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
[ 60, 9, 98, 7 ]
54
[ "60-9=51", "98+7=105", "105-51=54" ]
Current State: 54:[60, 9, 98, 7], Operations: [] Exploring Operation: 60-9=51, Resulting Numbers: [98, 7, 51] Generated Node #2: [98, 7, 51] from Operation: 60-9=51 Current State: 54:[98, 7, 51], Operations: ['60-9=51'] Exploring Operation: 98+7=105, Resulting Numbers: [51, 105] Generated Node #3: [51, 105] from Operation: 98+7=105 Current State: 54:[51, 105], Operations: ['60-9=51', '98+7=105'] Exploring Operation: 105-51=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[60, 9, 98, 7], Operations: [] Exploring Operation: 98-60=38, Resulting Numbers: [9, 7, 38] Generated Node #0,0: 54:[9, 7, 38] Operation: 98-60=38 Exploring Operation: 98-9=89, Resulting Numbers: [60, 7, 89] Generated Node #0,1: 54:[60, 7, 89] Operation: 98-9=89 Exploring Operation: 98/7=14, Resulting Numbers: [60, 9, 14] Generated Node #0,2: 54:[60, 9, 14] Operation: 98/7=14 Exploring Operation: 98-7=91, Resulting Numbers: [60, 9, 91] Generated Node #0,3: 54:[60, 9, 91] Operation: 98-7=91 Exploring Operation: 60-7=53, Resulting Numbers: [9, 98, 53] Generated Node #0,4: 54:[9, 98, 53] Operation: 60-7=53 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[60, 9, 14], Operations: ['98/7=14'] Exploring Operation: 9+14=23, Resulting Numbers: [60, 23] Generated Node #0,2,0: 54:[60, 23] Operation: 9+14=23 Exploring Operation: 14-9=5, Resulting Numbers: [60, 5] Generated Node #0,2,1: 54:[60, 5] Operation: 14-9=5 Exploring Operation: 60-14=46, Resulting Numbers: [9, 46] Generated Node #0,2,2: 54:[9, 46] Operation: 60-14=46 Exploring Operation: 60+9=69, Resulting Numbers: [14, 69] Generated Node #0,2,3: 54:[14, 69] Operation: 60+9=69 Exploring Operation: 60-9=51, Resulting Numbers: [14, 51] Generated Node #0,2,4: 54:[14, 51] Operation: 60-9=51 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 54:[60, 5], Operations: ['98/7=14', '14-9=5'] Exploring Operation: 60*5=300, Resulting Numbers: [300] 300,54 unequal: No Solution Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,54 unequal: No Solution Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 54:[14, 51], Operations: ['98/7=14', '60-9=51'] Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 14+51=65, Resulting Numbers: [65] 65,54 unequal: No Solution Exploring Operation: 14*51=714, Resulting Numbers: [714] 714,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 54:[9, 46], Operations: ['98/7=14', '60-14=46'] Exploring Operation: 9*46=414, Resulting Numbers: [414] 414,54 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 9+46=55, Resulting Numbers: [55] 55,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 54:[60, 23], Operations: ['98/7=14', '9+14=23'] Exploring Operation: 60*23=1380, Resulting Numbers: [1380] 1380,54 unequal: No Solution Exploring Operation: 60+23=83, Resulting Numbers: [83] 83,54 unequal: No Solution Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 54:[14, 69], Operations: ['98/7=14', '60+9=69'] Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,54 unequal: No Solution Exploring Operation: 14+69=83, Resulting Numbers: [83] 83,54 unequal: No Solution Exploring Operation: 14*69=966, Resulting Numbers: [966] 966,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[9, 7, 38], Operations: ['98-60=38'] Exploring Operation: 38-9=29, Resulting Numbers: [7, 29] Generated Node #0,0,0: 54:[7, 29] Operation: 38-9=29 Exploring Operation: 7+38=45, Resulting Numbers: [9, 45] Generated Node #0,0,1: 54:[9, 45] Operation: 7+38=45 Exploring Operation: 9-7=2, Resulting Numbers: [38, 2] Generated Node #0,0,2: 54:[38, 2] Operation: 9-7=2 Exploring Operation: 9+38=47, Resulting Numbers: [7, 47] Generated Node #0,0,3: 54:[7, 47] Operation: 9+38=47 Exploring Operation: 38-7=31, Resulting Numbers: [9, 31] Generated Node #0,0,4: 54:[9, 31] Operation: 38-7=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[7, 29], Operations: ['98-60=38', '38-9=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,54 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 54:[9, 31], Operations: ['98-60=38', '38-7=31'] Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,54 unequal: No Solution Exploring Operation: 9*31=279, Resulting Numbers: [279] 279,54 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 54:[7, 47], Operations: ['98-60=38', '9+38=47'] Exploring Operation: 7*47=329, Resulting Numbers: [329] 329,54 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,54 unequal: No Solution Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[60, 9, 98, 7], Operations: [] Exploring Operation: 98-60=38, Resulting Numbers: [9, 7, 38] Generated Node #0,0: 54:[9, 7, 38] Operation: 98-60=38 Moving to Node #0,0 Current State: 54:[9, 7, 38], Operations: ['98-60=38'] Exploring Operation: 9+38=47, Resulting Numbers: [7, 47] Generated Node #0,0,3: 54:[7, 47] Operation: 9+38=47 Moving to Node #0,0,3 Current State: 54:[7, 47], Operations: ['98-60=38', '9+38=47'] Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.961806
hs_5
mult_heuristic
[ 38, 24, 25, 68 ]
57
[ "38-24=14", "68-25=43", "14+43=57" ]
Current State: 57:[38, 24, 25, 68], Operations: [] Exploring Operation: 38-24=14, Resulting Numbers: [25, 68, 14] Generated Node #2: [25, 68, 14] from Operation: 38-24=14 Current State: 57:[25, 68, 14], Operations: ['38-24=14'] Exploring Operation: 68-25=43, Resulting Numbers: [14, 43] Generated Node #3: [14, 43] from Operation: 68-25=43 Current State: 57:[14, 43], Operations: ['38-24=14', '68-25=43'] Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[38, 24, 25, 68], Operations: [] Exploring Operation: 38+24=62, Resulting Numbers: [25, 68, 62] Generated Node #0,0: 57:[25, 68, 62] Operation: 38+24=62 Moving to Node #0,0 Current State: 57:[25, 68, 62], Operations: ['38+24=62'] Exploring Operation: 68-62=6, Resulting Numbers: [25, 6] Generated Node #0,0,0: 57:[25, 6] Operation: 68-62=6 Moving to Node #0,0,0 Current State: 57:[25, 6], Operations: ['38+24=62', '68-62=6'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,57 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 2, 22, 13, 83 ]
81
[ "22/2=11", "83-13=70", "11+70=81" ]
Current State: 81:[2, 22, 13, 83], Operations: [] Exploring Operation: 22/2=11, Resulting Numbers: [13, 83, 11] Generated Node #2: [13, 83, 11] from Operation: 22/2=11 Current State: 81:[13, 83, 11], Operations: ['22/2=11'] Exploring Operation: 83-13=70, Resulting Numbers: [11, 70] Generated Node #3: [11, 70] from Operation: 83-13=70 Current State: 81:[11, 70], Operations: ['22/2=11', '83-13=70'] Exploring Operation: 11+70=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[2, 22, 13, 83], Operations: [] Exploring Operation: 2*13=26, Resulting Numbers: [22, 83, 26] Generated Node #0,0: 81:[22, 83, 26] Operation: 2*13=26 Exploring Operation: 22-13=9, Resulting Numbers: [2, 83, 9] Generated Node #0,1: 81:[2, 83, 9] Operation: 22-13=9 Exploring Operation: 22/2=11, Resulting Numbers: [13, 83, 11] Generated Node #0,2: 81:[13, 83, 11] Operation: 22/2=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[2, 83, 9], Operations: ['22-13=9'] Exploring Operation: 2+9=11, Resulting Numbers: [83, 11] Generated Node #0,1,0: 81:[83, 11] Operation: 2+9=11 Exploring Operation: 83-2=81, Resulting Numbers: [9, 81] Generated Node #0,1,1: 81:[9, 81] Operation: 83-2=81 Exploring Operation: 2+83=85, Resulting Numbers: [9, 85] Generated Node #0,1,2: 81:[9, 85] Operation: 2+83=85 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[9, 81], Operations: ['22-13=9', '83-2=81'] Exploring Operation: 81-9=72, Resulting Numbers: [72] 72,81 unequal: No Solution Exploring Operation: 81/9=9, Resulting Numbers: [9] 9,81 unequal: No Solution Exploring Operation: 9+81=90, Resulting Numbers: [90] 90,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[83, 11], Operations: ['22-13=9', '2+9=11'] Exploring Operation: 83*11=913, Resulting Numbers: [913] 913,81 unequal: No Solution Exploring Operation: 83-11=72, Resulting Numbers: [72] 72,81 unequal: No Solution Exploring Operation: 83+11=94, Resulting Numbers: [94] 94,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 81:[9, 85], Operations: ['22-13=9', '2+83=85'] Exploring Operation: 9*85=765, Resulting Numbers: [765] 765,81 unequal: No Solution Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 9+85=94, Resulting Numbers: [94] 94,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[22, 83, 26], Operations: ['2*13=26'] Exploring Operation: 83-22=61, Resulting Numbers: [26, 61] Generated Node #0,0,0: 81:[26, 61] Operation: 83-22=61 Exploring Operation: 22+26=48, Resulting Numbers: [83, 48] Generated Node #0,0,1: 81:[83, 48] Operation: 22+26=48 Exploring Operation: 26-22=4, Resulting Numbers: [83, 4] Generated Node #0,0,2: 81:[83, 4] Operation: 26-22=4 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 81:[83, 4], Operations: ['2*13=26', '26-22=4'] Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,81 unequal: No Solution Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,81 unequal: No Solution Exploring Operation: 83*4=332, Resulting Numbers: [332] 332,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[26, 61], Operations: ['2*13=26', '83-22=61'] Exploring Operation: 26+61=87, Resulting Numbers: [87] 87,81 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,81 unequal: No Solution Exploring Operation: 26*61=1586, Resulting Numbers: [1586] 1586,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 81:[83, 48], Operations: ['2*13=26', '22+26=48'] Exploring Operation: 83*48=3984, Resulting Numbers: [3984] 3984,81 unequal: No Solution Exploring Operation: 83+48=131, Resulting Numbers: [131] 131,81 unequal: No Solution Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[13, 83, 11], Operations: ['22/2=11'] Exploring Operation: 13-11=2, Resulting Numbers: [83, 2] Generated Node #0,2,0: 81:[83, 2] Operation: 13-11=2 Exploring Operation: 13+11=24, Resulting Numbers: [83, 24] Generated Node #0,2,1: 81:[83, 24] Operation: 13+11=24 Exploring Operation: 83-13=70, Resulting Numbers: [11, 70] Generated Node #0,2,2: 81:[11, 70] Operation: 83-13=70 Moving to Node #0,2,0 Current State: 81:[83, 2], Operations: ['22/2=11', '13-11=2'] Exploring Operation: 83*2=166, Resulting Numbers: [166] 166,81 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[2, 22, 13, 83], Operations: [] Exploring Operation: 22/2=11, Resulting Numbers: [13, 83, 11] Generated Node #0,2: 81:[13, 83, 11] Operation: 22/2=11 Moving to Node #0,2 Current State: 81:[13, 83, 11], Operations: ['22/2=11'] Exploring Operation: 13-11=2, Resulting Numbers: [83, 2] Generated Node #0,2,0: 81:[83, 2] Operation: 13-11=2 Moving to Node #0,2,0 Current State: 81:[83, 2], Operations: ['22/2=11', '13-11=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 21, 96, 96, 73 ]
73
[ "96-96=0", "21*0=0", "73+0=73" ]
Current State: 73:[21, 96, 96, 73], Operations: [] Exploring Operation: 96-96=0, Resulting Numbers: [21, 73, 0] Generated Node #2: [21, 73, 0] from Operation: 96-96=0 Current State: 73:[21, 73, 0], Operations: ['96-96=0'] Exploring Operation: 21*0=0, Resulting Numbers: [73, 0] Generated Node #3: [73, 0] from Operation: 21*0=0 Current State: 73:[73, 0], Operations: ['96-96=0', '21*0=0'] Exploring Operation: 73+0=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[21, 96, 96, 73], Operations: [] Exploring Operation: 21+96=117, Resulting Numbers: [96, 73, 117] Generated Node #0,0: 73:[96, 73, 117] Operation: 21+96=117 Exploring Operation: 96-21=75, Resulting Numbers: [96, 73, 75] Generated Node #0,1: 73:[96, 73, 75] Operation: 96-21=75 Exploring Operation: 96-21=75, Resulting Numbers: [96, 73, 75] Generated Node #0,2: 73:[96, 73, 75] Operation: 96-21=75 Moving to Node #0,1 Current State: 73:[96, 73, 75], Operations: ['96-21=75'] Exploring Operation: 96-73=23, Resulting Numbers: [75, 23] Generated Node #0,1,0: 73:[75, 23] Operation: 96-73=23 Exploring Operation: 75-73=2, Resulting Numbers: [96, 2] Generated Node #0,1,1: 73:[96, 2] Operation: 75-73=2 Exploring Operation: 96-75=21, Resulting Numbers: [73, 21] Generated Node #0,1,2: 73:[73, 21] Operation: 96-75=21 Moving to Node #0,2 Current State: 73:[96, 73, 75], Operations: ['96-21=75'] Exploring Operation: 96-73=23, Resulting Numbers: [75, 23] Generated Node #0,2,0: 73:[75, 23] Operation: 96-73=23 Exploring Operation: 75-73=2, Resulting Numbers: [96, 2] Generated Node #0,2,1: 73:[96, 2] Operation: 75-73=2 Exploring Operation: 96-75=21, Resulting Numbers: [73, 21] Generated Node #0,2,2: 73:[73, 21] Operation: 96-75=21 Moving to Node #0,0 Current State: 73:[96, 73, 117], Operations: ['21+96=117'] Exploring Operation: 117-73=44, Resulting Numbers: [96, 44] Generated Node #0,0,0: 73:[96, 44] Operation: 117-73=44 Exploring Operation: 96-73=23, Resulting Numbers: [117, 23] Generated Node #0,0,1: 73:[117, 23] Operation: 96-73=23 Exploring Operation: 117-96=21, Resulting Numbers: [73, 21] Generated Node #0,0,2: 73:[73, 21] Operation: 117-96=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[96, 44], Operations: ['21+96=117', '117-73=44'] Exploring Operation: 96*44=4224, Resulting Numbers: [4224] 4224,73 unequal: No Solution Exploring Operation: 96+44=140, Resulting Numbers: [140] 140,73 unequal: No Solution Exploring Operation: 96-44=52, Resulting Numbers: [52] 52,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 73:[73, 21], Operations: ['21+96=117', '117-96=21'] Exploring Operation: 73*21=1533, Resulting Numbers: [1533] 1533,73 unequal: No Solution Exploring Operation: 73+21=94, Resulting Numbers: [94] 94,73 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[117, 23], Operations: ['21+96=117', '96-73=23'] Exploring Operation: 117-23=94, Resulting Numbers: [94] 94,73 unequal: No Solution Exploring Operation: 117*23=2691, Resulting Numbers: [2691] 2691,73 unequal: No Solution Exploring Operation: 117+23=140, Resulting Numbers: [140] 140,73 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: 73:[75, 23], Operations: ['96-21=75', '96-73=23'] Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,73 unequal: No Solution Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[73, 21], Operations: ['96-21=75', '96-75=21'] Exploring Operation: 73+21=94, Resulting Numbers: [94] 94,73 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 73*21=1533, Resulting Numbers: [1533] 1533,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[73, 21], Operations: ['96-21=75', '96-75=21'] Exploring Operation: 73+21=94, Resulting Numbers: [94] 94,73 unequal: No Solution Exploring Operation: 73*21=1533, Resulting Numbers: [1533] 1533,73 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[75, 23], Operations: ['96-21=75', '96-73=23'] Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,73 unequal: No Solution Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[96, 2], Operations: ['96-21=75', '75-73=2'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,73 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,73 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[96, 2], Operations: ['96-21=75', '75-73=2'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,73 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,73 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,73 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 17, 33, 75, 10 ]
85
[ "33-17=16", "10*16=160", "160-75=85" ]
Current State: 85:[17, 33, 75, 10], Operations: [] Exploring Operation: 33-17=16, Resulting Numbers: [75, 10, 16] Generated Node #2: [75, 10, 16] from Operation: 33-17=16 Current State: 85:[75, 10, 16], Operations: ['33-17=16'] Exploring Operation: 10*16=160, Resulting Numbers: [75, 160] Generated Node #3: [75, 160] from Operation: 10*16=160 Current State: 85:[75, 160], Operations: ['33-17=16', '10*16=160'] Exploring Operation: 160-75=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[17, 33, 75, 10], Operations: [] Exploring Operation: 33-17=16, Resulting Numbers: [75, 10, 16] Generated Node #0,0: 85:[75, 10, 16] Operation: 33-17=16 Moving to Node #0,0 Current State: 85:[75, 10, 16], Operations: ['33-17=16'] Exploring Operation: 75+10=85, Resulting Numbers: [16, 85] Generated Node #0,0,0: 85:[16, 85] Operation: 75+10=85 Moving to Node #0,0,0 Current State: 85:[16, 85], Operations: ['33-17=16', '75+10=85'] Exploring Operation: 16+85=101, Resulting Numbers: [101] 101,85 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 41, 59, 12, 77 ]
56
[ "77-41=36", "36/12=3", "59-3=56" ]
Current State: 56:[41, 59, 12, 77], Operations: [] Exploring Operation: 77-41=36, Resulting Numbers: [59, 12, 36] Generated Node #2: [59, 12, 36] from Operation: 77-41=36 Current State: 56:[59, 12, 36], Operations: ['77-41=36'] Exploring Operation: 36/12=3, Resulting Numbers: [59, 3] Generated Node #3: [59, 3] from Operation: 36/12=3 Current State: 56:[59, 3], Operations: ['77-41=36', '36/12=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[41, 59, 12, 77], Operations: [] Exploring Operation: 77-41=36, Resulting Numbers: [59, 12, 36] Generated Node #0,0: 56:[59, 12, 36] Operation: 77-41=36 Moving to Node #0,0 Current State: 56:[59, 12, 36], Operations: ['77-41=36'] Exploring Operation: 36/12=3, Resulting Numbers: [59, 3] Generated Node #0,0,0: 56:[59, 3] Operation: 36/12=3 Moving to Node #0,0,0 Current State: 56:[59, 3], Operations: ['77-41=36', '36/12=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[41, 59, 12, 77], Operations: [] Exploring Operation: 77-41=36, Resulting Numbers: [59, 12, 36] Generated Node #0,0: 56:[59, 12, 36] Operation: 77-41=36 Moving to Node #0,0 Current State: 56:[59, 12, 36], Operations: ['77-41=36'] Exploring Operation: 36/12=3, Resulting Numbers: [59, 3] Generated Node #0,0,0: 56:[59, 3] Operation: 36/12=3 Moving to Node #0,0,0 Current State: 56:[59, 3], Operations: ['77-41=36', '36/12=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 21, 40, 84, 65 ]
100
[ "84/21=4", "65-40=25", "4*25=100" ]
Current State: 100:[21, 40, 84, 65], Operations: [] Exploring Operation: 84/21=4, Resulting Numbers: [40, 65, 4] Generated Node #2: [40, 65, 4] from Operation: 84/21=4 Current State: 100:[40, 65, 4], Operations: ['84/21=4'] Exploring Operation: 65-40=25, Resulting Numbers: [4, 25] Generated Node #3: [4, 25] from Operation: 65-40=25 Current State: 100:[4, 25], Operations: ['84/21=4', '65-40=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[21, 40, 84, 65], Operations: [] Exploring Operation: 84-40=44, Resulting Numbers: [21, 65, 44] Generated Node #0,0: 100:[21, 65, 44] Operation: 84-40=44 Exploring Operation: 65-40=25, Resulting Numbers: [21, 84, 25] Generated Node #0,1: 100:[21, 84, 25] Operation: 65-40=25 Exploring Operation: 84-65=19, Resulting Numbers: [21, 40, 19] Generated Node #0,2: 100:[21, 40, 19] Operation: 84-65=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[21, 40, 19], Operations: ['84-65=19'] Exploring Operation: 40-19=21, Resulting Numbers: [21, 21] Generated Node #0,2,0: 100:[21, 21] Operation: 40-19=21 Exploring Operation: 40-21=19, Resulting Numbers: [19, 19] Generated Node #0,2,1: 100:[19, 19] Operation: 40-21=19 Exploring Operation: 21-19=2, Resulting Numbers: [40, 2] Generated Node #0,2,2: 100:[40, 2] Operation: 21-19=2 Moving to Node #0,2,0 Current State: 100:[21, 21], Operations: ['84-65=19', '40-19=21'] Exploring Operation: 21+21=42, Resulting Numbers: [42] 42,100 unequal: No Solution Exploring Operation: 21-21=0, Resulting Numbers: [0] 0,100 unequal: No Solution Exploring Operation: 21/21=1, Resulting Numbers: [1] 1,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[19, 19], Operations: ['84-65=19', '40-21=19'] Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,100 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,100 unequal: No Solution Moving to Node #0,2,2 Current State: 100:[40, 2], Operations: ['84-65=19', '21-19=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,100 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[21, 84, 25], Operations: ['65-40=25'] Exploring Operation: 21+84=105, Resulting Numbers: [25, 105] Generated Node #0,1,0: 100:[25, 105] Operation: 21+84=105 Exploring Operation: 84/21=4, Resulting Numbers: [25, 4] Generated Node #0,1,1: 100:[25, 4] Operation: 84/21=4 Exploring Operation: 84+25=109, Resulting Numbers: [21, 109] Generated Node #0,1,2: 100:[21, 109] Operation: 84+25=109 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[25, 4], Operations: ['65-40=25', '84/21=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[21, 40, 84, 65], Operations: [] Exploring Operation: 65-40=25, Resulting Numbers: [21, 84, 25] Generated Node #0,1: 100:[21, 84, 25] Operation: 65-40=25 Moving to Node #0,1 Current State: 100:[21, 84, 25], Operations: ['65-40=25'] Exploring Operation: 84/21=4, Resulting Numbers: [25, 4] Generated Node #0,1,1: 100:[25, 4] Operation: 84/21=4 Moving to Node #0,1,1 Current State: 100:[25, 4], Operations: ['65-40=25', '84/21=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 97, 70, 19, 99 ]
49
[ "97+70=167", "19+99=118", "167-118=49" ]
Current State: 49:[97, 70, 19, 99], Operations: [] Exploring Operation: 97+70=167, Resulting Numbers: [19, 99, 167] Generated Node #2: [19, 99, 167] from Operation: 97+70=167 Current State: 49:[19, 99, 167], Operations: ['97+70=167'] Exploring Operation: 19+99=118, Resulting Numbers: [167, 118] Generated Node #3: [167, 118] from Operation: 19+99=118 Current State: 49:[167, 118], Operations: ['97+70=167', '19+99=118'] Exploring Operation: 167-118=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[97, 70, 19, 99], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [70, 19, 2] Generated Node #0,0: 49:[70, 19, 2] Operation: 99-97=2 Exploring Operation: 99-70=29, Resulting Numbers: [97, 19, 29] Generated Node #0,1: 49:[97, 19, 29] Operation: 99-70=29 Moving to Node #0,0 Current State: 49:[70, 19, 2], Operations: ['99-97=2'] Exploring Operation: 70-19=51, Resulting Numbers: [2, 51] Generated Node #0,0,0: 49:[2, 51] Operation: 70-19=51 Exploring Operation: 70/2=35, Resulting Numbers: [19, 35] Generated Node #0,0,1: 49:[19, 35] Operation: 70/2=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[2, 51], Operations: ['99-97=2', '70-19=51'] Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[97, 70, 19, 99], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [70, 19, 2] Generated Node #0,0: 49:[70, 19, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 49:[70, 19, 2], Operations: ['99-97=2'] Exploring Operation: 70-19=51, Resulting Numbers: [2, 51] Generated Node #0,0,0: 49:[2, 51] Operation: 70-19=51 Moving to Node #0,0,0 Current State: 49:[2, 51], Operations: ['99-97=2', '70-19=51'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 55, 53, 40, 65 ]
90
[ "55-53=2", "65*2=130", "130-40=90" ]
Current State: 90:[55, 53, 40, 65], Operations: [] Exploring Operation: 55-53=2, Resulting Numbers: [40, 65, 2] Generated Node #2: [40, 65, 2] from Operation: 55-53=2 Current State: 90:[40, 65, 2], Operations: ['55-53=2'] Exploring Operation: 65*2=130, Resulting Numbers: [40, 130] Generated Node #3: [40, 130] from Operation: 65*2=130 Current State: 90:[40, 130], Operations: ['55-53=2', '65*2=130'] Exploring Operation: 130-40=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[55, 53, 40, 65], Operations: [] Exploring Operation: 55-53=2, Resulting Numbers: [40, 65, 2] Generated Node #0,0: 90:[40, 65, 2] Operation: 55-53=2 Exploring Operation: 55-40=15, Resulting Numbers: [53, 65, 15] Generated Node #0,1: 90:[53, 65, 15] Operation: 55-40=15 Exploring Operation: 65-55=10, Resulting Numbers: [53, 40, 10] Generated Node #0,2: 90:[53, 40, 10] Operation: 65-55=10 Exploring Operation: 65-40=25, Resulting Numbers: [55, 53, 25] Generated Node #0,3: 90:[55, 53, 25] Operation: 65-40=25 Exploring Operation: 65-53=12, Resulting Numbers: [55, 40, 12] Generated Node #0,4: 90:[55, 40, 12] Operation: 65-53=12 Moving to Node #0,2 Current State: 90:[53, 40, 10], Operations: ['65-55=10'] Exploring Operation: 53+40=93, Resulting Numbers: [10, 93] Generated Node #0,2,0: 90:[10, 93] Operation: 53+40=93 Exploring Operation: 40-10=30, Resulting Numbers: [53, 30] Generated Node #0,2,1: 90:[53, 30] Operation: 40-10=30 Exploring Operation: 53-40=13, Resulting Numbers: [10, 13] Generated Node #0,2,2: 90:[10, 13] Operation: 53-40=13 Exploring Operation: 53-10=43, Resulting Numbers: [40, 43] Generated Node #0,2,3: 90:[40, 43] Operation: 53-10=43 Exploring Operation: 40/10=4, Resulting Numbers: [53, 4] Generated Node #0,2,4: 90:[53, 4] Operation: 40/10=4 Moving to Node #0,4 Current State: 90:[55, 40, 12], Operations: ['65-53=12'] Exploring Operation: 55-40=15, Resulting Numbers: [12, 15] Generated Node #0,4,0: 90:[12, 15] Operation: 55-40=15 Exploring Operation: 55+40=95, Resulting Numbers: [12, 95] Generated Node #0,4,1: 90:[12, 95] Operation: 55+40=95 Exploring Operation: 40+12=52, Resulting Numbers: [55, 52] Generated Node #0,4,2: 90:[55, 52] Operation: 40+12=52 Exploring Operation: 55-12=43, Resulting Numbers: [40, 43] Generated Node #0,4,3: 90:[40, 43] Operation: 55-12=43 Exploring Operation: 40-12=28, Resulting Numbers: [55, 28] Generated Node #0,4,4: 90:[55, 28] Operation: 40-12=28 Moving to Node #0,3 Current State: 90:[55, 53, 25], Operations: ['65-40=25'] Exploring Operation: 53+25=78, Resulting Numbers: [55, 78] Generated Node #0,3,0: 90:[55, 78] Operation: 53+25=78 Exploring Operation: 55-25=30, Resulting Numbers: [53, 30] Generated Node #0,3,1: 90:[53, 30] Operation: 55-25=30 Exploring Operation: 53-25=28, Resulting Numbers: [55, 28] Generated Node #0,3,2: 90:[55, 28] Operation: 53-25=28 Exploring Operation: 55+25=80, Resulting Numbers: [53, 80] Generated Node #0,3,3: 90:[53, 80] Operation: 55+25=80 Exploring Operation: 55-53=2, Resulting Numbers: [25, 2] Generated Node #0,3,4: 90:[25, 2] Operation: 55-53=2 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 90:[25, 2], Operations: ['65-40=25', '55-53=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,90 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 #0,3,1 Current State: 90:[53, 30], Operations: ['65-40=25', '55-25=30'] Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,90 unequal: No Solution Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,90 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 #0,3,2 Current State: 90:[55, 28], Operations: ['65-40=25', '53-25=28'] Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 55*28=1540, Resulting Numbers: [1540] 1540,90 unequal: No Solution Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,90 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 #0,3,3 Current State: 90:[53, 80], Operations: ['65-40=25', '55+25=80'] Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 53+80=133, Resulting Numbers: [133] 133,90 unequal: No Solution Exploring Operation: 53*80=4240, Resulting Numbers: [4240] 4240,90 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 #0,3,0 Current State: 90:[55, 78], Operations: ['65-40=25', '53+25=78'] Exploring Operation: 55*78=4290, Resulting Numbers: [4290] 4290,90 unequal: No Solution Exploring Operation: 55+78=133, Resulting Numbers: [133] 133,90 unequal: No Solution Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,90 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:[40, 65, 2], Operations: ['55-53=2'] Exploring Operation: 40+65=105, Resulting Numbers: [2, 105] Generated Node #0,0,0: 90:[2, 105] Operation: 40+65=105 Exploring Operation: 65-2=63, Resulting Numbers: [40, 63] Generated Node #0,0,1: 90:[40, 63] Operation: 65-2=63 Exploring Operation: 65-40=25, Resulting Numbers: [2, 25] Generated Node #0,0,2: 90:[2, 25] Operation: 65-40=25 Exploring Operation: 40/2=20, Resulting Numbers: [65, 20] Generated Node #0,0,3: 90:[65, 20] Operation: 40/2=20 Exploring Operation: 40+2=42, Resulting Numbers: [65, 42] Generated Node #0,0,4: 90:[65, 42] Operation: 40+2=42 Moving to Node #0,1 Current State: 90:[53, 65, 15], Operations: ['55-40=15'] Exploring Operation: 53+65=118, Resulting Numbers: [15, 118] Generated Node #0,1,0: 90:[15, 118] Operation: 53+65=118 Exploring Operation: 53-15=38, Resulting Numbers: [65, 38] Generated Node #0,1,1: 90:[65, 38] Operation: 53-15=38 Exploring Operation: 65+15=80, Resulting Numbers: [53, 80] Generated Node #0,1,2: 90:[53, 80] Operation: 65+15=80 Exploring Operation: 65-53=12, Resulting Numbers: [15, 12] Generated Node #0,1,3: 90:[15, 12] Operation: 65-53=12 Exploring Operation: 65-15=50, Resulting Numbers: [53, 50] Generated Node #0,1,4: 90:[53, 50] Operation: 65-15=50 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 90:[15, 12], Operations: ['55-40=15', '65-53=12'] Exploring Operation: 15*12=180, Resulting Numbers: [180] 180,90 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,90 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 #0,1,4 Current State: 90:[53, 50], Operations: ['55-40=15', '65-15=50'] Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,90 unequal: No Solution Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,90 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:[53, 80], Operations: ['55-40=15', '65+15=80'] Exploring Operation: 53*80=4240, Resulting Numbers: [4240] 4240,90 unequal: No Solution Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 53+80=133, Resulting Numbers: [133] 133,90 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:[65, 38], Operations: ['55-40=15', '53-15=38'] Exploring Operation: 65*38=2470, Resulting Numbers: [2470] 2470,90 unequal: No Solution Exploring Operation: 65-38=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 65+38=103, Resulting Numbers: [103] 103,90 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 #0,1,0 Current State: 90:[15, 118], Operations: ['55-40=15', '53+65=118'] Exploring Operation: 118-15=103, Resulting Numbers: [103] 103,90 unequal: No Solution Exploring Operation: 15+118=133, Resulting Numbers: [133] 133,90 unequal: No Solution Exploring Operation: 15*118=1770, Resulting Numbers: [1770] 1770,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 90:[10, 13], Operations: ['65-55=10', '53-40=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,90 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,90 unequal: No Solution Moving to Node #0,4,0 Current State: 90:[12, 15], Operations: ['65-53=12', '55-40=15'] Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,90 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[10, 93], Operations: ['65-55=10', '53+40=93'] Exploring Operation: 10*93=930, Resulting Numbers: [930] 930,90 unequal: No Solution Exploring Operation: 93-10=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 10+93=103, Resulting Numbers: [103] 103,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[2, 25], Operations: ['55-53=2', '65-40=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,90 unequal: No Solution Moving to Node #0,4,1 Current State: 90:[12, 95], Operations: ['65-53=12', '55+40=95'] Exploring Operation: 95-12=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 12*95=1140, Resulting Numbers: [1140] 1140,90 unequal: No Solution Exploring Operation: 12+95=107, Resulting Numbers: [107] 107,90 unequal: No Solution Moving to Node #0,2,3 Current State: 90:[40, 43], Operations: ['65-55=10', '53-10=43'] Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,90 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,90 unequal: No Solution Moving to Node #0,4,3 Current State: 90:[40, 43], Operations: ['65-53=12', '55-12=43'] Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,90 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[53, 30], Operations: ['65-55=10', '40-10=30'] Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,90 unequal: No Solution Moving to Node #0,2,4 Current State: 90:[53, 4], Operations: ['65-55=10', '40/10=4'] Exploring Operation: 53+4=57, Resulting Numbers: [57] 57,90 unequal: No Solution Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 53*4=212, Resulting Numbers: [212] 212,90 unequal: No Solution Moving to Node #0,4,4 Current State: 90:[55, 28], Operations: ['65-53=12', '40-12=28'] Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 55*28=1540, Resulting Numbers: [1540] 1540,90 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[2, 105], Operations: ['55-53=2', '40+65=105'] Exploring Operation: 2*105=210, Resulting Numbers: [210] 210,90 unequal: No Solution Exploring Operation: 105-2=103, Resulting Numbers: [103] 103,90 unequal: No Solution Exploring Operation: 2+105=107, Resulting Numbers: [107] 107,90 unequal: No Solution Moving to Node #0,4,2 Current State: 90:[55, 52], Operations: ['65-53=12', '40+12=52'] Exploring Operation: 55-52=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 55*52=2860, Resulting Numbers: [2860] 2860,90 unequal: No Solution Exploring Operation: 55+52=107, Resulting Numbers: [107] 107,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[65, 20], Operations: ['55-53=2', '40/2=20'] Exploring Operation: 65+20=85, Resulting Numbers: [85] 85,90 unequal: No Solution Exploring Operation: 65-20=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 65*20=1300, Resulting Numbers: [1300] 1300,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[40, 63], Operations: ['55-53=2', '65-2=63'] Exploring Operation: 40*63=2520, Resulting Numbers: [2520] 2520,90 unequal: No Solution Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 40+63=103, Resulting Numbers: [103] 103,90 unequal: No Solution Moving to Node #0,0,4 Current State: 90:[65, 42], Operations: ['55-53=2', '40+2=42'] Exploring Operation: 65*42=2730, Resulting Numbers: [2730] 2730,90 unequal: No Solution Exploring Operation: 65-42=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 65+42=107, Resulting Numbers: [107] 107,90 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 61, 3, 33, 21 ]
31
[ "61+33=94", "3*21=63", "94-63=31" ]
Current State: 31:[61, 3, 33, 21], Operations: [] Exploring Operation: 61+33=94, Resulting Numbers: [3, 21, 94] Generated Node #2: [3, 21, 94] from Operation: 61+33=94 Current State: 31:[3, 21, 94], Operations: ['61+33=94'] Exploring Operation: 3*21=63, Resulting Numbers: [94, 63] Generated Node #3: [94, 63] from Operation: 3*21=63 Current State: 31:[94, 63], Operations: ['61+33=94', '3*21=63'] Exploring Operation: 94-63=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[61, 3, 33, 21], Operations: [] Exploring Operation: 61-3=58, Resulting Numbers: [33, 21, 58] Generated Node #0,0: 31:[33, 21, 58] Operation: 61-3=58 Exploring Operation: 33-3=30, Resulting Numbers: [61, 21, 30] Generated Node #0,1: 31:[61, 21, 30] Operation: 33-3=30 Exploring Operation: 61-33=28, Resulting Numbers: [3, 21, 28] Generated Node #0,2: 31:[3, 21, 28] Operation: 61-33=28 Exploring Operation: 61-21=40, Resulting Numbers: [3, 33, 40] Generated Node #0,3: 31:[3, 33, 40] Operation: 61-21=40 Exploring Operation: 3+21=24, Resulting Numbers: [61, 33, 24] Generated Node #0,4: 31:[61, 33, 24] Operation: 3+21=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[33, 21, 58], Operations: ['61-3=58'] Exploring Operation: 21+58=79, Resulting Numbers: [33, 79] Generated Node #0,0,0: 31:[33, 79] Operation: 21+58=79 Exploring Operation: 58-33=25, Resulting Numbers: [21, 25] Generated Node #0,0,1: 31:[21, 25] Operation: 58-33=25 Exploring Operation: 33-21=12, Resulting Numbers: [58, 12] Generated Node #0,0,2: 31:[58, 12] Operation: 33-21=12 Exploring Operation: 33+21=54, Resulting Numbers: [58, 54] Generated Node #0,0,3: 31:[58, 54] Operation: 33+21=54 Exploring Operation: 58-21=37, Resulting Numbers: [33, 37] Generated Node #0,0,4: 31:[33, 37] Operation: 58-21=37 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 31:[33, 37], Operations: ['61-3=58', '58-21=37'] Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 33*37=1221, Resulting Numbers: [1221] 1221,31 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,31 unequal: No Solution No 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: 31:[21, 25], Operations: ['61-3=58', '58-33=25'] Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 21*25=525, Resulting Numbers: [525] 525,31 unequal: No Solution No 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: 31:[58, 12], Operations: ['61-3=58', '33-21=12'] Exploring Operation: 58-12=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 58+12=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 58*12=696, Resulting Numbers: [696] 696,31 unequal: No Solution No 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: 31:[33, 79], Operations: ['61-3=58', '21+58=79'] Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,31 unequal: No Solution Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,31 unequal: No Solution No 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: 31:[58, 54], Operations: ['61-3=58', '33+21=54'] Exploring Operation: 58-54=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 58+54=112, Resulting Numbers: [112] 112,31 unequal: No Solution Exploring Operation: 58*54=3132, Resulting Numbers: [3132] 3132,31 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: 31:[3, 33, 40], Operations: ['61-21=40'] Exploring Operation: 33/3=11, Resulting Numbers: [40, 11] Generated Node #0,3,0: 31:[40, 11] Operation: 33/3=11 Exploring Operation: 33-3=30, Resulting Numbers: [40, 30] Generated Node #0,3,1: 31:[40, 30] Operation: 33-3=30 Exploring Operation: 3+33=36, Resulting Numbers: [40, 36] Generated Node #0,3,2: 31:[40, 36] Operation: 3+33=36 Exploring Operation: 40-3=37, Resulting Numbers: [33, 37] Generated Node #0,3,3: 31:[33, 37] Operation: 40-3=37 Exploring Operation: 3+40=43, Resulting Numbers: [33, 43] Generated Node #0,3,4: 31:[33, 43] Operation: 3+40=43 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 31:[33, 37], Operations: ['61-21=40', '40-3=37'] Exploring Operation: 33*37=1221, Resulting Numbers: [1221] 1221,31 unequal: No Solution Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,31 unequal: No Solution No 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: 31:[40, 30], Operations: ['61-21=40', '33-3=30'] Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,31 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,31 unequal: No Solution No 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: 31:[40, 36], Operations: ['61-21=40', '3+33=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 40*36=1440, Resulting Numbers: [1440] 1440,31 unequal: No Solution No 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: 31:[33, 43], Operations: ['61-21=40', '3+40=43'] Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 33*43=1419, Resulting Numbers: [1419] 1419,31 unequal: No Solution Exploring Operation: 33+43=76, Resulting Numbers: [76] 76,31 unequal: No Solution No 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: 31:[40, 11], Operations: ['61-21=40', '33/3=11'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 40*11=440, Resulting Numbers: [440] 440,31 unequal: No Solution Exploring Operation: 40+11=51, Resulting Numbers: [51] 51,31 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: 31:[61, 33, 24], Operations: ['3+21=24'] Exploring Operation: 61+24=85, Resulting Numbers: [33, 85] Generated Node #0,4,0: 31:[33, 85] Operation: 61+24=85 Exploring Operation: 61-33=28, Resulting Numbers: [24, 28] Generated Node #0,4,1: 31:[24, 28] Operation: 61-33=28 Exploring Operation: 33-24=9, Resulting Numbers: [61, 9] Generated Node #0,4,2: 31:[61, 9] Operation: 33-24=9 Exploring Operation: 33+24=57, Resulting Numbers: [61, 57] Generated Node #0,4,3: 31:[61, 57] Operation: 33+24=57 Exploring Operation: 61-24=37, Resulting Numbers: [33, 37] Generated Node #0,4,4: 31:[33, 37] Operation: 61-24=37 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 31:[33, 37], Operations: ['3+21=24', '61-24=37'] Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 33*37=1221, Resulting Numbers: [1221] 1221,31 unequal: No Solution No 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: 31:[24, 28], Operations: ['3+21=24', '61-33=28'] Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,31 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,31 unequal: No Solution No 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: 31:[61, 9], Operations: ['3+21=24', '33-24=9'] Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,31 unequal: No Solution Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,31 unequal: No Solution No 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: 31:[33, 85], Operations: ['3+21=24', '61+24=85'] Exploring Operation: 85-33=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 33+85=118, Resulting Numbers: [118] 118,31 unequal: No Solution Exploring Operation: 33*85=2805, Resulting Numbers: [2805] 2805,31 unequal: No Solution No 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: 31:[61, 57], Operations: ['3+21=24', '33+24=57'] Exploring Operation: 61-57=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 61*57=3477, Resulting Numbers: [3477] 3477,31 unequal: No Solution Exploring Operation: 61+57=118, Resulting Numbers: [118] 118,31 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: 31:[61, 21, 30], Operations: ['33-3=30'] Exploring Operation: 21+30=51, Resulting Numbers: [61, 51] Generated Node #0,1,0: 31:[61, 51] Operation: 21+30=51 Exploring Operation: 61-30=31, Resulting Numbers: [21, 31] Generated Node #0,1,1: 31:[21, 31] Operation: 61-30=31 Exploring Operation: 61+21=82, Resulting Numbers: [30, 82] Generated Node #0,1,2: 31:[30, 82] Operation: 61+21=82 Exploring Operation: 61-21=40, Resulting Numbers: [30, 40] Generated Node #0,1,3: 31:[30, 40] Operation: 61-21=40 Exploring Operation: 30-21=9, Resulting Numbers: [61, 9] Generated Node #0,1,4: 31:[61, 9] Operation: 30-21=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 31:[21, 31], Operations: ['33-3=30', '61-30=31'] Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,31 unequal: No Solution No 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: 31:[30, 40], Operations: ['33-3=30', '61-21=40'] Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,31 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,31 unequal: No Solution No 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: 31:[61, 51], Operations: ['33-3=30', '21+30=51'] Exploring Operation: 61*51=3111, Resulting Numbers: [3111] 3111,31 unequal: No Solution Exploring Operation: 61+51=112, Resulting Numbers: [112] 112,31 unequal: No Solution Exploring Operation: 61-51=10, Resulting Numbers: [10] 10,31 unequal: No Solution No 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: 31:[30, 82], Operations: ['33-3=30', '61+21=82'] Exploring Operation: 82-30=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 30+82=112, Resulting Numbers: [112] 112,31 unequal: No Solution Exploring Operation: 30*82=2460, Resulting Numbers: [2460] 2460,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 31:[61, 9], Operations: ['33-3=30', '30-21=9'] Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,31 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: 31:[3, 21, 28], Operations: ['61-33=28'] Exploring Operation: 28-3=25, Resulting Numbers: [21, 25] Generated Node #0,2,0: 31:[21, 25] Operation: 28-3=25 Exploring Operation: 21-3=18, Resulting Numbers: [28, 18] Generated Node #0,2,1: 31:[28, 18] Operation: 21-3=18 Exploring Operation: 3+28=31, Resulting Numbers: [21, 31] Generated Node #0,2,2: 31:[21, 31] Operation: 3+28=31 Exploring Operation: 3+21=24, Resulting Numbers: [28, 24] Generated Node #0,2,3: 31:[28, 24] Operation: 3+21=24 Exploring Operation: 21/3=7, Resulting Numbers: [28, 7] Generated Node #0,2,4: 31:[28, 7] Operation: 21/3=7 Moving to Node #0,2,2 Current State: 31:[21, 31], Operations: ['61-33=28', '3+28=31'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,31 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[28, 24], Operations: ['61-33=28', '3+21=24'] Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,31 unequal: No Solution Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[21, 25], Operations: ['61-33=28', '28-3=25'] Exploring Operation: 21*25=525, Resulting Numbers: [525] 525,31 unequal: No Solution Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[28, 18], Operations: ['61-33=28', '21-3=18'] Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,31 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,31 unequal: No Solution Moving to Node #0,2,4 Current State: 31:[28, 7], Operations: ['61-33=28', '21/3=7'] Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,31 unequal: No Solution Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 87, 40, 17, 32 ]
96
[ "87-40=47", "17+32=49", "47+49=96" ]
Current State: 96:[87, 40, 17, 32], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [17, 32, 47] Generated Node #2: [17, 32, 47] from Operation: 87-40=47 Current State: 96:[17, 32, 47], Operations: ['87-40=47'] Exploring Operation: 17+32=49, Resulting Numbers: [47, 49] Generated Node #3: [47, 49] from Operation: 17+32=49 Current State: 96:[47, 49], Operations: ['87-40=47', '17+32=49'] Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[87, 40, 17, 32], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [17, 32, 47] Generated Node #0,0: 96:[17, 32, 47] Operation: 87-40=47 Moving to Node #0,0 Current State: 96:[17, 32, 47], Operations: ['87-40=47'] Exploring Operation: 17+32=49, Resulting Numbers: [47, 49] Generated Node #0,0,0: 96:[47, 49] Operation: 17+32=49 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[47, 49], Operations: ['87-40=47', '17+32=49'] Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[87, 40, 17, 32], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [17, 32, 47] Generated Node #0,0: 96:[17, 32, 47] Operation: 87-40=47 Moving to Node #0,0 Current State: 96:[17, 32, 47], Operations: ['87-40=47'] Exploring Operation: 17+32=49, Resulting Numbers: [47, 49] Generated Node #0,0,0: 96:[47, 49] Operation: 17+32=49 Moving to Node #0,0,0 Current State: 96:[47, 49], Operations: ['87-40=47', '17+32=49'] Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 10, 79, 48, 70 ]
47
[ "79-10=69", "70-48=22", "69-22=47" ]
Current State: 47:[10, 79, 48, 70], Operations: [] Exploring Operation: 79-10=69, Resulting Numbers: [48, 70, 69] Generated Node #2: [48, 70, 69] from Operation: 79-10=69 Current State: 47:[48, 70, 69], Operations: ['79-10=69'] Exploring Operation: 70-48=22, Resulting Numbers: [69, 22] Generated Node #3: [69, 22] from Operation: 70-48=22 Current State: 47:[69, 22], Operations: ['79-10=69', '70-48=22'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[10, 79, 48, 70], Operations: [] Exploring Operation: 79-10=69, Resulting Numbers: [48, 70, 69] Generated Node #0,0: 47:[48, 70, 69] Operation: 79-10=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[48, 70, 69], Operations: ['79-10=69'] Exploring Operation: 70-48=22, Resulting Numbers: [69, 22] Generated Node #0,0,0: 47:[69, 22] Operation: 70-48=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[69, 22], Operations: ['79-10=69', '70-48=22'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[10, 79, 48, 70], Operations: [] Exploring Operation: 79-10=69, Resulting Numbers: [48, 70, 69] Generated Node #0,0: 47:[48, 70, 69] Operation: 79-10=69 Moving to Node #0,0 Current State: 47:[48, 70, 69], Operations: ['79-10=69'] Exploring Operation: 70-48=22, Resulting Numbers: [69, 22] Generated Node #0,0,0: 47:[69, 22] Operation: 70-48=22 Moving to Node #0,0,0 Current State: 47:[69, 22], Operations: ['79-10=69', '70-48=22'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 55, 98, 16, 99 ]
70
[ "55+98=153", "99-16=83", "153-83=70" ]
Current State: 70:[55, 98, 16, 99], Operations: [] Exploring Operation: 55+98=153, Resulting Numbers: [16, 99, 153] Generated Node #2: [16, 99, 153] from Operation: 55+98=153 Current State: 70:[16, 99, 153], Operations: ['55+98=153'] Exploring Operation: 99-16=83, Resulting Numbers: [153, 83] Generated Node #3: [153, 83] from Operation: 99-16=83 Current State: 70:[153, 83], Operations: ['55+98=153', '99-16=83'] Exploring Operation: 153-83=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[55, 98, 16, 99], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [98, 16, 44] Generated Node #0,0: 70:[98, 16, 44] Operation: 99-55=44 Exploring Operation: 98-55=43, Resulting Numbers: [16, 99, 43] Generated Node #0,1: 70:[16, 99, 43] Operation: 98-55=43 Exploring Operation: 99-98=1, Resulting Numbers: [55, 16, 1] Generated Node #0,2: 70:[55, 16, 1] Operation: 99-98=1 Moving to Node #0,2 Current State: 70:[55, 16, 1], Operations: ['99-98=1'] Exploring Operation: 55-16=39, Resulting Numbers: [1, 39] Generated Node #0,2,0: 70:[1, 39] Operation: 55-16=39 Exploring Operation: 55+16=71, Resulting Numbers: [1, 71] Generated Node #0,2,1: 70:[1, 71] Operation: 55+16=71 Exploring Operation: 55+1=56, Resulting Numbers: [16, 56] Generated Node #0,2,2: 70:[16, 56] Operation: 55+1=56 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 70:[1, 71], Operations: ['99-98=1', '55+16=71'] Exploring Operation: 71/1=71, Resulting Numbers: [71] 71,70 unequal: No Solution Exploring Operation: 1*71=71, Resulting Numbers: [71] 71,70 unequal: No Solution Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[55, 98, 16, 99], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [55, 16, 1] Generated Node #0,2: 70:[55, 16, 1] Operation: 99-98=1 Moving to Node #0,2 Current State: 70:[55, 16, 1], Operations: ['99-98=1'] Exploring Operation: 55+16=71, Resulting Numbers: [1, 71] Generated Node #0,2,1: 70:[1, 71] Operation: 55+16=71 Moving to Node #0,2,1 Current State: 70:[1, 71], Operations: ['99-98=1', '55+16=71'] Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 80, 86, 60, 5 ]
58
[ "80+60=140", "140/5=28", "86-28=58" ]
Current State: 58:[80, 86, 60, 5], Operations: [] Exploring Operation: 80+60=140, Resulting Numbers: [86, 5, 140] Generated Node #2: [86, 5, 140] from Operation: 80+60=140 Current State: 58:[86, 5, 140], Operations: ['80+60=140'] Exploring Operation: 140/5=28, Resulting Numbers: [86, 28] Generated Node #3: [86, 28] from Operation: 140/5=28 Current State: 58:[86, 28], Operations: ['80+60=140', '140/5=28'] Exploring Operation: 86-28=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[80, 86, 60, 5], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [60, 5, 6] Generated Node #0,0: 58:[60, 5, 6] Operation: 86-80=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[60, 5, 6], Operations: ['86-80=6'] Exploring Operation: 5*6=30, Resulting Numbers: [60, 30] Generated Node #0,0,0: 58:[60, 30] Operation: 5*6=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[60, 30], Operations: ['86-80=6', '5*6=30'] Exploring Operation: 60/30=2, Resulting Numbers: [2] 2,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 28, 75, 61, 88 ]
46
[ "28+75=103", "61+88=149", "149-103=46" ]
Current State: 46:[28, 75, 61, 88], Operations: [] Exploring Operation: 28+75=103, Resulting Numbers: [61, 88, 103] Generated Node #2: [61, 88, 103] from Operation: 28+75=103 Current State: 46:[61, 88, 103], Operations: ['28+75=103'] Exploring Operation: 61+88=149, Resulting Numbers: [103, 149] Generated Node #3: [103, 149] from Operation: 61+88=149 Current State: 46:[103, 149], Operations: ['28+75=103', '61+88=149'] Exploring Operation: 149-103=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[28, 75, 61, 88], Operations: [] Exploring Operation: 88-75=13, Resulting Numbers: [28, 61, 13] Generated Node #0,0: 46:[28, 61, 13] Operation: 88-75=13 Exploring Operation: 88-61=27, Resulting Numbers: [28, 75, 27] Generated Node #0,1: 46:[28, 75, 27] Operation: 88-61=27 Exploring Operation: 75-61=14, Resulting Numbers: [28, 88, 14] Generated Node #0,2: 46:[28, 88, 14] Operation: 75-61=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[28, 61, 13], Operations: ['88-75=13'] Exploring Operation: 61-28=33, Resulting Numbers: [13, 33] Generated Node #0,0,0: 46:[13, 33] Operation: 61-28=33 Exploring Operation: 61-13=48, Resulting Numbers: [28, 48] Generated Node #0,0,1: 46:[28, 48] Operation: 61-13=48 Exploring Operation: 28+13=41, Resulting Numbers: [61, 41] Generated Node #0,0,2: 46:[61, 41] Operation: 28+13=41 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 46:[28, 48], Operations: ['88-75=13', '61-13=48'] Exploring Operation: 28*48=1344, Resulting Numbers: [1344] 1344,46 unequal: No Solution Exploring Operation: 28+48=76, Resulting Numbers: [76] 76,46 unequal: No Solution Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,46 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 #0,0,0 Current State: 46:[13, 33], Operations: ['88-75=13', '61-28=33'] Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,46 unequal: No Solution Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[28, 75, 61, 88], Operations: [] Exploring Operation: 88-75=13, Resulting Numbers: [28, 61, 13] Generated Node #0,0: 46:[28, 61, 13] Operation: 88-75=13 Moving to Node #0,0 Current State: 46:[28, 61, 13], Operations: ['88-75=13'] Exploring Operation: 61-28=33, Resulting Numbers: [13, 33] Generated Node #0,0,0: 46:[13, 33] Operation: 61-28=33 Moving to Node #0,0,0 Current State: 46:[13, 33], Operations: ['88-75=13', '61-28=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 64, 12, 18, 14 ]
100
[ "14-12=2", "18*2=36", "64+36=100" ]
Current State: 100:[64, 12, 18, 14], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [64, 18, 2] Generated Node #2: [64, 18, 2] from Operation: 14-12=2 Current State: 100:[64, 18, 2], Operations: ['14-12=2'] Exploring Operation: 18*2=36, Resulting Numbers: [64, 36] Generated Node #3: [64, 36] from Operation: 18*2=36 Current State: 100:[64, 36], Operations: ['14-12=2', '18*2=36'] Exploring Operation: 64+36=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[64, 12, 18, 14], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [64, 18, 2] Generated Node #0,0: 100:[64, 18, 2] Operation: 14-12=2 Exploring Operation: 64-12=52, Resulting Numbers: [18, 14, 52] Generated Node #0,1: 100:[18, 14, 52] Operation: 64-12=52 Exploring Operation: 64-18=46, Resulting Numbers: [12, 14, 46] Generated Node #0,2: 100:[12, 14, 46] Operation: 64-18=46 Exploring Operation: 18-14=4, Resulting Numbers: [64, 12, 4] Generated Node #0,3: 100:[64, 12, 4] Operation: 18-14=4 Exploring Operation: 64-14=50, Resulting Numbers: [12, 18, 50] Generated Node #0,4: 100:[12, 18, 50] Operation: 64-14=50 Moving to Node #0,4 Current State: 100:[12, 18, 50], Operations: ['64-14=50'] Exploring Operation: 50-18=32, Resulting Numbers: [12, 32] Generated Node #0,4,0: 100:[12, 32] Operation: 50-18=32 Exploring Operation: 50-12=38, Resulting Numbers: [18, 38] Generated Node #0,4,1: 100:[18, 38] Operation: 50-12=38 Exploring Operation: 12+18=30, Resulting Numbers: [50, 30] Generated Node #0,4,2: 100:[50, 30] Operation: 12+18=30 Exploring Operation: 12+50=62, Resulting Numbers: [18, 62] Generated Node #0,4,3: 100:[18, 62] Operation: 12+50=62 Exploring Operation: 18-12=6, Resulting Numbers: [50, 6] Generated Node #0,4,4: 100:[50, 6] Operation: 18-12=6 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 100:[50, 6], Operations: ['64-14=50', '18-12=6'] Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 100:[50, 30], Operations: ['64-14=50', '12+18=30'] Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,100 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 50*30=1500, Resulting Numbers: [1500] 1500,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 100:[12, 32], Operations: ['64-14=50', '50-18=32'] Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 100:[18, 38], Operations: ['64-14=50', '50-12=38'] Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,100 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 100:[18, 62], Operations: ['64-14=50', '12+50=62'] Exploring Operation: 18+62=80, Resulting Numbers: [80] 80,100 unequal: No Solution Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 18*62=1116, Resulting Numbers: [1116] 1116,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 100:[18, 14, 52], Operations: ['64-12=52'] Exploring Operation: 18-14=4, Resulting Numbers: [52, 4] Generated Node #0,1,0: 100:[52, 4] Operation: 18-14=4 Exploring Operation: 18+14=32, Resulting Numbers: [52, 32] Generated Node #0,1,1: 100:[52, 32] Operation: 18+14=32 Exploring Operation: 52-18=34, Resulting Numbers: [14, 34] Generated Node #0,1,2: 100:[14, 34] Operation: 52-18=34 Exploring Operation: 52-14=38, Resulting Numbers: [18, 38] Generated Node #0,1,3: 100:[18, 38] Operation: 52-14=38 Exploring Operation: 14+52=66, Resulting Numbers: [18, 66] Generated Node #0,1,4: 100:[18, 66] Operation: 14+52=66 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[52, 4], Operations: ['64-12=52', '18-14=4'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,100 unequal: No Solution Exploring Operation: 52*4=208, Resulting Numbers: [208] 208,100 unequal: No Solution Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 100:[52, 32], Operations: ['64-12=52', '18+14=32'] Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,100 unequal: No Solution Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,100 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[14, 34], Operations: ['64-12=52', '52-18=34'] Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 14*34=476, Resulting Numbers: [476] 476,100 unequal: No Solution Exploring Operation: 14+34=48, Resulting Numbers: [48] 48,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 100:[18, 38], Operations: ['64-12=52', '52-14=38'] Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,100 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 100:[18, 66], Operations: ['64-12=52', '14+52=66'] Exploring Operation: 18*66=1188, Resulting Numbers: [1188] 1188,100 unequal: No Solution Exploring Operation: 66-18=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 18+66=84, Resulting Numbers: [84] 84,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 100:[12, 14, 46], Operations: ['64-18=46'] Exploring Operation: 12+14=26, Resulting Numbers: [46, 26] Generated Node #0,2,0: 100:[46, 26] Operation: 12+14=26 Exploring Operation: 46-14=32, Resulting Numbers: [12, 32] Generated Node #0,2,1: 100:[12, 32] Operation: 46-14=32 Exploring Operation: 12+46=58, Resulting Numbers: [14, 58] Generated Node #0,2,2: 100:[14, 58] Operation: 12+46=58 Exploring Operation: 14+46=60, Resulting Numbers: [12, 60] Generated Node #0,2,3: 100:[12, 60] Operation: 14+46=60 Exploring Operation: 14-12=2, Resulting Numbers: [46, 2] Generated Node #0,2,4: 100:[46, 2] Operation: 14-12=2 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 100:[46, 2], Operations: ['64-18=46', '14-12=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,100 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[46, 26], Operations: ['64-18=46', '12+14=26'] Exploring Operation: 46+26=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 46*26=1196, Resulting Numbers: [1196] 1196,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[12, 32], Operations: ['64-18=46', '46-14=32'] Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,100 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[14, 58], Operations: ['64-18=46', '12+46=58'] Exploring Operation: 14+58=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 14*58=812, Resulting Numbers: [812] 812,100 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 100:[12, 60], Operations: ['64-18=46', '14+46=60'] Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 12+60=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 12*60=720, Resulting Numbers: [720] 720,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 100:[64, 18, 2], Operations: ['14-12=2'] Exploring Operation: 64-2=62, Resulting Numbers: [18, 62] Generated Node #0,0,0: 100:[18, 62] Operation: 64-2=62 Exploring Operation: 64/2=32, Resulting Numbers: [18, 32] Generated Node #0,0,1: 100:[18, 32] Operation: 64/2=32 Exploring Operation: 64-18=46, Resulting Numbers: [2, 46] Generated Node #0,0,2: 100:[2, 46] Operation: 64-18=46 Exploring Operation: 18/2=9, Resulting Numbers: [64, 9] Generated Node #0,0,3: 100:[64, 9] Operation: 18/2=9 Exploring Operation: 18+2=20, Resulting Numbers: [64, 20] Generated Node #0,0,4: 100:[64, 20] Operation: 18+2=20 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 100:[2, 46], Operations: ['14-12=2', '64-18=46'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[18, 32], Operations: ['14-12=2', '64/2=32'] Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[18, 62], Operations: ['14-12=2', '64-2=62'] Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 18*62=1116, Resulting Numbers: [1116] 1116,100 unequal: No Solution Exploring Operation: 18+62=80, Resulting Numbers: [80] 80,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 100:[64, 20], Operations: ['14-12=2', '18+2=20'] Exploring Operation: 64*20=1280, Resulting Numbers: [1280] 1280,100 unequal: No Solution Exploring Operation: 64+20=84, Resulting Numbers: [84] 84,100 unequal: No Solution Exploring Operation: 64-20=44, Resulting Numbers: [44] 44,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 100:[64, 9], Operations: ['14-12=2', '18/2=9'] Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 64*9=576, Resulting Numbers: [576] 576,100 unequal: No Solution Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,100 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: 100:[64, 12, 4], Operations: ['18-14=4'] Exploring Operation: 64/4=16, Resulting Numbers: [12, 16] Generated Node #0,3,0: 100:[12, 16] Operation: 64/4=16 Exploring Operation: 64-4=60, Resulting Numbers: [12, 60] Generated Node #0,3,1: 100:[12, 60] Operation: 64-4=60 Exploring Operation: 64-12=52, Resulting Numbers: [4, 52] Generated Node #0,3,2: 100:[4, 52] Operation: 64-12=52 Exploring Operation: 12*4=48, Resulting Numbers: [64, 48] Generated Node #0,3,3: 100:[64, 48] Operation: 12*4=48 Exploring Operation: 12/4=3, Resulting Numbers: [64, 3] Generated Node #0,3,4: 100:[64, 3] Operation: 12/4=3 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 100:[4, 52], Operations: ['18-14=4', '64-12=52'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,100 unequal: No Solution Exploring Operation: 4*52=208, Resulting Numbers: [208] 208,100 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 #0,3,0 Current State: 100:[12, 16], Operations: ['18-14=4', '64/4=16'] Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,100 unequal: No Solution Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 100:[12, 60], Operations: ['18-14=4', '64-4=60'] Exploring Operation: 12*60=720, Resulting Numbers: [720] 720,100 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 12+60=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,100 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 #0,3,4 Current State: 100:[64, 3], Operations: ['18-14=4', '12/4=3'] Exploring Operation: 64+3=67, Resulting Numbers: [67] 67,100 unequal: No Solution Exploring Operation: 64*3=192, Resulting Numbers: [192] 192,100 unequal: No Solution Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,100 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 #0,3,3 Current State: 100:[64, 48], Operations: ['18-14=4', '12*4=48'] Exploring Operation: 64+48=112, Resulting Numbers: [112] 112,100 unequal: No Solution Exploring Operation: 64-48=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 64*48=3072, Resulting Numbers: [3072] 3072,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 45, 95, 65, 58 ]
90
[ "58-45=13", "65/13=5", "95-5=90" ]
Current State: 90:[45, 95, 65, 58], Operations: [] Exploring Operation: 58-45=13, Resulting Numbers: [95, 65, 13] Generated Node #2: [95, 65, 13] from Operation: 58-45=13 Current State: 90:[95, 65, 13], Operations: ['58-45=13'] Exploring Operation: 65/13=5, Resulting Numbers: [95, 5] Generated Node #3: [95, 5] from Operation: 65/13=5 Current State: 90:[95, 5], Operations: ['58-45=13', '65/13=5'] Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[45, 95, 65, 58], Operations: [] Exploring Operation: 65-58=7, Resulting Numbers: [45, 95, 7] Generated Node #0,0: 90:[45, 95, 7] Operation: 65-58=7 Exploring Operation: 95-65=30, Resulting Numbers: [45, 58, 30] Generated Node #0,1: 90:[45, 58, 30] Operation: 95-65=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[45, 95, 7], Operations: ['65-58=7'] Exploring Operation: 95-45=50, Resulting Numbers: [7, 50] Generated Node #0,0,0: 90:[7, 50] Operation: 95-45=50 Exploring Operation: 95-7=88, Resulting Numbers: [45, 88] Generated Node #0,0,1: 90:[45, 88] Operation: 95-7=88 Moving to Node #0,0,1 Current State: 90:[45, 88], Operations: ['65-58=7', '95-7=88'] Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,90 unequal: No Solution Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[7, 50], Operations: ['65-58=7', '95-45=50'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,90 unequal: No Solution Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,90 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 Current State: 90:[45, 58, 30], Operations: ['95-65=30'] Exploring Operation: 58-45=13, Resulting Numbers: [30, 13] Generated Node #0,1,0: 90:[30, 13] Operation: 58-45=13 Exploring Operation: 58+30=88, Resulting Numbers: [45, 88] Generated Node #0,1,1: 90:[45, 88] Operation: 58+30=88 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[30, 13], Operations: ['95-65=30', '58-45=13'] Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,90 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[45, 88], Operations: ['95-65=30', '58+30=88'] Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,90 unequal: No Solution Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 27, 36, 85, 25 ]
47
[ "27+36=63", "85+25=110", "110-63=47" ]
Current State: 47:[27, 36, 85, 25], Operations: [] Exploring Operation: 27+36=63, Resulting Numbers: [85, 25, 63] Generated Node #2: [85, 25, 63] from Operation: 27+36=63 Current State: 47:[85, 25, 63], Operations: ['27+36=63'] Exploring Operation: 85+25=110, Resulting Numbers: [63, 110] Generated Node #3: [63, 110] from Operation: 85+25=110 Current State: 47:[63, 110], Operations: ['27+36=63', '85+25=110'] Exploring Operation: 110-63=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[27, 36, 85, 25], Operations: [] Exploring Operation: 85-36=49, Resulting Numbers: [27, 25, 49] Generated Node #0,0: 47:[27, 25, 49] Operation: 85-36=49 Exploring Operation: 85-27=58, Resulting Numbers: [36, 25, 58] Generated Node #0,1: 47:[36, 25, 58] Operation: 85-27=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[27, 25, 49], Operations: ['85-36=49'] Exploring Operation: 49-25=24, Resulting Numbers: [27, 24] Generated Node #0,0,0: 47:[27, 24] Operation: 49-25=24 Exploring Operation: 27+25=52, Resulting Numbers: [49, 52] Generated Node #0,0,1: 47:[49, 52] Operation: 27+25=52 Moving to Node #0,0,1 Current State: 47:[49, 52], Operations: ['85-36=49', '27+25=52'] Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[27, 24], Operations: ['85-36=49', '49-25=24'] Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,47 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:[36, 25, 58], Operations: ['85-27=58'] Exploring Operation: 36+25=61, Resulting Numbers: [58, 61] Generated Node #0,1,0: 47:[58, 61] Operation: 36+25=61 Exploring Operation: 58-25=33, Resulting Numbers: [36, 33] Generated Node #0,1,1: 47:[36, 33] Operation: 58-25=33 Moving to Node #0,1,0 Current State: 47:[58, 61], Operations: ['85-27=58', '36+25=61'] Exploring Operation: 58+61=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[36, 33], Operations: ['85-27=58', '58-25=33'] Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,47 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 84, 63, 7, 61 ]
86
[ "84-63=21", "7*21=147", "147-61=86" ]
Current State: 86:[84, 63, 7, 61], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [7, 61, 21] Generated Node #2: [7, 61, 21] from Operation: 84-63=21 Current State: 86:[7, 61, 21], Operations: ['84-63=21'] Exploring Operation: 7*21=147, Resulting Numbers: [61, 147] Generated Node #3: [61, 147] from Operation: 7*21=147 Current State: 86:[61, 147], Operations: ['84-63=21', '7*21=147'] Exploring Operation: 147-61=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[84, 63, 7, 61], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [84, 7, 2] Generated Node #0,0: 86:[84, 7, 2] Operation: 63-61=2 Exploring Operation: 63/7=9, Resulting Numbers: [84, 61, 9] Generated Node #0,1: 86:[84, 61, 9] Operation: 63/7=9 Exploring Operation: 63-7=56, Resulting Numbers: [84, 61, 56] Generated Node #0,2: 86:[84, 61, 56] Operation: 63-7=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[84, 7, 2], Operations: ['63-61=2'] Exploring Operation: 84+7=91, Resulting Numbers: [2, 91] Generated Node #0,0,0: 86:[2, 91] Operation: 84+7=91 Exploring Operation: 7-2=5, Resulting Numbers: [84, 5] Generated Node #0,0,1: 86:[84, 5] Operation: 7-2=5 Exploring Operation: 84+2=86, Resulting Numbers: [7, 86] Generated Node #0,0,2: 86:[7, 86] Operation: 84+2=86 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[2, 91], Operations: ['63-61=2', '84+7=91'] Exploring Operation: 2*91=182, Resulting Numbers: [182] 182,86 unequal: No Solution Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,86 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[84, 5], Operations: ['63-61=2', '7-2=5'] Exploring Operation: 84*5=420, Resulting Numbers: [420] 420,86 unequal: No Solution Exploring Operation: 84+5=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 86:[7, 86], Operations: ['63-61=2', '84+2=86'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,86 unequal: No Solution Exploring Operation: 7*86=602, Resulting Numbers: [602] 602,86 unequal: No Solution Exploring Operation: 7+86=93, Resulting Numbers: [93] 93,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[84, 61, 9], Operations: ['63/7=9'] Exploring Operation: 61+9=70, Resulting Numbers: [84, 70] Generated Node #0,1,0: 86:[84, 70] Operation: 61+9=70 Exploring Operation: 84+9=93, Resulting Numbers: [61, 93] Generated Node #0,1,1: 86:[61, 93] Operation: 84+9=93 Exploring Operation: 61-9=52, Resulting Numbers: [84, 52] Generated Node #0,1,2: 86:[84, 52] Operation: 61-9=52 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 86:[84, 52], Operations: ['63/7=9', '61-9=52'] Exploring Operation: 84*52=4368, Resulting Numbers: [4368] 4368,86 unequal: No Solution Exploring Operation: 84-52=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 84+52=136, Resulting Numbers: [136] 136,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 86:[84, 70], Operations: ['63/7=9', '61+9=70'] Exploring Operation: 84+70=154, Resulting Numbers: [154] 154,86 unequal: No Solution Exploring Operation: 84*70=5880, Resulting Numbers: [5880] 5880,86 unequal: No Solution Exploring Operation: 84-70=14, Resulting Numbers: [14] 14,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[61, 93], Operations: ['63/7=9', '84+9=93'] Exploring Operation: 61*93=5673, Resulting Numbers: [5673] 5673,86 unequal: No Solution Exploring Operation: 93-61=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 61+93=154, Resulting Numbers: [154] 154,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[84, 61, 56], Operations: ['63-7=56'] Exploring Operation: 84-61=23, Resulting Numbers: [56, 23] Generated Node #0,2,0: 86:[56, 23] Operation: 84-61=23 Exploring Operation: 84-56=28, Resulting Numbers: [61, 28] Generated Node #0,2,1: 86:[61, 28] Operation: 84-56=28 Exploring Operation: 61-56=5, Resulting Numbers: [84, 5] Generated Node #0,2,2: 86:[84, 5] Operation: 61-56=5 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 86:[84, 5], Operations: ['63-7=56', '61-56=5'] Exploring Operation: 84*5=420, Resulting Numbers: [420] 420,86 unequal: No Solution Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,86 unequal: No Solution Exploring Operation: 84+5=89, Resulting Numbers: [89] 89,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 86:[56, 23], Operations: ['63-7=56', '84-61=23'] Exploring Operation: 56-23=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 56+23=79, Resulting Numbers: [79] 79,86 unequal: No Solution Exploring Operation: 56*23=1288, Resulting Numbers: [1288] 1288,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[61, 28], Operations: ['63-7=56', '84-56=28'] Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 92, 94, 28, 65 ]
79
[ "94-92=2", "28/2=14", "65+14=79" ]
Current State: 79:[92, 94, 28, 65], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [28, 65, 2] Generated Node #2: [28, 65, 2] from Operation: 94-92=2 Current State: 79:[28, 65, 2], Operations: ['94-92=2'] Exploring Operation: 28/2=14, Resulting Numbers: [65, 14] Generated Node #3: [65, 14] from Operation: 28/2=14 Current State: 79:[65, 14], Operations: ['94-92=2', '28/2=14'] Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[92, 94, 28, 65], Operations: [] Exploring Operation: 94-28=66, Resulting Numbers: [92, 65, 66] Generated Node #0,0: 79:[92, 65, 66] Operation: 94-28=66 Moving to Node #0,0 Current State: 79:[92, 65, 66], Operations: ['94-28=66'] Exploring Operation: 92-65=27, Resulting Numbers: [66, 27] Generated Node #0,0,0: 79:[66, 27] Operation: 92-65=27 Moving to Node #0,0,0 Current State: 79:[66, 27], Operations: ['94-28=66', '92-65=27'] Exploring Operation: 66+27=93, Resulting Numbers: [93] 93,79 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 65, 31, 72, 33 ]
71
[ "65-31=34", "72+33=105", "105-34=71" ]
Current State: 71:[65, 31, 72, 33], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [72, 33, 34] Generated Node #2: [72, 33, 34] from Operation: 65-31=34 Current State: 71:[72, 33, 34], Operations: ['65-31=34'] Exploring Operation: 72+33=105, Resulting Numbers: [34, 105] Generated Node #3: [34, 105] from Operation: 72+33=105 Current State: 71:[34, 105], Operations: ['65-31=34', '72+33=105'] Exploring Operation: 105-34=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[65, 31, 72, 33], Operations: [] Exploring Operation: 31+33=64, Resulting Numbers: [65, 72, 64] Generated Node #0,0: 71:[65, 72, 64] Operation: 31+33=64 Exploring Operation: 72-31=41, Resulting Numbers: [65, 33, 41] Generated Node #0,1: 71:[65, 33, 41] Operation: 72-31=41 Exploring Operation: 65+33=98, Resulting Numbers: [31, 72, 98] Generated Node #0,2: 71:[31, 72, 98] Operation: 65+33=98 Exploring Operation: 65+31=96, Resulting Numbers: [72, 33, 96] Generated Node #0,3: 71:[72, 33, 96] Operation: 65+31=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[65, 72, 64], Operations: ['31+33=64'] Exploring Operation: 72-65=7, Resulting Numbers: [64, 7] Generated Node #0,0,0: 71:[64, 7] Operation: 72-65=7 Exploring Operation: 65-64=1, Resulting Numbers: [72, 1] Generated Node #0,0,1: 71:[72, 1] Operation: 65-64=1 Exploring Operation: 72-64=8, Resulting Numbers: [65, 8] Generated Node #0,0,2: 71:[65, 8] Operation: 72-64=8 Exploring Operation: 65+64=129, Resulting Numbers: [72, 129] Generated Node #0,0,3: 71:[72, 129] Operation: 65+64=129 Moving to Node #0,0,3 Current State: 71:[72, 129], Operations: ['31+33=64', '65+64=129'] Exploring Operation: 72*129=9288, Resulting Numbers: [9288] 9288,71 unequal: No Solution Exploring Operation: 72+129=201, Resulting Numbers: [201] 201,71 unequal: No Solution Exploring Operation: 129-72=57, Resulting Numbers: [57] 57,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[65, 8], Operations: ['31+33=64', '72-64=8'] Exploring Operation: 65+8=73, Resulting Numbers: [73] 73,71 unequal: No Solution Exploring Operation: 65*8=520, Resulting Numbers: [520] 520,71 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[72, 1], Operations: ['31+33=64', '65-64=1'] Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,71 unequal: No Solution Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[65, 31, 72, 33], Operations: [] Exploring Operation: 31+33=64, Resulting Numbers: [65, 72, 64] Generated Node #0,0: 71:[65, 72, 64] Operation: 31+33=64 Moving to Node #0,0 Current State: 71:[65, 72, 64], Operations: ['31+33=64'] Exploring Operation: 65-64=1, Resulting Numbers: [72, 1] Generated Node #0,0,1: 71:[72, 1] Operation: 65-64=1 Moving to Node #0,0,1 Current State: 71:[72, 1], Operations: ['31+33=64', '65-64=1'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 90, 94, 13, 34 ]
17
[ "94-90=4", "34-13=21", "21-4=17" ]
Current State: 17:[90, 94, 13, 34], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [13, 34, 4] Generated Node #2: [13, 34, 4] from Operation: 94-90=4 Current State: 17:[13, 34, 4], Operations: ['94-90=4'] Exploring Operation: 34-13=21, Resulting Numbers: [4, 21] Generated Node #3: [4, 21] from Operation: 34-13=21 Current State: 17:[4, 21], Operations: ['94-90=4', '34-13=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[90, 94, 13, 34], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [13, 34, 4] Generated Node #0,0: 17:[13, 34, 4] Operation: 94-90=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[13, 34, 4], Operations: ['94-90=4'] Exploring Operation: 34-13=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 17:[4, 21] Operation: 34-13=21 Moving to Node #0,0,0 Current State: 17:[4, 21], Operations: ['94-90=4', '34-13=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[90, 94, 13, 34], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [13, 34, 4] Generated Node #0,0: 17:[13, 34, 4] Operation: 94-90=4 Moving to Node #0,0 Current State: 17:[13, 34, 4], Operations: ['94-90=4'] Exploring Operation: 34-13=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 17:[4, 21] Operation: 34-13=21 Moving to Node #0,0,0 Current State: 17:[4, 21], Operations: ['94-90=4', '34-13=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 39, 3, 96, 16 ]
99
[ "39/3=13", "96+16=112", "112-13=99" ]
Current State: 99:[39, 3, 96, 16], Operations: [] Exploring Operation: 39/3=13, Resulting Numbers: [96, 16, 13] Generated Node #2: [96, 16, 13] from Operation: 39/3=13 Current State: 99:[96, 16, 13], Operations: ['39/3=13'] Exploring Operation: 96+16=112, Resulting Numbers: [13, 112] Generated Node #3: [13, 112] from Operation: 96+16=112 Current State: 99:[13, 112], Operations: ['39/3=13', '96+16=112'] Exploring Operation: 112-13=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[39, 3, 96, 16], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [39, 3, 6] Generated Node #0,0: 99:[39, 3, 6] Operation: 96/16=6 Exploring Operation: 39/3=13, Resulting Numbers: [96, 16, 13] Generated Node #0,1: 99:[96, 16, 13] Operation: 39/3=13 Exploring Operation: 39-3=36, Resulting Numbers: [96, 16, 36] Generated Node #0,2: 99:[96, 16, 36] Operation: 39-3=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[39, 3, 6], Operations: ['96/16=6'] Exploring Operation: 39-6=33, Resulting Numbers: [3, 33] Generated Node #0,0,0: 99:[3, 33] Operation: 39-6=33 Exploring Operation: 39/3=13, Resulting Numbers: [6, 13] Generated Node #0,0,1: 99:[6, 13] Operation: 39/3=13 Exploring Operation: 39-3=36, Resulting Numbers: [6, 36] Generated Node #0,0,2: 99:[6, 36] Operation: 39-3=36 Moving to Node #0,0,0 Current State: 99:[3, 33], Operations: ['96/16=6', '39-6=33'] Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[39, 3, 96, 16], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [39, 3, 6] Generated Node #0,0: 99:[39, 3, 6] Operation: 96/16=6 Moving to Node #0,0 Current State: 99:[39, 3, 6], Operations: ['96/16=6'] Exploring Operation: 39-6=33, Resulting Numbers: [3, 33] Generated Node #0,0,0: 99:[3, 33] Operation: 39-6=33 Moving to Node #0,0,0 Current State: 99:[3, 33], Operations: ['96/16=6', '39-6=33'] Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 3, 14, 2, 89 ]
43
[ "89-2=87", "87/3=29", "14+29=43" ]
Current State: 43:[3, 14, 2, 89], Operations: [] Exploring Operation: 89-2=87, Resulting Numbers: [3, 14, 87] Generated Node #2: [3, 14, 87] from Operation: 89-2=87 Current State: 43:[3, 14, 87], Operations: ['89-2=87'] Exploring Operation: 87/3=29, Resulting Numbers: [14, 29] Generated Node #3: [14, 29] from Operation: 87/3=29 Current State: 43:[14, 29], Operations: ['89-2=87', '87/3=29'] Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[3, 14, 2, 89], Operations: [] Exploring Operation: 3*2=6, Resulting Numbers: [14, 89, 6] Generated Node #0,0: 43:[14, 89, 6] Operation: 3*2=6 Exploring Operation: 3+14=17, Resulting Numbers: [2, 89, 17] Generated Node #0,1: 43:[2, 89, 17] Operation: 3+14=17 Exploring Operation: 3+2=5, Resulting Numbers: [14, 89, 5] Generated Node #0,2: 43:[14, 89, 5] Operation: 3+2=5 Exploring Operation: 14*2=28, Resulting Numbers: [3, 89, 28] Generated Node #0,3: 43:[3, 89, 28] Operation: 14*2=28 Exploring Operation: 3*14=42, Resulting Numbers: [2, 89, 42] Generated Node #0,4: 43:[2, 89, 42] Operation: 3*14=42 Moving to Node #0,4 Current State: 43:[2, 89, 42], Operations: ['3*14=42'] Exploring Operation: 2+42=44, Resulting Numbers: [89, 44] Generated Node #0,4,0: 43:[89, 44] Operation: 2+42=44 Exploring Operation: 89-42=47, Resulting Numbers: [2, 47] Generated Node #0,4,1: 43:[2, 47] Operation: 89-42=47 Exploring Operation: 89-2=87, Resulting Numbers: [42, 87] Generated Node #0,4,2: 43:[42, 87] Operation: 89-2=87 Exploring Operation: 42-2=40, Resulting Numbers: [89, 40] Generated Node #0,4,3: 43:[89, 40] Operation: 42-2=40 Exploring Operation: 2+89=91, Resulting Numbers: [42, 91] Generated Node #0,4,4: 43:[42, 91] Operation: 2+89=91 Moving to Node #0,3 Current State: 43:[3, 89, 28], Operations: ['14*2=28'] Exploring Operation: 28-3=25, Resulting Numbers: [89, 25] Generated Node #0,3,0: 43:[89, 25] Operation: 28-3=25 Exploring Operation: 89-28=61, Resulting Numbers: [3, 61] Generated Node #0,3,1: 43:[3, 61] Operation: 89-28=61 Exploring Operation: 89-3=86, Resulting Numbers: [28, 86] Generated Node #0,3,2: 43:[28, 86] Operation: 89-3=86 Exploring Operation: 3+89=92, Resulting Numbers: [28, 92] Generated Node #0,3,3: 43:[28, 92] Operation: 3+89=92 Exploring Operation: 3+28=31, Resulting Numbers: [89, 31] Generated Node #0,3,4: 43:[89, 31] Operation: 3+28=31 Moving to Node #0,0 Current State: 43:[14, 89, 6], Operations: ['3*2=6'] Exploring Operation: 89-14=75, Resulting Numbers: [6, 75] Generated Node #0,0,0: 43:[6, 75] Operation: 89-14=75 Exploring Operation: 89-6=83, Resulting Numbers: [14, 83] Generated Node #0,0,1: 43:[14, 83] Operation: 89-6=83 Exploring Operation: 89+6=95, Resulting Numbers: [14, 95] Generated Node #0,0,2: 43:[14, 95] Operation: 89+6=95 Exploring Operation: 14+6=20, Resulting Numbers: [89, 20] Generated Node #0,0,3: 43:[89, 20] Operation: 14+6=20 Exploring Operation: 14-6=8, Resulting Numbers: [89, 8] Generated Node #0,0,4: 43:[89, 8] Operation: 14-6=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[6, 75], Operations: ['3*2=6', '89-14=75'] Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 6*75=450, Resulting Numbers: [450] 450,43 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:[14, 83], Operations: ['3*2=6', '89-6=83'] Exploring Operation: 14*83=1162, Resulting Numbers: [1162] 1162,43 unequal: No Solution Exploring Operation: 14+83=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,43 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:[89, 20], Operations: ['3*2=6', '14+6=20'] Exploring Operation: 89+20=109, Resulting Numbers: [109] 109,43 unequal: No Solution Exploring Operation: 89*20=1780, Resulting Numbers: [1780] 1780,43 unequal: No Solution Exploring Operation: 89-20=69, Resulting Numbers: [69] 69,43 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:[14, 95], Operations: ['3*2=6', '89+6=95'] Exploring Operation: 14*95=1330, Resulting Numbers: [1330] 1330,43 unequal: No Solution Exploring Operation: 14+95=109, Resulting Numbers: [109] 109,43 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,43 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 #0,0,4 Current State: 43:[89, 8], Operations: ['3*2=6', '14-6=8'] Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 43:[2, 89, 17], Operations: ['3+14=17'] Exploring Operation: 2*17=34, Resulting Numbers: [89, 34] Generated Node #0,1,0: 43:[89, 34] Operation: 2*17=34 Exploring Operation: 2+89=91, Resulting Numbers: [17, 91] Generated Node #0,1,1: 43:[17, 91] Operation: 2+89=91 Exploring Operation: 89-2=87, Resulting Numbers: [17, 87] Generated Node #0,1,2: 43:[17, 87] Operation: 89-2=87 Exploring Operation: 2+17=19, Resulting Numbers: [89, 19] Generated Node #0,1,3: 43:[89, 19] Operation: 2+17=19 Exploring Operation: 89-17=72, Resulting Numbers: [2, 72] Generated Node #0,1,4: 43:[2, 72] Operation: 89-17=72 Moving to Node #0,2 Current State: 43:[14, 89, 5], Operations: ['3+2=5'] Exploring Operation: 89-14=75, Resulting Numbers: [5, 75] Generated Node #0,2,0: 43:[5, 75] Operation: 89-14=75 Exploring Operation: 14-5=9, Resulting Numbers: [89, 9] Generated Node #0,2,1: 43:[89, 9] Operation: 14-5=9 Exploring Operation: 14*5=70, Resulting Numbers: [89, 70] Generated Node #0,2,2: 43:[89, 70] Operation: 14*5=70 Exploring Operation: 89-5=84, Resulting Numbers: [14, 84] Generated Node #0,2,3: 43:[14, 84] Operation: 89-5=84 Exploring Operation: 14+5=19, Resulting Numbers: [89, 19] Generated Node #0,2,4: 43:[89, 19] Operation: 14+5=19 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 43:[5, 75], Operations: ['3+2=5', '89-14=75'] Exploring Operation: 75-5=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 5*75=375, Resulting Numbers: [375] 375,43 unequal: No Solution Exploring Operation: 5+75=80, Resulting Numbers: [80] 80,43 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 #0,2,3 Current State: 43:[14, 84], Operations: ['3+2=5', '89-5=84'] Exploring Operation: 14+84=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 14*84=1176, Resulting Numbers: [1176] 1176,43 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,43 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 #0,2,4 Current State: 43:[89, 19], Operations: ['3+2=5', '14+5=19'] Exploring Operation: 89*19=1691, Resulting Numbers: [1691] 1691,43 unequal: No Solution Exploring Operation: 89+19=108, Resulting Numbers: [108] 108,43 unequal: No Solution Exploring Operation: 89-19=70, Resulting Numbers: [70] 70,43 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 #0,2,2 Current State: 43:[89, 70], Operations: ['3+2=5', '14*5=70'] Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 89+70=159, Resulting Numbers: [159] 159,43 unequal: No Solution Exploring Operation: 89*70=6230, Resulting Numbers: [6230] 6230,43 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 #0,2,1 Current State: 43:[89, 9], Operations: ['3+2=5', '14-5=9'] Exploring Operation: 89+9=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 89*9=801, Resulting Numbers: [801] 801,43 unequal: No Solution Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,1 Current State: 43:[2, 47], Operations: ['3*14=42', '89-42=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,43 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,43 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,43 unequal: No Solution Moving to Node #0,4,2 Current State: 43:[42, 87], Operations: ['3*14=42', '89-2=87'] Exploring Operation: 42+87=129, Resulting Numbers: [129] 129,43 unequal: No Solution Exploring Operation: 42*87=3654, Resulting Numbers: [3654] 3654,43 unequal: No Solution Exploring Operation: 87-42=45, Resulting Numbers: [45] 45,43 unequal: No Solution Moving to Node #0,4,0 Current State: 43:[89, 44], Operations: ['3*14=42', '2+42=44'] Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 89*44=3916, Resulting Numbers: [3916] 3916,43 unequal: No Solution Exploring Operation: 89+44=133, Resulting Numbers: [133] 133,43 unequal: No Solution Moving to Node #0,4,4 Current State: 43:[42, 91], Operations: ['3*14=42', '2+89=91'] Exploring Operation: 42+91=133, Resulting Numbers: [133] 133,43 unequal: No Solution Exploring Operation: 91-42=49, Resulting Numbers: [49] 49,43 unequal: No Solution Exploring Operation: 42*91=3822, Resulting Numbers: [3822] 3822,43 unequal: No Solution Moving to Node #0,4,3 Current State: 43:[89, 40], Operations: ['3*14=42', '42-2=40'] Exploring Operation: 89*40=3560, Resulting Numbers: [3560] 3560,43 unequal: No Solution Exploring Operation: 89+40=129, Resulting Numbers: [129] 129,43 unequal: No Solution Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[89, 34], Operations: ['3+14=17', '2*17=34'] Exploring Operation: 89+34=123, Resulting Numbers: [123] 123,43 unequal: No Solution Exploring Operation: 89*34=3026, Resulting Numbers: [3026] 3026,43 unequal: No Solution Exploring Operation: 89-34=55, Resulting Numbers: [55] 55,43 unequal: No Solution Moving to Node #0,3,2 Current State: 43:[28, 86], Operations: ['14*2=28', '89-3=86'] Exploring Operation: 28+86=114, Resulting Numbers: [114] 114,43 unequal: No Solution Exploring Operation: 28*86=2408, Resulting Numbers: [2408] 2408,43 unequal: No Solution Exploring Operation: 86-28=58, Resulting Numbers: [58] 58,43 unequal: No Solution Moving to Node #0,3,1 Current State: 43:[3, 61], Operations: ['14*2=28', '89-28=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,43 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,43 unequal: No Solution Moving to Node #0,3,4 Current State: 43:[89, 31], Operations: ['14*2=28', '3+28=31'] Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,43 unequal: No Solution Exploring Operation: 89*31=2759, Resulting Numbers: [2759] 2759,43 unequal: No Solution Exploring Operation: 89+31=120, Resulting Numbers: [120] 120,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[28, 92], Operations: ['14*2=28', '3+89=92'] Exploring Operation: 28*92=2576, Resulting Numbers: [2576] 2576,43 unequal: No Solution Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 28+92=120, Resulting Numbers: [120] 120,43 unequal: No Solution Moving to Node #0,3,0 Current State: 43:[89, 25], Operations: ['14*2=28', '28-3=25'] Exploring Operation: 89+25=114, Resulting Numbers: [114] 114,43 unequal: No Solution Exploring Operation: 89*25=2225, Resulting Numbers: [2225] 2225,43 unequal: No Solution Exploring Operation: 89-25=64, Resulting Numbers: [64] 64,43 unequal: No Solution Moving to Node #0,1,4 Current State: 43:[2, 72], Operations: ['3+14=17', '89-17=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 2*72=144, Resulting Numbers: [144] 144,43 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,43 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[17, 87], Operations: ['3+14=17', '89-2=87'] Exploring Operation: 17*87=1479, Resulting Numbers: [1479] 1479,43 unequal: No Solution Exploring Operation: 17+87=104, Resulting Numbers: [104] 104,43 unequal: No Solution Exploring Operation: 87-17=70, Resulting Numbers: [70] 70,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[89, 19], Operations: ['3+14=17', '2+17=19'] Exploring Operation: 89+19=108, Resulting Numbers: [108] 108,43 unequal: No Solution Exploring Operation: 89*19=1691, Resulting Numbers: [1691] 1691,43 unequal: No Solution Exploring Operation: 89-19=70, Resulting Numbers: [70] 70,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[17, 91], Operations: ['3+14=17', '2+89=91'] Exploring Operation: 17*91=1547, Resulting Numbers: [1547] 1547,43 unequal: No Solution Exploring Operation: 91-17=74, Resulting Numbers: [74] 74,43 unequal: No Solution Exploring Operation: 17+91=108, Resulting Numbers: [108] 108,43 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 15, 5, 99, 3 ]
33
[ "15+99=114", "114/3=38", "38-5=33" ]
Current State: 33:[15, 5, 99, 3], Operations: [] Exploring Operation: 15+99=114, Resulting Numbers: [5, 3, 114] Generated Node #2: [5, 3, 114] from Operation: 15+99=114 Current State: 33:[5, 3, 114], Operations: ['15+99=114'] Exploring Operation: 114/3=38, Resulting Numbers: [5, 38] Generated Node #3: [5, 38] from Operation: 114/3=38 Current State: 33:[5, 38], Operations: ['15+99=114', '114/3=38'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[15, 5, 99, 3], Operations: [] Exploring Operation: 15/5=3, Resulting Numbers: [99, 3, 3] Generated Node #0,0: 33:[99, 3, 3] Operation: 15/5=3 Exploring Operation: 99-5=94, Resulting Numbers: [15, 3, 94] Generated Node #0,1: 33:[15, 3, 94] Operation: 99-5=94 Exploring Operation: 15-5=10, Resulting Numbers: [99, 3, 10] Generated Node #0,2: 33:[99, 3, 10] Operation: 15-5=10 Exploring Operation: 99/3=33, Resulting Numbers: [15, 5, 33] Generated Node #0,3: 33:[15, 5, 33] Operation: 99/3=33 Exploring Operation: 99-15=84, Resulting Numbers: [5, 3, 84] Generated Node #0,4: 33:[5, 3, 84] Operation: 99-15=84 Moving to Node #0,3 Current State: 33:[15, 5, 33], Operations: ['99/3=33'] Exploring Operation: 33-15=18, Resulting Numbers: [5, 18] Generated Node #0,3,0: 33:[5, 18] Operation: 33-15=18 Exploring Operation: 15/5=3, Resulting Numbers: [33, 3] Generated Node #0,3,1: 33:[33, 3] Operation: 15/5=3 Exploring Operation: 15+5=20, Resulting Numbers: [33, 20] Generated Node #0,3,2: 33:[33, 20] Operation: 15+5=20 Exploring Operation: 15-5=10, Resulting Numbers: [33, 10] Generated Node #0,3,3: 33:[33, 10] Operation: 15-5=10 Exploring Operation: 5+33=38, Resulting Numbers: [15, 38] Generated Node #0,3,4: 33:[15, 38] Operation: 5+33=38 Moving to Node #0,4 Current State: 33:[5, 3, 84], Operations: ['99-15=84'] Exploring Operation: 5-3=2, Resulting Numbers: [84, 2] Generated Node #0,4,0: 33:[84, 2] Operation: 5-3=2 Exploring Operation: 84-5=79, Resulting Numbers: [3, 79] Generated Node #0,4,1: 33:[3, 79] Operation: 84-5=79 Exploring Operation: 5+3=8, Resulting Numbers: [84, 8] Generated Node #0,4,2: 33:[84, 8] Operation: 5+3=8 Exploring Operation: 84-3=81, Resulting Numbers: [5, 81] Generated Node #0,4,3: 33:[5, 81] Operation: 84-3=81 Exploring Operation: 84/3=28, Resulting Numbers: [5, 28] Generated Node #0,4,4: 33:[5, 28] Operation: 84/3=28 Moving to Node #0,1 Current State: 33:[15, 3, 94], Operations: ['99-5=94'] Exploring Operation: 15+3=18, Resulting Numbers: [94, 18] Generated Node #0,1,0: 33:[94, 18] Operation: 15+3=18 Exploring Operation: 94-15=79, Resulting Numbers: [3, 79] Generated Node #0,1,1: 33:[3, 79] Operation: 94-15=79 Exploring Operation: 15/3=5, Resulting Numbers: [94, 5] Generated Node #0,1,2: 33:[94, 5] Operation: 15/3=5 Exploring Operation: 94-3=91, Resulting Numbers: [15, 91] Generated Node #0,1,3: 33:[15, 91] Operation: 94-3=91 Exploring Operation: 15-3=12, Resulting Numbers: [94, 12] Generated Node #0,1,4: 33:[94, 12] Operation: 15-3=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[3, 79], Operations: ['99-5=94', '94-15=79'] Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,33 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,33 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 33:[15, 91], Operations: ['99-5=94', '94-3=91'] Exploring Operation: 15+91=106, Resulting Numbers: [106] 106,33 unequal: No Solution Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,33 unequal: No Solution Exploring Operation: 15*91=1365, Resulting Numbers: [1365] 1365,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 33:[94, 12], Operations: ['99-5=94', '15-3=12'] Exploring Operation: 94+12=106, Resulting Numbers: [106] 106,33 unequal: No Solution Exploring Operation: 94*12=1128, Resulting Numbers: [1128] 1128,33 unequal: No Solution Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 33:[94, 5], Operations: ['99-5=94', '15/3=5'] Exploring Operation: 94*5=470, Resulting Numbers: [470] 470,33 unequal: No Solution Exploring Operation: 94+5=99, Resulting Numbers: [99] 99,33 unequal: No Solution Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[94, 18], Operations: ['99-5=94', '15+3=18'] Exploring Operation: 94-18=76, Resulting Numbers: [76] 76,33 unequal: No Solution Exploring Operation: 94*18=1692, Resulting Numbers: [1692] 1692,33 unequal: No Solution Exploring Operation: 94+18=112, Resulting Numbers: [112] 112,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 33:[99, 3, 3], Operations: ['15/5=3'] Exploring Operation: 99-3=96, Resulting Numbers: [3, 96] Generated Node #0,0,0: 33:[3, 96] Operation: 99-3=96 Exploring Operation: 99/3=33, Resulting Numbers: [3, 33] Generated Node #0,0,1: 33:[3, 33] Operation: 99/3=33 Exploring Operation: 99/3=33, Resulting Numbers: [3, 33] Generated Node #0,0,2: 33:[3, 33] Operation: 99/3=33 Exploring Operation: 3*3=9, Resulting Numbers: [99, 9] Generated Node #0,0,3: 33:[99, 9] Operation: 3*3=9 Exploring Operation: 99-3=96, Resulting Numbers: [3, 96] Generated Node #0,0,4: 33:[3, 96] Operation: 99-3=96 Moving to Node #0,2 Current State: 33:[99, 3, 10], Operations: ['15-5=10'] Exploring Operation: 99-3=96, Resulting Numbers: [10, 96] Generated Node #0,2,0: 33:[10, 96] Operation: 99-3=96 Exploring Operation: 99/3=33, Resulting Numbers: [10, 33] Generated Node #0,2,1: 33:[10, 33] Operation: 99/3=33 Exploring Operation: 3+10=13, Resulting Numbers: [99, 13] Generated Node #0,2,2: 33:[99, 13] Operation: 3+10=13 Exploring Operation: 99-10=89, Resulting Numbers: [3, 89] Generated Node #0,2,3: 33:[3, 89] Operation: 99-10=89 Exploring Operation: 3*10=30, Resulting Numbers: [99, 30] Generated Node #0,2,4: 33:[99, 30] Operation: 3*10=30 Moving to Node #0,3,1 Current State: 33:[33, 3], Operations: ['99/3=33', '15/5=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,33 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,33 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,33 unequal: No Solution Moving to Node #0,0,2 Current State: 33:[3, 33], Operations: ['15/5=3', '99/3=33'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,33 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[3, 33], Operations: ['15/5=3', '99/3=33'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,33 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,33 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,33 unequal: No Solution Moving to Node #0,3,3 Current State: 33:[33, 10], Operations: ['99/3=33', '15-5=10'] Exploring Operation: 33+10=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,33 unequal: No Solution Exploring Operation: 33*10=330, Resulting Numbers: [330] 330,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[10, 33], Operations: ['15-5=10', '99/3=33'] Exploring Operation: 10*33=330, Resulting Numbers: [330] 330,33 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,33 unequal: No Solution Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,33 unequal: No Solution Moving to Node #0,4,4 Current State: 33:[5, 28], Operations: ['99-15=84', '84/3=28'] Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[15, 5, 99, 3], Operations: [] Exploring Operation: 99-15=84, Resulting Numbers: [5, 3, 84] Generated Node #0,4: 33:[5, 3, 84] Operation: 99-15=84 Moving to Node #0,4 Current State: 33:[5, 3, 84], Operations: ['99-15=84'] Exploring Operation: 84/3=28, Resulting Numbers: [5, 28] Generated Node #0,4,4: 33:[5, 28] Operation: 84/3=28 Moving to Node #0,4,4 Current State: 33:[5, 28], Operations: ['99-15=84', '84/3=28'] Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.940972
hs_5
mult_heuristic
[ 53, 93, 19, 95 ]
87
[ "95-93=2", "53*2=106", "106-19=87" ]
Current State: 87:[53, 93, 19, 95], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [53, 19, 2] Generated Node #2: [53, 19, 2] from Operation: 95-93=2 Current State: 87:[53, 19, 2], Operations: ['95-93=2'] Exploring Operation: 53*2=106, Resulting Numbers: [19, 106] Generated Node #3: [19, 106] from Operation: 53*2=106 Current State: 87:[19, 106], Operations: ['95-93=2', '53*2=106'] Exploring Operation: 106-19=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[53, 93, 19, 95], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [93, 19, 42] Generated Node #0,0: 87:[93, 19, 42] Operation: 95-53=42 Exploring Operation: 53+19=72, Resulting Numbers: [93, 95, 72] Generated Node #0,1: 87:[93, 95, 72] Operation: 53+19=72 Exploring Operation: 53-19=34, Resulting Numbers: [93, 95, 34] Generated Node #0,2: 87:[93, 95, 34] Operation: 53-19=34 Exploring Operation: 93-53=40, Resulting Numbers: [19, 95, 40] Generated Node #0,3: 87:[19, 95, 40] Operation: 93-53=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[93, 95, 34], Operations: ['53-19=34'] Exploring Operation: 93-34=59, Resulting Numbers: [95, 59] Generated Node #0,2,0: 87:[95, 59] Operation: 93-34=59 Exploring Operation: 93+34=127, Resulting Numbers: [95, 127] Generated Node #0,2,1: 87:[95, 127] Operation: 93+34=127 Exploring Operation: 95-93=2, Resulting Numbers: [34, 2] Generated Node #0,2,2: 87:[34, 2] Operation: 95-93=2 Exploring Operation: 95-34=61, Resulting Numbers: [93, 61] Generated Node #0,2,3: 87:[93, 61] Operation: 95-34=61 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 87:[34, 2], Operations: ['53-19=34', '95-93=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 87:[93, 61], Operations: ['53-19=34', '95-34=61'] Exploring Operation: 93*61=5673, Resulting Numbers: [5673] 5673,87 unequal: No Solution Exploring Operation: 93-61=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 93+61=154, Resulting Numbers: [154] 154,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[95, 59], Operations: ['53-19=34', '93-34=59'] Exploring Operation: 95+59=154, Resulting Numbers: [154] 154,87 unequal: No Solution Exploring Operation: 95-59=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 95*59=5605, Resulting Numbers: [5605] 5605,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 87:[95, 127], Operations: ['53-19=34', '93+34=127'] Exploring Operation: 127-95=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 95*127=12065, Resulting Numbers: [12065] 12065,87 unequal: No Solution Exploring Operation: 95+127=222, Resulting Numbers: [222] 222,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[93, 19, 42], Operations: ['95-53=42'] Exploring Operation: 42-19=23, Resulting Numbers: [93, 23] Generated Node #0,0,0: 87:[93, 23] Operation: 42-19=23 Exploring Operation: 93-42=51, Resulting Numbers: [19, 51] Generated Node #0,0,1: 87:[19, 51] Operation: 93-42=51 Exploring Operation: 19+42=61, Resulting Numbers: [93, 61] Generated Node #0,0,2: 87:[93, 61] Operation: 19+42=61 Exploring Operation: 93-19=74, Resulting Numbers: [42, 74] Generated Node #0,0,3: 87:[42, 74] Operation: 93-19=74 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[93, 23], Operations: ['95-53=42', '42-19=23'] Exploring Operation: 93*23=2139, Resulting Numbers: [2139] 2139,87 unequal: No Solution Exploring Operation: 93+23=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 93-23=70, Resulting Numbers: [70] 70,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[42, 74], Operations: ['95-53=42', '93-19=74'] Exploring Operation: 74-42=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 42+74=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 42*74=3108, Resulting Numbers: [3108] 3108,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[19, 51], Operations: ['95-53=42', '93-42=51'] Exploring Operation: 19*51=969, Resulting Numbers: [969] 969,87 unequal: No Solution Exploring Operation: 19+51=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[93, 61], Operations: ['95-53=42', '19+42=61'] Exploring Operation: 93-61=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 93*61=5673, Resulting Numbers: [5673] 5673,87 unequal: No Solution Exploring Operation: 93+61=154, Resulting Numbers: [154] 154,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[93, 95, 72], Operations: ['53+19=72'] Exploring Operation: 95-72=23, Resulting Numbers: [93, 23] Generated Node #0,1,0: 87:[93, 23] Operation: 95-72=23 Exploring Operation: 93+72=165, Resulting Numbers: [95, 165] Generated Node #0,1,1: 87:[95, 165] Operation: 93+72=165 Exploring Operation: 95-93=2, Resulting Numbers: [72, 2] Generated Node #0,1,2: 87:[72, 2] Operation: 95-93=2 Exploring Operation: 93-72=21, Resulting Numbers: [95, 21] Generated Node #0,1,3: 87:[95, 21] Operation: 93-72=21 Moving to Node #0,1,0 Current State: 87:[93, 23], Operations: ['53+19=72', '95-72=23'] Exploring Operation: 93+23=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 93-23=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 93*23=2139, Resulting Numbers: [2139] 2139,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[95, 21], Operations: ['53+19=72', '93-72=21'] Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 95+21=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 95*21=1995, Resulting Numbers: [1995] 1995,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[72, 2], Operations: ['53+19=72', '95-93=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[95, 165], Operations: ['53+19=72', '93+72=165'] Exploring Operation: 95+165=260, Resulting Numbers: [260] 260,87 unequal: No Solution Exploring Operation: 95*165=15675, Resulting Numbers: [15675] 15675,87 unequal: No Solution Exploring Operation: 165-95=70, Resulting Numbers: [70] 70,87 unequal: No Solution No 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: 87:[19, 95, 40], Operations: ['93-53=40'] Exploring Operation: 19+40=59, Resulting Numbers: [95, 59] Generated Node #0,3,0: 87:[95, 59] Operation: 19+40=59 Exploring Operation: 95/19=5, Resulting Numbers: [40, 5] Generated Node #0,3,1: 87:[40, 5] Operation: 95/19=5 Exploring Operation: 95-19=76, Resulting Numbers: [40, 76] Generated Node #0,3,2: 87:[40, 76] Operation: 95-19=76 Exploring Operation: 40-19=21, Resulting Numbers: [95, 21] Generated Node #0,3,3: 87:[95, 21] Operation: 40-19=21 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 87:[40, 5], Operations: ['93-53=40', '95/19=5'] Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,87 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 40*5=200, Resulting Numbers: [200] 200,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 87:[95, 21], Operations: ['93-53=40', '40-19=21'] Exploring Operation: 95+21=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 95*21=1995, Resulting Numbers: [1995] 1995,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 87:[40, 76], Operations: ['93-53=40', '95-19=76'] Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 40+76=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 40*76=3040, Resulting Numbers: [3040] 3040,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 87:[95, 59], Operations: ['93-53=40', '19+40=59'] Exploring Operation: 95*59=5605, Resulting Numbers: [5605] 5605,87 unequal: No Solution Exploring Operation: 95-59=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 95+59=154, Resulting Numbers: [154] 154,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 42, 75, 80, 8 ]
29
[ "42+75=117", "80+8=88", "117-88=29" ]
Current State: 29:[42, 75, 80, 8], Operations: [] Exploring Operation: 42+75=117, Resulting Numbers: [80, 8, 117] Generated Node #2: [80, 8, 117] from Operation: 42+75=117 Current State: 29:[80, 8, 117], Operations: ['42+75=117'] Exploring Operation: 80+8=88, Resulting Numbers: [117, 88] Generated Node #3: [117, 88] from Operation: 80+8=88 Current State: 29:[117, 88], Operations: ['42+75=117', '80+8=88'] Exploring Operation: 117-88=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[42, 75, 80, 8], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [42, 8, 5] Generated Node #0,0: 29:[42, 8, 5] Operation: 80-75=5 Exploring Operation: 75-42=33, Resulting Numbers: [80, 8, 33] Generated Node #0,1: 29:[80, 8, 33] Operation: 75-42=33 Moving to Node #0,0 Current State: 29:[42, 8, 5], Operations: ['80-75=5'] Exploring Operation: 8*5=40, Resulting Numbers: [42, 40] Generated Node #0,0,0: 29:[42, 40] Operation: 8*5=40 Exploring Operation: 42-8=34, Resulting Numbers: [5, 34] Generated Node #0,0,1: 29:[5, 34] Operation: 42-8=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[42, 40], Operations: ['80-75=5', '8*5=40'] Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[5, 34], Operations: ['80-75=5', '42-8=34'] Exploring Operation: 5+34=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[42, 75, 80, 8], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [42, 8, 5] Generated Node #0,0: 29:[42, 8, 5] Operation: 80-75=5 Moving to Node #0,0 Current State: 29:[42, 8, 5], Operations: ['80-75=5'] Exploring Operation: 42-8=34, Resulting Numbers: [5, 34] Generated Node #0,0,1: 29:[5, 34] Operation: 42-8=34 Moving to Node #0,0,1 Current State: 29:[5, 34], Operations: ['80-75=5', '42-8=34'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 27, 66, 57, 99 ]
33
[ "27*66=1782", "99+1782=1881", "1881/57=33" ]
Current State: 33:[27, 66, 57, 99], Operations: [] Exploring Operation: 27*66=1782, Resulting Numbers: [57, 99, 1782] Generated Node #2: [57, 99, 1782] from Operation: 27*66=1782 Current State: 33:[57, 99, 1782], Operations: ['27*66=1782'] Exploring Operation: 99+1782=1881, Resulting Numbers: [57, 1881] Generated Node #3: [57, 1881] from Operation: 99+1782=1881 Current State: 33:[57, 1881], Operations: ['27*66=1782', '99+1782=1881'] Exploring Operation: 1881/57=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[27, 66, 57, 99], Operations: [] Exploring Operation: 99-66=33, Resulting Numbers: [27, 57, 33] Generated Node #0,0: 33:[27, 57, 33] Operation: 99-66=33 Exploring Operation: 66-57=9, Resulting Numbers: [27, 99, 9] Generated Node #0,1: 33:[27, 99, 9] Operation: 66-57=9 Exploring Operation: 99-57=42, Resulting Numbers: [27, 66, 42] Generated Node #0,2: 33:[27, 66, 42] Operation: 99-57=42 Exploring Operation: 66-27=39, Resulting Numbers: [57, 99, 39] Generated Node #0,3: 33:[57, 99, 39] Operation: 66-27=39 Moving to Node #0,0 Current State: 33:[27, 57, 33], Operations: ['99-66=33'] Exploring Operation: 27+57=84, Resulting Numbers: [33, 84] Generated Node #0,0,0: 33:[33, 84] Operation: 27+57=84 Exploring Operation: 57-27=30, Resulting Numbers: [33, 30] Generated Node #0,0,1: 33:[33, 30] Operation: 57-27=30 Exploring Operation: 57-33=24, Resulting Numbers: [27, 24] Generated Node #0,0,2: 33:[27, 24] Operation: 57-33=24 Exploring Operation: 33-27=6, Resulting Numbers: [57, 6] Generated Node #0,0,3: 33:[57, 6] Operation: 33-27=6 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[33, 30], Operations: ['99-66=33', '57-27=30'] Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,33 unequal: No Solution Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,33 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[27, 24], Operations: ['99-66=33', '57-33=24'] Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,33 unequal: No Solution Exploring Operation: 27*24=648, Resulting Numbers: [648] 648,33 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 33:[57, 6], Operations: ['99-66=33', '33-27=6'] Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,33 unequal: No Solution Exploring Operation: 57*6=342, Resulting Numbers: [342] 342,33 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[33, 84], Operations: ['99-66=33', '27+57=84'] Exploring Operation: 33*84=2772, Resulting Numbers: [2772] 2772,33 unequal: No Solution Exploring Operation: 84-33=51, Resulting Numbers: [51] 51,33 unequal: No Solution Exploring Operation: 33+84=117, Resulting Numbers: [117] 117,33 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: 33:[27, 66, 42], Operations: ['99-57=42'] Exploring Operation: 66-27=39, Resulting Numbers: [42, 39] Generated Node #0,2,0: 33:[42, 39] Operation: 66-27=39 Exploring Operation: 27+66=93, Resulting Numbers: [42, 93] Generated Node #0,2,1: 33:[42, 93] Operation: 27+66=93 Exploring Operation: 42-27=15, Resulting Numbers: [66, 15] Generated Node #0,2,2: 33:[66, 15] Operation: 42-27=15 Exploring Operation: 66-42=24, Resulting Numbers: [27, 24] Generated Node #0,2,3: 33:[27, 24] Operation: 66-42=24 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 33:[42, 39], Operations: ['99-57=42', '66-27=39'] Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,33 unequal: No Solution Exploring Operation: 42*39=1638, Resulting Numbers: [1638] 1638,33 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 33:[27, 24], Operations: ['99-57=42', '66-42=24'] Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,33 unequal: No Solution Exploring Operation: 27*24=648, Resulting Numbers: [648] 648,33 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 33:[66, 15], Operations: ['99-57=42', '42-27=15'] Exploring Operation: 66*15=990, Resulting Numbers: [990] 990,33 unequal: No Solution Exploring Operation: 66+15=81, Resulting Numbers: [81] 81,33 unequal: No Solution Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 33:[42, 93], Operations: ['99-57=42', '27+66=93'] Exploring Operation: 42+93=135, Resulting Numbers: [135] 135,33 unequal: No Solution Exploring Operation: 42*93=3906, Resulting Numbers: [3906] 3906,33 unequal: No Solution Exploring Operation: 93-42=51, Resulting Numbers: [51] 51,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 33:[27, 99, 9], Operations: ['66-57=9'] Exploring Operation: 99-9=90, Resulting Numbers: [27, 90] Generated Node #0,1,0: 33:[27, 90] Operation: 99-9=90 Exploring Operation: 27/9=3, Resulting Numbers: [99, 3] Generated Node #0,1,1: 33:[99, 3] Operation: 27/9=3 Exploring Operation: 99-27=72, Resulting Numbers: [9, 72] Generated Node #0,1,2: 33:[9, 72] Operation: 99-27=72 Exploring Operation: 99/9=11, Resulting Numbers: [27, 11] Generated Node #0,1,3: 33:[27, 11] Operation: 99/9=11 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 33:[27, 11], Operations: ['66-57=9', '99/9=11'] Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,33 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 33:[9, 72], Operations: ['66-57=9', '99-27=72'] Exploring Operation: 9+72=81, Resulting Numbers: [81] 81,33 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,33 unequal: No Solution Exploring Operation: 9*72=648, Resulting Numbers: [648] 648,33 unequal: No Solution Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[27, 90], Operations: ['66-57=9', '99-9=90'] Exploring Operation: 27*90=2430, Resulting Numbers: [2430] 2430,33 unequal: No Solution Exploring Operation: 27+90=117, Resulting Numbers: [117] 117,33 unequal: No Solution Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[99, 3], Operations: ['66-57=9', '27/9=3'] Exploring Operation: 99*3=297, Resulting Numbers: [297] 297,33 unequal: No Solution Exploring Operation: 99+3=102, Resulting Numbers: [102] 102,33 unequal: No Solution Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,33 unequal: No Solution Exploring Operation: 99/3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[27, 66, 57, 99], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [27, 99, 9] Generated Node #0,1: 33:[27, 99, 9] Operation: 66-57=9 Moving to Node #0,1 Current State: 33:[27, 99, 9], Operations: ['66-57=9'] Exploring Operation: 27/9=3, Resulting Numbers: [99, 3] Generated Node #0,1,1: 33:[99, 3] Operation: 27/9=3 Moving to Node #0,1,1 Current State: 33:[99, 3], Operations: ['66-57=9', '27/9=3'] Exploring Operation: 99/3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_4
sum_heuristic
[ 71, 2, 84, 29 ]
32
[ "84-71=13", "29-13=16", "2*16=32" ]
Current State: 32:[71, 2, 84, 29], Operations: [] Exploring Operation: 84-71=13, Resulting Numbers: [2, 29, 13] Generated Node #2: [2, 29, 13] from Operation: 84-71=13 Current State: 32:[2, 29, 13], Operations: ['84-71=13'] Exploring Operation: 29-13=16, Resulting Numbers: [2, 16] Generated Node #3: [2, 16] from Operation: 29-13=16 Current State: 32:[2, 16], Operations: ['84-71=13', '29-13=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[71, 2, 84, 29], Operations: [] Exploring Operation: 84-71=13, Resulting Numbers: [2, 29, 13] Generated Node #0,0: 32:[2, 29, 13] Operation: 84-71=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[2, 29, 13], Operations: ['84-71=13'] Exploring Operation: 29-13=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 32:[2, 16] Operation: 29-13=16 Moving to Node #0,0,0 Current State: 32:[2, 16], Operations: ['84-71=13', '29-13=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[71, 2, 84, 29], Operations: [] Exploring Operation: 84-71=13, Resulting Numbers: [2, 29, 13] Generated Node #0,0: 32:[2, 29, 13] Operation: 84-71=13 Moving to Node #0,0 Current State: 32:[2, 29, 13], Operations: ['84-71=13'] Exploring Operation: 29-13=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 32:[2, 16] Operation: 29-13=16 Moving to Node #0,0,0 Current State: 32:[2, 16], Operations: ['84-71=13', '29-13=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 70, 91, 84, 16 ]
93
[ "70+91=161", "84-16=68", "161-68=93" ]
Current State: 93:[70, 91, 84, 16], Operations: [] Exploring Operation: 70+91=161, Resulting Numbers: [84, 16, 161] Generated Node #2: [84, 16, 161] from Operation: 70+91=161 Current State: 93:[84, 16, 161], Operations: ['70+91=161'] Exploring Operation: 84-16=68, Resulting Numbers: [161, 68] Generated Node #3: [161, 68] from Operation: 84-16=68 Current State: 93:[161, 68], Operations: ['70+91=161', '84-16=68'] Exploring Operation: 161-68=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[70, 91, 84, 16], Operations: [] Exploring Operation: 70+16=86, Resulting Numbers: [91, 84, 86] Generated Node #0,0: 93:[91, 84, 86] Operation: 70+16=86 Exploring Operation: 84-70=14, Resulting Numbers: [91, 16, 14] Generated Node #0,1: 93:[91, 16, 14] Operation: 84-70=14 Moving to Node #0,0 Current State: 93:[91, 84, 86], Operations: ['70+16=86'] Exploring Operation: 86-84=2, Resulting Numbers: [91, 2] Generated Node #0,0,0: 93:[91, 2] Operation: 86-84=2 Exploring Operation: 91-84=7, Resulting Numbers: [86, 7] Generated Node #0,0,1: 93:[86, 7] Operation: 91-84=7 Moving to Node #0,1 Current State: 93:[91, 16, 14], Operations: ['84-70=14'] Exploring Operation: 16-14=2, Resulting Numbers: [91, 2] Generated Node #0,1,0: 93:[91, 2] Operation: 16-14=2 Exploring Operation: 16+14=30, Resulting Numbers: [91, 30] Generated Node #0,1,1: 93:[91, 30] Operation: 16+14=30 Moving to Node #0,0,0 Current State: 93:[91, 2], Operations: ['70+16=86', '86-84=2'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,93 unequal: No Solution Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[70, 91, 84, 16], Operations: [] Exploring Operation: 70+16=86, Resulting Numbers: [91, 84, 86] Generated Node #0,0: 93:[91, 84, 86] Operation: 70+16=86 Moving to Node #0,0 Current State: 93:[91, 84, 86], Operations: ['70+16=86'] Exploring Operation: 86-84=2, Resulting Numbers: [91, 2] Generated Node #0,0,0: 93:[91, 2] Operation: 86-84=2 Moving to Node #0,0,0 Current State: 93:[91, 2], Operations: ['70+16=86', '86-84=2'] Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 64, 4, 6, 35 ]
75
[ "64+35=99", "4*6=24", "99-24=75" ]
Current State: 75:[64, 4, 6, 35], Operations: [] Exploring Operation: 64+35=99, Resulting Numbers: [4, 6, 99] Generated Node #2: [4, 6, 99] from Operation: 64+35=99 Current State: 75:[4, 6, 99], Operations: ['64+35=99'] Exploring Operation: 4*6=24, Resulting Numbers: [99, 24] Generated Node #3: [99, 24] from Operation: 4*6=24 Current State: 75:[99, 24], Operations: ['64+35=99', '4*6=24'] Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[64, 4, 6, 35], Operations: [] Exploring Operation: 64+6=70, Resulting Numbers: [4, 35, 70] Generated Node #0,0: 75:[4, 35, 70] Operation: 64+6=70 Exploring Operation: 64/4=16, Resulting Numbers: [6, 35, 16] Generated Node #0,1: 75:[6, 35, 16] Operation: 64/4=16 Exploring Operation: 35-6=29, Resulting Numbers: [64, 4, 29] Generated Node #0,2: 75:[64, 4, 29] Operation: 35-6=29 Exploring Operation: 64-35=29, Resulting Numbers: [4, 6, 29] Generated Node #0,3: 75:[4, 6, 29] Operation: 64-35=29 Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[4, 6, 29], Operations: ['64-35=29'] Exploring Operation: 29-6=23, Resulting Numbers: [4, 23] Generated Node #0,3,0: 75:[4, 23] Operation: 29-6=23 Exploring Operation: 29-4=25, Resulting Numbers: [6, 25] Generated Node #0,3,1: 75:[6, 25] Operation: 29-4=25 Exploring Operation: 6-4=2, Resulting Numbers: [29, 2] Generated Node #0,3,2: 75:[29, 2] Operation: 6-4=2 Exploring Operation: 4*6=24, Resulting Numbers: [29, 24] Generated Node #0,3,3: 75:[29, 24] Operation: 4*6=24 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 75:[6, 25], Operations: ['64-35=29', '29-4=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,75 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 75:[4, 23], Operations: ['64-35=29', '29-6=23'] Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,75 unequal: No Solution Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 75:[29, 2], Operations: ['64-35=29', '6-4=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,75 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 75:[29, 24], Operations: ['64-35=29', '4*6=24'] Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,75 unequal: No Solution Exploring Operation: 29*24=696, Resulting Numbers: [696] 696,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[6, 35, 16], Operations: ['64/4=16'] Exploring Operation: 16-6=10, Resulting Numbers: [35, 10] Generated Node #0,1,0: 75:[35, 10] Operation: 16-6=10 Exploring Operation: 35-6=29, Resulting Numbers: [16, 29] Generated Node #0,1,1: 75:[16, 29] Operation: 35-6=29 Exploring Operation: 35-16=19, Resulting Numbers: [6, 19] Generated Node #0,1,2: 75:[6, 19] Operation: 35-16=19 Exploring Operation: 6+16=22, Resulting Numbers: [35, 22] Generated Node #0,1,3: 75:[35, 22] Operation: 6+16=22 Moving to Node #0,1,1 Current State: 75:[16, 29], Operations: ['64/4=16', '35-6=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,75 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[6, 19], Operations: ['64/4=16', '35-16=19'] Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,75 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[35, 22], Operations: ['64/4=16', '6+16=22'] Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,75 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[35, 10], Operations: ['64/4=16', '16-6=10'] Exploring Operation: 35+10=45, Resulting Numbers: [45] 45,75 unequal: No Solution Exploring Operation: 35*10=350, Resulting Numbers: [350] 350,75 unequal: No Solution Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[4, 35, 70], Operations: ['64+6=70'] Exploring Operation: 35-4=31, Resulting Numbers: [70, 31] Generated Node #0,0,0: 75:[70, 31] Operation: 35-4=31 Exploring Operation: 70/35=2, Resulting Numbers: [4, 2] Generated Node #0,0,1: 75:[4, 2] Operation: 70/35=2 Exploring Operation: 4+70=74, Resulting Numbers: [35, 74] Generated Node #0,0,2: 75:[35, 74] Operation: 4+70=74 Exploring Operation: 70-35=35, Resulting Numbers: [4, 35] Generated Node #0,0,3: 75:[4, 35] Operation: 70-35=35 Moving to Node #0,0,1 Current State: 75:[4, 2], Operations: ['64+6=70', '70/35=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[35, 74], Operations: ['64+6=70', '4+70=74'] Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 35+74=109, Resulting Numbers: [109] 109,75 unequal: No Solution Exploring Operation: 35*74=2590, Resulting Numbers: [2590] 2590,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[70, 31], Operations: ['64+6=70', '35-4=31'] Exploring Operation: 70+31=101, Resulting Numbers: [101] 101,75 unequal: No Solution Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 70*31=2170, Resulting Numbers: [2170] 2170,75 unequal: No Solution Moving to Node #0,0,3 Current State: 75:[4, 35], Operations: ['64+6=70', '70-35=35'] Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[64, 4, 29], Operations: ['35-6=29'] Exploring Operation: 64/4=16, Resulting Numbers: [29, 16] Generated Node #0,2,0: 75:[29, 16] Operation: 64/4=16 Exploring Operation: 64-29=35, Resulting Numbers: [4, 35] Generated Node #0,2,1: 75:[4, 35] Operation: 64-29=35 Exploring Operation: 64+4=68, Resulting Numbers: [29, 68] Generated Node #0,2,2: 75:[29, 68] Operation: 64+4=68 Exploring Operation: 29-4=25, Resulting Numbers: [64, 25] Generated Node #0,2,3: 75:[64, 25] Operation: 29-4=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 75:[29, 16], Operations: ['35-6=29', '64/4=16'] Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,75 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,75 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 75:[4, 35], Operations: ['35-6=29', '64-29=35'] Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,75 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 75:[29, 68], Operations: ['35-6=29', '64+4=68'] Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 29+68=97, Resulting Numbers: [97] 97,75 unequal: No Solution Exploring Operation: 29*68=1972, Resulting Numbers: [1972] 1972,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 75:[64, 25], Operations: ['35-6=29', '29-4=25'] Exploring Operation: 64+25=89, Resulting Numbers: [89] 89,75 unequal: No Solution Exploring Operation: 64*25=1600, Resulting Numbers: [1600] 1600,75 unequal: No Solution Exploring Operation: 64-25=39, Resulting Numbers: [39] 39,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 7, 30, 27, 5 ]
69
[ "7+30=37", "27+5=32", "37+32=69" ]
Current State: 69:[7, 30, 27, 5], Operations: [] Exploring Operation: 7+30=37, Resulting Numbers: [27, 5, 37] Generated Node #2: [27, 5, 37] from Operation: 7+30=37 Current State: 69:[27, 5, 37], Operations: ['7+30=37'] Exploring Operation: 27+5=32, Resulting Numbers: [37, 32] Generated Node #3: [37, 32] from Operation: 27+5=32 Current State: 69:[37, 32], Operations: ['7+30=37', '27+5=32'] Exploring Operation: 37+32=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[7, 30, 27, 5], Operations: [] Exploring Operation: 27-7=20, Resulting Numbers: [30, 5, 20] Generated Node #0,0: 69:[30, 5, 20] Operation: 27-7=20 Exploring Operation: 30/5=6, Resulting Numbers: [7, 27, 6] Generated Node #0,1: 69:[7, 27, 6] Operation: 30/5=6 Exploring Operation: 30-27=3, Resulting Numbers: [7, 5, 3] Generated Node #0,2: 69:[7, 5, 3] Operation: 30-27=3 Exploring Operation: 30-7=23, Resulting Numbers: [27, 5, 23] Generated Node #0,3: 69:[27, 5, 23] Operation: 30-7=23 Exploring Operation: 30-5=25, Resulting Numbers: [7, 27, 25] Generated Node #0,4: 69:[7, 27, 25] Operation: 30-5=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[7, 5, 3], Operations: ['30-27=3'] Exploring Operation: 7-3=4, Resulting Numbers: [5, 4] Generated Node #0,2,0: 69:[5, 4] Operation: 7-3=4 Exploring Operation: 7*3=21, Resulting Numbers: [5, 21] Generated Node #0,2,1: 69:[5, 21] Operation: 7*3=21 Exploring Operation: 7+5=12, Resulting Numbers: [3, 12] Generated Node #0,2,2: 69:[3, 12] Operation: 7+5=12 Exploring Operation: 7-5=2, Resulting Numbers: [3, 2] Generated Node #0,2,3: 69:[3, 2] Operation: 7-5=2 Exploring Operation: 5-3=2, Resulting Numbers: [7, 2] Generated Node #0,2,4: 69:[7, 2] Operation: 5-3=2 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 69:[3, 2], Operations: ['30-27=3', '7-5=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,69 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 69:[5, 4], Operations: ['30-27=3', '7-3=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,69 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 69:[5, 21], Operations: ['30-27=3', '7*3=21'] Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,69 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 #0,2,4 Current State: 69:[7, 2], Operations: ['30-27=3', '5-3=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 69:[3, 12], Operations: ['30-27=3', '7+5=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[27, 5, 23], Operations: ['30-7=23'] Exploring Operation: 27-5=22, Resulting Numbers: [23, 22] Generated Node #0,3,0: 69:[23, 22] Operation: 27-5=22 Exploring Operation: 23-5=18, Resulting Numbers: [27, 18] Generated Node #0,3,1: 69:[27, 18] Operation: 23-5=18 Exploring Operation: 5+23=28, Resulting Numbers: [27, 28] Generated Node #0,3,2: 69:[27, 28] Operation: 5+23=28 Exploring Operation: 27+5=32, Resulting Numbers: [23, 32] Generated Node #0,3,3: 69:[23, 32] Operation: 27+5=32 Exploring Operation: 27-23=4, Resulting Numbers: [5, 4] Generated Node #0,3,4: 69:[5, 4] Operation: 27-23=4 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 69:[23, 22], Operations: ['30-7=23', '27-5=22'] Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,69 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,69 unequal: No Solution Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,69 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 #0,3,4 Current State: 69:[5, 4], Operations: ['30-7=23', '27-23=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,69 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 #0,3,1 Current State: 69:[27, 18], Operations: ['30-7=23', '23-5=18'] Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,69 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,69 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 #0,3,2 Current State: 69:[27, 28], Operations: ['30-7=23', '5+23=28'] Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,69 unequal: No Solution Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,69 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 #0,3,3 Current State: 69:[23, 32], Operations: ['30-7=23', '27+5=32'] Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 23+32=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 23*32=736, Resulting Numbers: [736] 736,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 69:[7, 27, 25], Operations: ['30-5=25'] Exploring Operation: 25-7=18, Resulting Numbers: [27, 18] Generated Node #0,4,0: 69:[27, 18] Operation: 25-7=18 Exploring Operation: 7+25=32, Resulting Numbers: [27, 32] Generated Node #0,4,1: 69:[27, 32] Operation: 7+25=32 Exploring Operation: 27-25=2, Resulting Numbers: [7, 2] Generated Node #0,4,2: 69:[7, 2] Operation: 27-25=2 Exploring Operation: 7+27=34, Resulting Numbers: [25, 34] Generated Node #0,4,3: 69:[25, 34] Operation: 7+27=34 Exploring Operation: 27-7=20, Resulting Numbers: [25, 20] Generated Node #0,4,4: 69:[25, 20] Operation: 27-7=20 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 69:[7, 2], Operations: ['30-5=25', '27-25=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 69:[25, 20], Operations: ['30-5=25', '27-7=20'] Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,69 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 69:[27, 18], Operations: ['30-5=25', '25-7=18'] Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 69:[27, 32], Operations: ['30-5=25', '7+25=32'] Exploring Operation: 27*32=864, Resulting Numbers: [864] 864,69 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 27+32=59, Resulting Numbers: [59] 59,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 69:[25, 34], Operations: ['30-5=25', '7+27=34'] Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,69 unequal: No Solution Exploring Operation: 25*34=850, Resulting Numbers: [850] 850,69 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,69 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 #0,1 Current State: 69:[7, 27, 6], Operations: ['30/5=6'] Exploring Operation: 7-6=1, Resulting Numbers: [27, 1] Generated Node #0,1,0: 69:[27, 1] Operation: 7-6=1 Exploring Operation: 7+6=13, Resulting Numbers: [27, 13] Generated Node #0,1,1: 69:[27, 13] Operation: 7+6=13 Exploring Operation: 27-7=20, Resulting Numbers: [6, 20] Generated Node #0,1,2: 69:[6, 20] Operation: 27-7=20 Exploring Operation: 7+27=34, Resulting Numbers: [6, 34] Generated Node #0,1,3: 69:[6, 34] Operation: 7+27=34 Exploring Operation: 27-6=21, Resulting Numbers: [7, 21] Generated Node #0,1,4: 69:[7, 21] Operation: 27-6=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[27, 1], Operations: ['30/5=6', '7-6=1'] Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,69 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 27-1=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 #0,1,2 Current State: 69:[6, 20], Operations: ['30/5=6', '27-7=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,69 unequal: No Solution Exploring Operation: 6+20=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 #0,1,4 Current State: 69:[7, 21], Operations: ['30/5=6', '27-6=21'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 7*21=147, Resulting Numbers: [147] 147,69 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,69 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:[27, 13], Operations: ['30/5=6', '7+6=13'] Exploring Operation: 27*13=351, Resulting Numbers: [351] 351,69 unequal: No Solution Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,69 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:[6, 34], Operations: ['30/5=6', '7+27=34'] Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,69 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,69 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:[30, 5, 20], Operations: ['27-7=20'] Exploring Operation: 30/5=6, Resulting Numbers: [20, 6] Generated Node #0,0,0: 69:[20, 6] Operation: 30/5=6 Exploring Operation: 30-20=10, Resulting Numbers: [5, 10] Generated Node #0,0,1: 69:[5, 10] Operation: 30-20=10 Exploring Operation: 5+20=25, Resulting Numbers: [30, 25] Generated Node #0,0,2: 69:[30, 25] Operation: 5+20=25 Exploring Operation: 30-5=25, Resulting Numbers: [20, 25] Generated Node #0,0,3: 69:[20, 25] Operation: 30-5=25 Exploring Operation: 20/5=4, Resulting Numbers: [30, 4] Generated Node #0,0,4: 69:[30, 4] Operation: 20/5=4 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 69:[20, 25], Operations: ['27-7=20', '30-5=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,69 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,69 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:[20, 6], Operations: ['27-7=20', '30/5=6'] Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,69 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:[30, 4], Operations: ['27-7=20', '20/5=4'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,69 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 #0,0,1 Current State: 69:[5, 10], Operations: ['27-7=20', '30-20=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,69 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:[30, 25], Operations: ['27-7=20', '5+20=25'] Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 30+25=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 30*25=750, Resulting Numbers: [750] 750,69 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 No solution found.
0
hs_5
mult_heuristic
[ 37, 9, 34, 11 ]
41
[ "37*9=333", "34*11=374", "374-333=41" ]
Current State: 41:[37, 9, 34, 11], Operations: [] Exploring Operation: 37*9=333, Resulting Numbers: [34, 11, 333] Generated Node #2: [34, 11, 333] from Operation: 37*9=333 Current State: 41:[34, 11, 333], Operations: ['37*9=333'] Exploring Operation: 34*11=374, Resulting Numbers: [333, 374] Generated Node #3: [333, 374] from Operation: 34*11=374 Current State: 41:[333, 374], Operations: ['37*9=333', '34*11=374'] Exploring Operation: 374-333=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[37, 9, 34, 11], Operations: [] Exploring Operation: 9+11=20, Resulting Numbers: [37, 34, 20] Generated Node #0,0: 41:[37, 34, 20] Operation: 9+11=20 Exploring Operation: 9+34=43, Resulting Numbers: [37, 11, 43] Generated Node #0,1: 41:[37, 11, 43] Operation: 9+34=43 Exploring Operation: 34+11=45, Resulting Numbers: [37, 9, 45] Generated Node #0,2: 41:[37, 9, 45] Operation: 34+11=45 Moving to Node #0,0 Current State: 41:[37, 34, 20], Operations: ['9+11=20'] Exploring Operation: 37-20=17, Resulting Numbers: [34, 17] Generated Node #0,0,0: 41:[34, 17] Operation: 37-20=17 Exploring Operation: 37+20=57, Resulting Numbers: [34, 57] Generated Node #0,0,1: 41:[34, 57] Operation: 37+20=57 Exploring Operation: 34+20=54, Resulting Numbers: [37, 54] Generated Node #0,0,2: 41:[37, 54] Operation: 34+20=54 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[37, 54], Operations: ['9+11=20', '34+20=54'] Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 37*54=1998, Resulting Numbers: [1998] 1998,41 unequal: No Solution Exploring Operation: 37+54=91, Resulting Numbers: [91] 91,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[34, 57], Operations: ['9+11=20', '37+20=57'] Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[34, 17], Operations: ['9+11=20', '37-20=17'] Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,41 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,41 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: 41:[37, 11, 43], Operations: ['9+34=43'] Exploring Operation: 43-11=32, Resulting Numbers: [37, 32] Generated Node #0,1,0: 41:[37, 32] Operation: 43-11=32 Exploring Operation: 37-11=26, Resulting Numbers: [43, 26] Generated Node #0,1,1: 41:[43, 26] Operation: 37-11=26 Exploring Operation: 37+11=48, Resulting Numbers: [43, 48] Generated Node #0,1,2: 41:[43, 48] Operation: 37+11=48 Moving to Node #0,2 Current State: 41:[37, 9, 45], Operations: ['34+11=45'] Exploring Operation: 45-9=36, Resulting Numbers: [37, 36] Generated Node #0,2,0: 41:[37, 36] Operation: 45-9=36 Exploring Operation: 37+9=46, Resulting Numbers: [45, 46] Generated Node #0,2,1: 41:[45, 46] Operation: 37+9=46 Exploring Operation: 37-9=28, Resulting Numbers: [45, 28] Generated Node #0,2,2: 41:[45, 28] Operation: 37-9=28 Moving to Node #0,1,2 Current State: 41:[43, 48], Operations: ['9+34=43', '37+11=48'] Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 43*48=2064, Resulting Numbers: [2064] 2064,41 unequal: No Solution Exploring Operation: 43+48=91, Resulting Numbers: [91] 91,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[37, 36], Operations: ['34+11=45', '45-9=36'] Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,41 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[45, 46], Operations: ['34+11=45', '37+9=46'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[37, 32], Operations: ['9+34=43', '43-11=32'] Exploring Operation: 37+32=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 37-32=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 37*32=1184, Resulting Numbers: [1184] 1184,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[45, 28], Operations: ['34+11=45', '37-9=28'] Exploring Operation: 45*28=1260, Resulting Numbers: [1260] 1260,41 unequal: No Solution Exploring Operation: 45+28=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[43, 26], Operations: ['9+34=43', '37-11=26'] Exploring Operation: 43+26=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 43*26=1118, Resulting Numbers: [1118] 1118,41 unequal: No Solution Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 48, 55, 8, 71 ]
96
[ "48/8=6", "71-55=16", "6*16=96" ]
Current State: 96:[48, 55, 8, 71], Operations: [] Exploring Operation: 48/8=6, Resulting Numbers: [55, 71, 6] Generated Node #2: [55, 71, 6] from Operation: 48/8=6 Current State: 96:[55, 71, 6], Operations: ['48/8=6'] Exploring Operation: 71-55=16, Resulting Numbers: [6, 16] Generated Node #3: [6, 16] from Operation: 71-55=16 Current State: 96:[6, 16], Operations: ['48/8=6', '71-55=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[48, 55, 8, 71], Operations: [] Exploring Operation: 71-55=16, Resulting Numbers: [48, 8, 16] Generated Node #0,0: 96:[48, 8, 16] Operation: 71-55=16 Exploring Operation: 71-48=23, Resulting Numbers: [55, 8, 23] Generated Node #0,1: 96:[55, 8, 23] Operation: 71-48=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[48, 8, 16], Operations: ['71-55=16'] Exploring Operation: 48-16=32, Resulting Numbers: [8, 32] Generated Node #0,0,0: 96:[8, 32] Operation: 48-16=32 Exploring Operation: 48/8=6, Resulting Numbers: [16, 6] Generated Node #0,0,1: 96:[16, 6] Operation: 48/8=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[8, 32], Operations: ['71-55=16', '48-16=32'] Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[16, 6], Operations: ['71-55=16', '48/8=6'] Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[48, 55, 8, 71], Operations: [] Exploring Operation: 71-55=16, Resulting Numbers: [48, 8, 16] Generated Node #0,0: 96:[48, 8, 16] Operation: 71-55=16 Moving to Node #0,0 Current State: 96:[48, 8, 16], Operations: ['71-55=16'] Exploring Operation: 48/8=6, Resulting Numbers: [16, 6] Generated Node #0,0,1: 96:[16, 6] Operation: 48/8=6 Moving to Node #0,0,1 Current State: 96:[16, 6], Operations: ['71-55=16', '48/8=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 52, 44, 97, 52 ]
97
[ "52-52=0", "44*0=0", "97+0=97" ]
Current State: 97:[52, 44, 97, 52], Operations: [] Exploring Operation: 52-52=0, Resulting Numbers: [44, 97, 0] Generated Node #2: [44, 97, 0] from Operation: 52-52=0 Current State: 97:[44, 97, 0], Operations: ['52-52=0'] Exploring Operation: 44*0=0, Resulting Numbers: [97, 0] Generated Node #3: [97, 0] from Operation: 44*0=0 Current State: 97:[97, 0], Operations: ['52-52=0', '44*0=0'] Exploring Operation: 97+0=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[52, 44, 97, 52], Operations: [] Exploring Operation: 44+52=96, Resulting Numbers: [52, 97, 96] Generated Node #0,0: 97:[52, 97, 96] Operation: 44+52=96 Exploring Operation: 52+52=104, Resulting Numbers: [44, 97, 104] Generated Node #0,1: 97:[44, 97, 104] Operation: 52+52=104 Exploring Operation: 52+44=96, Resulting Numbers: [97, 52, 96] Generated Node #0,2: 97:[97, 52, 96] Operation: 52+44=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[52, 97, 96], Operations: ['44+52=96'] Exploring Operation: 52+97=149, Resulting Numbers: [96, 149] Generated Node #0,0,0: 97:[96, 149] Operation: 52+97=149 Exploring Operation: 52+96=148, Resulting Numbers: [97, 148] Generated Node #0,0,1: 97:[97, 148] Operation: 52+96=148 Exploring Operation: 97-52=45, Resulting Numbers: [96, 45] Generated Node #0,0,2: 97:[96, 45] Operation: 97-52=45 Moving to Node #0,0,1 Current State: 97:[97, 148], Operations: ['44+52=96', '52+96=148'] Exploring Operation: 148-97=51, Resulting Numbers: [51] 51,97 unequal: No Solution Exploring Operation: 97+148=245, Resulting Numbers: [245] 245,97 unequal: No Solution Exploring Operation: 97*148=14356, Resulting Numbers: [14356] 14356,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[96, 149], Operations: ['44+52=96', '52+97=149'] Exploring Operation: 96*149=14304, Resulting Numbers: [14304] 14304,97 unequal: No Solution Exploring Operation: 96+149=245, Resulting Numbers: [245] 245,97 unequal: No Solution Exploring Operation: 149-96=53, Resulting Numbers: [53] 53,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[96, 45], Operations: ['44+52=96', '97-52=45'] Exploring Operation: 96+45=141, Resulting Numbers: [141] 141,97 unequal: No Solution Exploring Operation: 96-45=51, Resulting Numbers: [51] 51,97 unequal: No Solution Exploring Operation: 96*45=4320, Resulting Numbers: [4320] 4320,97 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 Current State: 97:[97, 52, 96], Operations: ['52+44=96'] Exploring Operation: 97+52=149, Resulting Numbers: [96, 149] Generated Node #0,2,0: 97:[96, 149] Operation: 97+52=149 Exploring Operation: 52+96=148, Resulting Numbers: [97, 148] Generated Node #0,2,1: 97:[97, 148] Operation: 52+96=148 Exploring Operation: 97-52=45, Resulting Numbers: [96, 45] Generated Node #0,2,2: 97:[96, 45] Operation: 97-52=45 Moving to Node #0,2,1 Current State: 97:[97, 148], Operations: ['52+44=96', '52+96=148'] Exploring Operation: 97*148=14356, Resulting Numbers: [14356] 14356,97 unequal: No Solution Exploring Operation: 148-97=51, Resulting Numbers: [51] 51,97 unequal: No Solution Exploring Operation: 97+148=245, Resulting Numbers: [245] 245,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[96, 149], Operations: ['52+44=96', '97+52=149'] Exploring Operation: 96+149=245, Resulting Numbers: [245] 245,97 unequal: No Solution Exploring Operation: 149-96=53, Resulting Numbers: [53] 53,97 unequal: No Solution Exploring Operation: 96*149=14304, Resulting Numbers: [14304] 14304,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[96, 45], Operations: ['52+44=96', '97-52=45'] Exploring Operation: 96-45=51, Resulting Numbers: [51] 51,97 unequal: No Solution Exploring Operation: 96+45=141, Resulting Numbers: [141] 141,97 unequal: No Solution Exploring Operation: 96*45=4320, Resulting Numbers: [4320] 4320,97 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 Current State: 97:[44, 97, 104], Operations: ['52+52=104'] Exploring Operation: 97-44=53, Resulting Numbers: [104, 53] Generated Node #0,1,0: 97:[104, 53] Operation: 97-44=53 Exploring Operation: 44+97=141, Resulting Numbers: [104, 141] Generated Node #0,1,1: 97:[104, 141] Operation: 44+97=141 Exploring Operation: 104-44=60, Resulting Numbers: [97, 60] Generated Node #0,1,2: 97:[97, 60] Operation: 104-44=60 Moving to Node #0,1,2 Current State: 97:[97, 60], Operations: ['52+52=104', '104-44=60'] Exploring Operation: 97+60=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 97-60=37, Resulting Numbers: [37] 37,97 unequal: No Solution Exploring Operation: 97*60=5820, Resulting Numbers: [5820] 5820,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[104, 53], Operations: ['52+52=104', '97-44=53'] Exploring Operation: 104*53=5512, Resulting Numbers: [5512] 5512,97 unequal: No Solution Exploring Operation: 104+53=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 104-53=51, Resulting Numbers: [51] 51,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[104, 141], Operations: ['52+52=104', '44+97=141'] Exploring Operation: 104+141=245, Resulting Numbers: [245] 245,97 unequal: No Solution Exploring Operation: 104*141=14664, Resulting Numbers: [14664] 14664,97 unequal: No Solution Exploring Operation: 141-104=37, Resulting Numbers: [37] 37,97 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
[ 76, 64, 74, 4 ]
58
[ "76-64=12", "74-4=70", "70-12=58" ]
Current State: 58:[76, 64, 74, 4], Operations: [] Exploring Operation: 76-64=12, Resulting Numbers: [74, 4, 12] Generated Node #2: [74, 4, 12] from Operation: 76-64=12 Current State: 58:[74, 4, 12], Operations: ['76-64=12'] Exploring Operation: 74-4=70, Resulting Numbers: [12, 70] Generated Node #3: [12, 70] from Operation: 74-4=70 Current State: 58:[12, 70], Operations: ['76-64=12', '74-4=70'] Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[76, 64, 74, 4], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [64, 4, 2] Generated Node #0,0: 58:[64, 4, 2] Operation: 76-74=2 Moving to Node #0,0 Current State: 58:[64, 4, 2], Operations: ['76-74=2'] Exploring Operation: 64-4=60, Resulting Numbers: [2, 60] Generated Node #0,0,0: 58:[2, 60] Operation: 64-4=60 Moving to Node #0,0,0 Current State: 58:[2, 60], Operations: ['76-74=2', '64-4=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[76, 64, 74, 4], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [64, 4, 2] Generated Node #0,0: 58:[64, 4, 2] Operation: 76-74=2 Moving to Node #0,0 Current State: 58:[64, 4, 2], Operations: ['76-74=2'] Exploring Operation: 64-4=60, Resulting Numbers: [2, 60] Generated Node #0,0,0: 58:[2, 60] Operation: 64-4=60 Moving to Node #0,0,0 Current State: 58:[2, 60], Operations: ['76-74=2', '64-4=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 90, 57, 39, 15 ]
24
[ "90/15=6", "57-39=18", "6+18=24" ]
Current State: 24:[90, 57, 39, 15], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [57, 39, 6] Generated Node #2: [57, 39, 6] from Operation: 90/15=6 Current State: 24:[57, 39, 6], Operations: ['90/15=6'] Exploring Operation: 57-39=18, Resulting Numbers: [6, 18] Generated Node #3: [6, 18] from Operation: 57-39=18 Current State: 24:[6, 18], Operations: ['90/15=6', '57-39=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[90, 57, 39, 15], Operations: [] Exploring Operation: 90-57=33, Resulting Numbers: [39, 15, 33] Generated Node #0,0: 24:[39, 15, 33] Operation: 90-57=33 Exploring Operation: 90/15=6, Resulting Numbers: [57, 39, 6] Generated Node #0,1: 24:[57, 39, 6] Operation: 90/15=6 Moving to Node #0,0 Current State: 24:[39, 15, 33], Operations: ['90-57=33'] Exploring Operation: 39-15=24, Resulting Numbers: [33, 24] Generated Node #0,0,0: 24:[33, 24] Operation: 39-15=24 Exploring Operation: 39-33=6, Resulting Numbers: [15, 6] Generated Node #0,0,1: 24:[15, 6] Operation: 39-33=6 Moving to Node #0,1 Current State: 24:[57, 39, 6], Operations: ['90/15=6'] Exploring Operation: 57-39=18, Resulting Numbers: [6, 18] Generated Node #0,1,0: 24:[6, 18] Operation: 57-39=18 Exploring Operation: 57-6=51, Resulting Numbers: [39, 51] Generated Node #0,1,1: 24:[39, 51] Operation: 57-6=51 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[6, 18], Operations: ['90/15=6', '57-39=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[90, 57, 39, 15], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [57, 39, 6] Generated Node #0,1: 24:[57, 39, 6] Operation: 90/15=6 Moving to Node #0,1 Current State: 24:[57, 39, 6], Operations: ['90/15=6'] Exploring Operation: 57-39=18, Resulting Numbers: [6, 18] Generated Node #0,1,0: 24:[6, 18] Operation: 57-39=18 Moving to Node #0,1,0 Current State: 24:[6, 18], Operations: ['90/15=6', '57-39=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 5, 81, 9, 4 ]
89
[ "81-5=76", "9+4=13", "76+13=89" ]
Current State: 89:[5, 81, 9, 4], Operations: [] Exploring Operation: 81-5=76, Resulting Numbers: [9, 4, 76] Generated Node #2: [9, 4, 76] from Operation: 81-5=76 Current State: 89:[9, 4, 76], Operations: ['81-5=76'] Exploring Operation: 9+4=13, Resulting Numbers: [76, 13] Generated Node #3: [76, 13] from Operation: 9+4=13 Current State: 89:[76, 13], Operations: ['81-5=76', '9+4=13'] Exploring Operation: 76+13=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[5, 81, 9, 4], Operations: [] Exploring Operation: 5*9=45, Resulting Numbers: [81, 4, 45] Generated Node #0,0: 89:[81, 4, 45] Operation: 5*9=45 Moving to Node #0,0 Current State: 89:[81, 4, 45], Operations: ['5*9=45'] Exploring Operation: 81+4=85, Resulting Numbers: [45, 85] Generated Node #0,0,0: 89:[45, 85] Operation: 81+4=85 Moving to Node #0,0,0 Current State: 89:[45, 85], Operations: ['5*9=45', '81+4=85'] Exploring Operation: 45+85=130, Resulting Numbers: [130] 130,89 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 22, 48, 1, 32 ]
34
[ "22*48=1056", "1056/32=33", "1+33=34" ]
Current State: 34:[22, 48, 1, 32], Operations: [] Exploring Operation: 22*48=1056, Resulting Numbers: [1, 32, 1056] Generated Node #2: [1, 32, 1056] from Operation: 22*48=1056 Current State: 34:[1, 32, 1056], Operations: ['22*48=1056'] Exploring Operation: 1056/32=33, Resulting Numbers: [1, 33] Generated Node #3: [1, 33] from Operation: 1056/32=33 Current State: 34:[1, 33], Operations: ['22*48=1056', '1056/32=33'] Exploring Operation: 1+33=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[22, 48, 1, 32], Operations: [] Exploring Operation: 48-32=16, Resulting Numbers: [22, 1, 16] Generated Node #0,0: 34:[22, 1, 16] Operation: 48-32=16 Moving to Node #0,0 Current State: 34:[22, 1, 16], Operations: ['48-32=16'] Exploring Operation: 22-1=21, Resulting Numbers: [16, 21] Generated Node #0,0,0: 34:[16, 21] Operation: 22-1=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[16, 21], Operations: ['48-32=16', '22-1=21'] Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,34 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
[ 3, 29, 3, 80 ]
42
[ "3*3=9", "80-29=51", "51-9=42" ]
Current State: 42:[3, 29, 3, 80], Operations: [] Exploring Operation: 3*3=9, Resulting Numbers: [29, 80, 9] Generated Node #2: [29, 80, 9] from Operation: 3*3=9 Current State: 42:[29, 80, 9], Operations: ['3*3=9'] Exploring Operation: 80-29=51, Resulting Numbers: [9, 51] Generated Node #3: [9, 51] from Operation: 80-29=51 Current State: 42:[9, 51], Operations: ['3*3=9', '80-29=51'] Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[3, 29, 3, 80], Operations: [] Exploring Operation: 80-29=51, Resulting Numbers: [3, 3, 51] Generated Node #0,0: 42:[3, 3, 51] Operation: 80-29=51 Moving to Node #0,0 Current State: 42:[3, 3, 51], Operations: ['80-29=51'] Exploring Operation: 51/3=17, Resulting Numbers: [3, 17] Generated Node #0,0,0: 42:[3, 17] Operation: 51/3=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[3, 17], Operations: ['80-29=51', '51/3=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,42 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
[ 35, 2, 38, 22 ]
97
[ "35+2=37", "38+22=60", "37+60=97" ]
Current State: 97:[35, 2, 38, 22], Operations: [] Exploring Operation: 35+2=37, Resulting Numbers: [38, 22, 37] Generated Node #2: [38, 22, 37] from Operation: 35+2=37 Current State: 97:[38, 22, 37], Operations: ['35+2=37'] Exploring Operation: 38+22=60, Resulting Numbers: [37, 60] Generated Node #3: [37, 60] from Operation: 38+22=60 Current State: 97:[37, 60], Operations: ['35+2=37', '38+22=60'] Exploring Operation: 37+60=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[35, 2, 38, 22], Operations: [] Exploring Operation: 2*38=76, Resulting Numbers: [35, 22, 76] Generated Node #0,0: 97:[35, 22, 76] Operation: 2*38=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[35, 22, 76], Operations: ['2*38=76'] Exploring Operation: 35+22=57, Resulting Numbers: [76, 57] Generated Node #0,0,0: 97:[76, 57] Operation: 35+22=57 Moving to Node #0,0,0 Current State: 97:[76, 57], Operations: ['2*38=76', '35+22=57'] Exploring Operation: 76+57=133, Resulting Numbers: [133] 133,97 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
[ 97, 40, 35, 6 ]
73
[ "97+40=137", "35*6=210", "210-137=73" ]
Current State: 73:[97, 40, 35, 6], Operations: [] Exploring Operation: 97+40=137, Resulting Numbers: [35, 6, 137] Generated Node #2: [35, 6, 137] from Operation: 97+40=137 Current State: 73:[35, 6, 137], Operations: ['97+40=137'] Exploring Operation: 35*6=210, Resulting Numbers: [137, 210] Generated Node #3: [137, 210] from Operation: 35*6=210 Current State: 73:[137, 210], Operations: ['97+40=137', '35*6=210'] Exploring Operation: 210-137=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[97, 40, 35, 6], Operations: [] Exploring Operation: 35+6=41, Resulting Numbers: [97, 40, 41] Generated Node #0,0: 73:[97, 40, 41] Operation: 35+6=41 Exploring Operation: 40+6=46, Resulting Numbers: [97, 35, 46] Generated Node #0,1: 73:[97, 35, 46] Operation: 40+6=46 Exploring Operation: 97-6=91, Resulting Numbers: [40, 35, 91] Generated Node #0,2: 73:[40, 35, 91] Operation: 97-6=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[97, 40, 41], Operations: ['35+6=41'] Exploring Operation: 40+41=81, Resulting Numbers: [97, 81] Generated Node #0,0,0: 73:[97, 81] Operation: 40+41=81 Exploring Operation: 97-41=56, Resulting Numbers: [40, 56] Generated Node #0,0,1: 73:[40, 56] Operation: 97-41=56 Exploring Operation: 97-40=57, Resulting Numbers: [41, 57] Generated Node #0,0,2: 73:[41, 57] Operation: 97-40=57 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[97, 81], Operations: ['35+6=41', '40+41=81'] Exploring Operation: 97+81=178, Resulting Numbers: [178] 178,73 unequal: No Solution Exploring Operation: 97*81=7857, Resulting Numbers: [7857] 7857,73 unequal: No Solution Exploring Operation: 97-81=16, Resulting Numbers: [16] 16,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[41, 57], Operations: ['35+6=41', '97-40=57'] Exploring Operation: 41*57=2337, Resulting Numbers: [2337] 2337,73 unequal: No Solution Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[40, 56], Operations: ['35+6=41', '97-41=56'] Exploring Operation: 56-40=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 40*56=2240, Resulting Numbers: [2240] 2240,73 unequal: No Solution Exploring Operation: 40+56=96, Resulting Numbers: [96] 96,73 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 #0,1 Current State: 73:[97, 35, 46], Operations: ['40+6=46'] Exploring Operation: 97-46=51, Resulting Numbers: [35, 51] Generated Node #0,1,0: 73:[35, 51] Operation: 97-46=51 Exploring Operation: 97-35=62, Resulting Numbers: [46, 62] Generated Node #0,1,1: 73:[46, 62] Operation: 97-35=62 Exploring Operation: 35+46=81, Resulting Numbers: [97, 81] Generated Node #0,1,2: 73:[97, 81] Operation: 35+46=81 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 73:[97, 81], Operations: ['40+6=46', '35+46=81'] Exploring Operation: 97+81=178, Resulting Numbers: [178] 178,73 unequal: No Solution Exploring Operation: 97*81=7857, Resulting Numbers: [7857] 7857,73 unequal: No Solution Exploring Operation: 97-81=16, Resulting Numbers: [16] 16,73 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 #0,1,1 Current State: 73:[46, 62], Operations: ['40+6=46', '97-35=62'] Exploring Operation: 46*62=2852, Resulting Numbers: [2852] 2852,73 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 46+62=108, Resulting Numbers: [108] 108,73 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 #0,1,0 Current State: 73:[35, 51], Operations: ['40+6=46', '97-46=51'] Exploring Operation: 35+51=86, Resulting Numbers: [86] 86,73 unequal: No Solution Exploring Operation: 35*51=1785, Resulting Numbers: [1785] 1785,73 unequal: No Solution Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[40, 35, 91], Operations: ['97-6=91'] Exploring Operation: 91-40=51, Resulting Numbers: [35, 51] Generated Node #0,2,0: 73:[35, 51] Operation: 91-40=51 Exploring Operation: 40+35=75, Resulting Numbers: [91, 75] Generated Node #0,2,1: 73:[91, 75] Operation: 40+35=75 Exploring Operation: 91-35=56, Resulting Numbers: [40, 56] Generated Node #0,2,2: 73:[40, 56] Operation: 91-35=56 Moving to Node #0,2,1 Current State: 73:[91, 75], Operations: ['97-6=91', '40+35=75'] Exploring Operation: 91*75=6825, Resulting Numbers: [6825] 6825,73 unequal: No Solution Exploring Operation: 91+75=166, Resulting Numbers: [166] 166,73 unequal: No Solution Exploring Operation: 91-75=16, Resulting Numbers: [16] 16,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[40, 56], Operations: ['97-6=91', '91-35=56'] Exploring Operation: 40*56=2240, Resulting Numbers: [2240] 2240,73 unequal: No Solution Exploring Operation: 56-40=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 40+56=96, Resulting Numbers: [96] 96,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[35, 51], Operations: ['97-6=91', '91-40=51'] Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 35*51=1785, Resulting Numbers: [1785] 1785,73 unequal: No Solution Exploring Operation: 35+51=86, Resulting Numbers: [86] 86,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 85, 33, 40, 30 ]
18
[ "85-33=52", "40+30=70", "70-52=18" ]
Current State: 18:[85, 33, 40, 30], Operations: [] Exploring Operation: 85-33=52, Resulting Numbers: [40, 30, 52] Generated Node #2: [40, 30, 52] from Operation: 85-33=52 Current State: 18:[40, 30, 52], Operations: ['85-33=52'] Exploring Operation: 40+30=70, Resulting Numbers: [52, 70] Generated Node #3: [52, 70] from Operation: 40+30=70 Current State: 18:[52, 70], Operations: ['85-33=52', '40+30=70'] Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[85, 33, 40, 30], Operations: [] Exploring Operation: 85-40=45, Resulting Numbers: [33, 30, 45] Generated Node #0,0: 18:[33, 30, 45] Operation: 85-40=45 Exploring Operation: 85-30=55, Resulting Numbers: [33, 40, 55] Generated Node #0,1: 18:[33, 40, 55] Operation: 85-30=55 Exploring Operation: 85-33=52, Resulting Numbers: [40, 30, 52] Generated Node #0,2: 18:[40, 30, 52] Operation: 85-33=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[33, 30, 45], Operations: ['85-40=45'] Exploring Operation: 45-33=12, Resulting Numbers: [30, 12] Generated Node #0,0,0: 18:[30, 12] Operation: 45-33=12 Exploring Operation: 33-30=3, Resulting Numbers: [45, 3] Generated Node #0,0,1: 18:[45, 3] Operation: 33-30=3 Exploring Operation: 45-30=15, Resulting Numbers: [33, 15] Generated Node #0,0,2: 18:[33, 15] Operation: 45-30=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[30, 12], Operations: ['85-40=45', '45-33=12'] Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,18 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[85, 33, 40, 30], Operations: [] Exploring Operation: 85-40=45, Resulting Numbers: [33, 30, 45] Generated Node #0,0: 18:[33, 30, 45] Operation: 85-40=45 Moving to Node #0,0 Current State: 18:[33, 30, 45], Operations: ['85-40=45'] Exploring Operation: 45-33=12, Resulting Numbers: [30, 12] Generated Node #0,0,0: 18:[30, 12] Operation: 45-33=12 Moving to Node #0,0,0 Current State: 18:[30, 12], Operations: ['85-40=45', '45-33=12'] Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 84, 65, 16, 4 ]
83
[ "84-65=19", "16*4=64", "19+64=83" ]
Current State: 83:[84, 65, 16, 4], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [16, 4, 19] Generated Node #2: [16, 4, 19] from Operation: 84-65=19 Current State: 83:[16, 4, 19], Operations: ['84-65=19'] Exploring Operation: 16*4=64, Resulting Numbers: [19, 64] Generated Node #3: [19, 64] from Operation: 16*4=64 Current State: 83:[19, 64], Operations: ['84-65=19', '16*4=64'] Exploring Operation: 19+64=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[84, 65, 16, 4], Operations: [] Exploring Operation: 16*4=64, Resulting Numbers: [84, 65, 64] Generated Node #0,0: 83:[84, 65, 64] Operation: 16*4=64 Moving to Node #0,0 Current State: 83:[84, 65, 64], Operations: ['16*4=64'] Exploring Operation: 65+64=129, Resulting Numbers: [84, 129] Generated Node #0,0,0: 83:[84, 129] Operation: 65+64=129 Moving to Node #0,0,0 Current State: 83:[84, 129], Operations: ['16*4=64', '65+64=129'] Exploring Operation: 129-84=45, Resulting Numbers: [45] 45,83 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 21, 7, 36, 54 ]
76
[ "21-7=14", "36+54=90", "90-14=76" ]
Current State: 76:[21, 7, 36, 54], Operations: [] Exploring Operation: 21-7=14, Resulting Numbers: [36, 54, 14] Generated Node #2: [36, 54, 14] from Operation: 21-7=14 Current State: 76:[36, 54, 14], Operations: ['21-7=14'] Exploring Operation: 36+54=90, Resulting Numbers: [14, 90] Generated Node #3: [14, 90] from Operation: 36+54=90 Current State: 76:[14, 90], Operations: ['21-7=14', '36+54=90'] Exploring Operation: 90-14=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[21, 7, 36, 54], Operations: [] Exploring Operation: 54-7=47, Resulting Numbers: [21, 36, 47] Generated Node #0,0: 76:[21, 36, 47] Operation: 54-7=47 Exploring Operation: 21+54=75, Resulting Numbers: [7, 36, 75] Generated Node #0,1: 76:[7, 36, 75] Operation: 21+54=75 Exploring Operation: 21/7=3, Resulting Numbers: [36, 54, 3] Generated Node #0,2: 76:[36, 54, 3] Operation: 21/7=3 Exploring Operation: 54-36=18, Resulting Numbers: [21, 7, 18] Generated Node #0,3: 76:[21, 7, 18] Operation: 54-36=18 Exploring Operation: 54-21=33, Resulting Numbers: [7, 36, 33] Generated Node #0,4: 76:[7, 36, 33] Operation: 54-21=33 Moving to Node #0,1 Current State: 76:[7, 36, 75], Operations: ['21+54=75'] Exploring Operation: 75-7=68, Resulting Numbers: [36, 68] Generated Node #0,1,0: 76:[36, 68] Operation: 75-7=68 Exploring Operation: 75-36=39, Resulting Numbers: [7, 39] Generated Node #0,1,1: 76:[7, 39] Operation: 75-36=39 Exploring Operation: 36-7=29, Resulting Numbers: [75, 29] Generated Node #0,1,2: 76:[75, 29] Operation: 36-7=29 Exploring Operation: 7+36=43, Resulting Numbers: [75, 43] Generated Node #0,1,3: 76:[75, 43] Operation: 7+36=43 Exploring Operation: 7+75=82, Resulting Numbers: [36, 82] Generated Node #0,1,4: 76:[36, 82] Operation: 7+75=82 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[7, 39], Operations: ['21+54=75', '75-36=39'] Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 7*39=273, Resulting Numbers: [273] 273,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 76:[75, 43], Operations: ['21+54=75', '7+36=43'] Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,76 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 76:[36, 82], Operations: ['21+54=75', '7+75=82'] Exploring Operation: 82-36=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 36*82=2952, Resulting Numbers: [2952] 2952,76 unequal: No Solution Exploring Operation: 36+82=118, Resulting Numbers: [118] 118,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[36, 68], Operations: ['21+54=75', '75-7=68'] Exploring Operation: 36*68=2448, Resulting Numbers: [2448] 2448,76 unequal: No Solution Exploring Operation: 36+68=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 76:[75, 29], Operations: ['21+54=75', '36-7=29'] Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,76 unequal: No Solution Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,76 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: 76:[21, 7, 18], Operations: ['54-36=18'] Exploring Operation: 21-7=14, Resulting Numbers: [18, 14] Generated Node #0,3,0: 76:[18, 14] Operation: 21-7=14 Exploring Operation: 21+18=39, Resulting Numbers: [7, 39] Generated Node #0,3,1: 76:[7, 39] Operation: 21+18=39 Exploring Operation: 7+18=25, Resulting Numbers: [21, 25] Generated Node #0,3,2: 76:[21, 25] Operation: 7+18=25 Exploring Operation: 21/7=3, Resulting Numbers: [18, 3] Generated Node #0,3,3: 76:[18, 3] Operation: 21/7=3 Exploring Operation: 21-18=3, Resulting Numbers: [7, 3] Generated Node #0,3,4: 76:[7, 3] Operation: 21-18=3 Moving to Node #0,4 Current State: 76:[7, 36, 33], Operations: ['54-21=33'] Exploring Operation: 7+33=40, Resulting Numbers: [36, 40] Generated Node #0,4,0: 76:[36, 40] Operation: 7+33=40 Exploring Operation: 7+36=43, Resulting Numbers: [33, 43] Generated Node #0,4,1: 76:[33, 43] Operation: 7+36=43 Exploring Operation: 36-33=3, Resulting Numbers: [7, 3] Generated Node #0,4,2: 76:[7, 3] Operation: 36-33=3 Exploring Operation: 33-7=26, Resulting Numbers: [36, 26] Generated Node #0,4,3: 76:[36, 26] Operation: 33-7=26 Exploring Operation: 36+33=69, Resulting Numbers: [7, 69] Generated Node #0,4,4: 76:[7, 69] Operation: 36+33=69 Moving to Node #0,0 Current State: 76:[21, 36, 47], Operations: ['54-7=47'] Exploring Operation: 36+47=83, Resulting Numbers: [21, 83] Generated Node #0,0,0: 76:[21, 83] Operation: 36+47=83 Exploring Operation: 47-21=26, Resulting Numbers: [36, 26] Generated Node #0,0,1: 76:[36, 26] Operation: 47-21=26 Exploring Operation: 36-21=15, Resulting Numbers: [47, 15] Generated Node #0,0,2: 76:[47, 15] Operation: 36-21=15 Exploring Operation: 21+47=68, Resulting Numbers: [36, 68] Generated Node #0,0,3: 76:[36, 68] Operation: 21+47=68 Exploring Operation: 47-36=11, Resulting Numbers: [21, 11] Generated Node #0,0,4: 76:[21, 11] Operation: 47-36=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[21, 83], Operations: ['54-7=47', '36+47=83'] Exploring Operation: 83-21=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 21+83=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 21*83=1743, Resulting Numbers: [1743] 1743,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[36, 26], Operations: ['54-7=47', '47-21=26'] Exploring Operation: 36*26=936, Resulting Numbers: [936] 936,76 unequal: No Solution Exploring Operation: 36+26=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 76:[21, 11], Operations: ['54-7=47', '47-36=11'] Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,76 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 76:[36, 68], Operations: ['54-7=47', '21+47=68'] Exploring Operation: 36+68=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 36*68=2448, Resulting Numbers: [2448] 2448,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[47, 15], Operations: ['54-7=47', '36-21=15'] Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 47+15=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 47*15=705, Resulting Numbers: [705] 705,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 76:[36, 54, 3], Operations: ['21/7=3'] Exploring Operation: 36+3=39, Resulting Numbers: [54, 39] Generated Node #0,2,0: 76:[54, 39] Operation: 36+3=39 Exploring Operation: 54-36=18, Resulting Numbers: [3, 18] Generated Node #0,2,1: 76:[3, 18] Operation: 54-36=18 Exploring Operation: 54/3=18, Resulting Numbers: [36, 18] Generated Node #0,2,2: 76:[36, 18] Operation: 54/3=18 Exploring Operation: 54-3=51, Resulting Numbers: [36, 51] Generated Node #0,2,3: 76:[36, 51] Operation: 54-3=51 Exploring Operation: 36+54=90, Resulting Numbers: [3, 90] Generated Node #0,2,4: 76:[3, 90] Operation: 36+54=90 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 76:[3, 18], Operations: ['21/7=3', '54-36=18'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,76 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[36, 18], Operations: ['21/7=3', '54/3=18'] Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 36/18=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 36+18=54, Resulting Numbers: [54] 54,76 unequal: No Solution Exploring Operation: 36*18=648, Resulting Numbers: [648] 648,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 76:[36, 51], Operations: ['21/7=3', '54-3=51'] Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 36*51=1836, Resulting Numbers: [1836] 1836,76 unequal: No Solution Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 76:[3, 90], Operations: ['21/7=3', '36+54=90'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,76 unequal: No Solution Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,76 unequal: No Solution Exploring Operation: 3*90=270, Resulting Numbers: [270] 270,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[54, 39], Operations: ['21/7=3', '36+3=39'] Exploring Operation: 54*39=2106, Resulting Numbers: [2106] 2106,76 unequal: No Solution Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 54+39=93, Resulting Numbers: [93] 93,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 76:[18, 3], Operations: ['54-36=18', '21/7=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,76 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,76 unequal: No Solution Moving to Node #0,3,4 Current State: 76:[7, 3], Operations: ['54-36=18', '21-18=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,76 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,76 unequal: No Solution Moving to Node #0,4,2 Current State: 76:[7, 3], Operations: ['54-21=33', '36-33=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,76 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,76 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,76 unequal: No Solution Moving to Node #0,4,0 Current State: 76:[36, 40], Operations: ['54-21=33', '7+33=40'] Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,76 unequal: No Solution Exploring Operation: 36*40=1440, Resulting Numbers: [1440] 1440,76 unequal: No Solution Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[21, 7, 36, 54], Operations: [] Exploring Operation: 54-21=33, Resulting Numbers: [7, 36, 33] Generated Node #0,4: 76:[7, 36, 33] Operation: 54-21=33 Moving to Node #0,4 Current State: 76:[7, 36, 33], Operations: ['54-21=33'] Exploring Operation: 7+33=40, Resulting Numbers: [36, 40] Generated Node #0,4,0: 76:[36, 40] Operation: 7+33=40 Moving to Node #0,4,0 Current State: 76:[36, 40], Operations: ['54-21=33', '7+33=40'] Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.917535
hs_5
sum_heuristic
[ 2, 3, 65, 28 ]
32
[ "2+3=5", "65-28=37", "37-5=32" ]
Current State: 32:[2, 3, 65, 28], Operations: [] Exploring Operation: 2+3=5, Resulting Numbers: [65, 28, 5] Generated Node #2: [65, 28, 5] from Operation: 2+3=5 Current State: 32:[65, 28, 5], Operations: ['2+3=5'] Exploring Operation: 65-28=37, Resulting Numbers: [5, 37] Generated Node #3: [5, 37] from Operation: 65-28=37 Current State: 32:[5, 37], Operations: ['2+3=5', '65-28=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[2, 3, 65, 28], Operations: [] Exploring Operation: 65-28=37, Resulting Numbers: [2, 3, 37] Generated Node #0,0: 32:[2, 3, 37] Operation: 65-28=37 Exploring Operation: 65-3=62, Resulting Numbers: [2, 28, 62] Generated Node #0,1: 32:[2, 28, 62] Operation: 65-3=62 Moving to Node #0,0 Current State: 32:[2, 3, 37], Operations: ['65-28=37'] Exploring Operation: 37-2=35, Resulting Numbers: [3, 35] Generated Node #0,0,0: 32:[3, 35] Operation: 37-2=35 Exploring Operation: 37-3=34, Resulting Numbers: [2, 34] Generated Node #0,0,1: 32:[2, 34] Operation: 37-3=34 Moving to Node #0,1 Current State: 32:[2, 28, 62], Operations: ['65-3=62'] Exploring Operation: 62/2=31, Resulting Numbers: [28, 31] Generated Node #0,1,0: 32:[28, 31] Operation: 62/2=31 Exploring Operation: 62-28=34, Resulting Numbers: [2, 34] Generated Node #0,1,1: 32:[2, 34] Operation: 62-28=34 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[2, 34], Operations: ['65-3=62', '62-28=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[2, 3, 65, 28], Operations: [] Exploring Operation: 65-3=62, Resulting Numbers: [2, 28, 62] Generated Node #0,1: 32:[2, 28, 62] Operation: 65-3=62 Moving to Node #0,1 Current State: 32:[2, 28, 62], Operations: ['65-3=62'] Exploring Operation: 62-28=34, Resulting Numbers: [2, 34] Generated Node #0,1,1: 32:[2, 34] Operation: 62-28=34 Moving to Node #0,1,1 Current State: 32:[2, 34], Operations: ['65-3=62', '62-28=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 94, 6, 31, 48 ]
21
[ "94+6=100", "31+48=79", "100-79=21" ]
Current State: 21:[94, 6, 31, 48], Operations: [] Exploring Operation: 94+6=100, Resulting Numbers: [31, 48, 100] Generated Node #2: [31, 48, 100] from Operation: 94+6=100 Current State: 21:[31, 48, 100], Operations: ['94+6=100'] Exploring Operation: 31+48=79, Resulting Numbers: [100, 79] Generated Node #3: [100, 79] from Operation: 31+48=79 Current State: 21:[100, 79], Operations: ['94+6=100', '31+48=79'] Exploring Operation: 100-79=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[94, 6, 31, 48], Operations: [] Exploring Operation: 94-6=88, Resulting Numbers: [31, 48, 88] Generated Node #0,0: 21:[31, 48, 88] Operation: 94-6=88 Exploring Operation: 48-31=17, Resulting Numbers: [94, 6, 17] Generated Node #0,1: 21:[94, 6, 17] Operation: 48-31=17 Exploring Operation: 94-31=63, Resulting Numbers: [6, 48, 63] Generated Node #0,2: 21:[6, 48, 63] Operation: 94-31=63 Exploring Operation: 94-48=46, Resulting Numbers: [6, 31, 46] Generated Node #0,3: 21:[6, 31, 46] Operation: 94-48=46 Exploring Operation: 48/6=8, Resulting Numbers: [94, 31, 8] Generated Node #0,4: 21:[94, 31, 8] Operation: 48/6=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[6, 31, 46], Operations: ['94-48=46'] Exploring Operation: 46-6=40, Resulting Numbers: [31, 40] Generated Node #0,3,0: 21:[31, 40] Operation: 46-6=40 Exploring Operation: 31-6=25, Resulting Numbers: [46, 25] Generated Node #0,3,1: 21:[46, 25] Operation: 31-6=25 Exploring Operation: 46-31=15, Resulting Numbers: [6, 15] Generated Node #0,3,2: 21:[6, 15] Operation: 46-31=15 Exploring Operation: 6+46=52, Resulting Numbers: [31, 52] Generated Node #0,3,3: 21:[31, 52] Operation: 6+46=52 Exploring Operation: 6+31=37, Resulting Numbers: [46, 37] Generated Node #0,3,4: 21:[46, 37] Operation: 6+31=37 Moving to Node #0,3,2 Current State: 21:[6, 15], Operations: ['94-48=46', '46-31=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,21 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[94, 6, 31, 48], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [6, 31, 46] Generated Node #0,3: 21:[6, 31, 46] Operation: 94-48=46 Moving to Node #0,3 Current State: 21:[6, 31, 46], Operations: ['94-48=46'] Exploring Operation: 46-31=15, Resulting Numbers: [6, 15] Generated Node #0,3,2: 21:[6, 15] Operation: 46-31=15 Moving to Node #0,3,2 Current State: 21:[6, 15], Operations: ['94-48=46', '46-31=15'] Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 18, 74, 69, 9 ]
81
[ "74-69=5", "18*5=90", "90-9=81" ]
Current State: 81:[18, 74, 69, 9], Operations: [] Exploring Operation: 74-69=5, Resulting Numbers: [18, 9, 5] Generated Node #2: [18, 9, 5] from Operation: 74-69=5 Current State: 81:[18, 9, 5], Operations: ['74-69=5'] Exploring Operation: 18*5=90, Resulting Numbers: [9, 90] Generated Node #3: [9, 90] from Operation: 18*5=90 Current State: 81:[9, 90], Operations: ['74-69=5', '18*5=90'] Exploring Operation: 90-9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[18, 74, 69, 9], Operations: [] Exploring Operation: 18+69=87, Resulting Numbers: [74, 9, 87] Generated Node #0,0: 81:[74, 9, 87] Operation: 18+69=87 Exploring Operation: 69+9=78, Resulting Numbers: [18, 74, 78] Generated Node #0,1: 81:[18, 74, 78] Operation: 69+9=78 Exploring Operation: 18+9=27, Resulting Numbers: [74, 69, 27] Generated Node #0,2: 81:[74, 69, 27] Operation: 18+9=27 Exploring Operation: 74-69=5, Resulting Numbers: [18, 9, 5] Generated Node #0,3: 81:[18, 9, 5] Operation: 74-69=5 Exploring Operation: 18-9=9, Resulting Numbers: [74, 69, 9] Generated Node #0,4: 81:[74, 69, 9] Operation: 18-9=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[18, 9, 5], Operations: ['74-69=5'] Exploring Operation: 18+5=23, Resulting Numbers: [9, 23] Generated Node #0,3,0: 81:[9, 23] Operation: 18+5=23 Exploring Operation: 18+9=27, Resulting Numbers: [5, 27] Generated Node #0,3,1: 81:[5, 27] Operation: 18+9=27 Exploring Operation: 18-9=9, Resulting Numbers: [5, 9] Generated Node #0,3,2: 81:[5, 9] Operation: 18-9=9 Exploring Operation: 18-5=13, Resulting Numbers: [9, 13] Generated Node #0,3,3: 81:[9, 13] Operation: 18-5=13 Exploring Operation: 18/9=2, Resulting Numbers: [5, 2] Generated Node #0,3,4: 81:[5, 2] Operation: 18/9=2 Moving to Node #0,3,1 Current State: 81:[5, 27], Operations: ['74-69=5', '18+9=27'] Exploring Operation: 5+27=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 5*27=135, Resulting Numbers: [135] 135,81 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,81 unequal: No Solution Moving to Node #0,3,2 Current State: 81:[5, 9], Operations: ['74-69=5', '18-9=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,81 unequal: No Solution Moving to Node #0,3,4 Current State: 81:[5, 2], Operations: ['74-69=5', '18/9=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,81 unequal: No Solution Moving to Node #0,3,0 Current State: 81:[9, 23], Operations: ['74-69=5', '18+5=23'] Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 9*23=207, Resulting Numbers: [207] 207,81 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,81 unequal: No Solution Moving to Node #0,3,3 Current State: 81:[9, 13], Operations: ['74-69=5', '18-5=13'] Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,81 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[74, 9, 87], Operations: ['18+69=87'] Exploring Operation: 74-9=65, Resulting Numbers: [87, 65] Generated Node #0,0,0: 81:[87, 65] Operation: 74-9=65 Exploring Operation: 87-9=78, Resulting Numbers: [74, 78] Generated Node #0,0,1: 81:[74, 78] Operation: 87-9=78 Exploring Operation: 9+87=96, Resulting Numbers: [74, 96] Generated Node #0,0,2: 81:[74, 96] Operation: 9+87=96 Exploring Operation: 74+9=83, Resulting Numbers: [87, 83] Generated Node #0,0,3: 81:[87, 83] Operation: 74+9=83 Exploring Operation: 87-74=13, Resulting Numbers: [9, 13] Generated Node #0,0,4: 81:[9, 13] Operation: 87-74=13 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 81:[9, 13], Operations: ['18+69=87', '87-74=13'] Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,81 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 81:[87, 83], Operations: ['18+69=87', '74+9=83'] Exploring Operation: 87+83=170, Resulting Numbers: [170] 170,81 unequal: No Solution Exploring Operation: 87-83=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 87*83=7221, Resulting Numbers: [7221] 7221,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 81:[74, 78], Operations: ['18+69=87', '87-9=78'] Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 74*78=5772, Resulting Numbers: [5772] 5772,81 unequal: No Solution Exploring Operation: 74+78=152, Resulting Numbers: [152] 152,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[87, 65], Operations: ['18+69=87', '74-9=65'] Exploring Operation: 87+65=152, Resulting Numbers: [152] 152,81 unequal: No Solution Exploring Operation: 87*65=5655, Resulting Numbers: [5655] 5655,81 unequal: No Solution Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 81:[74, 96], Operations: ['18+69=87', '9+87=96'] Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 74+96=170, Resulting Numbers: [170] 170,81 unequal: No Solution Exploring Operation: 74*96=7104, Resulting Numbers: [7104] 7104,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[18, 74, 78], Operations: ['69+9=78'] Exploring Operation: 74-18=56, Resulting Numbers: [78, 56] Generated Node #0,1,0: 81:[78, 56] Operation: 74-18=56 Exploring Operation: 78-74=4, Resulting Numbers: [18, 4] Generated Node #0,1,1: 81:[18, 4] Operation: 78-74=4 Exploring Operation: 18+74=92, Resulting Numbers: [78, 92] Generated Node #0,1,2: 81:[78, 92] Operation: 18+74=92 Exploring Operation: 18+78=96, Resulting Numbers: [74, 96] Generated Node #0,1,3: 81:[74, 96] Operation: 18+78=96 Exploring Operation: 78-18=60, Resulting Numbers: [74, 60] Generated Node #0,1,4: 81:[74, 60] Operation: 78-18=60 Moving to Node #0,1,1 Current State: 81:[18, 4], Operations: ['69+9=78', '78-74=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,81 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[78, 92], Operations: ['69+9=78', '18+74=92'] Exploring Operation: 78+92=170, Resulting Numbers: [170] 170,81 unequal: No Solution Exploring Operation: 92-78=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 78*92=7176, Resulting Numbers: [7176] 7176,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[74, 96], Operations: ['69+9=78', '18+78=96'] Exploring Operation: 74*96=7104, Resulting Numbers: [7104] 7104,81 unequal: No Solution Exploring Operation: 74+96=170, Resulting Numbers: [170] 170,81 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[78, 56], Operations: ['69+9=78', '74-18=56'] Exploring Operation: 78*56=4368, Resulting Numbers: [4368] 4368,81 unequal: No Solution Exploring Operation: 78-56=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 78+56=134, Resulting Numbers: [134] 134,81 unequal: No Solution Moving to Node #0,1,4 Current State: 81:[74, 60], Operations: ['69+9=78', '78-18=60'] Exploring Operation: 74*60=4440, Resulting Numbers: [4440] 4440,81 unequal: No Solution Exploring Operation: 74+60=134, Resulting Numbers: [134] 134,81 unequal: No Solution Exploring Operation: 74-60=14, Resulting Numbers: [14] 14,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[74, 69, 27], Operations: ['18+9=27'] Exploring Operation: 69-27=42, Resulting Numbers: [74, 42] Generated Node #0,2,0: 81:[74, 42] Operation: 69-27=42 Exploring Operation: 74+27=101, Resulting Numbers: [69, 101] Generated Node #0,2,1: 81:[69, 101] Operation: 74+27=101 Exploring Operation: 69+27=96, Resulting Numbers: [74, 96] Generated Node #0,2,2: 81:[74, 96] Operation: 69+27=96 Exploring Operation: 74-69=5, Resulting Numbers: [27, 5] Generated Node #0,2,3: 81:[27, 5] Operation: 74-69=5 Exploring Operation: 74-27=47, Resulting Numbers: [69, 47] Generated Node #0,2,4: 81:[69, 47] Operation: 74-27=47 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 81:[27, 5], Operations: ['18+9=27', '74-69=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,81 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[74, 42], Operations: ['18+9=27', '69-27=42'] Exploring Operation: 74*42=3108, Resulting Numbers: [3108] 3108,81 unequal: No Solution Exploring Operation: 74+42=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 74-42=32, Resulting Numbers: [32] 32,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 81:[74, 96], Operations: ['18+9=27', '69+27=96'] Exploring Operation: 74*96=7104, Resulting Numbers: [7104] 7104,81 unequal: No Solution Exploring Operation: 74+96=170, Resulting Numbers: [170] 170,81 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 81:[69, 101], Operations: ['18+9=27', '74+27=101'] Exploring Operation: 69+101=170, Resulting Numbers: [170] 170,81 unequal: No Solution Exploring Operation: 69*101=6969, Resulting Numbers: [6969] 6969,81 unequal: No Solution Exploring Operation: 101-69=32, Resulting Numbers: [32] 32,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 81:[69, 47], Operations: ['18+9=27', '74-27=47'] Exploring Operation: 69+47=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 69-47=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 69*47=3243, Resulting Numbers: [3243] 3243,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 81:[74, 69, 9], Operations: ['18-9=9'] Exploring Operation: 74-69=5, Resulting Numbers: [9, 5] Generated Node #0,4,0: 81:[9, 5] Operation: 74-69=5 Exploring Operation: 74-9=65, Resulting Numbers: [69, 65] Generated Node #0,4,1: 81:[69, 65] Operation: 74-9=65 Exploring Operation: 69-9=60, Resulting Numbers: [74, 60] Generated Node #0,4,2: 81:[74, 60] Operation: 69-9=60 Exploring Operation: 69+9=78, Resulting Numbers: [74, 78] Generated Node #0,4,3: 81:[74, 78] Operation: 69+9=78 Exploring Operation: 74+9=83, Resulting Numbers: [69, 83] Generated Node #0,4,4: 81:[69, 83] Operation: 74+9=83 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 81:[9, 5], Operations: ['18-9=9', '74-69=5'] Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 81:[74, 78], Operations: ['18-9=9', '69+9=78'] Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 74*78=5772, Resulting Numbers: [5772] 5772,81 unequal: No Solution Exploring Operation: 74+78=152, Resulting Numbers: [152] 152,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 81:[69, 83], Operations: ['18-9=9', '74+9=83'] Exploring Operation: 69*83=5727, Resulting Numbers: [5727] 5727,81 unequal: No Solution Exploring Operation: 69+83=152, Resulting Numbers: [152] 152,81 unequal: No Solution Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 81:[69, 65], Operations: ['18-9=9', '74-9=65'] Exploring Operation: 69+65=134, Resulting Numbers: [134] 134,81 unequal: No Solution Exploring Operation: 69-65=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 69*65=4485, Resulting Numbers: [4485] 4485,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 81:[74, 60], Operations: ['18-9=9', '69-9=60'] Exploring Operation: 74-60=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 74*60=4440, Resulting Numbers: [4440] 4440,81 unequal: No Solution Exploring Operation: 74+60=134, Resulting Numbers: [134] 134,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 7, 19, 36, 28 ]
25
[ "19-7=12", "36/12=3", "28-3=25" ]
Current State: 25:[7, 19, 36, 28], Operations: [] Exploring Operation: 19-7=12, Resulting Numbers: [36, 28, 12] Generated Node #2: [36, 28, 12] from Operation: 19-7=12 Current State: 25:[36, 28, 12], Operations: ['19-7=12'] Exploring Operation: 36/12=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 36/12=3 Current State: 25:[28, 3], Operations: ['19-7=12', '36/12=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[7, 19, 36, 28], Operations: [] Exploring Operation: 36-28=8, Resulting Numbers: [7, 19, 8] Generated Node #0,0: 25:[7, 19, 8] Operation: 36-28=8 Moving to Node #0,0 Current State: 25:[7, 19, 8], Operations: ['36-28=8'] Exploring Operation: 7+19=26, Resulting Numbers: [8, 26] Generated Node #0,0,0: 25:[8, 26] Operation: 7+19=26 Moving to Node #0,0,0 Current State: 25:[8, 26], Operations: ['36-28=8', '7+19=26'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,25 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 82, 66, 97, 97 ]
46
[ "82+66=148", "97+97=194", "194-148=46" ]
Current State: 46:[82, 66, 97, 97], Operations: [] Exploring Operation: 82+66=148, Resulting Numbers: [97, 97, 148] Generated Node #2: [97, 97, 148] from Operation: 82+66=148 Current State: 46:[97, 97, 148], Operations: ['82+66=148'] Exploring Operation: 97+97=194, Resulting Numbers: [148, 194] Generated Node #3: [148, 194] from Operation: 97+97=194 Current State: 46:[148, 194], Operations: ['82+66=148', '97+97=194'] Exploring Operation: 194-148=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[82, 66, 97, 97], Operations: [] Exploring Operation: 97/97=1, Resulting Numbers: [82, 66, 1] Generated Node #0,0: 46:[82, 66, 1] Operation: 97/97=1 Exploring Operation: 97-97=0, Resulting Numbers: [82, 66, 0] Generated Node #0,1: 46:[82, 66, 0] Operation: 97-97=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[82, 66, 1], Operations: ['97/97=1'] Exploring Operation: 82-1=81, Resulting Numbers: [66, 81] Generated Node #0,0,0: 46:[66, 81] Operation: 82-1=81 Exploring Operation: 82-66=16, Resulting Numbers: [1, 16] Generated Node #0,0,1: 46:[1, 16] Operation: 82-66=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 46:[1, 16], Operations: ['97/97=1', '82-66=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,46 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,46 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 #0,0,0 Current State: 46:[66, 81], Operations: ['97/97=1', '82-1=81'] Exploring Operation: 81-66=15, Resulting Numbers: [15] 15,46 unequal: No Solution Exploring Operation: 66+81=147, Resulting Numbers: [147] 147,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[82, 66, 0], Operations: ['97-97=0'] Exploring Operation: 82*0=0, Resulting Numbers: [66, 0] Generated Node #0,1,0: 46:[66, 0] Operation: 82*0=0 Exploring Operation: 82-66=16, Resulting Numbers: [0, 16] Generated Node #0,1,1: 46:[0, 16] Operation: 82-66=16 Moving to Node #0,1,1 Current State: 46:[0, 16], Operations: ['97-97=0', '82-66=16'] Exploring Operation: 0+16=16, Resulting Numbers: [16] 16,46 unequal: No Solution Exploring Operation: 0*16=0, Resulting Numbers: [0] 0,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[66, 0], Operations: ['97-97=0', '82*0=0'] Exploring Operation: 66*0=0, Resulting Numbers: [0] 0,46 unequal: No Solution Exploring Operation: 66+0=66, Resulting Numbers: [66] 66,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 91, 34, 70, 63 ]
37
[ "91-70=21", "63/21=3", "34+3=37" ]
Current State: 37:[91, 34, 70, 63], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [34, 63, 21] Generated Node #2: [34, 63, 21] from Operation: 91-70=21 Current State: 37:[34, 63, 21], Operations: ['91-70=21'] Exploring Operation: 63/21=3, Resulting Numbers: [34, 3] Generated Node #3: [34, 3] from Operation: 63/21=3 Current State: 37:[34, 3], Operations: ['91-70=21', '63/21=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[91, 34, 70, 63], Operations: [] Exploring Operation: 91-34=57, Resulting Numbers: [70, 63, 57] Generated Node #0,0: 37:[70, 63, 57] Operation: 91-34=57 Exploring Operation: 91-70=21, Resulting Numbers: [34, 63, 21] Generated Node #0,1: 37:[34, 63, 21] Operation: 91-70=21 Exploring Operation: 91-63=28, Resulting Numbers: [34, 70, 28] Generated Node #0,2: 37:[34, 70, 28] Operation: 91-63=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[34, 63, 21], Operations: ['91-70=21'] Exploring Operation: 63/21=3, Resulting Numbers: [34, 3] Generated Node #0,1,0: 37:[34, 3] Operation: 63/21=3 Exploring Operation: 63-34=29, Resulting Numbers: [21, 29] Generated Node #0,1,1: 37:[21, 29] Operation: 63-34=29 Exploring Operation: 63-21=42, Resulting Numbers: [34, 42] Generated Node #0,1,2: 37:[34, 42] Operation: 63-21=42 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[34, 42], Operations: ['91-70=21', '63-21=42'] Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,37 unequal: No Solution Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,37 unequal: No Solution Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[21, 29], Operations: ['91-70=21', '63-34=29'] Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,37 unequal: No Solution Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,37 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[34, 3], Operations: ['91-70=21', '63/21=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[91, 34, 70, 63], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [34, 63, 21] Generated Node #0,1: 37:[34, 63, 21] Operation: 91-70=21 Moving to Node #0,1 Current State: 37:[34, 63, 21], Operations: ['91-70=21'] Exploring Operation: 63/21=3, Resulting Numbers: [34, 3] Generated Node #0,1,0: 37:[34, 3] Operation: 63/21=3 Moving to Node #0,1,0 Current State: 37:[34, 3], Operations: ['91-70=21', '63/21=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 10, 38, 48, 30 ]
89
[ "30/10=3", "38+48=86", "3+86=89" ]
Current State: 89:[10, 38, 48, 30], Operations: [] Exploring Operation: 30/10=3, Resulting Numbers: [38, 48, 3] Generated Node #2: [38, 48, 3] from Operation: 30/10=3 Current State: 89:[38, 48, 3], Operations: ['30/10=3'] Exploring Operation: 38+48=86, Resulting Numbers: [3, 86] Generated Node #3: [3, 86] from Operation: 38+48=86 Current State: 89:[3, 86], Operations: ['30/10=3', '38+48=86'] Exploring Operation: 3+86=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[10, 38, 48, 30], Operations: [] Exploring Operation: 10+38=48, Resulting Numbers: [48, 30, 48] Generated Node #0,0: 89:[48, 30, 48] Operation: 10+38=48 Exploring Operation: 10+30=40, Resulting Numbers: [38, 48, 40] Generated Node #0,1: 89:[38, 48, 40] Operation: 10+30=40 Exploring Operation: 38+48=86, Resulting Numbers: [10, 30, 86] Generated Node #0,2: 89:[10, 30, 86] Operation: 38+48=86 Exploring Operation: 10+48=58, Resulting Numbers: [38, 30, 58] Generated Node #0,3: 89:[38, 30, 58] Operation: 10+48=58 Exploring Operation: 38+30=68, Resulting Numbers: [10, 48, 68] Generated Node #0,4: 89:[10, 48, 68] Operation: 38+30=68 Moving to Node #0,0 Current State: 89:[48, 30, 48], Operations: ['10+38=48'] Exploring Operation: 48-30=18, Resulting Numbers: [48, 18] Generated Node #0,0,0: 89:[48, 18] Operation: 48-30=18 Exploring Operation: 48+30=78, Resulting Numbers: [48, 78] Generated Node #0,0,1: 89:[48, 78] Operation: 48+30=78 Exploring Operation: 48-30=18, Resulting Numbers: [48, 18] Generated Node #0,0,2: 89:[48, 18] Operation: 48-30=18 Exploring Operation: 48+48=96, Resulting Numbers: [30, 96] Generated Node #0,0,3: 89:[30, 96] Operation: 48+48=96 Exploring Operation: 30+48=78, Resulting Numbers: [48, 78] Generated Node #0,0,4: 89:[48, 78] Operation: 30+48=78 Moving to Node #0,2 Current State: 89:[10, 30, 86], Operations: ['38+48=86'] Exploring Operation: 10+86=96, Resulting Numbers: [30, 96] Generated Node #0,2,0: 89:[30, 96] Operation: 10+86=96 Exploring Operation: 30/10=3, Resulting Numbers: [86, 3] Generated Node #0,2,1: 89:[86, 3] Operation: 30/10=3 Exploring Operation: 86-10=76, Resulting Numbers: [30, 76] Generated Node #0,2,2: 89:[30, 76] Operation: 86-10=76 Exploring Operation: 30-10=20, Resulting Numbers: [86, 20] Generated Node #0,2,3: 89:[86, 20] Operation: 30-10=20 Exploring Operation: 10+30=40, Resulting Numbers: [86, 40] Generated Node #0,2,4: 89:[86, 40] Operation: 10+30=40 Moving to Node #0,4 Current State: 89:[10, 48, 68], Operations: ['38+30=68'] Exploring Operation: 10+68=78, Resulting Numbers: [48, 78] Generated Node #0,4,0: 89:[48, 78] Operation: 10+68=78 Exploring Operation: 10+48=58, Resulting Numbers: [68, 58] Generated Node #0,4,1: 89:[68, 58] Operation: 10+48=58 Exploring Operation: 48+68=116, Resulting Numbers: [10, 116] Generated Node #0,4,2: 89:[10, 116] Operation: 48+68=116 Exploring Operation: 48-10=38, Resulting Numbers: [68, 38] Generated Node #0,4,3: 89:[68, 38] Operation: 48-10=38 Exploring Operation: 68-10=58, Resulting Numbers: [48, 58] Generated Node #0,4,4: 89:[48, 58] Operation: 68-10=58 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 89:[48, 78], Operations: ['38+30=68', '10+68=78'] Exploring Operation: 78-48=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 48+78=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 48*78=3744, Resulting Numbers: [3744] 3744,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 89:[68, 58], Operations: ['38+30=68', '10+48=58'] Exploring Operation: 68+58=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 68*58=3944, Resulting Numbers: [3944] 3944,89 unequal: No Solution Exploring Operation: 68-58=10, Resulting Numbers: [10] 10,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 89:[68, 38], Operations: ['38+30=68', '48-10=38'] Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 68+38=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 68*38=2584, Resulting Numbers: [2584] 2584,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 89:[48, 58], Operations: ['38+30=68', '68-10=58'] Exploring Operation: 48+58=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 48*58=2784, Resulting Numbers: [2784] 2784,89 unequal: No Solution Exploring Operation: 58-48=10, Resulting Numbers: [10] 10,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 89:[10, 116], Operations: ['38+30=68', '48+68=116'] Exploring Operation: 116-10=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 10+116=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 10*116=1160, Resulting Numbers: [1160] 1160,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[38, 48, 40], Operations: ['10+30=40'] Exploring Operation: 48-38=10, Resulting Numbers: [40, 10] Generated Node #0,1,0: 89:[40, 10] Operation: 48-38=10 Exploring Operation: 38+40=78, Resulting Numbers: [48, 78] Generated Node #0,1,1: 89:[48, 78] Operation: 38+40=78 Exploring Operation: 40-38=2, Resulting Numbers: [48, 2] Generated Node #0,1,2: 89:[48, 2] Operation: 40-38=2 Exploring Operation: 48+40=88, Resulting Numbers: [38, 88] Generated Node #0,1,3: 89:[38, 88] Operation: 48+40=88 Exploring Operation: 38+48=86, Resulting Numbers: [40, 86] Generated Node #0,1,4: 89:[40, 86] Operation: 38+48=86 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[48, 78], Operations: ['10+30=40', '38+40=78'] Exploring Operation: 48+78=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 78-48=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 48*78=3744, Resulting Numbers: [3744] 3744,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 89:[38, 88], Operations: ['10+30=40', '48+40=88'] Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 38+88=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 38*88=3344, Resulting Numbers: [3344] 3344,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 89:[40, 86], Operations: ['10+30=40', '38+48=86'] Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 40+86=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 40*86=3440, Resulting Numbers: [3440] 3440,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[40, 10], Operations: ['10+30=40', '48-38=10'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,89 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,89 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[48, 2], Operations: ['10+30=40', '40-38=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,89 unequal: No Solution Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,89 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: 89:[38, 30, 58], Operations: ['10+48=58'] Exploring Operation: 30+58=88, Resulting Numbers: [38, 88] Generated Node #0,3,0: 89:[38, 88] Operation: 30+58=88 Exploring Operation: 38+58=96, Resulting Numbers: [30, 96] Generated Node #0,3,1: 89:[30, 96] Operation: 38+58=96 Exploring Operation: 38-30=8, Resulting Numbers: [58, 8] Generated Node #0,3,2: 89:[58, 8] Operation: 38-30=8 Exploring Operation: 38+30=68, Resulting Numbers: [58, 68] Generated Node #0,3,3: 89:[58, 68] Operation: 38+30=68 Exploring Operation: 58-30=28, Resulting Numbers: [38, 28] Generated Node #0,3,4: 89:[38, 28] Operation: 58-30=28 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 89:[38, 88], Operations: ['10+48=58', '30+58=88'] Exploring Operation: 38+88=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 38*88=3344, Resulting Numbers: [3344] 3344,89 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 89:[58, 68], Operations: ['10+48=58', '38+30=68'] Exploring Operation: 68-58=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 58+68=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 58*68=3944, Resulting Numbers: [3944] 3944,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 89:[30, 96], Operations: ['10+48=58', '38+58=96'] Exploring Operation: 30*96=2880, Resulting Numbers: [2880] 2880,89 unequal: No Solution Exploring Operation: 96-30=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 30+96=126, Resulting Numbers: [126] 126,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 89:[58, 8], Operations: ['10+48=58', '38-30=8'] Exploring Operation: 58*8=464, Resulting Numbers: [464] 464,89 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 89:[38, 28], Operations: ['10+48=58', '58-30=28'] Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 38*28=1064, Resulting Numbers: [1064] 1064,89 unequal: No Solution Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 89:[48, 78], Operations: ['10+38=48', '48+30=78'] Exploring Operation: 48*78=3744, Resulting Numbers: [3744] 3744,89 unequal: No Solution Exploring Operation: 48+78=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 78-48=30, Resulting Numbers: [30] 30,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[86, 40], Operations: ['38+48=86', '10+30=40'] Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,89 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,89 unequal: No Solution Moving to Node #0,0,4 Current State: 89:[48, 78], Operations: ['10+38=48', '30+48=78'] Exploring Operation: 78-48=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 48+78=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 48*78=3744, Resulting Numbers: [3744] 3744,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[30, 96], Operations: ['38+48=86', '10+86=96'] Exploring Operation: 30*96=2880, Resulting Numbers: [2880] 2880,89 unequal: No Solution Exploring Operation: 30+96=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 96-30=66, Resulting Numbers: [66] 66,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[30, 96], Operations: ['10+38=48', '48+48=96'] Exploring Operation: 96-30=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 30*96=2880, Resulting Numbers: [2880] 2880,89 unequal: No Solution Exploring Operation: 30+96=126, Resulting Numbers: [126] 126,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[30, 76], Operations: ['38+48=86', '86-10=76'] Exploring Operation: 30*76=2280, Resulting Numbers: [2280] 2280,89 unequal: No Solution Exploring Operation: 30+76=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[86, 20], Operations: ['38+48=86', '30-10=20'] Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,89 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[86, 3], Operations: ['38+48=86', '30/10=3'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,89 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[10, 38, 48, 30], Operations: [] Exploring Operation: 38+48=86, Resulting Numbers: [10, 30, 86] Generated Node #0,2: 89:[10, 30, 86] Operation: 38+48=86 Moving to Node #0,2 Current State: 89:[10, 30, 86], Operations: ['38+48=86'] Exploring Operation: 30/10=3, Resulting Numbers: [86, 3] Generated Node #0,2,1: 89:[86, 3] Operation: 30/10=3 Moving to Node #0,2,1 Current State: 89:[86, 3], Operations: ['38+48=86', '30/10=3'] Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
0.909722
hs_5
sum_heuristic
[ 11, 74, 66, 4 ]
72
[ "66/11=6", "74+4=78", "78-6=72" ]
Current State: 72:[11, 74, 66, 4], Operations: [] Exploring Operation: 66/11=6, Resulting Numbers: [74, 4, 6] Generated Node #2: [74, 4, 6] from Operation: 66/11=6 Current State: 72:[74, 4, 6], Operations: ['66/11=6'] Exploring Operation: 74+4=78, Resulting Numbers: [6, 78] Generated Node #3: [6, 78] from Operation: 74+4=78 Current State: 72:[6, 78], Operations: ['66/11=6', '74+4=78'] Exploring Operation: 78-6=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[11, 74, 66, 4], Operations: [] Exploring Operation: 74-66=8, Resulting Numbers: [11, 4, 8] Generated Node #0,0: 72:[11, 4, 8] Operation: 74-66=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[11, 4, 8], Operations: ['74-66=8'] Exploring Operation: 11-8=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 72:[4, 3] Operation: 11-8=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[4, 3], Operations: ['74-66=8', '11-8=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,72 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 No solution found.
0
hs_1
mult_heuristic
[ 25, 67, 37, 26 ]
31
[ "67-25=42", "37-26=11", "42-11=31" ]
Current State: 31:[25, 67, 37, 26], Operations: [] Exploring Operation: 67-25=42, Resulting Numbers: [37, 26, 42] Generated Node #2: [37, 26, 42] from Operation: 67-25=42 Current State: 31:[37, 26, 42], Operations: ['67-25=42'] Exploring Operation: 37-26=11, Resulting Numbers: [42, 11] Generated Node #3: [42, 11] from Operation: 37-26=11 Current State: 31:[42, 11], Operations: ['67-25=42', '37-26=11'] Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[25, 67, 37, 26], Operations: [] Exploring Operation: 67-26=41, Resulting Numbers: [25, 37, 41] Generated Node #0,0: 31:[25, 37, 41] Operation: 67-26=41 Exploring Operation: 67-25=42, Resulting Numbers: [37, 26, 42] Generated Node #0,1: 31:[37, 26, 42] Operation: 67-25=42 Exploring Operation: 67-37=30, Resulting Numbers: [25, 26, 30] Generated Node #0,2: 31:[25, 26, 30] Operation: 67-37=30 Moving to Node #0,2 Current State: 31:[25, 26, 30], Operations: ['67-37=30'] Exploring Operation: 25+30=55, Resulting Numbers: [26, 55] Generated Node #0,2,0: 31:[26, 55] Operation: 25+30=55 Exploring Operation: 25+26=51, Resulting Numbers: [30, 51] Generated Node #0,2,1: 31:[30, 51] Operation: 25+26=51 Exploring Operation: 26-25=1, Resulting Numbers: [30, 1] Generated Node #0,2,2: 31:[30, 1] Operation: 26-25=1 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[30, 51], Operations: ['67-37=30', '25+26=51'] Exploring Operation: 30*51=1530, Resulting Numbers: [1530] 1530,31 unequal: No Solution Exploring Operation: 30+51=81, Resulting Numbers: [81] 81,31 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[26, 55], Operations: ['67-37=30', '25+30=55'] Exploring Operation: 26*55=1430, Resulting Numbers: [1430] 1430,31 unequal: No Solution Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 26+55=81, Resulting Numbers: [81] 81,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[30, 1], Operations: ['67-37=30', '26-25=1'] Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[25, 67, 37, 26], Operations: [] Exploring Operation: 67-37=30, Resulting Numbers: [25, 26, 30] Generated Node #0,2: 31:[25, 26, 30] Operation: 67-37=30 Moving to Node #0,2 Current State: 31:[25, 26, 30], Operations: ['67-37=30'] Exploring Operation: 26-25=1, Resulting Numbers: [30, 1] Generated Node #0,2,2: 31:[30, 1] Operation: 26-25=1 Moving to Node #0,2,2 Current State: 31:[30, 1], Operations: ['67-37=30', '26-25=1'] Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 47, 71, 13, 5 ]
67
[ "47+5=52", "52/13=4", "71-4=67" ]
Current State: 67:[47, 71, 13, 5], Operations: [] Exploring Operation: 47+5=52, Resulting Numbers: [71, 13, 52] Generated Node #2: [71, 13, 52] from Operation: 47+5=52 Current State: 67:[71, 13, 52], Operations: ['47+5=52'] Exploring Operation: 52/13=4, Resulting Numbers: [71, 4] Generated Node #3: [71, 4] from Operation: 52/13=4 Current State: 67:[71, 4], Operations: ['47+5=52', '52/13=4'] Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[47, 71, 13, 5], Operations: [] Exploring Operation: 13+5=18, Resulting Numbers: [47, 71, 18] Generated Node #0,0: 67:[47, 71, 18] Operation: 13+5=18 Exploring Operation: 13*5=65, Resulting Numbers: [47, 71, 65] Generated Node #0,1: 67:[47, 71, 65] Operation: 13*5=65 Exploring Operation: 47+13=60, Resulting Numbers: [71, 5, 60] Generated Node #0,2: 67:[71, 5, 60] Operation: 47+13=60 Exploring Operation: 47+5=52, Resulting Numbers: [71, 13, 52] Generated Node #0,3: 67:[71, 13, 52] Operation: 47+5=52 Moving to Node #0,1 Current State: 67:[47, 71, 65], Operations: ['13*5=65'] Exploring Operation: 71-47=24, Resulting Numbers: [65, 24] Generated Node #0,1,0: 67:[65, 24] Operation: 71-47=24 Exploring Operation: 47+65=112, Resulting Numbers: [71, 112] Generated Node #0,1,1: 67:[71, 112] Operation: 47+65=112 Exploring Operation: 47+71=118, Resulting Numbers: [65, 118] Generated Node #0,1,2: 67:[65, 118] Operation: 47+71=118 Exploring Operation: 65-47=18, Resulting Numbers: [71, 18] Generated Node #0,1,3: 67:[71, 18] Operation: 65-47=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[65, 24], Operations: ['13*5=65', '71-47=24'] Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,67 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,67 unequal: No Solution Exploring Operation: 65*24=1560, Resulting Numbers: [1560] 1560,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[71, 112], Operations: ['13*5=65', '47+65=112'] Exploring Operation: 71+112=183, Resulting Numbers: [183] 183,67 unequal: No Solution Exploring Operation: 112-71=41, Resulting Numbers: [41] 41,67 unequal: No Solution Exploring Operation: 71*112=7952, Resulting Numbers: [7952] 7952,67 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 #0,1,2 Current State: 67:[65, 118], Operations: ['13*5=65', '47+71=118'] Exploring Operation: 65*118=7670, Resulting Numbers: [7670] 7670,67 unequal: No Solution Exploring Operation: 118-65=53, Resulting Numbers: [53] 53,67 unequal: No Solution Exploring Operation: 65+118=183, Resulting Numbers: [183] 183,67 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:[71, 18], Operations: ['13*5=65', '65-47=18'] Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,67 unequal: No Solution Exploring Operation: 71+18=89, Resulting Numbers: [89] 89,67 unequal: No Solution Exploring Operation: 71*18=1278, Resulting Numbers: [1278] 1278,67 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:[71, 5, 60], Operations: ['47+13=60'] Exploring Operation: 60-5=55, Resulting Numbers: [71, 55] Generated Node #0,2,0: 67:[71, 55] Operation: 60-5=55 Exploring Operation: 5+60=65, Resulting Numbers: [71, 65] Generated Node #0,2,1: 67:[71, 65] Operation: 5+60=65 Exploring Operation: 71+5=76, Resulting Numbers: [60, 76] Generated Node #0,2,2: 67:[60, 76] Operation: 71+5=76 Exploring Operation: 71-5=66, Resulting Numbers: [60, 66] Generated Node #0,2,3: 67:[60, 66] Operation: 71-5=66 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[71, 65], Operations: ['47+13=60', '5+60=65'] Exploring Operation: 71*65=4615, Resulting Numbers: [4615] 4615,67 unequal: No Solution Exploring Operation: 71+65=136, Resulting Numbers: [136] 136,67 unequal: No Solution Exploring Operation: 71-65=6, Resulting Numbers: [6] 6,67 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 #0,2,3 Current State: 67:[60, 66], Operations: ['47+13=60', '71-5=66'] Exploring Operation: 60+66=126, Resulting Numbers: [126] 126,67 unequal: No Solution Exploring Operation: 60*66=3960, Resulting Numbers: [3960] 3960,67 unequal: No Solution Exploring Operation: 66-60=6, Resulting Numbers: [6] 6,67 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 #0,2,0 Current State: 67:[71, 55], Operations: ['47+13=60', '60-5=55'] Exploring Operation: 71+55=126, Resulting Numbers: [126] 126,67 unequal: No Solution Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,67 unequal: No Solution Exploring Operation: 71*55=3905, Resulting Numbers: [3905] 3905,67 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 #0,2,2 Current State: 67:[60, 76], Operations: ['47+13=60', '71+5=76'] Exploring Operation: 76-60=16, Resulting Numbers: [16] 16,67 unequal: No Solution Exploring Operation: 60*76=4560, Resulting Numbers: [4560] 4560,67 unequal: No Solution Exploring Operation: 60+76=136, Resulting Numbers: [136] 136,67 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: 67:[47, 71, 18], Operations: ['13+5=18'] Exploring Operation: 71-18=53, Resulting Numbers: [47, 53] Generated Node #0,0,0: 67:[47, 53] Operation: 71-18=53 Exploring Operation: 47+18=65, Resulting Numbers: [71, 65] Generated Node #0,0,1: 67:[71, 65] Operation: 47+18=65 Exploring Operation: 47-18=29, Resulting Numbers: [71, 29] Generated Node #0,0,2: 67:[71, 29] Operation: 47-18=29 Exploring Operation: 71+18=89, Resulting Numbers: [47, 89] Generated Node #0,0,3: 67:[47, 89] Operation: 71+18=89 Moving to Node #0,3 Current State: 67:[71, 13, 52], Operations: ['47+5=52'] Exploring Operation: 13+52=65, Resulting Numbers: [71, 65] Generated Node #0,3,0: 67:[71, 65] Operation: 13+52=65 Exploring Operation: 71+13=84, Resulting Numbers: [52, 84] Generated Node #0,3,1: 67:[52, 84] Operation: 71+13=84 Exploring Operation: 52-13=39, Resulting Numbers: [71, 39] Generated Node #0,3,2: 67:[71, 39] Operation: 52-13=39 Exploring Operation: 71-13=58, Resulting Numbers: [52, 58] Generated Node #0,3,3: 67:[52, 58] Operation: 71-13=58 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 67:[71, 65], Operations: ['47+5=52', '13+52=65'] Exploring Operation: 71-65=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 71+65=136, Resulting Numbers: [136] 136,67 unequal: No Solution Exploring Operation: 71*65=4615, Resulting Numbers: [4615] 4615,67 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:[52, 58], Operations: ['47+5=52', '71-13=58'] Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 52+58=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 52*58=3016, Resulting Numbers: [3016] 3016,67 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:[52, 84], Operations: ['47+5=52', '71+13=84'] Exploring Operation: 84-52=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 52*84=4368, Resulting Numbers: [4368] 4368,67 unequal: No Solution Exploring Operation: 52+84=136, Resulting Numbers: [136] 136,67 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:[71, 39], Operations: ['47+5=52', '52-13=39'] Exploring Operation: 71+39=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 71-39=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 71*39=2769, Resulting Numbers: [2769] 2769,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 67:[71, 65], Operations: ['13+5=18', '47+18=65'] Exploring Operation: 71-65=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 71+65=136, Resulting Numbers: [136] 136,67 unequal: No Solution Exploring Operation: 71*65=4615, Resulting Numbers: [4615] 4615,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[47, 53], Operations: ['13+5=18', '71-18=53'] Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 47*53=2491, Resulting Numbers: [2491] 2491,67 unequal: No Solution Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[47, 89], Operations: ['13+5=18', '71+18=89'] Exploring Operation: 89-47=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 47+89=136, Resulting Numbers: [136] 136,67 unequal: No Solution Exploring Operation: 47*89=4183, Resulting Numbers: [4183] 4183,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[71, 29], Operations: ['13+5=18', '47-18=29'] Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,67 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,67 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 56, 41, 24, 67 ]
72
[ "56+67=123", "123/41=3", "24*3=72" ]
Current State: 72:[56, 41, 24, 67], Operations: [] Exploring Operation: 56+67=123, Resulting Numbers: [41, 24, 123] Generated Node #2: [41, 24, 123] from Operation: 56+67=123 Current State: 72:[41, 24, 123], Operations: ['56+67=123'] Exploring Operation: 123/41=3, Resulting Numbers: [24, 3] Generated Node #3: [24, 3] from Operation: 123/41=3 Current State: 72:[24, 3], Operations: ['56+67=123', '123/41=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[56, 41, 24, 67], Operations: [] Exploring Operation: 56+24=80, Resulting Numbers: [41, 67, 80] Generated Node #0,0: 72:[41, 67, 80] Operation: 56+24=80 Exploring Operation: 67-56=11, Resulting Numbers: [41, 24, 11] Generated Node #0,1: 72:[41, 24, 11] Operation: 67-56=11 Exploring Operation: 56-41=15, Resulting Numbers: [24, 67, 15] Generated Node #0,2: 72:[24, 67, 15] Operation: 56-41=15 Exploring Operation: 56-24=32, Resulting Numbers: [41, 67, 32] Generated Node #0,3: 72:[41, 67, 32] Operation: 56-24=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[41, 24, 11], Operations: ['67-56=11'] Exploring Operation: 24+11=35, Resulting Numbers: [41, 35] Generated Node #0,1,0: 72:[41, 35] Operation: 24+11=35 Exploring Operation: 41-11=30, Resulting Numbers: [24, 30] Generated Node #0,1,1: 72:[24, 30] Operation: 41-11=30 Exploring Operation: 41-24=17, Resulting Numbers: [11, 17] Generated Node #0,1,2: 72:[11, 17] Operation: 41-24=17 Exploring Operation: 24-11=13, Resulting Numbers: [41, 13] Generated Node #0,1,3: 72:[41, 13] Operation: 24-11=13 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[11, 17], Operations: ['67-56=11', '41-24=17'] Exploring Operation: 11*17=187, Resulting Numbers: [187] 187,72 unequal: No Solution Exploring Operation: 11+17=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,72 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 #0,1,0 Current State: 72:[41, 35], Operations: ['67-56=11', '24+11=35'] Exploring Operation: 41+35=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 41*35=1435, Resulting Numbers: [1435] 1435,72 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,72 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:[24, 30], Operations: ['67-56=11', '41-11=30'] Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,72 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,72 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 #0,1,3 Current State: 72:[41, 13], Operations: ['67-56=11', '24-11=13'] Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,72 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,72 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 #0,2 Current State: 72:[24, 67, 15], Operations: ['56-41=15'] Exploring Operation: 67-24=43, Resulting Numbers: [15, 43] Generated Node #0,2,0: 72:[15, 43] Operation: 67-24=43 Exploring Operation: 24+15=39, Resulting Numbers: [67, 39] Generated Node #0,2,1: 72:[67, 39] Operation: 24+15=39 Exploring Operation: 24-15=9, Resulting Numbers: [67, 9] Generated Node #0,2,2: 72:[67, 9] Operation: 24-15=9 Exploring Operation: 67+15=82, Resulting Numbers: [24, 82] Generated Node #0,2,3: 72:[24, 82] Operation: 67+15=82 Moving to Node #0,2,2 Current State: 72:[67, 9], Operations: ['56-41=15', '24-15=9'] Exploring Operation: 67+9=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 67-9=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 67*9=603, Resulting Numbers: [603] 603,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[67, 39], Operations: ['56-41=15', '24+15=39'] Exploring Operation: 67*39=2613, Resulting Numbers: [2613] 2613,72 unequal: No Solution Exploring Operation: 67+39=106, Resulting Numbers: [106] 106,72 unequal: No Solution Exploring Operation: 67-39=28, Resulting Numbers: [28] 28,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[24, 82], Operations: ['56-41=15', '67+15=82'] Exploring Operation: 24*82=1968, Resulting Numbers: [1968] 1968,72 unequal: No Solution Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 24+82=106, Resulting Numbers: [106] 106,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[15, 43], Operations: ['56-41=15', '67-24=43'] Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 15+43=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 15*43=645, Resulting Numbers: [645] 645,72 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 Current State: 72:[41, 67, 32], Operations: ['56-24=32'] Exploring Operation: 67-32=35, Resulting Numbers: [41, 35] Generated Node #0,3,0: 72:[41, 35] Operation: 67-32=35 Exploring Operation: 41-32=9, Resulting Numbers: [67, 9] Generated Node #0,3,1: 72:[67, 9] Operation: 41-32=9 Exploring Operation: 67-41=26, Resulting Numbers: [32, 26] Generated Node #0,3,2: 72:[32, 26] Operation: 67-41=26 Exploring Operation: 41+32=73, Resulting Numbers: [67, 73] Generated Node #0,3,3: 72:[67, 73] Operation: 41+32=73 Moving to Node #0,3,1 Current State: 72:[67, 9], Operations: ['56-24=32', '41-32=9'] Exploring Operation: 67+9=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 67*9=603, Resulting Numbers: [603] 603,72 unequal: No Solution Exploring Operation: 67-9=58, Resulting Numbers: [58] 58,72 unequal: No Solution Moving to Node #0,3,2 Current State: 72:[32, 26], Operations: ['56-24=32', '67-41=26'] Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 32*26=832, Resulting Numbers: [832] 832,72 unequal: No Solution Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,72 unequal: No Solution Moving to Node #0,3,0 Current State: 72:[41, 35], Operations: ['56-24=32', '67-32=35'] Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 41*35=1435, Resulting Numbers: [1435] 1435,72 unequal: No Solution Exploring Operation: 41+35=76, Resulting Numbers: [76] 76,72 unequal: No Solution Moving to Node #0,3,3 Current State: 72:[67, 73], Operations: ['56-24=32', '41+32=73'] Exploring Operation: 67+73=140, Resulting Numbers: [140] 140,72 unequal: No Solution Exploring Operation: 67*73=4891, Resulting Numbers: [4891] 4891,72 unequal: No Solution Exploring Operation: 73-67=6, Resulting Numbers: [6] 6,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[41, 67, 80], Operations: ['56+24=80'] Exploring Operation: 67-41=26, Resulting Numbers: [80, 26] Generated Node #0,0,0: 72:[80, 26] Operation: 67-41=26 Exploring Operation: 80-41=39, Resulting Numbers: [67, 39] Generated Node #0,0,1: 72:[67, 39] Operation: 80-41=39 Exploring Operation: 41+67=108, Resulting Numbers: [80, 108] Generated Node #0,0,2: 72:[80, 108] Operation: 41+67=108 Exploring Operation: 80-67=13, Resulting Numbers: [41, 13] Generated Node #0,0,3: 72:[41, 13] Operation: 80-67=13 Moving to Node #0,0,3 Current State: 72:[41, 13], Operations: ['56+24=80', '80-67=13'] Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,72 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[67, 39], Operations: ['56+24=80', '80-41=39'] Exploring Operation: 67*39=2613, Resulting Numbers: [2613] 2613,72 unequal: No Solution Exploring Operation: 67-39=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 67+39=106, Resulting Numbers: [106] 106,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[80, 26], Operations: ['56+24=80', '67-41=26'] Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,72 unequal: No Solution Exploring Operation: 80*26=2080, Resulting Numbers: [2080] 2080,72 unequal: No Solution Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[80, 108], Operations: ['56+24=80', '41+67=108'] Exploring Operation: 80*108=8640, Resulting Numbers: [8640] 8640,72 unequal: No Solution Exploring Operation: 108-80=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 80+108=188, Resulting Numbers: [188] 188,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 1, 25, 30, 55 ]
61
[ "25-1=24", "30+55=85", "85-24=61" ]
Current State: 61:[1, 25, 30, 55], Operations: [] Exploring Operation: 25-1=24, Resulting Numbers: [30, 55, 24] Generated Node #2: [30, 55, 24] from Operation: 25-1=24 Current State: 61:[30, 55, 24], Operations: ['25-1=24'] Exploring Operation: 30+55=85, Resulting Numbers: [24, 85] Generated Node #3: [24, 85] from Operation: 30+55=85 Current State: 61:[24, 85], Operations: ['25-1=24', '30+55=85'] Exploring Operation: 85-24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[1, 25, 30, 55], Operations: [] Exploring Operation: 1+30=31, Resulting Numbers: [25, 55, 31] Generated Node #0,0: 61:[25, 55, 31] Operation: 1+30=31 Exploring Operation: 1+25=26, Resulting Numbers: [30, 55, 26] Generated Node #0,1: 61:[30, 55, 26] Operation: 1+25=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[25, 55, 31], Operations: ['1+30=31'] Exploring Operation: 25+31=56, Resulting Numbers: [55, 56] Generated Node #0,0,0: 61:[55, 56] Operation: 25+31=56 Exploring Operation: 25+55=80, Resulting Numbers: [31, 80] Generated Node #0,0,1: 61:[31, 80] Operation: 25+55=80 Moving to Node #0,0,0 Current State: 61:[55, 56], Operations: ['1+30=31', '25+31=56'] Exploring Operation: 56-55=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 55+56=111, Resulting Numbers: [111] 111,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[31, 80], Operations: ['1+30=31', '25+55=80'] Exploring Operation: 31+80=111, Resulting Numbers: [111] 111,61 unequal: No Solution Exploring Operation: 80-31=49, Resulting Numbers: [49] 49,61 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 Current State: 61:[30, 55, 26], Operations: ['1+25=26'] Exploring Operation: 30+26=56, Resulting Numbers: [55, 56] Generated Node #0,1,0: 61:[55, 56] Operation: 30+26=56 Exploring Operation: 55+26=81, Resulting Numbers: [30, 81] Generated Node #0,1,1: 61:[30, 81] Operation: 55+26=81 Moving to Node #0,1,0 Current State: 61:[55, 56], Operations: ['1+25=26', '30+26=56'] Exploring Operation: 55+56=111, Resulting Numbers: [111] 111,61 unequal: No Solution Exploring Operation: 56-55=1, Resulting Numbers: [1] 1,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[30, 81], Operations: ['1+25=26', '55+26=81'] Exploring Operation: 30+81=111, Resulting Numbers: [111] 111,61 unequal: No Solution Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,61 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
[ 63, 12, 18, 1 ]
93
[ "63+12=75", "18*1=18", "75+18=93" ]
Current State: 93:[63, 12, 18, 1], Operations: [] Exploring Operation: 63+12=75, Resulting Numbers: [18, 1, 75] Generated Node #2: [18, 1, 75] from Operation: 63+12=75 Current State: 93:[18, 1, 75], Operations: ['63+12=75'] Exploring Operation: 18*1=18, Resulting Numbers: [75, 18] Generated Node #3: [75, 18] from Operation: 18*1=18 Current State: 93:[75, 18], Operations: ['63+12=75', '18*1=18'] Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[63, 12, 18, 1], Operations: [] Exploring Operation: 12+18=30, Resulting Numbers: [63, 1, 30] Generated Node #0,0: 93:[63, 1, 30] Operation: 12+18=30 Exploring Operation: 63+18=81, Resulting Numbers: [12, 1, 81] Generated Node #0,1: 93:[12, 1, 81] Operation: 63+18=81 Exploring Operation: 63-18=45, Resulting Numbers: [12, 1, 45] Generated Node #0,2: 93:[12, 1, 45] Operation: 63-18=45 Exploring Operation: 63+12=75, Resulting Numbers: [18, 1, 75] Generated Node #0,3: 93:[18, 1, 75] Operation: 63+12=75 Moving to Node #0,1 Current State: 93:[12, 1, 81], Operations: ['63+18=81'] Exploring Operation: 1+81=82, Resulting Numbers: [12, 82] Generated Node #0,1,0: 93:[12, 82] Operation: 1+81=82 Exploring Operation: 12+81=93, Resulting Numbers: [1, 93] Generated Node #0,1,1: 93:[1, 93] Operation: 12+81=93 Exploring Operation: 12-1=11, Resulting Numbers: [81, 11] Generated Node #0,1,2: 93:[81, 11] Operation: 12-1=11 Exploring Operation: 12*1=12, Resulting Numbers: [81, 12] Generated Node #0,1,3: 93:[81, 12] Operation: 12*1=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[1, 93], Operations: ['63+18=81', '12+81=93'] Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[63, 12, 18, 1], Operations: [] Exploring Operation: 63+18=81, Resulting Numbers: [12, 1, 81] Generated Node #0,1: 93:[12, 1, 81] Operation: 63+18=81 Moving to Node #0,1 Current State: 93:[12, 1, 81], Operations: ['63+18=81'] Exploring Operation: 12+81=93, Resulting Numbers: [1, 93] Generated Node #0,1,1: 93:[1, 93] Operation: 12+81=93 Moving to Node #0,1,1 Current State: 93:[1, 93], Operations: ['63+18=81', '12+81=93'] Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 89, 47, 49, 90 ]
95
[ "89+47=136", "90-49=41", "136-41=95" ]
Current State: 95:[89, 47, 49, 90], Operations: [] Exploring Operation: 89+47=136, Resulting Numbers: [49, 90, 136] Generated Node #2: [49, 90, 136] from Operation: 89+47=136 Current State: 95:[49, 90, 136], Operations: ['89+47=136'] Exploring Operation: 90-49=41, Resulting Numbers: [136, 41] Generated Node #3: [136, 41] from Operation: 90-49=41 Current State: 95:[136, 41], Operations: ['89+47=136', '90-49=41'] Exploring Operation: 136-41=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[89, 47, 49, 90], Operations: [] Exploring Operation: 47+49=96, Resulting Numbers: [89, 90, 96] Generated Node #0,0: 95:[89, 90, 96] Operation: 47+49=96 Exploring Operation: 49-47=2, Resulting Numbers: [89, 90, 2] Generated Node #0,1: 95:[89, 90, 2] Operation: 49-47=2 Moving to Node #0,0 Current State: 95:[89, 90, 96], Operations: ['47+49=96'] Exploring Operation: 90-89=1, Resulting Numbers: [96, 1] Generated Node #0,0,0: 95:[96, 1] Operation: 90-89=1 Exploring Operation: 96-89=7, Resulting Numbers: [90, 7] Generated Node #0,0,1: 95:[90, 7] Operation: 96-89=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[96, 1], Operations: ['47+49=96', '90-89=1'] Exploring Operation: 96*1=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[89, 47, 49, 90], Operations: [] Exploring Operation: 47+49=96, Resulting Numbers: [89, 90, 96] Generated Node #0,0: 95:[89, 90, 96] Operation: 47+49=96 Moving to Node #0,0 Current State: 95:[89, 90, 96], Operations: ['47+49=96'] Exploring Operation: 90-89=1, Resulting Numbers: [96, 1] Generated Node #0,0,0: 95:[96, 1] Operation: 90-89=1 Moving to Node #0,0,0 Current State: 95:[96, 1], Operations: ['47+49=96', '90-89=1'] Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 90, 38, 13, 93 ]
75
[ "93-90=3", "38-13=25", "3*25=75" ]
Current State: 75:[90, 38, 13, 93], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [38, 13, 3] Generated Node #2: [38, 13, 3] from Operation: 93-90=3 Current State: 75:[38, 13, 3], Operations: ['93-90=3'] Exploring Operation: 38-13=25, Resulting Numbers: [3, 25] Generated Node #3: [3, 25] from Operation: 38-13=25 Current State: 75:[3, 25], Operations: ['93-90=3', '38-13=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[90, 38, 13, 93], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [38, 13, 3] Generated Node #0,0: 75:[38, 13, 3] Operation: 93-90=3 Moving to Node #0,0 Current State: 75:[38, 13, 3], Operations: ['93-90=3'] Exploring Operation: 38-13=25, Resulting Numbers: [3, 25] Generated Node #0,0,0: 75:[3, 25] Operation: 38-13=25 Moving to Node #0,0,0 Current State: 75:[3, 25], Operations: ['93-90=3', '38-13=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[90, 38, 13, 93], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [38, 13, 3] Generated Node #0,0: 75:[38, 13, 3] Operation: 93-90=3 Moving to Node #0,0 Current State: 75:[38, 13, 3], Operations: ['93-90=3'] Exploring Operation: 38-13=25, Resulting Numbers: [3, 25] Generated Node #0,0,0: 75:[3, 25] Operation: 38-13=25 Moving to Node #0,0,0 Current State: 75:[3, 25], Operations: ['93-90=3', '38-13=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 47, 46, 50, 41 ]
24
[ "47-41=6", "50-46=4", "6*4=24" ]
Current State: 24:[47, 46, 50, 41], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [46, 50, 6] Generated Node #2: [46, 50, 6] from Operation: 47-41=6 Current State: 24:[46, 50, 6], Operations: ['47-41=6'] Exploring Operation: 50-46=4, Resulting Numbers: [6, 4] Generated Node #3: [6, 4] from Operation: 50-46=4 Current State: 24:[6, 4], Operations: ['47-41=6', '50-46=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[47, 46, 50, 41], Operations: [] Exploring Operation: 47-46=1, Resulting Numbers: [50, 41, 1] Generated Node #0,0: 24:[50, 41, 1] Operation: 47-46=1 Exploring Operation: 50-47=3, Resulting Numbers: [46, 41, 3] Generated Node #0,1: 24:[46, 41, 3] Operation: 50-47=3 Exploring Operation: 50-46=4, Resulting Numbers: [47, 41, 4] Generated Node #0,2: 24:[47, 41, 4] Operation: 50-46=4 Exploring Operation: 50-41=9, Resulting Numbers: [47, 46, 9] Generated Node #0,3: 24:[47, 46, 9] Operation: 50-41=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[46, 41, 3], Operations: ['50-47=3'] Exploring Operation: 41-3=38, Resulting Numbers: [46, 38] Generated Node #0,1,0: 24:[46, 38] Operation: 41-3=38 Exploring Operation: 46-3=43, Resulting Numbers: [41, 43] Generated Node #0,1,1: 24:[41, 43] Operation: 46-3=43 Exploring Operation: 46+3=49, Resulting Numbers: [41, 49] Generated Node #0,1,2: 24:[41, 49] Operation: 46+3=49 Exploring Operation: 46-41=5, Resulting Numbers: [3, 5] Generated Node #0,1,3: 24:[3, 5] Operation: 46-41=5 Moving to Node #0,1,3 Current State: 24:[3, 5], Operations: ['50-47=3', '46-41=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[41, 43], Operations: ['50-47=3', '46-3=43'] Exploring Operation: 41+43=84, Resulting Numbers: [84] 84,24 unequal: No Solution Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 41*43=1763, Resulting Numbers: [1763] 1763,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[46, 38], Operations: ['50-47=3', '41-3=38'] Exploring Operation: 46+38=84, Resulting Numbers: [84] 84,24 unequal: No Solution Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 46*38=1748, Resulting Numbers: [1748] 1748,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[41, 49], Operations: ['50-47=3', '46+3=49'] Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 41*49=2009, Resulting Numbers: [2009] 2009,24 unequal: No Solution Exploring Operation: 41+49=90, Resulting Numbers: [90] 90,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[47, 41, 4], Operations: ['50-46=4'] Exploring Operation: 47-41=6, Resulting Numbers: [4, 6] Generated Node #0,2,0: 24:[4, 6] Operation: 47-41=6 Exploring Operation: 47-4=43, Resulting Numbers: [41, 43] Generated Node #0,2,1: 24:[41, 43] Operation: 47-4=43 Exploring Operation: 41-4=37, Resulting Numbers: [47, 37] Generated Node #0,2,2: 24:[47, 37] Operation: 41-4=37 Exploring Operation: 47+4=51, Resulting Numbers: [41, 51] Generated Node #0,2,3: 24:[41, 51] Operation: 47+4=51 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 24:[4, 6], Operations: ['50-46=4', '47-41=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,24 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[47, 46, 50, 41], Operations: [] Exploring Operation: 50-46=4, Resulting Numbers: [47, 41, 4] Generated Node #0,2: 24:[47, 41, 4] Operation: 50-46=4 Moving to Node #0,2 Current State: 24:[47, 41, 4], Operations: ['50-46=4'] Exploring Operation: 47-41=6, Resulting Numbers: [4, 6] Generated Node #0,2,0: 24:[4, 6] Operation: 47-41=6 Moving to Node #0,2,0 Current State: 24:[4, 6], Operations: ['50-46=4', '47-41=6'] Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 33, 99, 97, 30 ]
70
[ "99/33=3", "97-30=67", "3+67=70" ]
Current State: 70:[33, 99, 97, 30], Operations: [] Exploring Operation: 99/33=3, Resulting Numbers: [97, 30, 3] Generated Node #2: [97, 30, 3] from Operation: 99/33=3 Current State: 70:[97, 30, 3], Operations: ['99/33=3'] Exploring Operation: 97-30=67, Resulting Numbers: [3, 67] Generated Node #3: [3, 67] from Operation: 97-30=67 Current State: 70:[3, 67], Operations: ['99/33=3', '97-30=67'] Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[33, 99, 97, 30], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [33, 30, 2] Generated Node #0,0: 70:[33, 30, 2] Operation: 99-97=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[33, 30, 2], Operations: ['99-97=2'] Exploring Operation: 33-30=3, Resulting Numbers: [2, 3] Generated Node #0,0,0: 70:[2, 3] Operation: 33-30=3 Moving to Node #0,0,0 Current State: 70:[2, 3], Operations: ['99-97=2', '33-30=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 36, 37, 4, 59 ]
63
[ "37-36=1", "4+59=63", "1*63=63" ]
Current State: 63:[36, 37, 4, 59], Operations: [] Exploring Operation: 37-36=1, Resulting Numbers: [4, 59, 1] Generated Node #2: [4, 59, 1] from Operation: 37-36=1 Current State: 63:[4, 59, 1], Operations: ['37-36=1'] Exploring Operation: 4+59=63, Resulting Numbers: [1, 63] Generated Node #3: [1, 63] from Operation: 4+59=63 Current State: 63:[1, 63], Operations: ['37-36=1', '4+59=63'] Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[36, 37, 4, 59], Operations: [] Exploring Operation: 37-36=1, Resulting Numbers: [4, 59, 1] Generated Node #0,0: 63:[4, 59, 1] Operation: 37-36=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[4, 59, 1], Operations: ['37-36=1'] Exploring Operation: 4+59=63, Resulting Numbers: [1, 63] Generated Node #0,0,0: 63:[1, 63] Operation: 4+59=63 Moving to Node #0,0,0 Current State: 63:[1, 63], Operations: ['37-36=1', '4+59=63'] Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[36, 37, 4, 59], Operations: [] Exploring Operation: 37-36=1, Resulting Numbers: [4, 59, 1] Generated Node #0,0: 63:[4, 59, 1] Operation: 37-36=1 Moving to Node #0,0 Current State: 63:[4, 59, 1], Operations: ['37-36=1'] Exploring Operation: 4+59=63, Resulting Numbers: [1, 63] Generated Node #0,0,0: 63:[1, 63] Operation: 4+59=63 Moving to Node #0,0,0 Current State: 63:[1, 63], Operations: ['37-36=1', '4+59=63'] Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 4, 41, 34, 39 ]
50
[ "4+41=45", "39-34=5", "45+5=50" ]
Current State: 50:[4, 41, 34, 39], Operations: [] Exploring Operation: 4+41=45, Resulting Numbers: [34, 39, 45] Generated Node #2: [34, 39, 45] from Operation: 4+41=45 Current State: 50:[34, 39, 45], Operations: ['4+41=45'] Exploring Operation: 39-34=5, Resulting Numbers: [45, 5] Generated Node #3: [45, 5] from Operation: 39-34=5 Current State: 50:[45, 5], Operations: ['4+41=45', '39-34=5'] Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[4, 41, 34, 39], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [4, 34, 2] Generated Node #0,0: 50:[4, 34, 2] Operation: 41-39=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[4, 34, 2], Operations: ['41-39=2'] Exploring Operation: 34-4=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 50:[2, 30] Operation: 34-4=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[2, 30], Operations: ['41-39=2', '34-4=30'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,50 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
[ 76, 14, 24, 22 ]
45
[ "76+14=90", "24-22=2", "90/2=45" ]
Current State: 45:[76, 14, 24, 22], Operations: [] Exploring Operation: 76+14=90, Resulting Numbers: [24, 22, 90] Generated Node #2: [24, 22, 90] from Operation: 76+14=90 Current State: 45:[24, 22, 90], Operations: ['76+14=90'] Exploring Operation: 24-22=2, Resulting Numbers: [90, 2] Generated Node #3: [90, 2] from Operation: 24-22=2 Current State: 45:[90, 2], Operations: ['76+14=90', '24-22=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[76, 14, 24, 22], Operations: [] Exploring Operation: 76-22=54, Resulting Numbers: [14, 24, 54] Generated Node #0,0: 45:[14, 24, 54] Operation: 76-22=54 Exploring Operation: 76-14=62, Resulting Numbers: [24, 22, 62] Generated Node #0,1: 45:[24, 22, 62] Operation: 76-14=62 Exploring Operation: 24+22=46, Resulting Numbers: [76, 14, 46] Generated Node #0,2: 45:[76, 14, 46] Operation: 24+22=46 Exploring Operation: 76-24=52, Resulting Numbers: [14, 22, 52] Generated Node #0,3: 45:[14, 22, 52] Operation: 76-24=52 Moving to Node #0,3 Current State: 45:[14, 22, 52], Operations: ['76-24=52'] Exploring Operation: 52-22=30, Resulting Numbers: [14, 30] Generated Node #0,3,0: 45:[14, 30] Operation: 52-22=30 Exploring Operation: 14+22=36, Resulting Numbers: [52, 36] Generated Node #0,3,1: 45:[52, 36] Operation: 14+22=36 Exploring Operation: 22-14=8, Resulting Numbers: [52, 8] Generated Node #0,3,2: 45:[52, 8] Operation: 22-14=8 Exploring Operation: 52-14=38, Resulting Numbers: [22, 38] Generated Node #0,3,3: 45:[22, 38] Operation: 52-14=38 Moving to Node #0,0 Current State: 45:[14, 24, 54], Operations: ['76-22=54'] Exploring Operation: 24-14=10, Resulting Numbers: [54, 10] Generated Node #0,0,0: 45:[54, 10] Operation: 24-14=10 Exploring Operation: 54-24=30, Resulting Numbers: [14, 30] Generated Node #0,0,1: 45:[14, 30] Operation: 54-24=30 Exploring Operation: 54-14=40, Resulting Numbers: [24, 40] Generated Node #0,0,2: 45:[24, 40] Operation: 54-14=40 Exploring Operation: 14+24=38, Resulting Numbers: [54, 38] Generated Node #0,0,3: 45:[54, 38] Operation: 14+24=38 Moving to Node #0,2 Current State: 45:[76, 14, 46], Operations: ['24+22=46'] Exploring Operation: 46-14=32, Resulting Numbers: [76, 32] Generated Node #0,2,0: 45:[76, 32] Operation: 46-14=32 Exploring Operation: 76-46=30, Resulting Numbers: [14, 30] Generated Node #0,2,1: 45:[14, 30] Operation: 76-46=30 Exploring Operation: 76-14=62, Resulting Numbers: [46, 62] Generated Node #0,2,2: 45:[46, 62] Operation: 76-14=62 Exploring Operation: 76+14=90, Resulting Numbers: [46, 90] Generated Node #0,2,3: 45:[46, 90] Operation: 76+14=90 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[14, 30], Operations: ['24+22=46', '76-46=30'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,45 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 #0,2,2 Current State: 45:[46, 62], Operations: ['24+22=46', '76-14=62'] Exploring Operation: 46*62=2852, Resulting Numbers: [2852] 2852,45 unequal: No Solution Exploring Operation: 46+62=108, Resulting Numbers: [108] 108,45 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,45 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 #0,2,0 Current State: 45:[76, 32], Operations: ['24+22=46', '46-14=32'] Exploring Operation: 76+32=108, Resulting Numbers: [108] 108,45 unequal: No Solution Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 76*32=2432, Resulting Numbers: [2432] 2432,45 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 #0,2,3 Current State: 45:[46, 90], Operations: ['24+22=46', '76+14=90'] Exploring Operation: 46*90=4140, Resulting Numbers: [4140] 4140,45 unequal: No Solution Exploring Operation: 90-46=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 46+90=136, Resulting Numbers: [136] 136,45 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: 45:[24, 22, 62], Operations: ['76-14=62'] Exploring Operation: 24+22=46, Resulting Numbers: [62, 46] Generated Node #0,1,0: 45:[62, 46] Operation: 24+22=46 Exploring Operation: 24-22=2, Resulting Numbers: [62, 2] Generated Node #0,1,1: 45:[62, 2] Operation: 24-22=2 Exploring Operation: 62-24=38, Resulting Numbers: [22, 38] Generated Node #0,1,2: 45:[22, 38] Operation: 62-24=38 Exploring Operation: 62-22=40, Resulting Numbers: [24, 40] Generated Node #0,1,3: 45:[24, 40] Operation: 62-22=40 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[22, 38], Operations: ['76-14=62', '62-24=38'] Exploring Operation: 22*38=836, Resulting Numbers: [836] 836,45 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,45 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 #0,1,3 Current State: 45:[24, 40], Operations: ['76-14=62', '62-22=40'] Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,45 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[62, 46], Operations: ['76-14=62', '24+22=46'] Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 62+46=108, Resulting Numbers: [108] 108,45 unequal: No Solution Exploring Operation: 62*46=2852, Resulting Numbers: [2852] 2852,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[62, 2], Operations: ['76-14=62', '24-22=2'] Exploring Operation: 62*2=124, Resulting Numbers: [124] 124,45 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,45 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: 45:[52, 8], Operations: ['76-24=52', '22-14=8'] Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,45 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[54, 10], Operations: ['76-22=54', '24-14=10'] Exploring Operation: 54-10=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 54+10=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 54*10=540, Resulting Numbers: [540] 540,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[24, 40], Operations: ['76-22=54', '54-14=40'] Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,45 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[22, 38], Operations: ['76-24=52', '52-14=38'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 22*38=836, Resulting Numbers: [836] 836,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[14, 30], Operations: ['76-24=52', '52-22=30'] Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[14, 30], Operations: ['76-22=54', '54-24=30'] Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,45 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[54, 38], Operations: ['76-22=54', '14+24=38'] Exploring Operation: 54+38=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 54*38=2052, Resulting Numbers: [2052] 2052,45 unequal: No Solution Moving to Node #0,3,1 Current State: 45:[52, 36], Operations: ['76-24=52', '14+22=36'] Exploring Operation: 52*36=1872, Resulting Numbers: [1872] 1872,45 unequal: No Solution Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 52+36=88, Resulting Numbers: [88] 88,45 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 26, 7, 88, 96 ]
98
[ "96-26=70", "70/7=10", "88+10=98" ]
Current State: 98:[26, 7, 88, 96], Operations: [] Exploring Operation: 96-26=70, Resulting Numbers: [7, 88, 70] Generated Node #2: [7, 88, 70] from Operation: 96-26=70 Current State: 98:[7, 88, 70], Operations: ['96-26=70'] Exploring Operation: 70/7=10, Resulting Numbers: [88, 10] Generated Node #3: [88, 10] from Operation: 70/7=10 Current State: 98:[88, 10], Operations: ['96-26=70', '70/7=10'] Exploring Operation: 88+10=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[26, 7, 88, 96], Operations: [] Exploring Operation: 96-88=8, Resulting Numbers: [26, 7, 8] Generated Node #0,0: 98:[26, 7, 8] Operation: 96-88=8 Moving to Node #0,0 Current State: 98:[26, 7, 8], Operations: ['96-88=8'] Exploring Operation: 26-8=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 98:[7, 18] Operation: 26-8=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[7, 18], Operations: ['96-88=8', '26-8=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 55, 35, 95, 53 ]
66
[ "95-53=42", "55*42=2310", "2310/35=66" ]
Current State: 66:[55, 35, 95, 53], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [55, 35, 42] Generated Node #2: [55, 35, 42] from Operation: 95-53=42 Current State: 66:[55, 35, 42], Operations: ['95-53=42'] Exploring Operation: 55*42=2310, Resulting Numbers: [35, 2310] Generated Node #3: [35, 2310] from Operation: 55*42=2310 Current State: 66:[35, 2310], Operations: ['95-53=42', '55*42=2310'] Exploring Operation: 2310/35=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[55, 35, 95, 53], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [55, 35, 42] Generated Node #0,0: 66:[55, 35, 42] Operation: 95-53=42 Exploring Operation: 95-55=40, Resulting Numbers: [35, 53, 40] Generated Node #0,1: 66:[35, 53, 40] Operation: 95-55=40 Exploring Operation: 95-35=60, Resulting Numbers: [55, 53, 60] Generated Node #0,2: 66:[55, 53, 60] Operation: 95-35=60 Moving to Node #0,0 Current State: 66:[55, 35, 42], Operations: ['95-53=42'] Exploring Operation: 55-35=20, Resulting Numbers: [42, 20] Generated Node #0,0,0: 66:[42, 20] Operation: 55-35=20 Exploring Operation: 55-42=13, Resulting Numbers: [35, 13] Generated Node #0,0,1: 66:[35, 13] Operation: 55-42=13 Exploring Operation: 42-35=7, Resulting Numbers: [55, 7] Generated Node #0,0,2: 66:[55, 7] Operation: 42-35=7 Moving to Node #0,1 Current State: 66:[35, 53, 40], Operations: ['95-55=40'] Exploring Operation: 40-35=5, Resulting Numbers: [53, 5] Generated Node #0,1,0: 66:[53, 5] Operation: 40-35=5 Exploring Operation: 53-35=18, Resulting Numbers: [40, 18] Generated Node #0,1,1: 66:[40, 18] Operation: 53-35=18 Exploring Operation: 53-40=13, Resulting Numbers: [35, 13] Generated Node #0,1,2: 66:[35, 13] Operation: 53-40=13 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 66:[35, 13], Operations: ['95-55=40', '53-40=13'] Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,66 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 66:[40, 18], Operations: ['95-55=40', '53-35=18'] Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,66 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[53, 5], Operations: ['95-55=40', '40-35=5'] Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 53*5=265, Resulting Numbers: [265] 265,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 66:[55, 53, 60], Operations: ['95-35=60'] Exploring Operation: 60-55=5, Resulting Numbers: [53, 5] Generated Node #0,2,0: 66:[53, 5] Operation: 60-55=5 Exploring Operation: 55-53=2, Resulting Numbers: [60, 2] Generated Node #0,2,1: 66:[60, 2] Operation: 55-53=2 Exploring Operation: 60-53=7, Resulting Numbers: [55, 7] Generated Node #0,2,2: 66:[55, 7] Operation: 60-53=7 Moving to Node #0,0,1 Current State: 66:[35, 13], Operations: ['95-53=42', '55-42=13'] Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,66 unequal: No Solution Moving to Node #0,2,1 Current State: 66:[60, 2], Operations: ['95-35=60', '55-53=2'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[42, 20], Operations: ['95-53=42', '55-35=20'] Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 42+20=62, Resulting Numbers: [62] 62,66 unequal: No Solution Exploring Operation: 42*20=840, Resulting Numbers: [840] 840,66 unequal: No Solution Moving to Node #0,0,2 Current State: 66:[55, 7], Operations: ['95-53=42', '42-35=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,66 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,66 unequal: No Solution Moving to Node #0,2,2 Current State: 66:[55, 7], Operations: ['95-35=60', '60-53=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,66 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,66 unequal: No Solution Moving to Node #0,2,0 Current State: 66:[53, 5], Operations: ['95-35=60', '60-55=5'] Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 53*5=265, Resulting Numbers: [265] 265,66 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,66 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 77, 73, 4, 82 ]
53
[ "82-77=5", "4*5=20", "73-20=53" ]
Current State: 53:[77, 73, 4, 82], Operations: [] Exploring Operation: 82-77=5, Resulting Numbers: [73, 4, 5] Generated Node #2: [73, 4, 5] from Operation: 82-77=5 Current State: 53:[73, 4, 5], Operations: ['82-77=5'] Exploring Operation: 4*5=20, Resulting Numbers: [73, 20] Generated Node #3: [73, 20] from Operation: 4*5=20 Current State: 53:[73, 20], Operations: ['82-77=5', '4*5=20'] Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[77, 73, 4, 82], Operations: [] Exploring Operation: 77-4=73, Resulting Numbers: [73, 82, 73] Generated Node #0,0: 53:[73, 82, 73] Operation: 77-4=73 Exploring Operation: 73-4=69, Resulting Numbers: [77, 82, 69] Generated Node #0,1: 53:[77, 82, 69] Operation: 73-4=69 Moving to Node #0,0 Current State: 53:[73, 82, 73], Operations: ['77-4=73'] Exploring Operation: 82-73=9, Resulting Numbers: [73, 9] Generated Node #0,0,0: 53:[73, 9] Operation: 82-73=9 Exploring Operation: 82-73=9, Resulting Numbers: [73, 9] Generated Node #0,0,1: 53:[73, 9] Operation: 82-73=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[73, 9], Operations: ['77-4=73', '82-73=9'] Exploring Operation: 73+9=82, Resulting Numbers: [82] 82,53 unequal: No Solution Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[73, 9], Operations: ['77-4=73', '82-73=9'] Exploring Operation: 73+9=82, Resulting Numbers: [82] 82,53 unequal: No Solution Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 53:[77, 82, 69], Operations: ['73-4=69'] Exploring Operation: 82-77=5, Resulting Numbers: [69, 5] Generated Node #0,1,0: 53:[69, 5] Operation: 82-77=5 Exploring Operation: 82-69=13, Resulting Numbers: [77, 13] Generated Node #0,1,1: 53:[77, 13] Operation: 82-69=13 Moving to Node #0,1,0 Current State: 53:[69, 5], Operations: ['73-4=69', '82-77=5'] Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 69+5=74, Resulting Numbers: [74] 74,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[77, 13], Operations: ['73-4=69', '82-69=13'] Exploring Operation: 77+13=90, Resulting Numbers: [90] 90,53 unequal: No Solution Exploring Operation: 77-13=64, Resulting Numbers: [64] 64,53 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 9, 39, 69, 57 ]
55
[ "9+69=78", "78/39=2", "57-2=55" ]
Current State: 55:[9, 39, 69, 57], Operations: [] Exploring Operation: 9+69=78, Resulting Numbers: [39, 57, 78] Generated Node #2: [39, 57, 78] from Operation: 9+69=78 Current State: 55:[39, 57, 78], Operations: ['9+69=78'] Exploring Operation: 78/39=2, Resulting Numbers: [57, 2] Generated Node #3: [57, 2] from Operation: 78/39=2 Current State: 55:[57, 2], Operations: ['9+69=78', '78/39=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[9, 39, 69, 57], Operations: [] Exploring Operation: 69-9=60, Resulting Numbers: [39, 57, 60] Generated Node #0,0: 55:[39, 57, 60] Operation: 69-9=60 Exploring Operation: 69-57=12, Resulting Numbers: [9, 39, 12] Generated Node #0,1: 55:[9, 39, 12] Operation: 69-57=12 Exploring Operation: 9+39=48, Resulting Numbers: [69, 57, 48] Generated Node #0,2: 55:[69, 57, 48] Operation: 9+39=48 Moving to Node #0,1 Current State: 55:[9, 39, 12], Operations: ['69-57=12'] Exploring Operation: 12-9=3, Resulting Numbers: [39, 3] Generated Node #0,1,0: 55:[39, 3] Operation: 12-9=3 Exploring Operation: 39+12=51, Resulting Numbers: [9, 51] Generated Node #0,1,1: 55:[9, 51] Operation: 39+12=51 Exploring Operation: 9+39=48, Resulting Numbers: [12, 48] Generated Node #0,1,2: 55:[12, 48] Operation: 9+39=48 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 55:[9, 51], Operations: ['69-57=12', '39+12=51'] Exploring Operation: 9+51=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 9*51=459, Resulting Numbers: [459] 459,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 55:[12, 48], Operations: ['69-57=12', '9+39=48'] Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 12+48=60, Resulting Numbers: [60] 60,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[39, 3], Operations: ['69-57=12', '12-9=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,55 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: 55:[39, 57, 60], Operations: ['69-9=60'] Exploring Operation: 60-39=21, Resulting Numbers: [57, 21] Generated Node #0,0,0: 55:[57, 21] Operation: 60-39=21 Exploring Operation: 60-57=3, Resulting Numbers: [39, 3] Generated Node #0,0,1: 55:[39, 3] Operation: 60-57=3 Exploring Operation: 57-39=18, Resulting Numbers: [60, 18] Generated Node #0,0,2: 55:[60, 18] Operation: 57-39=18 Moving to Node #0,2 Current State: 55:[69, 57, 48], Operations: ['9+39=48'] Exploring Operation: 69-48=21, Resulting Numbers: [57, 21] Generated Node #0,2,0: 55:[57, 21] Operation: 69-48=21 Exploring Operation: 69-57=12, Resulting Numbers: [48, 12] Generated Node #0,2,1: 55:[48, 12] Operation: 69-57=12 Exploring Operation: 57-48=9, Resulting Numbers: [69, 9] Generated Node #0,2,2: 55:[69, 9] Operation: 57-48=9 Moving to Node #0,2,1 Current State: 55:[48, 12], Operations: ['9+39=48', '69-57=12'] Exploring Operation: 48+12=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[57, 21], Operations: ['69-9=60', '60-39=21'] Exploring Operation: 57+21=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 57*21=1197, Resulting Numbers: [1197] 1197,55 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,55 unequal: No Solution Moving to Node #0,2,0 Current State: 55:[57, 21], Operations: ['9+39=48', '69-48=21'] Exploring Operation: 57*21=1197, Resulting Numbers: [1197] 1197,55 unequal: No Solution Exploring Operation: 57+21=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[60, 18], Operations: ['69-9=60', '57-39=18'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 60*18=1080, Resulting Numbers: [1080] 1080,55 unequal: No Solution Exploring Operation: 60+18=78, Resulting Numbers: [78] 78,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[69, 9], Operations: ['9+39=48', '57-48=9'] Exploring Operation: 69-9=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 69+9=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 69*9=621, Resulting Numbers: [621] 621,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[39, 3], Operations: ['69-9=60', '60-57=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,55 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 68, 57, 63, 90 ]
53
[ "63-57=6", "90/6=15", "68-15=53" ]
Current State: 53:[68, 57, 63, 90], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [68, 90, 6] Generated Node #2: [68, 90, 6] from Operation: 63-57=6 Current State: 53:[68, 90, 6], Operations: ['63-57=6'] Exploring Operation: 90/6=15, Resulting Numbers: [68, 15] Generated Node #3: [68, 15] from Operation: 90/6=15 Current State: 53:[68, 15], Operations: ['63-57=6', '90/6=15'] Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[68, 57, 63, 90], Operations: [] Exploring Operation: 90-68=22, Resulting Numbers: [57, 63, 22] Generated Node #0,0: 53:[57, 63, 22] Operation: 90-68=22 Exploring Operation: 90-63=27, Resulting Numbers: [68, 57, 27] Generated Node #0,1: 53:[68, 57, 27] Operation: 90-63=27 Exploring Operation: 68-57=11, Resulting Numbers: [63, 90, 11] Generated Node #0,2: 53:[63, 90, 11] Operation: 68-57=11 Exploring Operation: 68-63=5, Resulting Numbers: [57, 90, 5] Generated Node #0,3: 53:[57, 90, 5] Operation: 68-63=5 Exploring Operation: 90-57=33, Resulting Numbers: [68, 63, 33] Generated Node #0,4: 53:[68, 63, 33] Operation: 90-57=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[57, 63, 22], Operations: ['90-68=22'] Exploring Operation: 57+22=79, Resulting Numbers: [63, 79] Generated Node #0,0,0: 53:[63, 79] Operation: 57+22=79 Exploring Operation: 63-57=6, Resulting Numbers: [22, 6] Generated Node #0,0,1: 53:[22, 6] Operation: 63-57=6 Exploring Operation: 63-22=41, Resulting Numbers: [57, 41] Generated Node #0,0,2: 53:[57, 41] Operation: 63-22=41 Exploring Operation: 57-22=35, Resulting Numbers: [63, 35] Generated Node #0,0,3: 53:[63, 35] Operation: 57-22=35 Exploring Operation: 63+22=85, Resulting Numbers: [57, 85] Generated Node #0,0,4: 53:[57, 85] Operation: 63+22=85 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 53:[57, 41], Operations: ['90-68=22', '63-22=41'] Exploring Operation: 57+41=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 57*41=2337, Resulting Numbers: [2337] 2337,53 unequal: No Solution No 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: 53:[63, 35], Operations: ['90-68=22', '57-22=35'] Exploring Operation: 63+35=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 63*35=2205, Resulting Numbers: [2205] 2205,53 unequal: No Solution Exploring Operation: 63-35=28, Resulting Numbers: [28] 28,53 unequal: No Solution No 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: 53:[63, 79], Operations: ['90-68=22', '57+22=79'] Exploring Operation: 79-63=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 63*79=4977, Resulting Numbers: [4977] 4977,53 unequal: No Solution Exploring Operation: 63+79=142, Resulting Numbers: [142] 142,53 unequal: No Solution No 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: 53:[57, 85], Operations: ['90-68=22', '63+22=85'] Exploring Operation: 57+85=142, Resulting Numbers: [142] 142,53 unequal: No Solution Exploring Operation: 57*85=4845, Resulting Numbers: [4845] 4845,53 unequal: No Solution Exploring Operation: 85-57=28, Resulting Numbers: [28] 28,53 unequal: No Solution No 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: 53:[22, 6], Operations: ['90-68=22', '63-57=6'] Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[68, 57, 27], Operations: ['90-63=27'] Exploring Operation: 68-57=11, Resulting Numbers: [27, 11] Generated Node #0,1,0: 53:[27, 11] Operation: 68-57=11 Exploring Operation: 68-27=41, Resulting Numbers: [57, 41] Generated Node #0,1,1: 53:[57, 41] Operation: 68-27=41 Exploring Operation: 57-27=30, Resulting Numbers: [68, 30] Generated Node #0,1,2: 53:[68, 30] Operation: 57-27=30 Exploring Operation: 68+27=95, Resulting Numbers: [57, 95] Generated Node #0,1,3: 53:[57, 95] Operation: 68+27=95 Exploring Operation: 57+27=84, Resulting Numbers: [68, 84] Generated Node #0,1,4: 53:[68, 84] Operation: 57+27=84 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[57, 41], Operations: ['90-63=27', '68-27=41'] Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 57*41=2337, Resulting Numbers: [2337] 2337,53 unequal: No Solution Exploring Operation: 57+41=98, Resulting Numbers: [98] 98,53 unequal: No Solution No 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: 53:[68, 30], Operations: ['90-63=27', '57-27=30'] Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,53 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,53 unequal: No Solution No 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: 53:[57, 95], Operations: ['90-63=27', '68+27=95'] Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 57*95=5415, Resulting Numbers: [5415] 5415,53 unequal: No Solution Exploring Operation: 57+95=152, Resulting Numbers: [152] 152,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 53:[68, 84], Operations: ['90-63=27', '57+27=84'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,53 unequal: No Solution Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,53 unequal: No Solution No 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: 53:[27, 11], Operations: ['90-63=27', '68-57=11'] Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 53:[68, 63, 33], Operations: ['90-57=33'] Exploring Operation: 68-33=35, Resulting Numbers: [63, 35] Generated Node #0,4,0: 53:[63, 35] Operation: 68-33=35 Exploring Operation: 63+33=96, Resulting Numbers: [68, 96] Generated Node #0,4,1: 53:[68, 96] Operation: 63+33=96 Exploring Operation: 63-33=30, Resulting Numbers: [68, 30] Generated Node #0,4,2: 53:[68, 30] Operation: 63-33=30 Exploring Operation: 68+33=101, Resulting Numbers: [63, 101] Generated Node #0,4,3: 53:[63, 101] Operation: 68+33=101 Exploring Operation: 68-63=5, Resulting Numbers: [33, 5] Generated Node #0,4,4: 53:[33, 5] Operation: 68-63=5 Moving to Node #0,4,0 Current State: 53:[63, 35], Operations: ['90-57=33', '68-33=35'] Exploring Operation: 63*35=2205, Resulting Numbers: [2205] 2205,53 unequal: No Solution Exploring Operation: 63+35=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 63-35=28, Resulting Numbers: [28] 28,53 unequal: No Solution Moving to Node #0,4,2 Current State: 53:[68, 30], Operations: ['90-57=33', '63-33=30'] Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,53 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,53 unequal: No Solution Moving to Node #0,4,1 Current State: 53:[68, 96], Operations: ['90-57=33', '63+33=96'] Exploring Operation: 68*96=6528, Resulting Numbers: [6528] 6528,53 unequal: No Solution Exploring Operation: 68+96=164, Resulting Numbers: [164] 164,53 unequal: No Solution Exploring Operation: 96-68=28, Resulting Numbers: [28] 28,53 unequal: No Solution Moving to Node #0,4,3 Current State: 53:[63, 101], Operations: ['90-57=33', '68+33=101'] Exploring Operation: 63+101=164, Resulting Numbers: [164] 164,53 unequal: No Solution Exploring Operation: 101-63=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 63*101=6363, Resulting Numbers: [6363] 6363,53 unequal: No Solution Moving to Node #0,4,4 Current State: 53:[33, 5], Operations: ['90-57=33', '68-63=5'] Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,53 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[63, 90, 11], Operations: ['68-57=11'] Exploring Operation: 63-11=52, Resulting Numbers: [90, 52] Generated Node #0,2,0: 53:[90, 52] Operation: 63-11=52 Exploring Operation: 90-11=79, Resulting Numbers: [63, 79] Generated Node #0,2,1: 53:[63, 79] Operation: 90-11=79 Exploring Operation: 63+11=74, Resulting Numbers: [90, 74] Generated Node #0,2,2: 53:[90, 74] Operation: 63+11=74 Exploring Operation: 90-63=27, Resulting Numbers: [11, 27] Generated Node #0,2,3: 53:[11, 27] Operation: 90-63=27 Exploring Operation: 90+11=101, Resulting Numbers: [63, 101] Generated Node #0,2,4: 53:[63, 101] Operation: 90+11=101 Moving to Node #0,2,1 Current State: 53:[63, 79], Operations: ['68-57=11', '90-11=79'] Exploring Operation: 79-63=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 63*79=4977, Resulting Numbers: [4977] 4977,53 unequal: No Solution Exploring Operation: 63+79=142, Resulting Numbers: [142] 142,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[90, 52], Operations: ['68-57=11', '63-11=52'] Exploring Operation: 90*52=4680, Resulting Numbers: [4680] 4680,53 unequal: No Solution Exploring Operation: 90-52=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 90+52=142, Resulting Numbers: [142] 142,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[90, 74], Operations: ['68-57=11', '63+11=74'] Exploring Operation: 90*74=6660, Resulting Numbers: [6660] 6660,53 unequal: No Solution Exploring Operation: 90-74=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 90+74=164, Resulting Numbers: [164] 164,53 unequal: No Solution Moving to Node #0,2,4 Current State: 53:[63, 101], Operations: ['68-57=11', '90+11=101'] Exploring Operation: 63+101=164, Resulting Numbers: [164] 164,53 unequal: No Solution Exploring Operation: 101-63=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 63*101=6363, Resulting Numbers: [6363] 6363,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[11, 27], Operations: ['68-57=11', '90-63=27'] Exploring Operation: 11*27=297, Resulting Numbers: [297] 297,53 unequal: No Solution Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 53:[57, 90, 5], Operations: ['68-63=5'] Exploring Operation: 57+5=62, Resulting Numbers: [90, 62] Generated Node #0,3,0: 53:[90, 62] Operation: 57+5=62 Exploring Operation: 90/5=18, Resulting Numbers: [57, 18] Generated Node #0,3,1: 53:[57, 18] Operation: 90/5=18 Exploring Operation: 57-5=52, Resulting Numbers: [90, 52] Generated Node #0,3,2: 53:[90, 52] Operation: 57-5=52 Exploring Operation: 90-5=85, Resulting Numbers: [57, 85] Generated Node #0,3,3: 53:[57, 85] Operation: 90-5=85 Exploring Operation: 90+5=95, Resulting Numbers: [57, 95] Generated Node #0,3,4: 53:[57, 95] Operation: 90+5=95 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 53:[57, 85], Operations: ['68-63=5', '90-5=85'] Exploring Operation: 85-57=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 57*85=4845, Resulting Numbers: [4845] 4845,53 unequal: No Solution Exploring Operation: 57+85=142, Resulting Numbers: [142] 142,53 unequal: No Solution No 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: 53:[90, 52], Operations: ['68-63=5', '57-5=52'] Exploring Operation: 90*52=4680, Resulting Numbers: [4680] 4680,53 unequal: No Solution Exploring Operation: 90-52=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 90+52=142, Resulting Numbers: [142] 142,53 unequal: No Solution No 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: 53:[57, 18], Operations: ['68-63=5', '90/5=18'] Exploring Operation: 57+18=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 57*18=1026, Resulting Numbers: [1026] 1026,53 unequal: No Solution Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,53 unequal: No Solution No 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: 53:[90, 62], Operations: ['68-63=5', '57+5=62'] Exploring Operation: 90*62=5580, Resulting Numbers: [5580] 5580,53 unequal: No Solution Exploring Operation: 90+62=152, Resulting Numbers: [152] 152,53 unequal: No Solution Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,53 unequal: No Solution No 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: 53:[57, 95], Operations: ['68-63=5', '90+5=95'] Exploring Operation: 57+95=152, Resulting Numbers: [152] 152,53 unequal: No Solution Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 57*95=5415, Resulting Numbers: [5415] 5415,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 13, 75, 8, 56 ]
85
[ "13*8=104", "75-56=19", "104-19=85" ]
Current State: 85:[13, 75, 8, 56], Operations: [] Exploring Operation: 13*8=104, Resulting Numbers: [75, 56, 104] Generated Node #2: [75, 56, 104] from Operation: 13*8=104 Current State: 85:[75, 56, 104], Operations: ['13*8=104'] Exploring Operation: 75-56=19, Resulting Numbers: [104, 19] Generated Node #3: [104, 19] from Operation: 75-56=19 Current State: 85:[104, 19], Operations: ['13*8=104', '75-56=19'] Exploring Operation: 104-19=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[13, 75, 8, 56], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [13, 8, 19] Generated Node #0,0: 85:[13, 8, 19] Operation: 75-56=19 Exploring Operation: 13+56=69, Resulting Numbers: [75, 8, 69] Generated Node #0,1: 85:[75, 8, 69] Operation: 13+56=69 Exploring Operation: 56/8=7, Resulting Numbers: [13, 75, 7] Generated Node #0,2: 85:[13, 75, 7] Operation: 56/8=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[13, 8, 19], Operations: ['75-56=19'] Exploring Operation: 13+8=21, Resulting Numbers: [19, 21] Generated Node #0,0,0: 85:[19, 21] Operation: 13+8=21 Exploring Operation: 13-8=5, Resulting Numbers: [19, 5] Generated Node #0,0,1: 85:[19, 5] Operation: 13-8=5 Exploring Operation: 19-13=6, Resulting Numbers: [8, 6] Generated Node #0,0,2: 85:[8, 6] Operation: 19-13=6 Moving to Node #0,0,1 Current State: 85:[19, 5], Operations: ['75-56=19', '13-8=5'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[8, 6], Operations: ['75-56=19', '19-13=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,85 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[19, 21], Operations: ['75-56=19', '13+8=21'] Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 19*21=399, Resulting Numbers: [399] 399,85 unequal: No Solution Exploring Operation: 19+21=40, Resulting Numbers: [40] 40,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[13, 75, 7], Operations: ['56/8=7'] Exploring Operation: 13-7=6, Resulting Numbers: [75, 6] Generated Node #0,2,0: 85:[75, 6] Operation: 13-7=6 Exploring Operation: 75+7=82, Resulting Numbers: [13, 82] Generated Node #0,2,1: 85:[13, 82] Operation: 75+7=82 Exploring Operation: 13+75=88, Resulting Numbers: [7, 88] Generated Node #0,2,2: 85:[7, 88] Operation: 13+75=88 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 85:[7, 88], Operations: ['56/8=7', '13+75=88'] Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 7*88=616, Resulting Numbers: [616] 616,85 unequal: No Solution Exploring Operation: 7+88=95, Resulting Numbers: [95] 95,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 85:[13, 82], Operations: ['56/8=7', '75+7=82'] Exploring Operation: 82-13=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 13+82=95, Resulting Numbers: [95] 95,85 unequal: No Solution Exploring Operation: 13*82=1066, Resulting Numbers: [1066] 1066,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 85:[75, 6], Operations: ['56/8=7', '13-7=6'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 75+6=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 75*6=450, Resulting Numbers: [450] 450,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[75, 8, 69], Operations: ['13+56=69'] Exploring Operation: 75+8=83, Resulting Numbers: [69, 83] Generated Node #0,1,0: 85:[69, 83] Operation: 75+8=83 Exploring Operation: 75-69=6, Resulting Numbers: [8, 6] Generated Node #0,1,1: 85:[8, 6] Operation: 75-69=6 Exploring Operation: 8+69=77, Resulting Numbers: [75, 77] Generated Node #0,1,2: 85:[75, 77] Operation: 8+69=77 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[8, 6], Operations: ['13+56=69', '75-69=6'] Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[69, 83], Operations: ['13+56=69', '75+8=83'] Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 69*83=5727, Resulting Numbers: [5727] 5727,85 unequal: No Solution Exploring Operation: 69+83=152, Resulting Numbers: [152] 152,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 85:[75, 77], Operations: ['13+56=69', '8+69=77'] Exploring Operation: 75*77=5775, Resulting Numbers: [5775] 5775,85 unequal: No Solution Exploring Operation: 75+77=152, Resulting Numbers: [152] 152,85 unequal: No Solution Exploring Operation: 77-75=2, Resulting Numbers: [2] 2,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 18, 30, 42, 92 ]
46
[ "18+42=60", "30*92=2760", "2760/60=46" ]
Current State: 46:[18, 30, 42, 92], Operations: [] Exploring Operation: 18+42=60, Resulting Numbers: [30, 92, 60] Generated Node #2: [30, 92, 60] from Operation: 18+42=60 Current State: 46:[30, 92, 60], Operations: ['18+42=60'] Exploring Operation: 30*92=2760, Resulting Numbers: [60, 2760] Generated Node #3: [60, 2760] from Operation: 30*92=2760 Current State: 46:[60, 2760], Operations: ['18+42=60', '30*92=2760'] Exploring Operation: 2760/60=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[18, 30, 42, 92], Operations: [] Exploring Operation: 92-42=50, Resulting Numbers: [18, 30, 50] Generated Node #0,0: 46:[18, 30, 50] Operation: 92-42=50 Exploring Operation: 92-18=74, Resulting Numbers: [30, 42, 74] Generated Node #0,1: 46:[30, 42, 74] Operation: 92-18=74 Exploring Operation: 92-30=62, Resulting Numbers: [18, 42, 62] Generated Node #0,2: 46:[18, 42, 62] Operation: 92-30=62 Moving to Node #0,0 Current State: 46:[18, 30, 50], Operations: ['92-42=50'] Exploring Operation: 18+30=48, Resulting Numbers: [50, 48] Generated Node #0,0,0: 46:[50, 48] Operation: 18+30=48 Exploring Operation: 30-18=12, Resulting Numbers: [50, 12] Generated Node #0,0,1: 46:[50, 12] Operation: 30-18=12 Exploring Operation: 50-30=20, Resulting Numbers: [18, 20] Generated Node #0,0,2: 46:[18, 20] Operation: 50-30=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[50, 48], Operations: ['92-42=50', '18+30=48'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,46 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,46 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 #0,0,2 Current State: 46:[18, 20], Operations: ['92-42=50', '50-30=20'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,46 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,46 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 #0,0,1 Current State: 46:[50, 12], Operations: ['92-42=50', '30-18=12'] Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,46 unequal: No Solution Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,46 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,46 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: 46:[18, 42, 62], Operations: ['92-30=62'] Exploring Operation: 62-42=20, Resulting Numbers: [18, 20] Generated Node #0,2,0: 46:[18, 20] Operation: 62-42=20 Exploring Operation: 42-18=24, Resulting Numbers: [62, 24] Generated Node #0,2,1: 46:[62, 24] Operation: 42-18=24 Exploring Operation: 62-18=44, Resulting Numbers: [42, 44] Generated Node #0,2,2: 46:[42, 44] Operation: 62-18=44 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 46:[42, 44], Operations: ['92-30=62', '62-18=44'] Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,46 unequal: No Solution Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 46:[18, 20], Operations: ['92-30=62', '62-42=20'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,46 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 46:[62, 24], Operations: ['92-30=62', '42-18=24'] Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,46 unequal: No Solution Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 46:[30, 42, 74], Operations: ['92-18=74'] Exploring Operation: 74-42=32, Resulting Numbers: [30, 32] Generated Node #0,1,0: 46:[30, 32] Operation: 74-42=32 Exploring Operation: 74-30=44, Resulting Numbers: [42, 44] Generated Node #0,1,1: 46:[42, 44] Operation: 74-30=44 Exploring Operation: 42-30=12, Resulting Numbers: [74, 12] Generated Node #0,1,2: 46:[74, 12] Operation: 42-30=12 Moving to Node #0,1,1 Current State: 46:[42, 44], Operations: ['92-18=74', '74-30=44'] Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[30, 32], Operations: ['92-18=74', '74-42=32'] Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,46 unequal: No Solution Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,46 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,1,2 Current State: 46:[74, 12], Operations: ['92-18=74', '42-30=12'] Exploring Operation: 74*12=888, Resulting Numbers: [888] 888,46 unequal: No Solution Exploring Operation: 74-12=62, Resulting Numbers: [62] 62,46 unequal: No Solution Exploring Operation: 74+12=86, Resulting Numbers: [86] 86,46 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 11, 55, 28, 19 ]
75
[ "11+55=66", "28-19=9", "66+9=75" ]
Current State: 75:[11, 55, 28, 19], Operations: [] Exploring Operation: 11+55=66, Resulting Numbers: [28, 19, 66] Generated Node #2: [28, 19, 66] from Operation: 11+55=66 Current State: 75:[28, 19, 66], Operations: ['11+55=66'] Exploring Operation: 28-19=9, Resulting Numbers: [66, 9] Generated Node #3: [66, 9] from Operation: 28-19=9 Current State: 75:[66, 9], Operations: ['11+55=66', '28-19=9'] Exploring Operation: 66+9=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[11, 55, 28, 19], Operations: [] Exploring Operation: 55-28=27, Resulting Numbers: [11, 19, 27] Generated Node #0,0: 75:[11, 19, 27] Operation: 55-28=27 Exploring Operation: 55/11=5, Resulting Numbers: [28, 19, 5] Generated Node #0,1: 75:[28, 19, 5] Operation: 55/11=5 Exploring Operation: 55+19=74, Resulting Numbers: [11, 28, 74] Generated Node #0,2: 75:[11, 28, 74] Operation: 55+19=74 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[28, 19, 5], Operations: ['55/11=5'] Exploring Operation: 19-5=14, Resulting Numbers: [28, 14] Generated Node #0,1,0: 75:[28, 14] Operation: 19-5=14 Exploring Operation: 19+5=24, Resulting Numbers: [28, 24] Generated Node #0,1,1: 75:[28, 24] Operation: 19+5=24 Exploring Operation: 28-19=9, Resulting Numbers: [5, 9] Generated Node #0,1,2: 75:[5, 9] Operation: 28-19=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 75:[28, 14], Operations: ['55/11=5', '19-5=14'] Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,75 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[28, 24], Operations: ['55/11=5', '19+5=24'] Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 75:[5, 9], Operations: ['55/11=5', '28-19=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,75 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[11, 28, 74], Operations: ['55+19=74'] Exploring Operation: 11+28=39, Resulting Numbers: [74, 39] Generated Node #0,2,0: 75:[74, 39] Operation: 11+28=39 Exploring Operation: 11+74=85, Resulting Numbers: [28, 85] Generated Node #0,2,1: 75:[28, 85] Operation: 11+74=85 Exploring Operation: 28-11=17, Resulting Numbers: [74, 17] Generated Node #0,2,2: 75:[74, 17] Operation: 28-11=17 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 75:[74, 17], Operations: ['55+19=74', '28-11=17'] Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,75 unequal: No Solution Exploring Operation: 74*17=1258, Resulting Numbers: [1258] 1258,75 unequal: No Solution Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 75:[28, 85], Operations: ['55+19=74', '11+74=85'] Exploring Operation: 85-28=57, Resulting Numbers: [57] 57,75 unequal: No Solution Exploring Operation: 28*85=2380, Resulting Numbers: [2380] 2380,75 unequal: No Solution Exploring Operation: 28+85=113, Resulting Numbers: [113] 113,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 75:[74, 39], Operations: ['55+19=74', '11+28=39'] Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,75 unequal: No Solution Exploring Operation: 74*39=2886, Resulting Numbers: [2886] 2886,75 unequal: No Solution Exploring Operation: 74+39=113, Resulting Numbers: [113] 113,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[11, 19, 27], Operations: ['55-28=27'] Exploring Operation: 11+19=30, Resulting Numbers: [27, 30] Generated Node #0,0,0: 75:[27, 30] Operation: 11+19=30 Exploring Operation: 27-11=16, Resulting Numbers: [19, 16] Generated Node #0,0,1: 75:[19, 16] Operation: 27-11=16 Exploring Operation: 19-11=8, Resulting Numbers: [27, 8] Generated Node #0,0,2: 75:[27, 8] Operation: 19-11=8 Moving to Node #0,0,1 Current State: 75:[19, 16], Operations: ['55-28=27', '27-11=16'] Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,75 unequal: No Solution Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[27, 8], Operations: ['55-28=27', '19-11=8'] Exploring Operation: 27*8=216, Resulting Numbers: [216] 216,75 unequal: No Solution Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,75 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[27, 30], Operations: ['55-28=27', '11+19=30'] Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,75 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,75 unequal: No Solution Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,75 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
[ 58, 62, 70, 72 ]
60
[ "58+62=120", "72-70=2", "120/2=60" ]
Current State: 60:[58, 62, 70, 72], Operations: [] Exploring Operation: 58+62=120, Resulting Numbers: [70, 72, 120] Generated Node #2: [70, 72, 120] from Operation: 58+62=120 Current State: 60:[70, 72, 120], Operations: ['58+62=120'] Exploring Operation: 72-70=2, Resulting Numbers: [120, 2] Generated Node #3: [120, 2] from Operation: 72-70=2 Current State: 60:[120, 2], Operations: ['58+62=120', '72-70=2'] Exploring Operation: 120/2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[58, 62, 70, 72], Operations: [] Exploring Operation: 72-62=10, Resulting Numbers: [58, 70, 10] Generated Node #0,0: 60:[58, 70, 10] Operation: 72-62=10 Exploring Operation: 72-58=14, Resulting Numbers: [62, 70, 14] Generated Node #0,1: 60:[62, 70, 14] Operation: 72-58=14 Exploring Operation: 72-70=2, Resulting Numbers: [58, 62, 2] Generated Node #0,2: 60:[58, 62, 2] Operation: 72-70=2 Moving to Node #0,2 Current State: 60:[58, 62, 2], Operations: ['72-70=2'] Exploring Operation: 62-58=4, Resulting Numbers: [2, 4] Generated Node #0,2,0: 60:[2, 4] Operation: 62-58=4 Exploring Operation: 58+2=60, Resulting Numbers: [62, 60] Generated Node #0,2,1: 60:[62, 60] Operation: 58+2=60 Exploring Operation: 62-2=60, Resulting Numbers: [58, 60] Generated Node #0,2,2: 60:[58, 60] Operation: 62-2=60 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[2, 4], Operations: ['72-70=2', '62-58=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,60 unequal: No Solution No 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: 60:[62, 60], Operations: ['72-70=2', '58+2=60'] Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,60 unequal: No Solution Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,60 unequal: No Solution No 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: 60:[58, 60], Operations: ['72-70=2', '62-2=60'] Exploring Operation: 58+60=118, Resulting Numbers: [118] 118,60 unequal: No Solution Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 58*60=3480, Resulting Numbers: [3480] 3480,60 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: 60:[58, 70, 10], Operations: ['72-62=10'] Exploring Operation: 70-58=12, Resulting Numbers: [10, 12] Generated Node #0,0,0: 60:[10, 12] Operation: 70-58=12 Exploring Operation: 70/10=7, Resulting Numbers: [58, 7] Generated Node #0,0,1: 60:[58, 7] Operation: 70/10=7 Exploring Operation: 70-10=60, Resulting Numbers: [58, 60] Generated Node #0,0,2: 60:[58, 60] Operation: 70-10=60 Moving to Node #0,1 Current State: 60:[62, 70, 14], Operations: ['72-58=14'] Exploring Operation: 70/14=5, Resulting Numbers: [62, 5] Generated Node #0,1,0: 60:[62, 5] Operation: 70/14=5 Exploring Operation: 70-62=8, Resulting Numbers: [14, 8] Generated Node #0,1,1: 60:[14, 8] Operation: 70-62=8 Exploring Operation: 70-14=56, Resulting Numbers: [62, 56] Generated Node #0,1,2: 60:[62, 56] Operation: 70-14=56 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[62, 5], Operations: ['72-58=14', '70/14=5'] Exploring Operation: 62*5=310, Resulting Numbers: [310] 310,60 unequal: No Solution Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,60 unequal: No Solution Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,60 unequal: No Solution No 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: 60:[14, 8], Operations: ['72-58=14', '70-62=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,60 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,60 unequal: No Solution No 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: 60:[62, 56], Operations: ['72-58=14', '70-14=56'] Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 62*56=3472, Resulting Numbers: [3472] 3472,60 unequal: No Solution Exploring Operation: 62+56=118, Resulting Numbers: [118] 118,60 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: 60:[10, 12], Operations: ['72-62=10', '70-58=12'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,60 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,60 unequal: No Solution Moving to Node #0,0,2 Current State: 60:[58, 60], Operations: ['72-62=10', '70-10=60'] Exploring Operation: 58*60=3480, Resulting Numbers: [3480] 3480,60 unequal: No Solution Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 58+60=118, Resulting Numbers: [118] 118,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[58, 7], Operations: ['72-62=10', '70/10=7'] Exploring Operation: 58*7=406, Resulting Numbers: [406] 406,60 unequal: No Solution Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,60 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 26, 65, 57, 15 ]
49
[ "26+65=91", "57-15=42", "91-42=49" ]
Current State: 49:[26, 65, 57, 15], Operations: [] Exploring Operation: 26+65=91, Resulting Numbers: [57, 15, 91] Generated Node #2: [57, 15, 91] from Operation: 26+65=91 Current State: 49:[57, 15, 91], Operations: ['26+65=91'] Exploring Operation: 57-15=42, Resulting Numbers: [91, 42] Generated Node #3: [91, 42] from Operation: 57-15=42 Current State: 49:[91, 42], Operations: ['26+65=91', '57-15=42'] Exploring Operation: 91-42=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[26, 65, 57, 15], Operations: [] Exploring Operation: 65-57=8, Resulting Numbers: [26, 15, 8] Generated Node #0,0: 49:[26, 15, 8] Operation: 65-57=8 Exploring Operation: 65-26=39, Resulting Numbers: [57, 15, 39] Generated Node #0,1: 49:[57, 15, 39] Operation: 65-26=39 Exploring Operation: 26-15=11, Resulting Numbers: [65, 57, 11] Generated Node #0,2: 49:[65, 57, 11] Operation: 26-15=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[57, 15, 39], Operations: ['65-26=39'] Exploring Operation: 57-15=42, Resulting Numbers: [39, 42] Generated Node #0,1,0: 49:[39, 42] Operation: 57-15=42 Exploring Operation: 57-39=18, Resulting Numbers: [15, 18] Generated Node #0,1,1: 49:[15, 18] Operation: 57-39=18 Exploring Operation: 15+39=54, Resulting Numbers: [57, 54] Generated Node #0,1,2: 49:[57, 54] Operation: 15+39=54 Moving to Node #0,1,2 Current State: 49:[57, 54], Operations: ['65-26=39', '15+39=54'] Exploring Operation: 57*54=3078, Resulting Numbers: [3078] 3078,49 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 57+54=111, Resulting Numbers: [111] 111,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[39, 42], Operations: ['65-26=39', '57-15=42'] Exploring Operation: 39*42=1638, Resulting Numbers: [1638] 1638,49 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 39+42=81, Resulting Numbers: [81] 81,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[15, 18], Operations: ['65-26=39', '57-39=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,49 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,49 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[26, 15, 8], Operations: ['65-57=8'] Exploring Operation: 26+15=41, Resulting Numbers: [8, 41] Generated Node #0,0,0: 49:[8, 41] Operation: 26+15=41 Exploring Operation: 26-15=11, Resulting Numbers: [8, 11] Generated Node #0,0,1: 49:[8, 11] Operation: 26-15=11 Exploring Operation: 26-8=18, Resulting Numbers: [15, 18] Generated Node #0,0,2: 49:[15, 18] Operation: 26-8=18 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[8, 11], Operations: ['65-57=8', '26-15=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,49 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[8, 41], Operations: ['65-57=8', '26+15=41'] Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,49 unequal: No Solution Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[26, 65, 57, 15], Operations: [] Exploring Operation: 65-57=8, Resulting Numbers: [26, 15, 8] Generated Node #0,0: 49:[26, 15, 8] Operation: 65-57=8 Moving to Node #0,0 Current State: 49:[26, 15, 8], Operations: ['65-57=8'] Exploring Operation: 26+15=41, Resulting Numbers: [8, 41] Generated Node #0,0,0: 49:[8, 41] Operation: 26+15=41 Moving to Node #0,0,0 Current State: 49:[8, 41], Operations: ['65-57=8', '26+15=41'] Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 80, 5, 90, 40 ]
80
[ "80*5=400", "400/40=10", "90-10=80" ]
Current State: 80:[80, 5, 90, 40], Operations: [] Exploring Operation: 80*5=400, Resulting Numbers: [90, 40, 400] Generated Node #2: [90, 40, 400] from Operation: 80*5=400 Current State: 80:[90, 40, 400], Operations: ['80*5=400'] Exploring Operation: 400/40=10, Resulting Numbers: [90, 10] Generated Node #3: [90, 10] from Operation: 400/40=10 Current State: 80:[90, 10], Operations: ['80*5=400', '400/40=10'] Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[80, 5, 90, 40], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [5, 40, 10] Generated Node #0,0: 80:[5, 40, 10] Operation: 90-80=10 Exploring Operation: 90/5=18, Resulting Numbers: [80, 40, 18] Generated Node #0,1: 80:[80, 40, 18] Operation: 90/5=18 Moving to Node #0,0 Current State: 80:[5, 40, 10], Operations: ['90-80=10'] Exploring Operation: 40/5=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 40/5=8 Exploring Operation: 10-5=5, Resulting Numbers: [40, 5] Generated Node #0,0,1: 80:[40, 5] Operation: 10-5=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['90-80=10', '40/5=8'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[80, 5, 90, 40], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [5, 40, 10] Generated Node #0,0: 80:[5, 40, 10] Operation: 90-80=10 Moving to Node #0,0 Current State: 80:[5, 40, 10], Operations: ['90-80=10'] Exploring Operation: 40/5=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 40/5=8 Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['90-80=10', '40/5=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 9, 15, 7, 4 ]
19
[ "9+7=16", "16/4=4", "15+4=19" ]
Current State: 19:[9, 15, 7, 4], Operations: [] Exploring Operation: 9+7=16, Resulting Numbers: [15, 4, 16] Generated Node #2: [15, 4, 16] from Operation: 9+7=16 Current State: 19:[15, 4, 16], Operations: ['9+7=16'] Exploring Operation: 16/4=4, Resulting Numbers: [15, 4] Generated Node #3: [15, 4] from Operation: 16/4=4 Current State: 19:[15, 4], Operations: ['9+7=16', '16/4=4'] Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[9, 15, 7, 4], Operations: [] Exploring Operation: 9+4=13, Resulting Numbers: [15, 7, 13] Generated Node #0,0: 19:[15, 7, 13] Operation: 9+4=13 Exploring Operation: 9+7=16, Resulting Numbers: [15, 4, 16] Generated Node #0,1: 19:[15, 4, 16] Operation: 9+7=16 Moving to Node #0,0 Current State: 19:[15, 7, 13], Operations: ['9+4=13'] Exploring Operation: 15+7=22, Resulting Numbers: [13, 22] Generated Node #0,0,0: 19:[13, 22] Operation: 15+7=22 Exploring Operation: 7+13=20, Resulting Numbers: [15, 20] Generated Node #0,0,1: 19:[15, 20] Operation: 7+13=20 Moving to Node #0,1 Current State: 19:[15, 4, 16], Operations: ['9+7=16'] Exploring Operation: 15+4=19, Resulting Numbers: [16, 19] Generated Node #0,1,0: 19:[16, 19] Operation: 15+4=19 Exploring Operation: 4+16=20, Resulting Numbers: [15, 20] Generated Node #0,1,1: 19:[15, 20] Operation: 4+16=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[16, 19], Operations: ['9+7=16', '15+4=19'] Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,19 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 #0,1,1 Current State: 19:[15, 20], Operations: ['9+7=16', '4+16=20'] Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 19:[15, 20], Operations: ['9+4=13', '7+13=20'] Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,19 unequal: No Solution Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[13, 22], Operations: ['9+4=13', '15+7=22'] Exploring Operation: 13+22=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,19 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 45, 24, 83, 9 ]
86
[ "24-9=15", "45/15=3", "83+3=86" ]
Current State: 86:[45, 24, 83, 9], Operations: [] Exploring Operation: 24-9=15, Resulting Numbers: [45, 83, 15] Generated Node #2: [45, 83, 15] from Operation: 24-9=15 Current State: 86:[45, 83, 15], Operations: ['24-9=15'] Exploring Operation: 45/15=3, Resulting Numbers: [83, 3] Generated Node #3: [83, 3] from Operation: 45/15=3 Current State: 86:[83, 3], Operations: ['24-9=15', '45/15=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[45, 24, 83, 9], Operations: [] Exploring Operation: 45/9=5, Resulting Numbers: [24, 83, 5] Generated Node #0,0: 86:[24, 83, 5] Operation: 45/9=5 Exploring Operation: 24+9=33, Resulting Numbers: [45, 83, 33] Generated Node #0,1: 86:[45, 83, 33] Operation: 24+9=33 Exploring Operation: 24-9=15, Resulting Numbers: [45, 83, 15] Generated Node #0,2: 86:[45, 83, 15] Operation: 24-9=15 Exploring Operation: 83-24=59, Resulting Numbers: [45, 9, 59] Generated Node #0,3: 86:[45, 9, 59] Operation: 83-24=59 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[45, 83, 33], Operations: ['24+9=33'] Exploring Operation: 83-33=50, Resulting Numbers: [45, 50] Generated Node #0,1,0: 86:[45, 50] Operation: 83-33=50 Exploring Operation: 45-33=12, Resulting Numbers: [83, 12] Generated Node #0,1,1: 86:[83, 12] Operation: 45-33=12 Exploring Operation: 83-45=38, Resulting Numbers: [33, 38] Generated Node #0,1,2: 86:[33, 38] Operation: 83-45=38 Exploring Operation: 45+33=78, Resulting Numbers: [83, 78] Generated Node #0,1,3: 86:[83, 78] Operation: 45+33=78 Moving to Node #0,1,0 Current State: 86:[45, 50], Operations: ['24+9=33', '83-33=50'] Exploring Operation: 45*50=2250, Resulting Numbers: [2250] 2250,86 unequal: No Solution Exploring Operation: 45+50=95, Resulting Numbers: [95] 95,86 unequal: No Solution Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,86 unequal: No Solution Moving to Node #0,1,3 Current State: 86:[83, 78], Operations: ['24+9=33', '45+33=78'] Exploring Operation: 83+78=161, Resulting Numbers: [161] 161,86 unequal: No Solution Exploring Operation: 83*78=6474, Resulting Numbers: [6474] 6474,86 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[83, 12], Operations: ['24+9=33', '45-33=12'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,86 unequal: No Solution Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,86 unequal: No Solution Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[33, 38], Operations: ['24+9=33', '83-45=38'] Exploring Operation: 33*38=1254, Resulting Numbers: [1254] 1254,86 unequal: No Solution Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[45, 83, 15], Operations: ['24-9=15'] Exploring Operation: 45/15=3, Resulting Numbers: [83, 3] Generated Node #0,2,0: 86:[83, 3] Operation: 45/15=3 Exploring Operation: 83+15=98, Resulting Numbers: [45, 98] Generated Node #0,2,1: 86:[45, 98] Operation: 83+15=98 Exploring Operation: 83-45=38, Resulting Numbers: [15, 38] Generated Node #0,2,2: 86:[15, 38] Operation: 83-45=38 Exploring Operation: 45-15=30, Resulting Numbers: [83, 30] Generated Node #0,2,3: 86:[83, 30] Operation: 45-15=30 Moving to Node #0,2,0 Current State: 86:[83, 3], Operations: ['24-9=15', '45/15=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[45, 24, 83, 9], Operations: [] Exploring Operation: 24-9=15, Resulting Numbers: [45, 83, 15] Generated Node #0,2: 86:[45, 83, 15] Operation: 24-9=15 Moving to Node #0,2 Current State: 86:[45, 83, 15], Operations: ['24-9=15'] Exploring Operation: 45/15=3, Resulting Numbers: [83, 3] Generated Node #0,2,0: 86:[83, 3] Operation: 45/15=3 Moving to Node #0,2,0 Current State: 86:[83, 3], Operations: ['24-9=15', '45/15=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 44, 82, 84, 6 ]
45
[ "44*84=3696", "3696-6=3690", "3690/82=45" ]
Current State: 45:[44, 82, 84, 6], Operations: [] Exploring Operation: 44*84=3696, Resulting Numbers: [82, 6, 3696] Generated Node #2: [82, 6, 3696] from Operation: 44*84=3696 Current State: 45:[82, 6, 3696], Operations: ['44*84=3696'] Exploring Operation: 3696-6=3690, Resulting Numbers: [82, 3690] Generated Node #3: [82, 3690] from Operation: 3696-6=3690 Current State: 45:[82, 3690], Operations: ['44*84=3696', '3696-6=3690'] Exploring Operation: 3690/82=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[44, 82, 84, 6], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [44, 6, 2] Generated Node #0,0: 45:[44, 6, 2] Operation: 84-82=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[44, 6, 2], Operations: ['84-82=2'] Exploring Operation: 6/2=3, Resulting Numbers: [44, 3] Generated Node #0,0,0: 45:[44, 3] Operation: 6/2=3 Moving to Node #0,0,0 Current State: 45:[44, 3], Operations: ['84-82=2', '6/2=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,45 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
[ 29, 61, 3, 2 ]
45
[ "29+3=32", "32/2=16", "61-16=45" ]
Current State: 45:[29, 61, 3, 2], Operations: [] Exploring Operation: 29+3=32, Resulting Numbers: [61, 2, 32] Generated Node #2: [61, 2, 32] from Operation: 29+3=32 Current State: 45:[61, 2, 32], Operations: ['29+3=32'] Exploring Operation: 32/2=16, Resulting Numbers: [61, 16] Generated Node #3: [61, 16] from Operation: 32/2=16 Current State: 45:[61, 16], Operations: ['29+3=32', '32/2=16'] Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[29, 61, 3, 2], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [3, 2, 32] Generated Node #0,0: 45:[3, 2, 32] Operation: 61-29=32 Exploring Operation: 29-3=26, Resulting Numbers: [61, 2, 26] Generated Node #0,1: 45:[61, 2, 26] Operation: 29-3=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[3, 2, 32], Operations: ['61-29=32'] Exploring Operation: 3+32=35, Resulting Numbers: [2, 35] Generated Node #0,0,0: 45:[2, 35] Operation: 3+32=35 Exploring Operation: 32/2=16, Resulting Numbers: [3, 16] Generated Node #0,0,1: 45:[3, 16] Operation: 32/2=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[3, 16], Operations: ['61-29=32', '32/2=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,45 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[2, 35], Operations: ['61-29=32', '3+32=35'] Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,45 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[61, 2, 26], Operations: ['29-3=26'] Exploring Operation: 26/2=13, Resulting Numbers: [61, 13] Generated Node #0,1,0: 45:[61, 13] Operation: 26/2=13 Exploring Operation: 61-26=35, Resulting Numbers: [2, 35] Generated Node #0,1,1: 45:[2, 35] Operation: 61-26=35 Moving to Node #0,1,1 Current State: 45:[2, 35], Operations: ['29-3=26', '61-26=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,45 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[61, 13], Operations: ['29-3=26', '26/2=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,45 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 67, 12, 24, 89 ]
24
[ "67+24=91", "91-89=2", "12*2=24" ]
Current State: 24:[67, 12, 24, 89], Operations: [] Exploring Operation: 67+24=91, Resulting Numbers: [12, 89, 91] Generated Node #2: [12, 89, 91] from Operation: 67+24=91 Current State: 24:[12, 89, 91], Operations: ['67+24=91'] Exploring Operation: 91-89=2, Resulting Numbers: [12, 2] Generated Node #3: [12, 2] from Operation: 91-89=2 Current State: 24:[12, 2], Operations: ['67+24=91', '91-89=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[67, 12, 24, 89], Operations: [] Exploring Operation: 89-67=22, Resulting Numbers: [12, 24, 22] Generated Node #0,0: 24:[12, 24, 22] Operation: 89-67=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[12, 24, 22], Operations: ['89-67=22'] Exploring Operation: 24-22=2, Resulting Numbers: [12, 2] Generated Node #0,0,0: 24:[12, 2] Operation: 24-22=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[12, 2], Operations: ['89-67=22', '24-22=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[67, 12, 24, 89], Operations: [] Exploring Operation: 89-67=22, Resulting Numbers: [12, 24, 22] Generated Node #0,0: 24:[12, 24, 22] Operation: 89-67=22 Moving to Node #0,0 Current State: 24:[12, 24, 22], Operations: ['89-67=22'] Exploring Operation: 24-22=2, Resulting Numbers: [12, 2] Generated Node #0,0,0: 24:[12, 2] Operation: 24-22=2 Moving to Node #0,0,0 Current State: 24:[12, 2], Operations: ['89-67=22', '24-22=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 10, 43, 95, 54 ]
94
[ "10+43=53", "95-54=41", "53+41=94" ]
Current State: 94:[10, 43, 95, 54], Operations: [] Exploring Operation: 10+43=53, Resulting Numbers: [95, 54, 53] Generated Node #2: [95, 54, 53] from Operation: 10+43=53 Current State: 94:[95, 54, 53], Operations: ['10+43=53'] Exploring Operation: 95-54=41, Resulting Numbers: [53, 41] Generated Node #3: [53, 41] from Operation: 95-54=41 Current State: 94:[53, 41], Operations: ['10+43=53', '95-54=41'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[10, 43, 95, 54], Operations: [] Exploring Operation: 43+54=97, Resulting Numbers: [10, 95, 97] Generated Node #0,0: 94:[10, 95, 97] Operation: 43+54=97 Exploring Operation: 54-10=44, Resulting Numbers: [43, 95, 44] Generated Node #0,1: 94:[43, 95, 44] Operation: 54-10=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[43, 95, 44], Operations: ['54-10=44'] Exploring Operation: 44-43=1, Resulting Numbers: [95, 1] Generated Node #0,1,0: 94:[95, 1] Operation: 44-43=1 Exploring Operation: 95-43=52, Resulting Numbers: [44, 52] Generated Node #0,1,1: 94:[44, 52] Operation: 95-43=52 Moving to Node #0,1,0 Current State: 94:[95, 1], Operations: ['54-10=44', '44-43=1'] Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[10, 43, 95, 54], Operations: [] Exploring Operation: 54-10=44, Resulting Numbers: [43, 95, 44] Generated Node #0,1: 94:[43, 95, 44] Operation: 54-10=44 Moving to Node #0,1 Current State: 94:[43, 95, 44], Operations: ['54-10=44'] Exploring Operation: 44-43=1, Resulting Numbers: [95, 1] Generated Node #0,1,0: 94:[95, 1] Operation: 44-43=1 Moving to Node #0,1,0 Current State: 94:[95, 1], Operations: ['54-10=44', '44-43=1'] Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 50, 35, 33, 71 ]
96
[ "35-33=2", "50/2=25", "71+25=96" ]
Current State: 96:[50, 35, 33, 71], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [50, 71, 2] Generated Node #2: [50, 71, 2] from Operation: 35-33=2 Current State: 96:[50, 71, 2], Operations: ['35-33=2'] Exploring Operation: 50/2=25, Resulting Numbers: [71, 25] Generated Node #3: [71, 25] from Operation: 50/2=25 Current State: 96:[71, 25], Operations: ['35-33=2', '50/2=25'] Exploring Operation: 71+25=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[50, 35, 33, 71], Operations: [] Exploring Operation: 71-50=21, Resulting Numbers: [35, 33, 21] Generated Node #0,0: 96:[35, 33, 21] Operation: 71-50=21 Exploring Operation: 71-33=38, Resulting Numbers: [50, 35, 38] Generated Node #0,1: 96:[50, 35, 38] Operation: 71-33=38 Exploring Operation: 35+71=106, Resulting Numbers: [50, 33, 106] Generated Node #0,2: 96:[50, 33, 106] Operation: 35+71=106 Exploring Operation: 71-35=36, Resulting Numbers: [50, 33, 36] Generated Node #0,3: 96:[50, 33, 36] Operation: 71-35=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[35, 33, 21], Operations: ['71-50=21'] Exploring Operation: 33-21=12, Resulting Numbers: [35, 12] Generated Node #0,0,0: 96:[35, 12] Operation: 33-21=12 Exploring Operation: 35-21=14, Resulting Numbers: [33, 14] Generated Node #0,0,1: 96:[33, 14] Operation: 35-21=14 Exploring Operation: 35-33=2, Resulting Numbers: [21, 2] Generated Node #0,0,2: 96:[21, 2] Operation: 35-33=2 Exploring Operation: 35+21=56, Resulting Numbers: [33, 56] Generated Node #0,0,3: 96:[33, 56] Operation: 35+21=56 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[35, 12], Operations: ['71-50=21', '33-21=12'] Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,96 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[33, 14], Operations: ['71-50=21', '35-21=14'] Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,96 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[21, 2], Operations: ['71-50=21', '35-33=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 96:[33, 56], Operations: ['71-50=21', '35+21=56'] Exploring Operation: 33*56=1848, Resulting Numbers: [1848] 1848,96 unequal: No Solution Exploring Operation: 33+56=89, Resulting Numbers: [89] 89,96 unequal: No Solution Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[50, 33, 36], Operations: ['71-35=36'] Exploring Operation: 50-36=14, Resulting Numbers: [33, 14] Generated Node #0,3,0: 96:[33, 14] Operation: 50-36=14 Exploring Operation: 36-33=3, Resulting Numbers: [50, 3] Generated Node #0,3,1: 96:[50, 3] Operation: 36-33=3 Exploring Operation: 50-33=17, Resulting Numbers: [36, 17] Generated Node #0,3,2: 96:[36, 17] Operation: 50-33=17 Exploring Operation: 50+36=86, Resulting Numbers: [33, 86] Generated Node #0,3,3: 96:[33, 86] Operation: 50+36=86 Moving to Node #0,3,1 Current State: 96:[50, 3], Operations: ['71-35=36', '36-33=3'] Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,96 unequal: No Solution Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,96 unequal: No Solution Moving to Node #0,3,0 Current State: 96:[33, 14], Operations: ['71-35=36', '50-36=14'] Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,96 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,96 unequal: No Solution Moving to Node #0,3,2 Current State: 96:[36, 17], Operations: ['71-35=36', '50-33=17'] Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,96 unequal: No Solution Moving to Node #0,3,3 Current State: 96:[33, 86], Operations: ['71-35=36', '50+36=86'] Exploring Operation: 33+86=119, Resulting Numbers: [119] 119,96 unequal: No Solution Exploring Operation: 33*86=2838, Resulting Numbers: [2838] 2838,96 unequal: No Solution Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[50, 35, 38], Operations: ['71-33=38'] Exploring Operation: 50-38=12, Resulting Numbers: [35, 12] Generated Node #0,1,0: 96:[35, 12] Operation: 50-38=12 Exploring Operation: 38-35=3, Resulting Numbers: [50, 3] Generated Node #0,1,1: 96:[50, 3] Operation: 38-35=3 Exploring Operation: 50+38=88, Resulting Numbers: [35, 88] Generated Node #0,1,2: 96:[35, 88] Operation: 50+38=88 Exploring Operation: 50-35=15, Resulting Numbers: [38, 15] Generated Node #0,1,3: 96:[38, 15] Operation: 50-35=15 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[50, 3], Operations: ['71-33=38', '38-35=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,96 unequal: No Solution Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[35, 12], Operations: ['71-33=38', '50-38=12'] Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,96 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,96 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 #0,1,3 Current State: 96:[38, 15], Operations: ['71-33=38', '50-35=15'] Exploring Operation: 38*15=570, Resulting Numbers: [570] 570,96 unequal: No Solution Exploring Operation: 38+15=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,96 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 #0,1,2 Current State: 96:[35, 88], Operations: ['71-33=38', '50+38=88'] Exploring Operation: 88-35=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 35*88=3080, Resulting Numbers: [3080] 3080,96 unequal: No Solution Exploring Operation: 35+88=123, Resulting Numbers: [123] 123,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[50, 33, 106], Operations: ['35+71=106'] Exploring Operation: 50+33=83, Resulting Numbers: [106, 83] Generated Node #0,2,0: 96:[106, 83] Operation: 50+33=83 Exploring Operation: 50-33=17, Resulting Numbers: [106, 17] Generated Node #0,2,1: 96:[106, 17] Operation: 50-33=17 Exploring Operation: 106-50=56, Resulting Numbers: [33, 56] Generated Node #0,2,2: 96:[33, 56] Operation: 106-50=56 Exploring Operation: 106-33=73, Resulting Numbers: [50, 73] Generated Node #0,2,3: 96:[50, 73] Operation: 106-33=73 Moving to Node #0,2,2 Current State: 96:[33, 56], Operations: ['35+71=106', '106-50=56'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 33+56=89, Resulting Numbers: [89] 89,96 unequal: No Solution Exploring Operation: 33*56=1848, Resulting Numbers: [1848] 1848,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[106, 17], Operations: ['35+71=106', '50-33=17'] Exploring Operation: 106-17=89, Resulting Numbers: [89] 89,96 unequal: No Solution Exploring Operation: 106*17=1802, Resulting Numbers: [1802] 1802,96 unequal: No Solution Exploring Operation: 106+17=123, Resulting Numbers: [123] 123,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[106, 83], Operations: ['35+71=106', '50+33=83'] Exploring Operation: 106*83=8798, Resulting Numbers: [8798] 8798,96 unequal: No Solution Exploring Operation: 106-83=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 106+83=189, Resulting Numbers: [189] 189,96 unequal: No Solution Moving to Node #0,2,3 Current State: 96:[50, 73], Operations: ['35+71=106', '106-33=73'] Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,96 unequal: No Solution Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,96 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
[ 87, 5, 20, 37 ]
54
[ "87-37=50", "20/5=4", "50+4=54" ]
Current State: 54:[87, 5, 20, 37], Operations: [] Exploring Operation: 87-37=50, Resulting Numbers: [5, 20, 50] Generated Node #2: [5, 20, 50] from Operation: 87-37=50 Current State: 54:[5, 20, 50], Operations: ['87-37=50'] Exploring Operation: 20/5=4, Resulting Numbers: [50, 4] Generated Node #3: [50, 4] from Operation: 20/5=4 Current State: 54:[50, 4], Operations: ['87-37=50', '20/5=4'] Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[87, 5, 20, 37], Operations: [] Exploring Operation: 87-20=67, Resulting Numbers: [5, 37, 67] Generated Node #0,0: 54:[5, 37, 67] Operation: 87-20=67 Exploring Operation: 87-37=50, Resulting Numbers: [5, 20, 50] Generated Node #0,1: 54:[5, 20, 50] Operation: 87-37=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[5, 20, 50], Operations: ['87-37=50'] Exploring Operation: 50/5=10, Resulting Numbers: [20, 10] Generated Node #0,1,0: 54:[20, 10] Operation: 50/5=10 Exploring Operation: 5+50=55, Resulting Numbers: [20, 55] Generated Node #0,1,1: 54:[20, 55] Operation: 5+50=55 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[20, 10], Operations: ['87-37=50', '50/5=10'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 54:[20, 55], Operations: ['87-37=50', '5+50=55'] Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,54 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[5, 37, 67], Operations: ['87-20=67'] Exploring Operation: 67-37=30, Resulting Numbers: [5, 30] Generated Node #0,0,0: 54:[5, 30] Operation: 67-37=30 Exploring Operation: 37-5=32, Resulting Numbers: [67, 32] Generated Node #0,0,1: 54:[67, 32] Operation: 37-5=32 Moving to Node #0,0,0 Current State: 54:[5, 30], Operations: ['87-20=67', '67-37=30'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[67, 32], Operations: ['87-20=67', '37-5=32'] Exploring Operation: 67+32=99, Resulting Numbers: [99] 99,54 unequal: No Solution Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,54 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
[ 4, 9, 10, 5 ]
31
[ "4*9=36", "10-5=5", "36-5=31" ]
Current State: 31:[4, 9, 10, 5], Operations: [] Exploring Operation: 4*9=36, Resulting Numbers: [10, 5, 36] Generated Node #2: [10, 5, 36] from Operation: 4*9=36 Current State: 31:[10, 5, 36], Operations: ['4*9=36'] Exploring Operation: 10-5=5, Resulting Numbers: [36, 5] Generated Node #3: [36, 5] from Operation: 10-5=5 Current State: 31:[36, 5], Operations: ['4*9=36', '10-5=5'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[4, 9, 10, 5], Operations: [] Exploring Operation: 4*9=36, Resulting Numbers: [10, 5, 36] Generated Node #0,0: 31:[10, 5, 36] Operation: 4*9=36 Exploring Operation: 4*10=40, Resulting Numbers: [9, 5, 40] Generated Node #0,1: 31:[9, 5, 40] Operation: 4*10=40 Exploring Operation: 4*5=20, Resulting Numbers: [9, 10, 20] Generated Node #0,2: 31:[9, 10, 20] Operation: 4*5=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[10, 5, 36], Operations: ['4*9=36'] Exploring Operation: 36-5=31, Resulting Numbers: [10, 31] Generated Node #0,0,0: 31:[10, 31] Operation: 36-5=31 Exploring Operation: 10*5=50, Resulting Numbers: [36, 50] Generated Node #0,0,1: 31:[36, 50] Operation: 10*5=50 Exploring Operation: 10+5=15, Resulting Numbers: [36, 15] Generated Node #0,0,2: 31:[36, 15] Operation: 10+5=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[10, 31], Operations: ['4*9=36', '36-5=31'] Exploring Operation: 10+31=41, Resulting Numbers: [41] 41,31 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 10*31=310, Resulting Numbers: [310] 310,31 unequal: No Solution No 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: 31:[36, 15], Operations: ['4*9=36', '10+5=15'] Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 36*15=540, Resulting Numbers: [540] 540,31 unequal: No Solution Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,31 unequal: No Solution No 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: 31:[36, 50], Operations: ['4*9=36', '10*5=50'] Exploring Operation: 36+50=86, Resulting Numbers: [86] 86,31 unequal: No Solution Exploring Operation: 36*50=1800, Resulting Numbers: [1800] 1800,31 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,31 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: 31:[9, 10, 20], Operations: ['4*5=20'] Exploring Operation: 9+10=19, Resulting Numbers: [20, 19] Generated Node #0,2,0: 31:[20, 19] Operation: 9+10=19 Exploring Operation: 10+20=30, Resulting Numbers: [9, 30] Generated Node #0,2,1: 31:[9, 30] Operation: 10+20=30 Exploring Operation: 9+20=29, Resulting Numbers: [10, 29] Generated Node #0,2,2: 31:[10, 29] Operation: 9+20=29 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 31:[20, 19], Operations: ['4*5=20', '9+10=19'] Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,31 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,31 unequal: No Solution No 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: 31:[9, 30], Operations: ['4*5=20', '10+20=30'] Exploring Operation: 9*30=270, Resulting Numbers: [270] 270,31 unequal: No Solution Exploring Operation: 9+30=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,31 unequal: No Solution No 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: 31:[10, 29], Operations: ['4*5=20', '9+20=29'] Exploring Operation: 10*29=290, Resulting Numbers: [290] 290,31 unequal: No Solution Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,31 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: 31:[9, 5, 40], Operations: ['4*10=40'] Exploring Operation: 9+5=14, Resulting Numbers: [40, 14] Generated Node #0,1,0: 31:[40, 14] Operation: 9+5=14 Exploring Operation: 40-9=31, Resulting Numbers: [5, 31] Generated Node #0,1,1: 31:[5, 31] Operation: 40-9=31 Exploring Operation: 9*5=45, Resulting Numbers: [40, 45] Generated Node #0,1,2: 31:[40, 45] Operation: 9*5=45 Moving to Node #0,1,2 Current State: 31:[40, 45], Operations: ['4*10=40', '9*5=45'] Exploring Operation: 40*45=1800, Resulting Numbers: [1800] 1800,31 unequal: No Solution Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,31 unequal: No Solution Exploring Operation: 40+45=85, Resulting Numbers: [85] 85,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[40, 14], Operations: ['4*10=40', '9+5=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,31 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[5, 31], Operations: ['4*10=40', '40-9=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,31 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,31 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
[ 94, 38, 3, 11 ]
99
[ "94+38=132", "3*11=33", "132-33=99" ]
Current State: 99:[94, 38, 3, 11], Operations: [] Exploring Operation: 94+38=132, Resulting Numbers: [3, 11, 132] Generated Node #2: [3, 11, 132] from Operation: 94+38=132 Current State: 99:[3, 11, 132], Operations: ['94+38=132'] Exploring Operation: 3*11=33, Resulting Numbers: [132, 33] Generated Node #3: [132, 33] from Operation: 3*11=33 Current State: 99:[132, 33], Operations: ['94+38=132', '3*11=33'] Exploring Operation: 132-33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[94, 38, 3, 11], Operations: [] Exploring Operation: 3*11=33, Resulting Numbers: [94, 38, 33] Generated Node #0,0: 99:[94, 38, 33] Operation: 3*11=33 Exploring Operation: 94+11=105, Resulting Numbers: [38, 3, 105] Generated Node #0,1: 99:[38, 3, 105] Operation: 94+11=105 Exploring Operation: 38-3=35, Resulting Numbers: [94, 11, 35] Generated Node #0,2: 99:[94, 11, 35] Operation: 38-3=35 Exploring Operation: 94+3=97, Resulting Numbers: [38, 11, 97] Generated Node #0,3: 99:[38, 11, 97] Operation: 94+3=97 Moving to Node #0,2 Current State: 99:[94, 11, 35], Operations: ['38-3=35'] Exploring Operation: 11+35=46, Resulting Numbers: [94, 46] Generated Node #0,2,0: 99:[94, 46] Operation: 11+35=46 Exploring Operation: 94-11=83, Resulting Numbers: [35, 83] Generated Node #0,2,1: 99:[35, 83] Operation: 94-11=83 Exploring Operation: 35-11=24, Resulting Numbers: [94, 24] Generated Node #0,2,2: 99:[94, 24] Operation: 35-11=24 Exploring Operation: 94+11=105, Resulting Numbers: [35, 105] Generated Node #0,2,3: 99:[35, 105] Operation: 94+11=105 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 99:[35, 105], Operations: ['38-3=35', '94+11=105'] Exploring Operation: 105/35=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 35*105=3675, Resulting Numbers: [3675] 3675,99 unequal: No Solution Exploring Operation: 35+105=140, Resulting Numbers: [140] 140,99 unequal: No Solution Exploring Operation: 105-35=70, Resulting Numbers: [70] 70,99 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 #0,2,2 Current State: 99:[94, 24], Operations: ['38-3=35', '35-11=24'] Exploring Operation: 94*24=2256, Resulting Numbers: [2256] 2256,99 unequal: No Solution Exploring Operation: 94+24=118, Resulting Numbers: [118] 118,99 unequal: No Solution Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,99 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 #0,2,0 Current State: 99:[94, 46], Operations: ['38-3=35', '11+35=46'] Exploring Operation: 94*46=4324, Resulting Numbers: [4324] 4324,99 unequal: No Solution Exploring Operation: 94-46=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 94+46=140, Resulting Numbers: [140] 140,99 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 #0,2,1 Current State: 99:[35, 83], Operations: ['38-3=35', '94-11=83'] Exploring Operation: 35*83=2905, Resulting Numbers: [2905] 2905,99 unequal: No Solution Exploring Operation: 35+83=118, Resulting Numbers: [118] 118,99 unequal: No Solution Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,99 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: 99:[38, 11, 97], Operations: ['94+3=97'] Exploring Operation: 38+11=49, Resulting Numbers: [97, 49] Generated Node #0,3,0: 99:[97, 49] Operation: 38+11=49 Exploring Operation: 97-11=86, Resulting Numbers: [38, 86] Generated Node #0,3,1: 99:[38, 86] Operation: 97-11=86 Exploring Operation: 11+97=108, Resulting Numbers: [38, 108] Generated Node #0,3,2: 99:[38, 108] Operation: 11+97=108 Exploring Operation: 38-11=27, Resulting Numbers: [97, 27] Generated Node #0,3,3: 99:[97, 27] Operation: 38-11=27 Moving to Node #0,0 Current State: 99:[94, 38, 33], Operations: ['3*11=33'] Exploring Operation: 94+33=127, Resulting Numbers: [38, 127] Generated Node #0,0,0: 99:[38, 127] Operation: 94+33=127 Exploring Operation: 94-38=56, Resulting Numbers: [33, 56] Generated Node #0,0,1: 99:[33, 56] Operation: 94-38=56 Exploring Operation: 38-33=5, Resulting Numbers: [94, 5] Generated Node #0,0,2: 99:[94, 5] Operation: 38-33=5 Exploring Operation: 94+38=132, Resulting Numbers: [33, 132] Generated Node #0,0,3: 99:[33, 132] Operation: 94+38=132 Moving to Node #0,1 Current State: 99:[38, 3, 105], Operations: ['94+11=105'] Exploring Operation: 38+3=41, Resulting Numbers: [105, 41] Generated Node #0,1,0: 99:[105, 41] Operation: 38+3=41 Exploring Operation: 105/3=35, Resulting Numbers: [38, 35] Generated Node #0,1,1: 99:[38, 35] Operation: 105/3=35 Exploring Operation: 105-3=102, Resulting Numbers: [38, 102] Generated Node #0,1,2: 99:[38, 102] Operation: 105-3=102 Exploring Operation: 38-3=35, Resulting Numbers: [105, 35] Generated Node #0,1,3: 99:[105, 35] Operation: 38-3=35 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[38, 35], Operations: ['94+11=105', '105/3=35'] Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 38+35=73, Resulting Numbers: [73] 73,99 unequal: No Solution Exploring Operation: 38*35=1330, Resulting Numbers: [1330] 1330,99 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 #0,1,2 Current State: 99:[38, 102], Operations: ['94+11=105', '105-3=102'] Exploring Operation: 102-38=64, Resulting Numbers: [64] 64,99 unequal: No Solution Exploring Operation: 38*102=3876, Resulting Numbers: [3876] 3876,99 unequal: No Solution Exploring Operation: 38+102=140, Resulting Numbers: [140] 140,99 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 #0,1,3 Current State: 99:[105, 35], Operations: ['94+11=105', '38-3=35'] Exploring Operation: 105*35=3675, Resulting Numbers: [3675] 3675,99 unequal: No Solution Exploring Operation: 105+35=140, Resulting Numbers: [140] 140,99 unequal: No Solution Exploring Operation: 105/35=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 105-35=70, Resulting Numbers: [70] 70,99 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 #0,1,0 Current State: 99:[105, 41], Operations: ['94+11=105', '38+3=41'] Exploring Operation: 105-41=64, Resulting Numbers: [64] 64,99 unequal: No Solution Exploring Operation: 105+41=146, Resulting Numbers: [146] 146,99 unequal: No Solution Exploring Operation: 105*41=4305, Resulting Numbers: [4305] 4305,99 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: 99:[94, 5], Operations: ['3*11=33', '38-33=5'] Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,99 unequal: No Solution Exploring Operation: 94*5=470, Resulting Numbers: [470] 470,99 unequal: No Solution Exploring Operation: 94+5=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[94, 38, 3, 11], Operations: [] Exploring Operation: 3*11=33, Resulting Numbers: [94, 38, 33] Generated Node #0,0: 99:[94, 38, 33] Operation: 3*11=33 Moving to Node #0,0 Current State: 99:[94, 38, 33], Operations: ['3*11=33'] Exploring Operation: 38-33=5, Resulting Numbers: [94, 5] Generated Node #0,0,2: 99:[94, 5] Operation: 38-33=5 Moving to Node #0,0,2 Current State: 99:[94, 5], Operations: ['3*11=33', '38-33=5'] Exploring Operation: 94+5=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.953993
hs_4
sum_heuristic
[ 57, 55, 10, 63 ]
83
[ "57-55=2", "10*2=20", "63+20=83" ]
Current State: 83:[57, 55, 10, 63], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [10, 63, 2] Generated Node #2: [10, 63, 2] from Operation: 57-55=2 Current State: 83:[10, 63, 2], Operations: ['57-55=2'] Exploring Operation: 10*2=20, Resulting Numbers: [63, 20] Generated Node #3: [63, 20] from Operation: 10*2=20 Current State: 83:[63, 20], Operations: ['57-55=2', '10*2=20'] Exploring Operation: 63+20=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[57, 55, 10, 63], Operations: [] Exploring Operation: 55+10=65, Resulting Numbers: [57, 63, 65] Generated Node #0,0: 83:[57, 63, 65] Operation: 55+10=65 Exploring Operation: 57+10=67, Resulting Numbers: [55, 63, 67] Generated Node #0,1: 83:[55, 63, 67] Operation: 57+10=67 Exploring Operation: 10+63=73, Resulting Numbers: [57, 55, 73] Generated Node #0,2: 83:[57, 55, 73] Operation: 10+63=73 Moving to Node #0,0 Current State: 83:[57, 63, 65], Operations: ['55+10=65'] Exploring Operation: 63+65=128, Resulting Numbers: [57, 128] Generated Node #0,0,0: 83:[57, 128] Operation: 63+65=128 Exploring Operation: 57+63=120, Resulting Numbers: [65, 120] Generated Node #0,0,1: 83:[65, 120] Operation: 57+63=120 Exploring Operation: 57+65=122, Resulting Numbers: [63, 122] Generated Node #0,0,2: 83:[63, 122] Operation: 57+65=122 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[65, 120], Operations: ['55+10=65', '57+63=120'] Exploring Operation: 65*120=7800, Resulting Numbers: [7800] 7800,83 unequal: No Solution Exploring Operation: 120-65=55, Resulting Numbers: [55] 55,83 unequal: No Solution Exploring Operation: 65+120=185, Resulting Numbers: [185] 185,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[63, 122], Operations: ['55+10=65', '57+65=122'] Exploring Operation: 63+122=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 63*122=7686, Resulting Numbers: [7686] 7686,83 unequal: No Solution Exploring Operation: 122-63=59, Resulting Numbers: [59] 59,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[57, 128], Operations: ['55+10=65', '63+65=128'] Exploring Operation: 128-57=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 57+128=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 57*128=7296, Resulting Numbers: [7296] 7296,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[55, 63, 67], Operations: ['57+10=67'] Exploring Operation: 63+67=130, Resulting Numbers: [55, 130] Generated Node #0,1,0: 83:[55, 130] Operation: 63+67=130 Exploring Operation: 55+67=122, Resulting Numbers: [63, 122] Generated Node #0,1,1: 83:[63, 122] Operation: 55+67=122 Exploring Operation: 55+63=118, Resulting Numbers: [67, 118] Generated Node #0,1,2: 83:[67, 118] Operation: 55+63=118 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 83:[67, 118], Operations: ['57+10=67', '55+63=118'] Exploring Operation: 67+118=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 67*118=7906, Resulting Numbers: [7906] 7906,83 unequal: No Solution Exploring Operation: 118-67=51, Resulting Numbers: [51] 51,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[63, 122], Operations: ['57+10=67', '55+67=122'] Exploring Operation: 63+122=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 63*122=7686, Resulting Numbers: [7686] 7686,83 unequal: No Solution Exploring Operation: 122-63=59, Resulting Numbers: [59] 59,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[55, 130], Operations: ['57+10=67', '63+67=130'] Exploring Operation: 55*130=7150, Resulting Numbers: [7150] 7150,83 unequal: No Solution Exploring Operation: 55+130=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 130-55=75, Resulting Numbers: [75] 75,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 83:[57, 55, 73], Operations: ['10+63=73'] Exploring Operation: 55+73=128, Resulting Numbers: [57, 128] Generated Node #0,2,0: 83:[57, 128] Operation: 55+73=128 Exploring Operation: 57+73=130, Resulting Numbers: [55, 130] Generated Node #0,2,1: 83:[55, 130] Operation: 57+73=130 Exploring Operation: 57+55=112, Resulting Numbers: [73, 112] Generated Node #0,2,2: 83:[73, 112] Operation: 57+55=112 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[73, 112], Operations: ['10+63=73', '57+55=112'] Exploring Operation: 73+112=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 112-73=39, Resulting Numbers: [39] 39,83 unequal: No Solution Exploring Operation: 73*112=8176, Resulting Numbers: [8176] 8176,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[57, 128], Operations: ['10+63=73', '55+73=128'] Exploring Operation: 57+128=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 57*128=7296, Resulting Numbers: [7296] 7296,83 unequal: No Solution Exploring Operation: 128-57=71, Resulting Numbers: [71] 71,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[55, 130], Operations: ['10+63=73', '57+73=130'] Exploring Operation: 130-55=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 55+130=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 55*130=7150, Resulting Numbers: [7150] 7150,83 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
[ 1, 16, 41, 32 ]
81
[ "32/16=2", "41*2=82", "82-1=81" ]
Current State: 81:[1, 16, 41, 32], Operations: [] Exploring Operation: 32/16=2, Resulting Numbers: [1, 41, 2] Generated Node #2: [1, 41, 2] from Operation: 32/16=2 Current State: 81:[1, 41, 2], Operations: ['32/16=2'] Exploring Operation: 41*2=82, Resulting Numbers: [1, 82] Generated Node #3: [1, 82] from Operation: 41*2=82 Current State: 81:[1, 82], Operations: ['32/16=2', '41*2=82'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[1, 16, 41, 32], Operations: [] Exploring Operation: 41-16=25, Resulting Numbers: [1, 32, 25] Generated Node #0,0: 81:[1, 32, 25] Operation: 41-16=25 Exploring Operation: 41+32=73, Resulting Numbers: [1, 16, 73] Generated Node #0,1: 81:[1, 16, 73] Operation: 41+32=73 Exploring Operation: 32-16=16, Resulting Numbers: [1, 41, 16] Generated Node #0,2: 81:[1, 41, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [1, 41, 2] Generated Node #0,3: 81:[1, 41, 2] Operation: 32/16=2 Exploring Operation: 41-32=9, Resulting Numbers: [1, 16, 9] Generated Node #0,4: 81:[1, 16, 9] Operation: 41-32=9 Moving to Node #0,0 Current State: 81:[1, 32, 25], Operations: ['41-16=25'] Exploring Operation: 32-25=7, Resulting Numbers: [1, 7] Generated Node #0,0,0: 81:[1, 7] Operation: 32-25=7 Exploring Operation: 32/1=32, Resulting Numbers: [25, 32] Generated Node #0,0,1: 81:[25, 32] Operation: 32/1=32 Exploring Operation: 1*32=32, Resulting Numbers: [25, 32] Generated Node #0,0,2: 81:[25, 32] Operation: 1*32=32 Exploring Operation: 32-1=31, Resulting Numbers: [25, 31] Generated Node #0,0,3: 81:[25, 31] Operation: 32-1=31 Exploring Operation: 1+25=26, Resulting Numbers: [32, 26] Generated Node #0,0,4: 81:[32, 26] Operation: 1+25=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[1, 7], Operations: ['41-16=25', '32-25=7'] Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,81 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 81:[25, 31], Operations: ['41-16=25', '32-1=31'] Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,81 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,81 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 81:[32, 26], Operations: ['41-16=25', '1+25=26'] Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 32*26=832, Resulting Numbers: [832] 832,81 unequal: No Solution Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[25, 32], Operations: ['41-16=25', '32/1=32'] Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,81 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 81:[25, 32], Operations: ['41-16=25', '1*32=32'] Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,81 unequal: No Solution Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,81 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: 81:[1, 16, 9], Operations: ['41-32=9'] Exploring Operation: 1*16=16, Resulting Numbers: [9, 16] Generated Node #0,4,0: 81:[9, 16] Operation: 1*16=16 Exploring Operation: 16+9=25, Resulting Numbers: [1, 25] Generated Node #0,4,1: 81:[1, 25] Operation: 16+9=25 Exploring Operation: 16-1=15, Resulting Numbers: [9, 15] Generated Node #0,4,2: 81:[9, 15] Operation: 16-1=15 Exploring Operation: 16-9=7, Resulting Numbers: [1, 7] Generated Node #0,4,3: 81:[1, 7] Operation: 16-9=7 Exploring Operation: 16/1=16, Resulting Numbers: [9, 16] Generated Node #0,4,4: 81:[9, 16] Operation: 16/1=16 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 81:[1, 25], Operations: ['41-32=9', '16+9=25'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 1*25=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 81:[1, 7], Operations: ['41-32=9', '16-9=7'] Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,81 unequal: No Solution Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 81:[9, 15], Operations: ['41-32=9', '16-1=15'] Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,81 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 81:[9, 16], Operations: ['41-32=9', '1*16=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 81:[9, 16], Operations: ['41-32=9', '16/1=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,81 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: 81:[1, 16, 73], Operations: ['41+32=73'] Exploring Operation: 1*16=16, Resulting Numbers: [73, 16] Generated Node #0,1,0: 81:[73, 16] Operation: 1*16=16 Exploring Operation: 16/1=16, Resulting Numbers: [73, 16] Generated Node #0,1,1: 81:[73, 16] Operation: 16/1=16 Exploring Operation: 16+73=89, Resulting Numbers: [1, 89] Generated Node #0,1,2: 81:[1, 89] Operation: 16+73=89 Exploring Operation: 16-1=15, Resulting Numbers: [73, 15] Generated Node #0,1,3: 81:[73, 15] Operation: 16-1=15 Exploring Operation: 1+73=74, Resulting Numbers: [16, 74] Generated Node #0,1,4: 81:[16, 74] Operation: 1+73=74 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 81:[1, 89], Operations: ['41+32=73', '16+73=89'] Exploring Operation: 1*89=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 1+89=90, Resulting Numbers: [90] 90,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 81:[73, 15], Operations: ['41+32=73', '16-1=15'] Exploring Operation: 73*15=1095, Resulting Numbers: [1095] 1095,81 unequal: No Solution Exploring Operation: 73+15=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 81:[16, 74], Operations: ['41+32=73', '1+73=74'] Exploring Operation: 16+74=90, Resulting Numbers: [90] 90,81 unequal: No Solution Exploring Operation: 16*74=1184, Resulting Numbers: [1184] 1184,81 unequal: No Solution Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[73, 16], Operations: ['41+32=73', '1*16=16'] Exploring Operation: 73+16=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 73*16=1168, Resulting Numbers: [1168] 1168,81 unequal: No Solution Exploring Operation: 73-16=57, Resulting Numbers: [57] 57,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[73, 16], Operations: ['41+32=73', '16/1=16'] Exploring Operation: 73+16=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 73-16=57, Resulting Numbers: [57] 57,81 unequal: No Solution Exploring Operation: 73*16=1168, Resulting Numbers: [1168] 1168,81 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: 81:[1, 41, 2], Operations: ['32/16=2'] Exploring Operation: 41*2=82, Resulting Numbers: [1, 82] Generated Node #0,3,0: 81:[1, 82] Operation: 41*2=82 Exploring Operation: 41-1=40, Resulting Numbers: [2, 40] Generated Node #0,3,1: 81:[2, 40] Operation: 41-1=40 Exploring Operation: 41-2=39, Resulting Numbers: [1, 39] Generated Node #0,3,2: 81:[1, 39] Operation: 41-2=39 Exploring Operation: 1+2=3, Resulting Numbers: [41, 3] Generated Node #0,3,3: 81:[41, 3] Operation: 1+2=3 Exploring Operation: 1*41=41, Resulting Numbers: [2, 41] Generated Node #0,3,4: 81:[2, 41] Operation: 1*41=41 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 81:[1, 82], Operations: ['32/16=2', '41*2=82'] Exploring Operation: 1+82=83, Resulting Numbers: [83] 83,81 unequal: No Solution Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[1, 16, 41, 32], Operations: [] Exploring Operation: 32/16=2, Resulting Numbers: [1, 41, 2] Generated Node #0,3: 81:[1, 41, 2] Operation: 32/16=2 Moving to Node #0,3 Current State: 81:[1, 41, 2], Operations: ['32/16=2'] Exploring Operation: 41*2=82, Resulting Numbers: [1, 82] Generated Node #0,3,0: 81:[1, 82] Operation: 41*2=82 Moving to Node #0,3,0 Current State: 81:[1, 82], Operations: ['32/16=2', '41*2=82'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.930556
hs_5
mult_heuristic
[ 36, 34, 78, 76 ]
80
[ "36-34=2", "78*2=156", "156-76=80" ]
Current State: 80:[36, 34, 78, 76], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [78, 76, 2] Generated Node #2: [78, 76, 2] from Operation: 36-34=2 Current State: 80:[78, 76, 2], Operations: ['36-34=2'] Exploring Operation: 78*2=156, Resulting Numbers: [76, 156] Generated Node #3: [76, 156] from Operation: 78*2=156 Current State: 80:[76, 156], Operations: ['36-34=2', '78*2=156'] Exploring Operation: 156-76=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[36, 34, 78, 76], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [78, 76, 2] Generated Node #0,0: 80:[78, 76, 2] Operation: 36-34=2 Exploring Operation: 76-36=40, Resulting Numbers: [34, 78, 40] Generated Node #0,1: 80:[34, 78, 40] Operation: 76-36=40 Exploring Operation: 76-34=42, Resulting Numbers: [36, 78, 42] Generated Node #0,2: 80:[36, 78, 42] Operation: 76-34=42 Moving to Node #0,0 Current State: 80:[78, 76, 2], Operations: ['36-34=2'] Exploring Operation: 78+2=80, Resulting Numbers: [76, 80] Generated Node #0,0,0: 80:[76, 80] Operation: 78+2=80 Exploring Operation: 76+2=78, Resulting Numbers: [78, 78] Generated Node #0,0,1: 80:[78, 78] Operation: 76+2=78 Exploring Operation: 78-76=2, Resulting Numbers: [2, 2] Generated Node #0,0,2: 80:[2, 2] Operation: 78-76=2 Moving to Node #0,1 Current State: 80:[34, 78, 40], Operations: ['76-36=40'] Exploring Operation: 78-34=44, Resulting Numbers: [40, 44] Generated Node #0,1,0: 80:[40, 44] Operation: 78-34=44 Exploring Operation: 40-34=6, Resulting Numbers: [78, 6] Generated Node #0,1,1: 80:[78, 6] Operation: 40-34=6 Exploring Operation: 34+40=74, Resulting Numbers: [78, 74] Generated Node #0,1,2: 80:[78, 74] Operation: 34+40=74 Moving to Node #0,2 Current State: 80:[36, 78, 42], Operations: ['76-34=42'] Exploring Operation: 42-36=6, Resulting Numbers: [78, 6] Generated Node #0,2,0: 80:[78, 6] Operation: 42-36=6 Exploring Operation: 36+42=78, Resulting Numbers: [78, 78] Generated Node #0,2,1: 80:[78, 78] Operation: 36+42=78 Exploring Operation: 78-36=42, Resulting Numbers: [42, 42] Generated Node #0,2,2: 80:[42, 42] Operation: 78-36=42 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[78, 6], Operations: ['76-34=42', '42-36=6'] Exploring Operation: 78/6=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 78+6=84, Resulting Numbers: [84] 84,80 unequal: No Solution Exploring Operation: 78-6=72, Resulting Numbers: [72] 72,80 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:[78, 78], Operations: ['76-34=42', '36+42=78'] Exploring Operation: 78-78=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 78/78=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 78+78=156, Resulting Numbers: [156] 156,80 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:[42, 42], Operations: ['76-34=42', '78-36=42'] Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,80 unequal: No Solution Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,80 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: 80:[2, 2], Operations: ['36-34=2', '78-76=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[78, 6], Operations: ['76-36=40', '40-34=6'] Exploring Operation: 78-6=72, Resulting Numbers: [72] 72,80 unequal: No Solution Exploring Operation: 78+6=84, Resulting Numbers: [84] 84,80 unequal: No Solution Exploring Operation: 78/6=13, Resulting Numbers: [13] 13,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[78, 78], Operations: ['36-34=2', '76+2=78'] Exploring Operation: 78-78=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 78/78=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 78+78=156, Resulting Numbers: [156] 156,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[40, 44], Operations: ['76-36=40', '78-34=44'] Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,80 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[76, 80], Operations: ['36-34=2', '78+2=80'] Exploring Operation: 76+80=156, Resulting Numbers: [156] 156,80 unequal: No Solution Exploring Operation: 80-76=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 76*80=6080, Resulting Numbers: [6080] 6080,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[78, 74], Operations: ['76-36=40', '34+40=74'] Exploring Operation: 78*74=5772, Resulting Numbers: [5772] 5772,80 unequal: No Solution Exploring Operation: 78+74=152, Resulting Numbers: [152] 152,80 unequal: No Solution Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,80 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 35, 5, 85, 40 ]
11
[ "5*85=425", "425-40=385", "385/35=11" ]
Current State: 11:[35, 5, 85, 40], Operations: [] Exploring Operation: 5*85=425, Resulting Numbers: [35, 40, 425] Generated Node #2: [35, 40, 425] from Operation: 5*85=425 Current State: 11:[35, 40, 425], Operations: ['5*85=425'] Exploring Operation: 425-40=385, Resulting Numbers: [35, 385] Generated Node #3: [35, 385] from Operation: 425-40=385 Current State: 11:[35, 385], Operations: ['5*85=425', '425-40=385'] Exploring Operation: 385/35=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[35, 5, 85, 40], Operations: [] Exploring Operation: 85-35=50, Resulting Numbers: [5, 40, 50] Generated Node #0,0: 11:[5, 40, 50] Operation: 85-35=50 Exploring Operation: 40/5=8, Resulting Numbers: [35, 85, 8] Generated Node #0,1: 11:[35, 85, 8] Operation: 40/5=8 Exploring Operation: 85/5=17, Resulting Numbers: [35, 40, 17] Generated Node #0,2: 11:[35, 40, 17] Operation: 85/5=17 Exploring Operation: 40-35=5, Resulting Numbers: [5, 85, 5] Generated Node #0,3: 11:[5, 85, 5] Operation: 40-35=5 Exploring Operation: 85-40=45, Resulting Numbers: [35, 5, 45] Generated Node #0,4: 11:[35, 5, 45] Operation: 85-40=45 Start Sub Search at level 1: Moving to Node #0,2 Current State: 11:[35, 40, 17], Operations: ['85/5=17'] Exploring Operation: 35+17=52, Resulting Numbers: [40, 52] Generated Node #0,2,0: 11:[40, 52] Operation: 35+17=52 Exploring Operation: 35-17=18, Resulting Numbers: [40, 18] Generated Node #0,2,1: 11:[40, 18] Operation: 35-17=18 Exploring Operation: 40-35=5, Resulting Numbers: [17, 5] Generated Node #0,2,2: 11:[17, 5] Operation: 40-35=5 Exploring Operation: 40-17=23, Resulting Numbers: [35, 23] Generated Node #0,2,3: 11:[35, 23] Operation: 40-17=23 Exploring Operation: 35+40=75, Resulting Numbers: [17, 75] Generated Node #0,2,4: 11:[17, 75] Operation: 35+40=75 Moving to Node #0,2,2 Current State: 11:[17, 5], Operations: ['85/5=17', '40-35=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,11 unequal: No Solution Moving to Node #0,2,3 Current State: 11:[35, 23], Operations: ['85/5=17', '40-17=23'] Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,11 unequal: No Solution Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[40, 18], Operations: ['85/5=17', '35-17=18'] Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,11 unequal: No Solution Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,11 unequal: No Solution Moving to Node #0,2,0 Current State: 11:[40, 52], Operations: ['85/5=17', '35+17=52'] Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,11 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,11 unequal: No Solution Moving to Node #0,2,4 Current State: 11:[17, 75], Operations: ['85/5=17', '35+40=75'] Exploring Operation: 17*75=1275, Resulting Numbers: [1275] 1275,11 unequal: No Solution Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 17+75=92, Resulting Numbers: [92] 92,11 unequal: No Solution No 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: 11:[35, 5, 45], Operations: ['85-40=45'] Exploring Operation: 35-5=30, Resulting Numbers: [45, 30] Generated Node #0,4,0: 11:[45, 30] Operation: 35-5=30 Exploring Operation: 35/5=7, Resulting Numbers: [45, 7] Generated Node #0,4,1: 11:[45, 7] Operation: 35/5=7 Exploring Operation: 45-35=10, Resulting Numbers: [5, 10] Generated Node #0,4,2: 11:[5, 10] Operation: 45-35=10 Exploring Operation: 45/5=9, Resulting Numbers: [35, 9] Generated Node #0,4,3: 11:[35, 9] Operation: 45/5=9 Exploring Operation: 45-5=40, Resulting Numbers: [35, 40] Generated Node #0,4,4: 11:[35, 40] Operation: 45-5=40 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 11:[5, 10], Operations: ['85-40=45', '45-35=10'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 11:[35, 9], Operations: ['85-40=45', '45/5=9'] Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,11 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 11:[45, 7], Operations: ['85-40=45', '35/5=7'] Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 45*7=315, Resulting Numbers: [315] 315,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 11:[45, 30], Operations: ['85-40=45', '35-5=30'] Exploring Operation: 45-30=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 45+30=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 45*30=1350, Resulting Numbers: [1350] 1350,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 11:[35, 40], Operations: ['85-40=45', '45-5=40'] Exploring Operation: 35*40=1400, Resulting Numbers: [1400] 1400,11 unequal: No Solution Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 35+40=75, Resulting Numbers: [75] 75,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[5, 40, 50], Operations: ['85-35=50'] Exploring Operation: 50-40=10, Resulting Numbers: [5, 10] Generated Node #0,0,0: 11:[5, 10] Operation: 50-40=10 Exploring Operation: 40-5=35, Resulting Numbers: [50, 35] Generated Node #0,0,1: 11:[50, 35] Operation: 40-5=35 Exploring Operation: 50-5=45, Resulting Numbers: [40, 45] Generated Node #0,0,2: 11:[40, 45] Operation: 50-5=45 Exploring Operation: 50/5=10, Resulting Numbers: [40, 10] Generated Node #0,0,3: 11:[40, 10] Operation: 50/5=10 Exploring Operation: 40/5=8, Resulting Numbers: [50, 8] Generated Node #0,0,4: 11:[50, 8] Operation: 40/5=8 Moving to Node #0,0,0 Current State: 11:[5, 10], Operations: ['85-35=50', '50-40=10'] Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[40, 10], Operations: ['85-35=50', '50/5=10'] Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,11 unequal: No Solution Moving to Node #0,0,4 Current State: 11:[50, 8], Operations: ['85-35=50', '40/5=8'] Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 50*8=400, Resulting Numbers: [400] 400,11 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[50, 35], Operations: ['85-35=50', '40-5=35'] Exploring Operation: 50+35=85, Resulting Numbers: [85] 85,11 unequal: No Solution Exploring Operation: 50*35=1750, Resulting Numbers: [1750] 1750,11 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[40, 45], Operations: ['85-35=50', '50-5=45'] Exploring Operation: 40*45=1800, Resulting Numbers: [1800] 1800,11 unequal: No Solution Exploring Operation: 40+45=85, Resulting Numbers: [85] 85,11 unequal: No Solution Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 11:[5, 85, 5], Operations: ['40-35=5'] Exploring Operation: 85/5=17, Resulting Numbers: [5, 17] Generated Node #0,3,0: 11:[5, 17] Operation: 85/5=17 Exploring Operation: 85/5=17, Resulting Numbers: [5, 17] Generated Node #0,3,1: 11:[5, 17] Operation: 85/5=17 Exploring Operation: 5+5=10, Resulting Numbers: [85, 10] Generated Node #0,3,2: 11:[85, 10] Operation: 5+5=10 Exploring Operation: 85-5=80, Resulting Numbers: [5, 80] Generated Node #0,3,3: 11:[5, 80] Operation: 85-5=80 Exploring Operation: 85-5=80, Resulting Numbers: [5, 80] Generated Node #0,3,4: 11:[5, 80] Operation: 85-5=80 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 11:[5, 17], Operations: ['40-35=5', '85/5=17'] Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,11 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 11:[5, 17], Operations: ['40-35=5', '85/5=17'] Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 11:[85, 10], Operations: ['40-35=5', '5+5=10'] Exploring Operation: 85-10=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 85*10=850, Resulting Numbers: [850] 850,11 unequal: No Solution Exploring Operation: 85+10=95, Resulting Numbers: [95] 95,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 11:[5, 80], Operations: ['40-35=5', '85-5=80'] Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,11 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,11 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,11 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 11:[5, 80], Operations: ['40-35=5', '85-5=80'] Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,11 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,11 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[35, 85, 8], Operations: ['40/5=8'] Exploring Operation: 85-35=50, Resulting Numbers: [8, 50] Generated Node #0,1,0: 11:[8, 50] Operation: 85-35=50 Exploring Operation: 85+8=93, Resulting Numbers: [35, 93] Generated Node #0,1,1: 11:[35, 93] Operation: 85+8=93 Exploring Operation: 35-8=27, Resulting Numbers: [85, 27] Generated Node #0,1,2: 11:[85, 27] Operation: 35-8=27 Exploring Operation: 85-8=77, Resulting Numbers: [35, 77] Generated Node #0,1,3: 11:[35, 77] Operation: 85-8=77 Exploring Operation: 35+8=43, Resulting Numbers: [85, 43] Generated Node #0,1,4: 11:[85, 43] Operation: 35+8=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[8, 50], Operations: ['40/5=8', '85-35=50'] Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,11 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 11:[85, 27], Operations: ['40/5=8', '35-8=27'] Exploring Operation: 85*27=2295, Resulting Numbers: [2295] 2295,11 unequal: No Solution Exploring Operation: 85-27=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 85+27=112, Resulting Numbers: [112] 112,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 11:[35, 77], Operations: ['40/5=8', '85-8=77'] Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 35+77=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 35*77=2695, Resulting Numbers: [2695] 2695,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 11:[35, 93], Operations: ['40/5=8', '85+8=93'] Exploring Operation: 93-35=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 35*93=3255, Resulting Numbers: [3255] 3255,11 unequal: No Solution Exploring Operation: 35+93=128, Resulting Numbers: [128] 128,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 11:[85, 43], Operations: ['40/5=8', '35+8=43'] Exploring Operation: 85*43=3655, Resulting Numbers: [3655] 3655,11 unequal: No Solution Exploring Operation: 85+43=128, Resulting Numbers: [128] 128,11 unequal: No Solution Exploring Operation: 85-43=42, Resulting Numbers: [42] 42,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 65, 17, 91, 34 ]
43
[ "65+17=82", "91+34=125", "125-82=43" ]
Current State: 43:[65, 17, 91, 34], Operations: [] Exploring Operation: 65+17=82, Resulting Numbers: [91, 34, 82] Generated Node #2: [91, 34, 82] from Operation: 65+17=82 Current State: 43:[91, 34, 82], Operations: ['65+17=82'] Exploring Operation: 91+34=125, Resulting Numbers: [82, 125] Generated Node #3: [82, 125] from Operation: 91+34=125 Current State: 43:[82, 125], Operations: ['65+17=82', '91+34=125'] Exploring Operation: 125-82=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[65, 17, 91, 34], Operations: [] Exploring Operation: 91-65=26, Resulting Numbers: [17, 34, 26] Generated Node #0,0: 43:[17, 34, 26] Operation: 91-65=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[17, 34, 26], Operations: ['91-65=26'] Exploring Operation: 17+26=43, Resulting Numbers: [34, 43] Generated Node #0,0,0: 43:[34, 43] Operation: 17+26=43 Moving to Node #0,0,0 Current State: 43:[34, 43], Operations: ['91-65=26', '17+26=43'] Exploring Operation: 34+43=77, Resulting Numbers: [77] 77,43 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
[ 8, 91, 4, 77 ]
16
[ "8/4=2", "91-77=14", "2+14=16" ]
Current State: 16:[8, 91, 4, 77], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [91, 77, 2] Generated Node #2: [91, 77, 2] from Operation: 8/4=2 Current State: 16:[91, 77, 2], Operations: ['8/4=2'] Exploring Operation: 91-77=14, Resulting Numbers: [2, 14] Generated Node #3: [2, 14] from Operation: 91-77=14 Current State: 16:[2, 14], Operations: ['8/4=2', '91-77=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[8, 91, 4, 77], Operations: [] Exploring Operation: 91-8=83, Resulting Numbers: [4, 77, 83] Generated Node #0,0: 16:[4, 77, 83] Operation: 91-8=83 Exploring Operation: 91-77=14, Resulting Numbers: [8, 4, 14] Generated Node #0,1: 16:[8, 4, 14] Operation: 91-77=14 Moving to Node #0,1 Current State: 16:[8, 4, 14], Operations: ['91-77=14'] Exploring Operation: 8/4=2, Resulting Numbers: [14, 2] Generated Node #0,1,0: 16:[14, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [14, 4] Generated Node #0,1,1: 16:[14, 4] Operation: 8-4=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[14, 2], Operations: ['91-77=14', '8/4=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[8, 91, 4, 77], Operations: [] Exploring Operation: 91-77=14, Resulting Numbers: [8, 4, 14] Generated Node #0,1: 16:[8, 4, 14] Operation: 91-77=14 Moving to Node #0,1 Current State: 16:[8, 4, 14], Operations: ['91-77=14'] Exploring Operation: 8/4=2, Resulting Numbers: [14, 2] Generated Node #0,1,0: 16:[14, 2] Operation: 8/4=2 Moving to Node #0,1,0 Current State: 16:[14, 2], Operations: ['91-77=14', '8/4=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 82, 83, 25, 39 ]
13
[ "83-82=1", "39-25=14", "14-1=13" ]
Current State: 13:[82, 83, 25, 39], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [25, 39, 1] Generated Node #2: [25, 39, 1] from Operation: 83-82=1 Current State: 13:[25, 39, 1], Operations: ['83-82=1'] Exploring Operation: 39-25=14, Resulting Numbers: [1, 14] Generated Node #3: [1, 14] from Operation: 39-25=14 Current State: 13:[1, 14], Operations: ['83-82=1', '39-25=14'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[82, 83, 25, 39], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [25, 39, 1] Generated Node #0,0: 13:[25, 39, 1] Operation: 83-82=1 Exploring Operation: 82-39=43, Resulting Numbers: [83, 25, 43] Generated Node #0,1: 13:[83, 25, 43] Operation: 82-39=43 Moving to Node #0,0 Current State: 13:[25, 39, 1], Operations: ['83-82=1'] Exploring Operation: 39-25=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 13:[1, 14] Operation: 39-25=14 Exploring Operation: 25-1=24, Resulting Numbers: [39, 24] Generated Node #0,0,1: 13:[39, 24] Operation: 25-1=24 Moving to Node #0,1 Current State: 13:[83, 25, 43], Operations: ['82-39=43'] Exploring Operation: 83-43=40, Resulting Numbers: [25, 40] Generated Node #0,1,0: 13:[25, 40] Operation: 83-43=40 Exploring Operation: 83-25=58, Resulting Numbers: [43, 58] Generated Node #0,1,1: 13:[43, 58] Operation: 83-25=58 Moving to Node #0,0,0 Current State: 13:[1, 14], Operations: ['83-82=1', '39-25=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[82, 83, 25, 39], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [25, 39, 1] Generated Node #0,0: 13:[25, 39, 1] Operation: 83-82=1 Moving to Node #0,0 Current State: 13:[25, 39, 1], Operations: ['83-82=1'] Exploring Operation: 39-25=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 13:[1, 14] Operation: 39-25=14 Moving to Node #0,0,0 Current State: 13:[1, 14], Operations: ['83-82=1', '39-25=14'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 17, 51, 63, 39 ]
50
[ "51/17=3", "39/3=13", "63-13=50" ]
Current State: 50:[17, 51, 63, 39], Operations: [] Exploring Operation: 51/17=3, Resulting Numbers: [63, 39, 3] Generated Node #2: [63, 39, 3] from Operation: 51/17=3 Current State: 50:[63, 39, 3], Operations: ['51/17=3'] Exploring Operation: 39/3=13, Resulting Numbers: [63, 13] Generated Node #3: [63, 13] from Operation: 39/3=13 Current State: 50:[63, 13], Operations: ['51/17=3', '39/3=13'] Exploring Operation: 63-13=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[17, 51, 63, 39], Operations: [] Exploring Operation: 63-39=24, Resulting Numbers: [17, 51, 24] Generated Node #0,0: 50:[17, 51, 24] Operation: 63-39=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[17, 51, 24], Operations: ['63-39=24'] Exploring Operation: 51/17=3, Resulting Numbers: [24, 3] Generated Node #0,0,0: 50:[24, 3] Operation: 51/17=3 Moving to Node #0,0,0 Current State: 50:[24, 3], Operations: ['63-39=24', '51/17=3'] Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,50 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
[ 51, 95, 22, 68 ]
19
[ "51+22=73", "73-68=5", "95/5=19" ]
Current State: 19:[51, 95, 22, 68], Operations: [] Exploring Operation: 51+22=73, Resulting Numbers: [95, 68, 73] Generated Node #2: [95, 68, 73] from Operation: 51+22=73 Current State: 19:[95, 68, 73], Operations: ['51+22=73'] Exploring Operation: 73-68=5, Resulting Numbers: [95, 5] Generated Node #3: [95, 5] from Operation: 73-68=5 Current State: 19:[95, 5], Operations: ['51+22=73', '73-68=5'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[51, 95, 22, 68], Operations: [] Exploring Operation: 95-51=44, Resulting Numbers: [22, 68, 44] Generated Node #0,0: 19:[22, 68, 44] Operation: 95-51=44 Exploring Operation: 68-51=17, Resulting Numbers: [95, 22, 17] Generated Node #0,1: 19:[95, 22, 17] Operation: 68-51=17 Exploring Operation: 95-68=27, Resulting Numbers: [51, 22, 27] Generated Node #0,2: 19:[51, 22, 27] Operation: 95-68=27 Moving to Node #0,2 Current State: 19:[51, 22, 27], Operations: ['95-68=27'] Exploring Operation: 51-22=29, Resulting Numbers: [27, 29] Generated Node #0,2,0: 19:[27, 29] Operation: 51-22=29 Exploring Operation: 27-22=5, Resulting Numbers: [51, 5] Generated Node #0,2,1: 19:[51, 5] Operation: 27-22=5 Exploring Operation: 51-27=24, Resulting Numbers: [22, 24] Generated Node #0,2,2: 19:[22, 24] Operation: 51-27=24 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 19:[22, 24], Operations: ['95-68=27', '51-27=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,19 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 19:[27, 29], Operations: ['95-68=27', '51-22=29'] Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,19 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 19:[51, 5], Operations: ['95-68=27', '27-22=5'] Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,19 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,19 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: 19:[22, 68, 44], Operations: ['95-51=44'] Exploring Operation: 68-44=24, Resulting Numbers: [22, 24] Generated Node #0,0,0: 19:[22, 24] Operation: 68-44=24 Exploring Operation: 68-22=46, Resulting Numbers: [44, 46] Generated Node #0,0,1: 19:[44, 46] Operation: 68-22=46 Exploring Operation: 44-22=22, Resulting Numbers: [68, 22] Generated Node #0,0,2: 19:[68, 22] Operation: 44-22=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[22, 24], Operations: ['95-51=44', '68-44=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,19 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 19:[44, 46], Operations: ['95-51=44', '68-22=46'] Exploring Operation: 44+46=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 46-44=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 44*46=2024, Resulting Numbers: [2024] 2024,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 19:[68, 22], Operations: ['95-51=44', '44-22=22'] Exploring Operation: 68+22=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 68*22=1496, Resulting Numbers: [1496] 1496,19 unequal: No Solution Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,19 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: 19:[95, 22, 17], Operations: ['68-51=17'] Exploring Operation: 95-22=73, Resulting Numbers: [17, 73] Generated Node #0,1,0: 19:[17, 73] Operation: 95-22=73 Exploring Operation: 22-17=5, Resulting Numbers: [95, 5] Generated Node #0,1,1: 19:[95, 5] Operation: 22-17=5 Exploring Operation: 95-17=78, Resulting Numbers: [22, 78] Generated Node #0,1,2: 19:[22, 78] Operation: 95-17=78 Moving to Node #0,1,0 Current State: 19:[17, 73], Operations: ['68-51=17', '95-22=73'] Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 17+73=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 17*73=1241, Resulting Numbers: [1241] 1241,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[22, 78], Operations: ['68-51=17', '95-17=78'] Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 22*78=1716, Resulting Numbers: [1716] 1716,19 unequal: No Solution Exploring Operation: 22+78=100, Resulting Numbers: [100] 100,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[95, 5], Operations: ['68-51=17', '22-17=5'] Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[51, 95, 22, 68], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [95, 22, 17] Generated Node #0,1: 19:[95, 22, 17] Operation: 68-51=17 Moving to Node #0,1 Current State: 19:[95, 22, 17], Operations: ['68-51=17'] Exploring Operation: 22-17=5, Resulting Numbers: [95, 5] Generated Node #0,1,1: 19:[95, 5] Operation: 22-17=5 Moving to Node #0,1,1 Current State: 19:[95, 5], Operations: ['68-51=17', '22-17=5'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.963542
hs_3
mult_heuristic
[ 56, 36, 24, 20 ]
26
[ "36*20=720", "720/24=30", "56-30=26" ]
Current State: 26:[56, 36, 24, 20], Operations: [] Exploring Operation: 36*20=720, Resulting Numbers: [56, 24, 720] Generated Node #2: [56, 24, 720] from Operation: 36*20=720 Current State: 26:[56, 24, 720], Operations: ['36*20=720'] Exploring Operation: 720/24=30, Resulting Numbers: [56, 30] Generated Node #3: [56, 30] from Operation: 720/24=30 Current State: 26:[56, 30], Operations: ['36*20=720', '720/24=30'] Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[56, 36, 24, 20], Operations: [] Exploring Operation: 56-36=20, Resulting Numbers: [24, 20, 20] Generated Node #0,0: 26:[24, 20, 20] Operation: 56-36=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[24, 20, 20], Operations: ['56-36=20'] Exploring Operation: 20/20=1, Resulting Numbers: [24, 1] Generated Node #0,0,0: 26:[24, 1] Operation: 20/20=1 Moving to Node #0,0,0 Current State: 26:[24, 1], Operations: ['56-36=20', '20/20=1'] Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 2, 36, 70, 44 ]
74
[ "44-36=8", "8/2=4", "70+4=74" ]
Current State: 74:[2, 36, 70, 44], Operations: [] Exploring Operation: 44-36=8, Resulting Numbers: [2, 70, 8] Generated Node #2: [2, 70, 8] from Operation: 44-36=8 Current State: 74:[2, 70, 8], Operations: ['44-36=8'] Exploring Operation: 8/2=4, Resulting Numbers: [70, 4] Generated Node #3: [70, 4] from Operation: 8/2=4 Current State: 74:[70, 4], Operations: ['44-36=8', '8/2=4'] Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[2, 36, 70, 44], Operations: [] Exploring Operation: 44-2=42, Resulting Numbers: [36, 70, 42] Generated Node #0,0: 74:[36, 70, 42] Operation: 44-2=42 Exploring Operation: 2+70=72, Resulting Numbers: [36, 44, 72] Generated Node #0,1: 74:[36, 44, 72] Operation: 2+70=72 Exploring Operation: 70/2=35, Resulting Numbers: [36, 44, 35] Generated Node #0,2: 74:[36, 44, 35] Operation: 70/2=35 Moving to Node #0,0 Current State: 74:[36, 70, 42], Operations: ['44-2=42'] Exploring Operation: 42-36=6, Resulting Numbers: [70, 6] Generated Node #0,0,0: 74:[70, 6] Operation: 42-36=6 Exploring Operation: 70-36=34, Resulting Numbers: [42, 34] Generated Node #0,0,1: 74:[42, 34] Operation: 70-36=34 Exploring Operation: 36+42=78, Resulting Numbers: [70, 78] Generated Node #0,0,2: 74:[70, 78] Operation: 36+42=78 Moving to Node #0,1 Current State: 74:[36, 44, 72], Operations: ['2+70=72'] Exploring Operation: 44-36=8, Resulting Numbers: [72, 8] Generated Node #0,1,0: 74:[72, 8] Operation: 44-36=8 Exploring Operation: 72/36=2, Resulting Numbers: [44, 2] Generated Node #0,1,1: 74:[44, 2] Operation: 72/36=2 Exploring Operation: 36+44=80, Resulting Numbers: [72, 80] Generated Node #0,1,2: 74:[72, 80] Operation: 36+44=80 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 74:[44, 2], Operations: ['2+70=72', '72/36=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,74 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,74 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 #0,1,0 Current State: 74:[72, 8], Operations: ['2+70=72', '44-36=8'] Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,74 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,74 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:[72, 80], Operations: ['2+70=72', '36+44=80'] Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 72+80=152, Resulting Numbers: [152] 152,74 unequal: No Solution Exploring Operation: 72*80=5760, Resulting Numbers: [5760] 5760,74 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: 74:[36, 44, 35], Operations: ['70/2=35'] Exploring Operation: 44+35=79, Resulting Numbers: [36, 79] Generated Node #0,2,0: 74:[36, 79] Operation: 44+35=79 Exploring Operation: 36+44=80, Resulting Numbers: [35, 80] Generated Node #0,2,1: 74:[35, 80] Operation: 36+44=80 Exploring Operation: 44-36=8, Resulting Numbers: [35, 8] Generated Node #0,2,2: 74:[35, 8] Operation: 44-36=8 Moving to Node #0,2,0 Current State: 74:[36, 79], Operations: ['70/2=35', '44+35=79'] Exploring Operation: 36+79=115, Resulting Numbers: [115] 115,74 unequal: No Solution Exploring Operation: 36*79=2844, Resulting Numbers: [2844] 2844,74 unequal: No Solution Exploring Operation: 79-36=43, Resulting Numbers: [43] 43,74 unequal: No Solution Moving to Node #0,0,2 Current State: 74:[70, 78], Operations: ['44-2=42', '36+42=78'] Exploring Operation: 70+78=148, Resulting Numbers: [148] 148,74 unequal: No Solution Exploring Operation: 78-70=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 70*78=5460, Resulting Numbers: [5460] 5460,74 unequal: No Solution Moving to Node #0,2,2 Current State: 74:[35, 8], Operations: ['70/2=35', '44-36=8'] Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,74 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,74 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,74 unequal: No Solution Moving to Node #0,2,1 Current State: 74:[35, 80], Operations: ['70/2=35', '36+44=80'] Exploring Operation: 80-35=45, Resulting Numbers: [45] 45,74 unequal: No Solution Exploring Operation: 35*80=2800, Resulting Numbers: [2800] 2800,74 unequal: No Solution Exploring Operation: 35+80=115, Resulting Numbers: [115] 115,74 unequal: No Solution Moving to Node #0,0,0 Current State: 74:[70, 6], Operations: ['44-2=42', '42-36=6'] Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 70*6=420, Resulting Numbers: [420] 420,74 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[42, 34], Operations: ['44-2=42', '70-36=34'] Exploring Operation: 42*34=1428, Resulting Numbers: [1428] 1428,74 unequal: No Solution Exploring Operation: 42+34=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,74 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 78, 78, 86, 21 ]
86
[ "78-78=0", "21*0=0", "86+0=86" ]
Current State: 86:[78, 78, 86, 21], Operations: [] Exploring Operation: 78-78=0, Resulting Numbers: [86, 21, 0] Generated Node #2: [86, 21, 0] from Operation: 78-78=0 Current State: 86:[86, 21, 0], Operations: ['78-78=0'] Exploring Operation: 21*0=0, Resulting Numbers: [86, 0] Generated Node #3: [86, 0] from Operation: 21*0=0 Current State: 86:[86, 0], Operations: ['78-78=0', '21*0=0'] Exploring Operation: 86+0=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[78, 78, 86, 21], Operations: [] Exploring Operation: 78/78=1, Resulting Numbers: [86, 21, 1] Generated Node #0,0: 86:[86, 21, 1] Operation: 78/78=1 Exploring Operation: 78-21=57, Resulting Numbers: [78, 86, 57] Generated Node #0,1: 86:[78, 86, 57] Operation: 78-21=57 Exploring Operation: 78+21=99, Resulting Numbers: [78, 86, 99] Generated Node #0,2: 86:[78, 86, 99] Operation: 78+21=99 Exploring Operation: 78-78=0, Resulting Numbers: [86, 21, 0] Generated Node #0,3: 86:[86, 21, 0] Operation: 78-78=0 Exploring Operation: 78+21=99, Resulting Numbers: [78, 86, 99] Generated Node #0,4: 86:[78, 86, 99] Operation: 78+21=99 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[86, 21, 1], Operations: ['78/78=1'] Exploring Operation: 21-1=20, Resulting Numbers: [86, 20] Generated Node #0,0,0: 86:[86, 20] Operation: 21-1=20 Exploring Operation: 86*1=86, Resulting Numbers: [21, 86] Generated Node #0,0,1: 86:[21, 86] Operation: 86*1=86 Exploring Operation: 86/1=86, Resulting Numbers: [21, 86] Generated Node #0,0,2: 86:[21, 86] Operation: 86/1=86 Exploring Operation: 21/1=21, Resulting Numbers: [86, 21] Generated Node #0,0,3: 86:[86, 21] Operation: 21/1=21 Exploring Operation: 21*1=21, Resulting Numbers: [86, 21] Generated Node #0,0,4: 86:[86, 21] Operation: 21*1=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[86, 20], Operations: ['78/78=1', '21-1=20'] Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,86 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,86 unequal: No Solution Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[21, 86], Operations: ['78/78=1', '86*1=86'] Exploring Operation: 21*86=1806, Resulting Numbers: [1806] 1806,86 unequal: No Solution Exploring Operation: 21+86=107, Resulting Numbers: [107] 107,86 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 86:[21, 86], Operations: ['78/78=1', '86/1=86'] Exploring Operation: 21+86=107, Resulting Numbers: [107] 107,86 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,86 unequal: No Solution Exploring Operation: 21*86=1806, Resulting Numbers: [1806] 1806,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 86:[86, 21], Operations: ['78/78=1', '21/1=21'] Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,86 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,86 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 86:[86, 21], Operations: ['78/78=1', '21*1=21'] Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,86 unequal: No Solution Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,86 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[78, 86, 99], Operations: ['78+21=99'] Exploring Operation: 86-78=8, Resulting Numbers: [99, 8] Generated Node #0,2,0: 86:[99, 8] Operation: 86-78=8 Exploring Operation: 78+86=164, Resulting Numbers: [99, 164] Generated Node #0,2,1: 86:[99, 164] Operation: 78+86=164 Exploring Operation: 78+99=177, Resulting Numbers: [86, 177] Generated Node #0,2,2: 86:[86, 177] Operation: 78+99=177 Exploring Operation: 99-78=21, Resulting Numbers: [86, 21] Generated Node #0,2,3: 86:[86, 21] Operation: 99-78=21 Exploring Operation: 99-86=13, Resulting Numbers: [78, 13] Generated Node #0,2,4: 86:[78, 13] Operation: 99-86=13 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 86:[99, 8], Operations: ['78+21=99', '86-78=8'] Exploring Operation: 99-8=91, Resulting Numbers: [91] 91,86 unequal: No Solution Exploring Operation: 99+8=107, Resulting Numbers: [107] 107,86 unequal: No Solution Exploring Operation: 99*8=792, Resulting Numbers: [792] 792,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 86:[86, 21], Operations: ['78+21=99', '99-78=21'] Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,86 unequal: No Solution Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,86 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 86:[78, 13], Operations: ['78+21=99', '99-86=13'] Exploring Operation: 78/13=6, Resulting Numbers: [6] 6,86 unequal: No Solution Exploring Operation: 78-13=65, Resulting Numbers: [65] 65,86 unequal: No Solution Exploring Operation: 78*13=1014, Resulting Numbers: [1014] 1014,86 unequal: No Solution Exploring Operation: 78+13=91, Resulting Numbers: [91] 91,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[99, 164], Operations: ['78+21=99', '78+86=164'] Exploring Operation: 164-99=65, Resulting Numbers: [65] 65,86 unequal: No Solution Exploring Operation: 99+164=263, Resulting Numbers: [263] 263,86 unequal: No Solution Exploring Operation: 99*164=16236, Resulting Numbers: [16236] 16236,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 86:[86, 177], Operations: ['78+21=99', '78+99=177'] Exploring Operation: 86*177=15222, Resulting Numbers: [15222] 15222,86 unequal: No Solution Exploring Operation: 86+177=263, Resulting Numbers: [263] 263,86 unequal: No Solution Exploring Operation: 177-86=91, Resulting Numbers: [91] 91,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[86, 21, 0], Operations: ['78-78=0'] Exploring Operation: 21+0=21, Resulting Numbers: [86, 21] Generated Node #0,3,0: 86:[86, 21] Operation: 21+0=21 Exploring Operation: 21-0=21, Resulting Numbers: [86, 21] Generated Node #0,3,1: 86:[86, 21] Operation: 21-0=21 Exploring Operation: 86-0=86, Resulting Numbers: [21, 86] Generated Node #0,3,2: 86:[21, 86] Operation: 86-0=86 Exploring Operation: 86+0=86, Resulting Numbers: [21, 86] Generated Node #0,3,3: 86:[21, 86] Operation: 86+0=86 Exploring Operation: 21*0=0, Resulting Numbers: [86, 0] Generated Node #0,3,4: 86:[86, 0] Operation: 21*0=0 Moving to Node #0,3,4 Current State: 86:[86, 0], Operations: ['78-78=0', '21*0=0'] Exploring Operation: 86-0=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[78, 78, 86, 21], Operations: [] Exploring Operation: 78-78=0, Resulting Numbers: [86, 21, 0] Generated Node #0,3: 86:[86, 21, 0] Operation: 78-78=0 Moving to Node #0,3 Current State: 86:[86, 21, 0], Operations: ['78-78=0'] Exploring Operation: 21*0=0, Resulting Numbers: [86, 0] Generated Node #0,3,4: 86:[86, 0] Operation: 21*0=0 Moving to Node #0,3,4 Current State: 86:[86, 0], Operations: ['78-78=0', '21*0=0'] Exploring Operation: 86-0=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_5
mult_heuristic
[ 78, 6, 40, 9 ]
62
[ "78/6=13", "40+9=49", "13+49=62" ]
Current State: 62:[78, 6, 40, 9], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [40, 9, 13] Generated Node #2: [40, 9, 13] from Operation: 78/6=13 Current State: 62:[40, 9, 13], Operations: ['78/6=13'] Exploring Operation: 40+9=49, Resulting Numbers: [13, 49] Generated Node #3: [13, 49] from Operation: 40+9=49 Current State: 62:[13, 49], Operations: ['78/6=13', '40+9=49'] Exploring Operation: 13+49=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[78, 6, 40, 9], Operations: [] Exploring Operation: 78-6=72, Resulting Numbers: [40, 9, 72] Generated Node #0,0: 62:[40, 9, 72] Operation: 78-6=72 Exploring Operation: 78-40=38, Resulting Numbers: [6, 9, 38] Generated Node #0,1: 62:[6, 9, 38] Operation: 78-40=38 Exploring Operation: 78-9=69, Resulting Numbers: [6, 40, 69] Generated Node #0,2: 62:[6, 40, 69] Operation: 78-9=69 Exploring Operation: 40-9=31, Resulting Numbers: [78, 6, 31] Generated Node #0,3: 62:[78, 6, 31] Operation: 40-9=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[6, 9, 38], Operations: ['78-40=38'] Exploring Operation: 6*9=54, Resulting Numbers: [38, 54] Generated Node #0,1,0: 62:[38, 54] Operation: 6*9=54 Exploring Operation: 38-9=29, Resulting Numbers: [6, 29] Generated Node #0,1,1: 62:[6, 29] Operation: 38-9=29 Exploring Operation: 38-6=32, Resulting Numbers: [9, 32] Generated Node #0,1,2: 62:[9, 32] Operation: 38-6=32 Exploring Operation: 9-6=3, Resulting Numbers: [38, 3] Generated Node #0,1,3: 62:[38, 3] Operation: 9-6=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[6, 29], Operations: ['78-40=38', '38-9=29'] Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,62 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,62 unequal: No Solution No 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: 62:[9, 32], Operations: ['78-40=38', '38-6=32'] Exploring Operation: 9*32=288, Resulting Numbers: [288] 288,62 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,62 unequal: No Solution No 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: 62:[38, 3], Operations: ['78-40=38', '9-6=3'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 38*3=114, Resulting Numbers: [114] 114,62 unequal: No Solution Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,62 unequal: No Solution No 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: 62:[38, 54], Operations: ['78-40=38', '6*9=54'] Exploring Operation: 38*54=2052, Resulting Numbers: [2052] 2052,62 unequal: No Solution Exploring Operation: 38+54=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[6, 40, 69], Operations: ['78-9=69'] Exploring Operation: 6+40=46, Resulting Numbers: [69, 46] Generated Node #0,2,0: 62:[69, 46] Operation: 6+40=46 Exploring Operation: 69-6=63, Resulting Numbers: [40, 63] Generated Node #0,2,1: 62:[40, 63] Operation: 69-6=63 Exploring Operation: 40-6=34, Resulting Numbers: [69, 34] Generated Node #0,2,2: 62:[69, 34] Operation: 40-6=34 Exploring Operation: 69-40=29, Resulting Numbers: [6, 29] Generated Node #0,2,3: 62:[6, 29] Operation: 69-40=29 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 62:[6, 29], Operations: ['78-9=69', '69-40=29'] Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,62 unequal: No Solution No 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: 62:[40, 63], Operations: ['78-9=69', '69-6=63'] Exploring Operation: 40+63=103, Resulting Numbers: [103] 103,62 unequal: No Solution Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 40*63=2520, Resulting Numbers: [2520] 2520,62 unequal: No Solution No 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: 62:[69, 34], Operations: ['78-9=69', '40-6=34'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 69*34=2346, Resulting Numbers: [2346] 2346,62 unequal: No Solution Exploring Operation: 69+34=103, Resulting Numbers: [103] 103,62 unequal: No Solution No 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: 62:[69, 46], Operations: ['78-9=69', '6+40=46'] Exploring Operation: 69+46=115, Resulting Numbers: [115] 115,62 unequal: No Solution Exploring Operation: 69*46=3174, Resulting Numbers: [3174] 3174,62 unequal: No Solution Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[78, 6, 31], Operations: ['40-9=31'] Exploring Operation: 78-31=47, Resulting Numbers: [6, 47] Generated Node #0,3,0: 62:[6, 47] Operation: 78-31=47 Exploring Operation: 78+6=84, Resulting Numbers: [31, 84] Generated Node #0,3,1: 62:[31, 84] Operation: 78+6=84 Exploring Operation: 78/6=13, Resulting Numbers: [31, 13] Generated Node #0,3,2: 62:[31, 13] Operation: 78/6=13 Exploring Operation: 78-6=72, Resulting Numbers: [31, 72] Generated Node #0,3,3: 62:[31, 72] Operation: 78-6=72 Moving to Node #0,3,3 Current State: 62:[31, 72], Operations: ['40-9=31', '78-6=72'] Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,62 unequal: No Solution Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,62 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,62 unequal: No Solution Moving to Node #0,3,2 Current State: 62:[31, 13], Operations: ['40-9=31', '78/6=13'] Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,62 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,62 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,62 unequal: No Solution Moving to Node #0,3,0 Current State: 62:[6, 47], Operations: ['40-9=31', '78-31=47'] Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,62 unequal: No Solution Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,62 unequal: No Solution Moving to Node #0,3,1 Current State: 62:[31, 84], Operations: ['40-9=31', '78+6=84'] Exploring Operation: 84-31=53, Resulting Numbers: [53] 53,62 unequal: No Solution Exploring Operation: 31+84=115, Resulting Numbers: [115] 115,62 unequal: No Solution Exploring Operation: 31*84=2604, Resulting Numbers: [2604] 2604,62 unequal: No Solution No 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: 62:[40, 9, 72], Operations: ['78-6=72'] Exploring Operation: 72/9=8, Resulting Numbers: [40, 8] Generated Node #0,0,0: 62:[40, 8] Operation: 72/9=8 Exploring Operation: 72-40=32, Resulting Numbers: [9, 32] Generated Node #0,0,1: 62:[9, 32] Operation: 72-40=32 Exploring Operation: 72-9=63, Resulting Numbers: [40, 63] Generated Node #0,0,2: 62:[40, 63] Operation: 72-9=63 Exploring Operation: 40-9=31, Resulting Numbers: [72, 31] Generated Node #0,0,3: 62:[72, 31] Operation: 40-9=31 Moving to Node #0,0,1 Current State: 62:[9, 32], Operations: ['78-6=72', '72-40=32'] Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 9*32=288, Resulting Numbers: [288] 288,62 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,62 unequal: No Solution Moving to Node #0,0,3 Current State: 62:[72, 31], Operations: ['78-6=72', '40-9=31'] Exploring Operation: 72*31=2232, Resulting Numbers: [2232] 2232,62 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 72+31=103, Resulting Numbers: [103] 103,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[40, 63], Operations: ['78-6=72', '72-9=63'] Exploring Operation: 40*63=2520, Resulting Numbers: [2520] 2520,62 unequal: No Solution Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 40+63=103, Resulting Numbers: [103] 103,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[40, 8], Operations: ['78-6=72', '72/9=8'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,62 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,62 unequal: No Solution Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 58, 66, 41, 2 ]
33
[ "58+41=99", "66*2=132", "132-99=33" ]
Current State: 33:[58, 66, 41, 2], Operations: [] Exploring Operation: 58+41=99, Resulting Numbers: [66, 2, 99] Generated Node #2: [66, 2, 99] from Operation: 58+41=99 Current State: 33:[66, 2, 99], Operations: ['58+41=99'] Exploring Operation: 66*2=132, Resulting Numbers: [99, 132] Generated Node #3: [99, 132] from Operation: 66*2=132 Current State: 33:[99, 132], Operations: ['58+41=99', '66*2=132'] Exploring Operation: 132-99=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[58, 66, 41, 2], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [41, 2, 8] Generated Node #0,0: 33:[41, 2, 8] Operation: 66-58=8 Exploring Operation: 66/2=33, Resulting Numbers: [58, 41, 33] Generated Node #0,1: 33:[58, 41, 33] Operation: 66/2=33 Moving to Node #0,0 Current State: 33:[41, 2, 8], Operations: ['66-58=8'] Exploring Operation: 41-8=33, Resulting Numbers: [2, 33] Generated Node #0,0,0: 33:[2, 33] Operation: 41-8=33 Exploring Operation: 41-2=39, Resulting Numbers: [8, 39] Generated Node #0,0,1: 33:[8, 39] Operation: 41-2=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[2, 33], Operations: ['66-58=8', '41-8=33'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,33 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[8, 39], Operations: ['66-58=8', '41-2=39'] Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,33 unequal: No Solution Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 33:[58, 41, 33], Operations: ['66/2=33'] Exploring Operation: 58-41=17, Resulting Numbers: [33, 17] Generated Node #0,1,0: 33:[33, 17] Operation: 58-41=17 Exploring Operation: 58-33=25, Resulting Numbers: [41, 25] Generated Node #0,1,1: 33:[41, 25] Operation: 58-33=25 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[33, 17], Operations: ['66/2=33', '58-41=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[41, 25], Operations: ['66/2=33', '58-33=25'] Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 41+25=66, Resulting Numbers: [66] 66,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic