016, Resulting Numbers: [2016] 2016,70 unequal: No Solution Exploring Operation: 56+36=92, Resulting Numbers: [92] 92,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 70:[40, 60], Operations: ['72-68=4', '56+4=60'] Exploring Operation: 40+60=100, Resulting Numbers: [100] 100,70 unequal: No Solution Exploring Operation: 40*60=2400, Resulting Numbers: [2400] 2400,70 unequal: No Solution Exploring Operation: 60-40=20, Resulting Numbers: [20] 20,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 37, 26, 1, 52 ]
36
[ "37+1=38", "52/26=2", "38-2=36" ]
Current State: 36:[37, 26, 1, 52], Operations: [] Exploring Operation: 37+1=38, Resulting Numbers: [26, 52, 38] Generated Node #2: [26, 52, 38] from Operation: 37+1=38 Current State: 36:[26, 52, 38], Operations: ['37+1=38'] Exploring Operation: 52/26=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 52/26=2 Current State: 36:[38, 2], Operations: ['37+1=38', '52/26=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[37, 26, 1, 52], Operations: [] Exploring Operation: 37-26=11, Resulting Numbers: [1, 52, 11] Generated Node #0,0: 36:[1, 52, 11] Operation: 37-26=11 Exploring Operation: 52/26=2, Resulting Numbers: [37, 1, 2] Generated Node #0,1: 36:[37, 1, 2] Operation: 52/26=2 Exploring Operation: 37-1=36, Resulting Numbers: [26, 52, 36] Generated Node #0,2: 36:[26, 52, 36] Operation: 37-1=36 Exploring Operation: 52-26=26, Resulting Numbers: [37, 1, 26] Generated Node #0,3: 36:[37, 1, 26] Operation: 52-26=26 Exploring Operation: 52-37=15, Resulting Numbers: [26, 1, 15] Generated Node #0,4: 36:[26, 1, 15] Operation: 52-37=15 Moving to Node #0,1 Current State: 36:[37, 1, 2], Operations: ['52/26=2'] Exploring Operation: 1*2=2, Resulting Numbers: [37, 2] Generated Node #0,1,0: 36:[37, 2] Operation: 1*2=2 Exploring Operation: 1+2=3, Resulting Numbers: [37, 3] Generated Node #0,1,1: 36:[37, 3] Operation: 1+2=3 Exploring Operation: 37*1=37, Resulting Numbers: [2, 37] Generated Node #0,1,2: 36:[2, 37] Operation: 37*1=37 Exploring Operation: 37-1=36, Resulting Numbers: [2, 36] Generated Node #0,1,3: 36:[2, 36] Operation: 37-1=36 Exploring Operation: 37/1=37, Resulting Numbers: [2, 37] Generated Node #0,1,4: 36:[2, 37] Operation: 37/1=37 Moving to Node #0,3 Current State: 36:[37, 1, 26], Operations: ['52-26=26'] Exploring Operation: 26-1=25, Resulting Numbers: [37, 25] Generated Node #0,3,0: 36:[37, 25] Operation: 26-1=25 Exploring Operation: 37*1=37, Resulting Numbers: [26, 37] Generated Node #0,3,1: 36:[26, 37] Operation: 37*1=37 Exploring Operation: 37-26=11, Resulting Numbers: [1, 11] Generated Node #0,3,2: 36:[1, 11] Operation: 37-26=11 Exploring Operation: 37-1=36, Resulting Numbers: [26, 36] Generated Node #0,3,3: 36:[26, 36] Operation: 37-1=36 Exploring Operation: 37/1=37, Resulting Numbers: [26, 37] Generated Node #0,3,4: 36:[26, 37] Operation: 37/1=37 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 36:[1, 11], Operations: ['52-26=26', '37-26=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,36 unequal: No Solution Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[37, 25], Operations: ['52-26=26', '26-1=25'] Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,36 unequal: No Solution Exploring Operation: 37*25=925, Resulting Numbers: [925] 925,36 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 36:[26, 36], Operations: ['52-26=26', '37-1=36'] Exploring Operation: 26+36=62, Resulting Numbers: [62] 62,36 unequal: No Solution Exploring Operation: 26*36=936, Resulting Numbers: [936] 936,36 unequal: No Solution Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 36:[26, 37], Operations: ['52-26=26', '37*1=37'] Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 26*37=962, Resulting Numbers: [962] 962,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 36:[26, 37], Operations: ['52-26=26', '37/1=37'] Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 26*37=962, Resulting Numbers: [962] 962,36 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: 36:[26, 1, 15], Operations: ['52-37=15'] Exploring Operation: 1+15=16, Resulting Numbers: [26, 16] Generated Node #0,4,0: 36:[26, 16] Operation: 1+15=16 Exploring Operation: 26-15=11, Resulting Numbers: [1, 11] Generated Node #0,4,1: 36:[1, 11] Operation: 26-15=11 Exploring Operation: 15-1=14, Resulting Numbers: [26, 14] Generated Node #0,4,2: 36:[26, 14] Operation: 15-1=14 Exploring Operation: 26-1=25, Resulting Numbers: [15, 25] Generated Node #0,4,3: 36:[15, 25] Operation: 26-1=25 Exploring Operation: 26+15=41, Resulting Numbers: [1, 41] Generated Node #0,4,4: 36:[1, 41] Operation: 26+15=41 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 36:[1, 11], Operations: ['52-37=15', '26-15=11'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 36:[1, 41], Operations: ['52-37=15', '26+15=41'] Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,36 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 36:[26, 16], Operations: ['52-37=15', '1+15=16'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 36:[26, 14], Operations: ['52-37=15', '15-1=14'] Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,36 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,36 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 36:[15, 25], Operations: ['52-37=15', '26-1=25'] Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,36 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,36 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,36 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: 36:[1, 52, 11], Operations: ['37-26=11'] Exploring Operation: 52-11=41, Resulting Numbers: [1, 41] Generated Node #0,0,0: 36:[1, 41] Operation: 52-11=41 Exploring Operation: 1*52=52, Resulting Numbers: [11, 52] Generated Node #0,0,1: 36:[11, 52] Operation: 1*52=52 Exploring Operation: 52-1=51, Resulting Numbers: [11, 51] Generated Node #0,0,2: 36:[11, 51] Operation: 52-1=51 Exploring Operation: 1+11=12, Resulting Numbers: [52, 12] Generated Node #0,0,3: 36:[52, 12] Operation: 1+11=12 Exploring Operation: 52/1=52, Resulting Numbers: [11, 52] Generated Node #0,0,4: 36:[11, 52] Operation: 52/1=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[1, 41], Operations: ['37-26=11', '52-11=41'] Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,36 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 36:[11, 51], Operations: ['37-26=11', '52-1=51'] Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,36 unequal: No Solution Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,36 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 36:[52, 12], Operations: ['37-26=11', '1+11=12'] Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,36 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,36 unequal: No Solution Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[11, 52], Operations: ['37-26=11', '1*52=52'] Exploring Operation: 11+52=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 11*52=572, Resulting Numbers: [572] 572,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 36:[11, 52], Operations: ['37-26=11', '52/1=52'] Exploring Operation: 11+52=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 11*52=572, Resulting Numbers: [572] 572,36 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 36:[26, 52, 36], Operations: ['37-1=36'] Exploring Operation: 26+52=78, Resulting Numbers: [36, 78] Generated Node #0,2,0: 36:[36, 78] Operation: 26+52=78 Exploring Operation: 52-36=16, Resulting Numbers: [26, 16] Generated Node #0,2,1: 36:[26, 16] Operation: 52-36=16 Exploring Operation: 36-26=10, Resulting Numbers: [52, 10] Generated Node #0,2,2: 36:[52, 10] Operation: 36-26=10 Exploring Operation: 52/26=2, Resulting Numbers: [36, 2] Generated Node #0,2,3: 36:[36, 2] Operation: 52/26=2 Exploring Operation: 52-26=26, Resulting Numbers: [36, 26] Generated Node #0,2,4: 36:[36, 26] Operation: 52-26=26 Moving to Node #0,1,3 Current State: 36:[2, 36], Operations: ['52/26=2', '37-1=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,36 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,36 unequal: No Solution Moving to Node #0,2,3 Current State: 36:[36, 2], Operations: ['37-1=36', '52/26=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,36 unequal: No Solution Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[37, 3], Operations: ['52/26=2', '1+2=3'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,36 unequal: No Solution Exploring Operation: 37*3=111, Resulting Numbers: [111] 111,36 unequal: No Solution Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[37, 2], Operations: ['52/26=2', '1*2=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,36 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,36 unequal: No Solution Moving to Node #0,1,4 Current State: 36:[2, 37], Operations: ['52/26=2', '37/1=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,36 unequal: No Solution Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[2, 37], Operations: ['52/26=2', '37*1=37'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,36 unequal: No Solution Moving to Node #0,2,4 Current State: 36:[36, 26], Operations: ['37-1=36', '52-26=26'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 36*26=936, Resulting Numbers: [936] 936,36 unequal: No Solution Exploring Operation: 36+26=62, Resulting Numbers: [62] 62,36 unequal: No Solution Moving to Node #0,2,1 Current State: 36:[26, 16], Operations: ['37-1=36', '52-36=16'] Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,36 unequal: No Solution Moving to Node #0,2,2 Current State: 36:[52, 10], Operations: ['37-1=36', '36-26=10'] Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,36 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,36 unequal: No Solution Moving to Node #0,2,0 Current State: 36:[36, 78], Operations: ['37-1=36', '26+52=78'] Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,36 unequal: No Solution Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,36 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 80, 8, 22, 94 ]
90
[ "80+8=88", "88/22=4", "94-4=90" ]
Current State: 90:[80, 8, 22, 94], Operations: [] Exploring Operation: 80+8=88, Resulting Numbers: [22, 94, 88] Generated Node #2: [22, 94, 88] from Operation: 80+8=88 Current State: 90:[22, 94, 88], Operations: ['80+8=88'] Exploring Operation: 88/22=4, Resulting Numbers: [94, 4] Generated Node #3: [94, 4] from Operation: 88/22=4 Current State: 90:[94, 4], Operations: ['80+8=88', '88/22=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[80, 8, 22, 94], Operations: [] Exploring Operation: 80+8=88, Resulting Numbers: [22, 94, 88] Generated Node #0,0: 90:[22, 94, 88] Operation: 80+8=88 Exploring Operation: 80/8=10, Resulting Numbers: [22, 94, 10] Generated Node #0,1: 90:[22, 94, 10] Operation: 80/8=10 Exploring Operation: 94-80=14, Resulting Numbers: [8, 22, 14] Generated Node #0,2: 90:[8, 22, 14] Operation: 94-80=14 Moving to Node #0,2 Current State: 90:[8, 22, 14], Operations: ['94-80=14'] Exploring Operation: 22-14=8, Resulting Numbers: [8, 8] Generated Node #0,2,0: 90:[8, 8] Operation: 22-14=8 Exploring Operation: 8+22=30, Resulting Numbers: [14, 30] Generated Node #0,2,1: 90:[14, 30] Operation: 8+22=30 Exploring Operation: 22-8=14, Resulting Numbers: [14, 14] Generated Node #0,2,2: 90:[14, 14] Operation: 22-8=14 Moving to Node #0,1 Current State: 90:[22, 94, 10], Operations: ['80/8=10'] Exploring Operation: 22-10=12, Resulting Numbers: [94, 12] Generated Node #0,1,0: 90:[94, 12] Operation: 22-10=12 Exploring Operation: 22+10=32, Resulting Numbers: [94, 32] Generated Node #0,1,1: 90:[94, 32] Operation: 22+10=32 Exploring Operation: 94-10=84, Resulting Numbers: [22, 84] Generated Node #0,1,2: 90:[22, 84] Operation: 94-10=84 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[94, 12], Operations: ['80/8=10', '22-10=12'] Exploring Operation: 94+12=106, Resulting Numbers: [106] 106,90 unequal: No Solution Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,90 unequal: No Solution Exploring Operation: 94*12=1128, Resulting Numbers: [1128] 1128,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[94, 32], Operations: ['80/8=10', '22+10=32'] Exploring Operation: 94+32=126, Resulting Numbers: [126] 126,90 unequal: No Solution Exploring Operation: 94-32=62, Resulting Numbers: [62] 62,90 unequal: No Solution Exploring Operation: 94*32=3008, Resulting Numbers: [3008] 3008,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[22, 84], Operations: ['80/8=10', '94-10=84'] Exploring Operation: 22+84=106, Resulting Numbers: [106] 106,90 unequal: No Solution Exploring Operation: 22*84=1848, Resulting Numbers: [1848] 1848,90 unequal: No Solution Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,90 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: 90:[22, 94, 88], Operations: ['80+8=88'] Exploring Operation: 94-88=6, Resulting Numbers: [22, 6] Generated Node #0,0,0: 90:[22, 6] Operation: 94-88=6 Exploring Operation: 94-22=72, Resulting Numbers: [88, 72] Generated Node #0,0,1: 90:[88, 72] Operation: 94-22=72 Exploring Operation: 88/22=4, Resulting Numbers: [94, 4] Generated Node #0,0,2: 90:[94, 4] Operation: 88/22=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[22, 6], Operations: ['80+8=88', '94-88=6'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,90 unequal: No Solution Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,90 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[94, 4], Operations: ['80+8=88', '88/22=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[80, 8, 22, 94], Operations: [] Exploring Operation: 80+8=88, Resulting Numbers: [22, 94, 88] Generated Node #0,0: 90:[22, 94, 88] Operation: 80+8=88 Moving to Node #0,0 Current State: 90:[22, 94, 88], Operations: ['80+8=88'] Exploring Operation: 88/22=4, Resulting Numbers: [94, 4] Generated Node #0,0,2: 90:[94, 4] Operation: 88/22=4 Moving to Node #0,0,2 Current State: 90:[94, 4], Operations: ['80+8=88', '88/22=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
sum_heuristic
[ 15, 88, 37, 5 ]
31
[ "88-15=73", "37+5=42", "73-42=31" ]
Current State: 31:[15, 88, 37, 5], Operations: [] Exploring Operation: 88-15=73, Resulting Numbers: [37, 5, 73] Generated Node #2: [37, 5, 73] from Operation: 88-15=73 Current State: 31:[37, 5, 73], Operations: ['88-15=73'] Exploring Operation: 37+5=42, Resulting Numbers: [73, 42] Generated Node #3: [73, 42] from Operation: 37+5=42 Current State: 31:[73, 42], Operations: ['88-15=73', '37+5=42'] Exploring Operation: 73-42=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[15, 88, 37, 5], Operations: [] Exploring Operation: 88-15=73, Resulting Numbers: [37, 5, 73] Generated Node #0,0: 31:[37, 5, 73] Operation: 88-15=73 Exploring Operation: 15+5=20, Resulting Numbers: [88, 37, 20] Generated Node #0,1: 31:[88, 37, 20] Operation: 15+5=20 Exploring Operation: 88-37=51, Resulting Numbers: [15, 5, 51] Generated Node #0,2: 31:[15, 5, 51] Operation: 88-37=51 Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[15, 5, 51], Operations: ['88-37=51'] Exploring Operation: 51-5=46, Resulting Numbers: [15, 46] Generated Node #0,2,0: 31:[15, 46] Operation: 51-5=46 Exploring Operation: 15+5=20, Resulting Numbers: [51, 20] Generated Node #0,2,1: 31:[51, 20] Operation: 15+5=20 Exploring Operation: 51-15=36, Resulting Numbers: [5, 36] Generated Node #0,2,2: 31:[5, 36] Operation: 51-15=36 Moving to Node #0,2,0 Current State: 31:[15, 46], Operations: ['88-37=51', '51-5=46'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[15, 88, 37, 5], Operations: [] Exploring Operation: 88-37=51, Resulting Numbers: [15, 5, 51] Generated Node #0,2: 31:[15, 5, 51] Operation: 88-37=51 Moving to Node #0,2 Current State: 31:[15, 5, 51], Operations: ['88-37=51'] Exploring Operation: 51-5=46, Resulting Numbers: [15, 46] Generated Node #0,2,0: 31:[15, 46] Operation: 51-5=46 Moving to Node #0,2,0 Current State: 31:[15, 46], Operations: ['88-37=51', '51-5=46'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 26, 1, 33, 2 ]
57
[ "26*1=26", "33-2=31", "26+31=57" ]
Current State: 57:[26, 1, 33, 2], Operations: [] Exploring Operation: 26*1=26, Resulting Numbers: [33, 2, 26] Generated Node #2: [33, 2, 26] from Operation: 26*1=26 Current State: 57:[33, 2, 26], Operations: ['26*1=26'] Exploring Operation: 33-2=31, Resulting Numbers: [26, 31] Generated Node #3: [26, 31] from Operation: 33-2=31 Current State: 57:[26, 31], Operations: ['26*1=26', '33-2=31'] Exploring Operation: 26+31=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[26, 1, 33, 2], Operations: [] Exploring Operation: 26+33=59, Resulting Numbers: [1, 2, 59] Generated Node #0,0: 57:[1, 2, 59] Operation: 26+33=59 Exploring Operation: 33-26=7, Resulting Numbers: [1, 2, 7] Generated Node #0,1: 57:[1, 2, 7] Operation: 33-26=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[1, 2, 59], Operations: ['26+33=59'] Exploring Operation: 1+2=3, Resulting Numbers: [59, 3] Generated Node #0,0,0: 57:[59, 3] Operation: 1+2=3 Exploring Operation: 59-1=58, Resulting Numbers: [2, 58] Generated Node #0,0,1: 57:[2, 58] Operation: 59-1=58 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[59, 3], Operations: ['26+33=59', '1+2=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,57 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 #0,0,1 Current State: 57:[2, 58], Operations: ['26+33=59', '59-1=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,57 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,57 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 #0,1 Current State: 57:[1, 2, 7], Operations: ['33-26=7'] Exploring Operation: 7-1=6, Resulting Numbers: [2, 6] Generated Node #0,1,0: 57:[2, 6] Operation: 7-1=6 Exploring Operation: 1+2=3, Resulting Numbers: [7, 3] Generated Node #0,1,1: 57:[7, 3] Operation: 1+2=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[2, 6], Operations: ['33-26=7', '7-1=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,57 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 57:[7, 3], Operations: ['33-26=7', '1+2=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,57 unequal: No Solution Exploring Operation: 7*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 No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic