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
[ 21, 5, 54, 46 ]
97
[ "21*5=105", "54-46=8", "105-8=97" ]
Current State: 97:[21, 5, 54, 46], Operations: [] Exploring Operation: 21*5=105, Resulting Numbers: [54, 46, 105] Generated Node #2: [54, 46, 105] from Operation: 21*5=105 Current State: 97:[54, 46, 105], Operations: ['21*5=105'] Exploring Operation: 54-46=8, Resulting Numbers: [105, 8] Generated Node #3: [105, 8] from Operation: 54-46=8 Current State: 97:[105, 8], Operations: ['21*5=105', '54-46=8'] Exploring Operation: 105-8=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[21, 5, 54, 46], Operations: [] Exploring Operation: 21*5=105, Resulting Numbers: [54, 46, 105] Generated Node #0,0: 97:[54, 46, 105] Operation: 21*5=105 Moving to Node #0,0 Current State: 97:[54, 46, 105], Operations: ['21*5=105'] Exploring Operation: 54+46=100, Resulting Numbers: [105, 100] Generated Node #0,0,0: 97:[105, 100] Operation: 54+46=100 Moving to Node #0,0,0 Current State: 97:[105, 100], Operations: ['21*5=105', '54+46=100'] Exploring Operation: 105-100=5, Resulting Numbers: [5] 5,97 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 2, 11, 20, 3 ]
89
[ "2+3=5", "20*5=100", "100-11=89" ]
Current State: 89:[2, 11, 20, 3], Operations: [] Exploring Operation: 2+3=5, Resulting Numbers: [11, 20, 5] Generated Node #2: [11, 20, 5] from Operation: 2+3=5 Current State: 89:[11, 20, 5], Operations: ['2+3=5'] Exploring Operation: 20*5=100, Resulting Numbers: [11, 100] Generated Node #3: [11, 100] from Operation: 20*5=100 Current State: 89:[11, 100], Operations: ['2+3=5', '20*5=100'] Exploring Operation: 100-11=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[2, 11, 20, 3], Operations: [] Exploring Operation: 11*3=33, Resulting Numbers: [2, 20, 33] Generated Node #0,0: 89:[2, 20, 33] Operation: 11*3=33 Exploring Operation: 2*20=40, Resulting Numbers: [11, 3, 40] Generated Node #0,1: 89:[11, 3, 40] Operation: 2*20=40 Exploring Operation: 2*3=6, Resulting Numbers: [11, 20, 6] Generated Node #0,2: 89:[11, 20, 6] Operation: 2*3=6 Exploring Operation: 20*3=60, Resulting Numbers: [2, 11, 60] Generated Node #0,3: 89:[2, 11, 60] Operation: 20*3=60 Exploring Operation: 2*11=22, Resulting Numbers: [20, 3, 22] Generated Node #0,4: 89:[20, 3, 22] Operation: 2*11=22 Moving to Node #0,3 Current State: 89:[2, 11, 60], Operations: ['20*3=60'] Exploring Operation: 11-2=9, Resulting Numbers: [60, 9] Generated Node #0,3,0: 89:[60, 9] Operation: 11-2=9 Exploring Operation: 2+11=13, Resulting Numbers: [60, 13] Generated Node #0,3,1: 89:[60, 13] Operation: 2+11=13 Exploring Operation: 2+60=62, Resulting Numbers: [11, 62] Generated Node #0,3,2: 89:[11, 62] Operation: 2+60=62 Exploring Operation: 11+60=71, Resulting Numbers: [2, 71] Generated Node #0,3,3: 89:[2, 71] Operation: 11+60=71 Exploring Operation: 2*11=22, Resulting Numbers: [60, 22] Generated Node #0,3,4: 89:[60, 22] Operation: 2*11=22 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 89:[60, 22], Operations: ['20*3=60', '2*11=22'] Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,89 unequal: No Solution Exploring Operation: 60+22=82, Resulting Numbers: [82] 82,89 unequal: No Solution Exploring Operation: 60*22=1320, Resulting Numbers: [1320] 1320,89 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:[60, 13], Operations: ['20*3=60', '2+11=13'] Exploring Operation: 60+13=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 60*13=780, Resulting Numbers: [780] 780,89 unequal: No Solution Exploring Operation: 60-13=47, Resulting Numbers: [47] 47,89 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:[11, 62], Operations: ['20*3=60', '2+60=62'] Exploring Operation: 11*62=682, Resulting Numbers: [682] 682,89 unequal: No Solution Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 11+62=73, Resulting Numbers: [73] 73,89 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:[2, 71], Operations: ['20*3=60', '11+60=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,89 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,89 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 #0,3,0 Current State: 89:[60, 9], Operations: ['20*3=60', '11-2=9'] Exploring Operation: 60+9=69, Resulting Numbers: [69] 69,89 unequal: No Solution Exploring Operation: 60*9=540, Resulting Numbers: [540] 540,89 unequal: No Solution Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 89:[2, 20, 33], Operations: ['11*3=33'] Exploring Operation: 2+33=35, Resulting Numbers: [20, 35] Generated Node #0,0,0: 89:[20, 35] Operation: 2+33=35 Exploring Operation: 2*20=40, Resulting Numbers: [33, 40] Generated Node #0,0,1: 89:[33, 40] Operation: 2*20=40 Exploring Operation: 2+20=22, Resulting Numbers: [33, 22] Generated Node #0,0,2: 89:[33, 22] Operation: 2+20=22 Exploring Operation: 2*33=66, Resulting Numbers: [20, 66] Generated Node #0,0,3: 89:[20, 66] Operation: 2*33=66 Exploring Operation: 20+33=53, Resulting Numbers: [2, 53] Generated Node #0,0,4: 89:[2, 53] Operation: 20+33=53 Moving to Node #0,1 Current State: 89:[11, 3, 40], Operations: ['2*20=40'] Exploring Operation: 11+3=14, Resulting Numbers: [40, 14] Generated Node #0,1,0: 89:[40, 14] Operation: 11+3=14 Exploring Operation: 11+40=51, Resulting Numbers: [3, 51] Generated Node #0,1,1: 89:[3, 51] Operation: 11+40=51 Exploring Operation: 3+40=43, Resulting Numbers: [11, 43] Generated Node #0,1,2: 89:[11, 43] Operation: 3+40=43 Exploring Operation: 11*3=33, Resulting Numbers: [40, 33] Generated Node #0,1,3: 89:[40, 33] Operation: 11*3=33 Exploring Operation: 3*40=120, Resulting Numbers: [11, 120] Generated Node #0,1,4: 89:[11, 120] Operation: 3*40=120 Moving to Node #0,4 Current State: 89:[20, 3, 22], Operations: ['2*11=22'] Exploring Operation: 20+3=23, Resulting Numbers: [22, 23] Generated Node #0,4,0: 89:[22, 23] Operation: 20+3=23 Exploring Operation: 3+22=25, Resulting Numbers: [20, 25] Generated Node #0,4,1: 89:[20, 25] Operation: 3+22=25 Exploring Operation: 3*22=66, Resulting Numbers: [20, 66] Generated Node #0,4,2: 89:[20, 66] Operation: 3*22=66 Exploring Operation: 20+22=42, Resulting Numbers: [3, 42] Generated Node #0,4,3: 89:[3, 42] Operation: 20+22=42 Exploring Operation: 20*3=60, Resulting Numbers: [22, 60] Generated Node #0,4,4: 89:[22, 60] Operation: 20*3=60 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 89:[20, 66], Operations: ['2*11=22', '3*22=66'] Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 20*66=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,89 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:[22, 60], Operations: ['2*11=22', '20*3=60'] Exploring Operation: 22*60=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,89 unequal: No Solution Exploring Operation: 22+60=82, Resulting Numbers: [82] 82,89 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 #0,4,0 Current State: 89:[22, 23], Operations: ['2*11=22', '20+3=23'] Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 22*23=506, Resulting Numbers: [506] 506,89 unequal: No Solution Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,89 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:[20, 25], Operations: ['2*11=22', '3+22=25'] Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,89 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,89 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,89 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:[3, 42], Operations: ['2*11=22', '20+22=42'] Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,89 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,89 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: 89:[11, 20, 6], Operations: ['2*3=6'] Exploring Operation: 11+6=17, Resulting Numbers: [20, 17] Generated Node #0,2,0: 89:[20, 17] Operation: 11+6=17 Exploring Operation: 11*6=66, Resulting Numbers: [20, 66] Generated Node #0,2,1: 89:[20, 66] Operation: 11*6=66 Exploring Operation: 11+20=31, Resulting Numbers: [6, 31] Generated Node #0,2,2: 89:[6, 31] Operation: 11+20=31 Exploring Operation: 20*6=120, Resulting Numbers: [11, 120] Generated Node #0,2,3: 89:[11, 120] Operation: 20*6=120 Exploring Operation: 20+6=26, Resulting Numbers: [11, 26] Generated Node #0,2,4: 89:[11, 26] Operation: 20+6=26 Moving to Node #0,0,3 Current State: 89:[20, 66], Operations: ['11*3=33', '2*33=66'] Exploring Operation: 20*66=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[20, 66], Operations: ['2*3=6', '11*6=66'] Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 20*66=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[40, 33], Operations: ['2*20=40', '11*3=33'] Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,89 unequal: No Solution Exploring Operation: 40+33=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 40*33=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[33, 40], Operations: ['11*3=33', '2*20=40'] Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,89 unequal: No Solution Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Moving to Node #0,1,4 Current State: 89:[11, 120], Operations: ['2*20=40', '3*40=120'] Exploring Operation: 11+120=131, Resulting Numbers: [131] 131,89 unequal: No Solution Exploring Operation: 11*120=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Exploring Operation: 120-11=109, Resulting Numbers: [109] 109,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[11, 120], Operations: ['2*3=6', '20*6=120'] Exploring Operation: 120-11=109, Resulting Numbers: [109] 109,89 unequal: No Solution Exploring Operation: 11*120=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Exploring Operation: 11+120=131, Resulting Numbers: [131] 131,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[20, 35], Operations: ['11*3=33', '2+33=35'] Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,89 unequal: No Solution Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,89 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,89 unequal: No Solution Moving to Node #0,0,4 Current State: 89:[2, 53], Operations: ['11*3=33', '20+33=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[33, 22], Operations: ['11*3=33', '2+20=22'] Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,89 unequal: No Solution Exploring Operation: 33*22=726, Resulting Numbers: [726] 726,89 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[11, 43], Operations: ['2*20=40', '3+40=43'] Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 11+43=54, Resulting Numbers: [54] 54,89 unequal: No Solution Exploring Operation: 11*43=473, Resulting Numbers: [473] 473,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[3, 51], Operations: ['2*20=40', '11+40=51'] Exploring Operation: 3*51=153, Resulting Numbers: [153] 153,89 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,89 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[40, 14], Operations: ['2*20=40', '11+3=14'] Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,89 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,89 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[6, 31], Operations: ['2*3=6', '11+20=31'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[11, 26], Operations: ['2*3=6', '20+6=26'] Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,89 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[20, 17], Operations: ['2*3=6', '11+6=17'] Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,89 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,89 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 81, 24, 1, 6 ]
63
[ "81-24=57", "1*6=6", "57+6=63" ]
Current State: 63:[81, 24, 1, 6], Operations: [] Exploring Operation: 81-24=57, Resulting Numbers: [1, 6, 57] Generated Node #2: [1, 6, 57] from Operation: 81-24=57 Current State: 63:[1, 6, 57], Operations: ['81-24=57'] Exploring Operation: 1*6=6, Resulting Numbers: [57, 6] Generated Node #3: [57, 6] from Operation: 1*6=6 Current State: 63:[57, 6], Operations: ['81-24=57', '1*6=6'] Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[81, 24, 1, 6], Operations: [] Exploring Operation: 81-24=57, Resulting Numbers: [1, 6, 57] Generated Node #0,0: 63:[1, 6, 57] Operation: 81-24=57 Moving to Node #0,0 Current State: 63:[1, 6, 57], Operations: ['81-24=57'] Exploring Operation: 6+57=63, Resulting Numbers: [1, 63] Generated Node #0,0,0: 63:[1, 63] Operation: 6+57=63 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[1, 63], Operations: ['81-24=57', '6+57=63'] Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[81, 24, 1, 6], Operations: [] Exploring Operation: 81-24=57, Resulting Numbers: [1, 6, 57] Generated Node #0,0: 63:[1, 6, 57] Operation: 81-24=57 Moving to Node #0,0 Current State: 63:[1, 6, 57], Operations: ['81-24=57'] Exploring Operation: 6+57=63, Resulting Numbers: [1, 63] Generated Node #0,0,0: 63:[1, 63] Operation: 6+57=63 Moving to Node #0,0,0 Current State: 63:[1, 63], Operations: ['81-24=57', '6+57=63'] Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 79, 28, 18, 17 ]
54
[ "79-28=51", "18*51=918", "918/17=54" ]
Current State: 54:[79, 28, 18, 17], Operations: [] Exploring Operation: 79-28=51, Resulting Numbers: [18, 17, 51] Generated Node #2: [18, 17, 51] from Operation: 79-28=51 Current State: 54:[18, 17, 51], Operations: ['79-28=51'] Exploring Operation: 18*51=918, Resulting Numbers: [17, 918] Generated Node #3: [17, 918] from Operation: 18*51=918 Current State: 54:[17, 918], Operations: ['79-28=51', '18*51=918'] Exploring Operation: 918/17=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[79, 28, 18, 17], Operations: [] Exploring Operation: 79-18=61, Resulting Numbers: [28, 17, 61] Generated Node #0,0: 54:[28, 17, 61] Operation: 79-18=61 Exploring Operation: 79-28=51, Resulting Numbers: [18, 17, 51] Generated Node #0,1: 54:[18, 17, 51] Operation: 79-28=51 Moving to Node #0,1 Current State: 54:[18, 17, 51], Operations: ['79-28=51'] Exploring Operation: 51/17=3, Resulting Numbers: [18, 3] Generated Node #0,1,0: 54:[18, 3] Operation: 51/17=3 Exploring Operation: 18-17=1, Resulting Numbers: [51, 1] Generated Node #0,1,1: 54:[51, 1] Operation: 18-17=1 Moving to Node #0,0 Current State: 54:[28, 17, 61], Operations: ['79-18=61'] Exploring Operation: 28-17=11, Resulting Numbers: [61, 11] Generated Node #0,0,0: 54:[61, 11] Operation: 28-17=11 Exploring Operation: 61-28=33, Resulting Numbers: [17, 33] Generated Node #0,0,1: 54:[17, 33] Operation: 61-28=33 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[17, 33], Operations: ['79-18=61', '61-28=33'] Exploring Operation: 17+33=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[61, 11], Operations: ['79-18=61', '28-17=11'] Exploring Operation: 61+11=72, Resulting Numbers: [72] 72,54 unequal: No Solution Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,54 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: 54:[18, 3], Operations: ['79-28=51', '51/17=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[79, 28, 18, 17], Operations: [] Exploring Operation: 79-28=51, Resulting Numbers: [18, 17, 51] Generated Node #0,1: 54:[18, 17, 51] Operation: 79-28=51 Moving to Node #0,1 Current State: 54:[18, 17, 51], Operations: ['79-28=51'] Exploring Operation: 51/17=3, Resulting Numbers: [18, 3] Generated Node #0,1,0: 54:[18, 3] Operation: 51/17=3 Moving to Node #0,1,0 Current State: 54:[18, 3], Operations: ['79-28=51', '51/17=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 88, 43, 57, 8 ]
25
[ "88/8=11", "57-43=14", "11+14=25" ]
Current State: 25:[88, 43, 57, 8], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [43, 57, 11] Generated Node #2: [43, 57, 11] from Operation: 88/8=11 Current State: 25:[43, 57, 11], Operations: ['88/8=11'] Exploring Operation: 57-43=14, Resulting Numbers: [11, 14] Generated Node #3: [11, 14] from Operation: 57-43=14 Current State: 25:[11, 14], Operations: ['88/8=11', '57-43=14'] Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[88, 43, 57, 8], Operations: [] Exploring Operation: 88-57=31, Resulting Numbers: [43, 8, 31] Generated Node #0,0: 25:[43, 8, 31] Operation: 88-57=31 Moving to Node #0,0 Current State: 25:[43, 8, 31], Operations: ['88-57=31'] Exploring Operation: 43-31=12, Resulting Numbers: [8, 12] Generated Node #0,0,0: 25:[8, 12] Operation: 43-31=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[8, 12], Operations: ['88-57=31', '43-31=12'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,25 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, 93, 19, 92 ]
54
[ "93-19=74", "92-74=18", "3*18=54" ]
Current State: 54:[3, 93, 19, 92], Operations: [] Exploring Operation: 93-19=74, Resulting Numbers: [3, 92, 74] Generated Node #2: [3, 92, 74] from Operation: 93-19=74 Current State: 54:[3, 92, 74], Operations: ['93-19=74'] Exploring Operation: 92-74=18, Resulting Numbers: [3, 18] Generated Node #3: [3, 18] from Operation: 92-74=18 Current State: 54:[3, 18], Operations: ['93-19=74', '92-74=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[3, 93, 19, 92], Operations: [] Exploring Operation: 93-92=1, Resulting Numbers: [3, 19, 1] Generated Node #0,0: 54:[3, 19, 1] Operation: 93-92=1 Moving to Node #0,0 Current State: 54:[3, 19, 1], Operations: ['93-92=1'] Exploring Operation: 19-1=18, Resulting Numbers: [3, 18] Generated Node #0,0,0: 54:[3, 18] Operation: 19-1=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[3, 18], Operations: ['93-92=1', '19-1=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[3, 93, 19, 92], Operations: [] Exploring Operation: 93-92=1, Resulting Numbers: [3, 19, 1] Generated Node #0,0: 54:[3, 19, 1] Operation: 93-92=1 Moving to Node #0,0 Current State: 54:[3, 19, 1], Operations: ['93-92=1'] Exploring Operation: 19-1=18, Resulting Numbers: [3, 18] Generated Node #0,0,0: 54:[3, 18] Operation: 19-1=18 Moving to Node #0,0,0 Current State: 54:[3, 18], Operations: ['93-92=1', '19-1=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 55, 22, 6, 9 ]
86
[ "55-9=46", "22*6=132", "132-46=86" ]
Current State: 86:[55, 22, 6, 9], Operations: [] Exploring Operation: 55-9=46, Resulting Numbers: [22, 6, 46] Generated Node #2: [22, 6, 46] from Operation: 55-9=46 Current State: 86:[22, 6, 46], Operations: ['55-9=46'] Exploring Operation: 22*6=132, Resulting Numbers: [46, 132] Generated Node #3: [46, 132] from Operation: 22*6=132 Current State: 86:[46, 132], Operations: ['55-9=46', '22*6=132'] Exploring Operation: 132-46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[55, 22, 6, 9], Operations: [] Exploring Operation: 55-22=33, Resulting Numbers: [6, 9, 33] Generated Node #0,0: 86:[6, 9, 33] Operation: 55-22=33 Exploring Operation: 55-9=46, Resulting Numbers: [22, 6, 46] Generated Node #0,1: 86:[22, 6, 46] Operation: 55-9=46 Exploring Operation: 55+22=77, Resulting Numbers: [6, 9, 77] Generated Node #0,2: 86:[6, 9, 77] Operation: 55+22=77 Moving to Node #0,2 Current State: 86:[6, 9, 77], Operations: ['55+22=77'] Exploring Operation: 9-6=3, Resulting Numbers: [77, 3] Generated Node #0,2,0: 86:[77, 3] Operation: 9-6=3 Exploring Operation: 9+77=86, Resulting Numbers: [6, 86] Generated Node #0,2,1: 86:[6, 86] Operation: 9+77=86 Exploring Operation: 6+77=83, Resulting Numbers: [9, 83] Generated Node #0,2,2: 86:[9, 83] Operation: 6+77=83 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[6, 86], Operations: ['55+22=77', '9+77=86'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,86 unequal: No Solution Exploring Operation: 6*86=516, Resulting Numbers: [516] 516,86 unequal: No Solution Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,86 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 #0,2,0 Current State: 86:[77, 3], Operations: ['55+22=77', '9-6=3'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 77*3=231, Resulting Numbers: [231] 231,86 unequal: No Solution Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,86 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 #0,2,2 Current State: 86:[9, 83], Operations: ['55+22=77', '6+77=83'] Exploring Operation: 9+83=92, Resulting Numbers: [92] 92,86 unequal: No Solution Exploring Operation: 9*83=747, Resulting Numbers: [747] 747,86 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,86 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: 86:[6, 9, 33], Operations: ['55-22=33'] Exploring Operation: 9+33=42, Resulting Numbers: [6, 42] Generated Node #0,0,0: 86:[6, 42] Operation: 9+33=42 Exploring Operation: 6+33=39, Resulting Numbers: [9, 39] Generated Node #0,0,1: 86:[9, 39] Operation: 6+33=39 Exploring Operation: 9-6=3, Resulting Numbers: [33, 3] Generated Node #0,0,2: 86:[33, 3] Operation: 9-6=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[6, 42], Operations: ['55-22=33', '9+33=42'] Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[9, 39], Operations: ['55-22=33', '6+33=39'] Exploring Operation: 9+39=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 9*39=351, Resulting Numbers: [351] 351,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[33, 3], Operations: ['55-22=33', '9-6=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,86 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,86 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: 86:[22, 6, 46], Operations: ['55-9=46'] Exploring Operation: 22+6=28, Resulting Numbers: [46, 28] Generated Node #0,1,0: 86:[46, 28] Operation: 22+6=28 Exploring Operation: 22+46=68, Resulting Numbers: [6, 68] Generated Node #0,1,1: 86:[6, 68] Operation: 22+46=68 Exploring Operation: 22-6=16, Resulting Numbers: [46, 16] Generated Node #0,1,2: 86:[46, 16] Operation: 22-6=16 Moving to Node #0,1,2 Current State: 86:[46, 16], Operations: ['55-9=46', '22-6=16'] Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[46, 28], Operations: ['55-9=46', '22+6=28'] Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 46+28=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 46*28=1288, Resulting Numbers: [1288] 1288,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[6, 68], Operations: ['55-9=46', '22+46=68'] Exploring Operation: 6+68=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 6*68=408, Resulting Numbers: [408] 408,86 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 16, 3, 80, 2 ]
97
[ "16+3=19", "80-2=78", "19+78=97" ]
Current State: 97:[16, 3, 80, 2], Operations: [] Exploring Operation: 16+3=19, Resulting Numbers: [80, 2, 19] Generated Node #2: [80, 2, 19] from Operation: 16+3=19 Current State: 97:[80, 2, 19], Operations: ['16+3=19'] Exploring Operation: 80-2=78, Resulting Numbers: [19, 78] Generated Node #3: [19, 78] from Operation: 80-2=78 Current State: 97:[19, 78], Operations: ['16+3=19', '80-2=78'] Exploring Operation: 19+78=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[16, 3, 80, 2], Operations: [] Exploring Operation: 16*3=48, Resulting Numbers: [80, 2, 48] Generated Node #0,0: 97:[80, 2, 48] Operation: 16*3=48 Moving to Node #0,0 Current State: 97:[80, 2, 48], Operations: ['16*3=48'] Exploring Operation: 2*48=96, Resulting Numbers: [80, 96] Generated Node #0,0,0: 97:[80, 96] Operation: 2*48=96 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[80, 96], Operations: ['16*3=48', '2*48=96'] Exploring Operation: 80+96=176, Resulting Numbers: [176] 176,97 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
[ 96, 58, 29, 8 ]
17
[ "96-58=38", "29-8=21", "38-21=17" ]
Current State: 17:[96, 58, 29, 8], Operations: [] Exploring Operation: 96-58=38, Resulting Numbers: [29, 8, 38] Generated Node #2: [29, 8, 38] from Operation: 96-58=38 Current State: 17:[29, 8, 38], Operations: ['96-58=38'] Exploring Operation: 29-8=21, Resulting Numbers: [38, 21] Generated Node #3: [38, 21] from Operation: 29-8=21 Current State: 17:[38, 21], Operations: ['96-58=38', '29-8=21'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[96, 58, 29, 8], Operations: [] Exploring Operation: 96-58=38, Resulting Numbers: [29, 8, 38] Generated Node #0,0: 17:[29, 8, 38] Operation: 96-58=38 Moving to Node #0,0 Current State: 17:[29, 8, 38], Operations: ['96-58=38'] Exploring Operation: 38-29=9, Resulting Numbers: [8, 9] Generated Node #0,0,0: 17:[8, 9] Operation: 38-29=9 Moving to Node #0,0,0 Current State: 17:[8, 9], Operations: ['96-58=38', '38-29=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[96, 58, 29, 8], Operations: [] Exploring Operation: 96-58=38, Resulting Numbers: [29, 8, 38] Generated Node #0,0: 17:[29, 8, 38] Operation: 96-58=38 Moving to Node #0,0 Current State: 17:[29, 8, 38], Operations: ['96-58=38'] Exploring Operation: 38-29=9, Resulting Numbers: [8, 9] Generated Node #0,0,0: 17:[8, 9] Operation: 38-29=9 Moving to Node #0,0,0 Current State: 17:[8, 9], Operations: ['96-58=38', '38-29=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 99, 21, 17, 14 ]
47
[ "99-21=78", "17+14=31", "78-31=47" ]
Current State: 47:[99, 21, 17, 14], Operations: [] Exploring Operation: 99-21=78, Resulting Numbers: [17, 14, 78] Generated Node #2: [17, 14, 78] from Operation: 99-21=78 Current State: 47:[17, 14, 78], Operations: ['99-21=78'] Exploring Operation: 17+14=31, Resulting Numbers: [78, 31] Generated Node #3: [78, 31] from Operation: 17+14=31 Current State: 47:[78, 31], Operations: ['99-21=78', '17+14=31'] Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[99, 21, 17, 14], Operations: [] Exploring Operation: 99-21=78, Resulting Numbers: [17, 14, 78] Generated Node #0,0: 47:[17, 14, 78] Operation: 99-21=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[17, 14, 78], Operations: ['99-21=78'] Exploring Operation: 17+14=31, Resulting Numbers: [78, 31] Generated Node #0,0,0: 47:[78, 31] Operation: 17+14=31 Moving to Node #0,0,0 Current State: 47:[78, 31], Operations: ['99-21=78', '17+14=31'] Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[99, 21, 17, 14], Operations: [] Exploring Operation: 99-21=78, Resulting Numbers: [17, 14, 78] Generated Node #0,0: 47:[17, 14, 78] Operation: 99-21=78 Moving to Node #0,0 Current State: 47:[17, 14, 78], Operations: ['99-21=78'] Exploring Operation: 17+14=31, Resulting Numbers: [78, 31] Generated Node #0,0,0: 47:[78, 31] Operation: 17+14=31 Moving to Node #0,0,0 Current State: 47:[78, 31], Operations: ['99-21=78', '17+14=31'] Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 3, 25, 40, 90 ]
15
[ "90/3=30", "40-25=15", "30-15=15" ]
Current State: 15:[3, 25, 40, 90], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [25, 40, 30] Generated Node #2: [25, 40, 30] from Operation: 90/3=30 Current State: 15:[25, 40, 30], Operations: ['90/3=30'] Exploring Operation: 40-25=15, Resulting Numbers: [30, 15] Generated Node #3: [30, 15] from Operation: 40-25=15 Current State: 15:[30, 15], Operations: ['90/3=30', '40-25=15'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[3, 25, 40, 90], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [25, 40, 30] Generated Node #0,0: 15:[25, 40, 30] Operation: 90/3=30 Exploring Operation: 90-40=50, Resulting Numbers: [3, 25, 50] Generated Node #0,1: 15:[3, 25, 50] Operation: 90-40=50 Exploring Operation: 90-25=65, Resulting Numbers: [3, 40, 65] Generated Node #0,2: 15:[3, 40, 65] Operation: 90-25=65 Exploring Operation: 25-3=22, Resulting Numbers: [40, 90, 22] Generated Node #0,3: 15:[40, 90, 22] Operation: 25-3=22 Exploring Operation: 40-25=15, Resulting Numbers: [3, 90, 15] Generated Node #0,4: 15:[3, 90, 15] Operation: 40-25=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[3, 25, 50], Operations: ['90-40=50'] Exploring Operation: 50-25=25, Resulting Numbers: [3, 25] Generated Node #0,1,0: 15:[3, 25] Operation: 50-25=25 Exploring Operation: 25-3=22, Resulting Numbers: [50, 22] Generated Node #0,1,1: 15:[50, 22] Operation: 25-3=22 Exploring Operation: 50/25=2, Resulting Numbers: [3, 2] Generated Node #0,1,2: 15:[3, 2] Operation: 50/25=2 Exploring Operation: 50-3=47, Resulting Numbers: [25, 47] Generated Node #0,1,3: 15:[25, 47] Operation: 50-3=47 Exploring Operation: 3+25=28, Resulting Numbers: [50, 28] Generated Node #0,1,4: 15:[50, 28] Operation: 3+25=28 Moving to Node #0,1,2 Current State: 15:[3, 2], Operations: ['90-40=50', '50/25=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[3, 25], Operations: ['90-40=50', '50-25=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,15 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[50, 22], Operations: ['90-40=50', '25-3=22'] Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,15 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,15 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[25, 47], Operations: ['90-40=50', '50-3=47'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 25*47=1175, Resulting Numbers: [1175] 1175,15 unequal: No Solution Exploring Operation: 25+47=72, Resulting Numbers: [72] 72,15 unequal: No Solution Moving to Node #0,1,4 Current State: 15:[50, 28], Operations: ['90-40=50', '3+25=28'] Exploring Operation: 50+28=78, Resulting Numbers: [78] 78,15 unequal: No Solution Exploring Operation: 50*28=1400, Resulting Numbers: [1400] 1400,15 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[25, 40, 30], Operations: ['90/3=30'] Exploring Operation: 40-30=10, Resulting Numbers: [25, 10] Generated Node #0,0,0: 15:[25, 10] Operation: 40-30=10 Exploring Operation: 25+30=55, Resulting Numbers: [40, 55] Generated Node #0,0,1: 15:[40, 55] Operation: 25+30=55 Exploring Operation: 40-25=15, Resulting Numbers: [30, 15] Generated Node #0,0,2: 15:[30, 15] Operation: 40-25=15 Exploring Operation: 30-25=5, Resulting Numbers: [40, 5] Generated Node #0,0,3: 15:[40, 5] Operation: 30-25=5 Exploring Operation: 25+40=65, Resulting Numbers: [30, 65] Generated Node #0,0,4: 15:[30, 65] Operation: 25+40=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[25, 10], Operations: ['90/3=30', '40-30=10'] Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,15 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[3, 25, 40, 90], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [25, 40, 30] Generated Node #0,0: 15:[25, 40, 30] Operation: 90/3=30 Moving to Node #0,0 Current State: 15:[25, 40, 30], Operations: ['90/3=30'] Exploring Operation: 40-30=10, Resulting Numbers: [25, 10] Generated Node #0,0,0: 15:[25, 10] Operation: 40-30=10 Moving to Node #0,0,0 Current State: 15:[25, 10], Operations: ['90/3=30', '40-30=10'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 97, 6, 72, 6 ]
11
[ "97-72=25", "6*6=36", "36-25=11" ]
Current State: 11:[97, 6, 72, 6], Operations: [] Exploring Operation: 97-72=25, Resulting Numbers: [6, 6, 25] Generated Node #2: [6, 6, 25] from Operation: 97-72=25 Current State: 11:[6, 6, 25], Operations: ['97-72=25'] Exploring Operation: 6*6=36, Resulting Numbers: [25, 36] Generated Node #3: [25, 36] from Operation: 6*6=36 Current State: 11:[25, 36], Operations: ['97-72=25', '6*6=36'] Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[97, 6, 72, 6], Operations: [] Exploring Operation: 72/6=12, Resulting Numbers: [97, 6, 12] Generated Node #0,0: 11:[97, 6, 12] Operation: 72/6=12 Exploring Operation: 97-72=25, Resulting Numbers: [6, 6, 25] Generated Node #0,1: 11:[6, 6, 25] Operation: 97-72=25 Moving to Node #0,1 Current State: 11:[6, 6, 25], Operations: ['97-72=25'] Exploring Operation: 25-6=19, Resulting Numbers: [6, 19] Generated Node #0,1,0: 11:[6, 19] Operation: 25-6=19 Exploring Operation: 25-6=19, Resulting Numbers: [6, 19] Generated Node #0,1,1: 11:[6, 19] Operation: 25-6=19 Moving to Node #0,0 Current State: 11:[97, 6, 12], Operations: ['72/6=12'] Exploring Operation: 97-12=85, Resulting Numbers: [6, 85] Generated Node #0,0,0: 11:[6, 85] Operation: 97-12=85 Exploring Operation: 97-6=91, Resulting Numbers: [12, 91] Generated Node #0,0,1: 11:[12, 91] Operation: 97-6=91 Moving to Node #0,1,0 Current State: 11:[6, 19], Operations: ['97-72=25', '25-6=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[6, 19], Operations: ['97-72=25', '25-6=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[6, 85], Operations: ['72/6=12', '97-12=85'] Exploring Operation: 6+85=91, Resulting Numbers: [91] 91,11 unequal: No Solution Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[12, 91], Operations: ['72/6=12', '97-6=91'] Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,11 unequal: No Solution Exploring Operation: 12+91=103, Resulting Numbers: [103] 103,11 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 52, 21, 14, 3 ]
26
[ "52*21=1092", "14*3=42", "1092/42=26" ]
Current State: 26:[52, 21, 14, 3], Operations: [] Exploring Operation: 52*21=1092, Resulting Numbers: [14, 3, 1092] Generated Node #2: [14, 3, 1092] from Operation: 52*21=1092 Current State: 26:[14, 3, 1092], Operations: ['52*21=1092'] Exploring Operation: 14*3=42, Resulting Numbers: [1092, 42] Generated Node #3: [1092, 42] from Operation: 14*3=42 Current State: 26:[1092, 42], Operations: ['52*21=1092', '14*3=42'] Exploring Operation: 1092/42=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[52, 21, 14, 3], Operations: [] Exploring Operation: 52-21=31, Resulting Numbers: [14, 3, 31] Generated Node #0,0: 26:[14, 3, 31] Operation: 52-21=31 Exploring Operation: 52-3=49, Resulting Numbers: [21, 14, 49] Generated Node #0,1: 26:[21, 14, 49] Operation: 52-3=49 Exploring Operation: 52-14=38, Resulting Numbers: [21, 3, 38] Generated Node #0,2: 26:[21, 3, 38] Operation: 52-14=38 Moving to Node #0,0 Current State: 26:[14, 3, 31], Operations: ['52-21=31'] Exploring Operation: 31-3=28, Resulting Numbers: [14, 28] Generated Node #0,0,0: 26:[14, 28] Operation: 31-3=28 Exploring Operation: 14-3=11, Resulting Numbers: [31, 11] Generated Node #0,0,1: 26:[31, 11] Operation: 14-3=11 Exploring Operation: 31-14=17, Resulting Numbers: [3, 17] Generated Node #0,0,2: 26:[3, 17] Operation: 31-14=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[14, 28], Operations: ['52-21=31', '31-3=28'] Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[3, 17], Operations: ['52-21=31', '31-14=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,26 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[31, 11], Operations: ['52-21=31', '14-3=11'] Exploring Operation: 31*11=341, Resulting Numbers: [341] 341,26 unequal: No Solution Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,26 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: 26:[21, 3, 38], Operations: ['52-14=38'] Exploring Operation: 38-3=35, Resulting Numbers: [21, 35] Generated Node #0,2,0: 26:[21, 35] Operation: 38-3=35 Exploring Operation: 21+3=24, Resulting Numbers: [38, 24] Generated Node #0,2,1: 26:[38, 24] Operation: 21+3=24 Exploring Operation: 38-21=17, Resulting Numbers: [3, 17] Generated Node #0,2,2: 26:[3, 17] Operation: 38-21=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 26:[3, 17], Operations: ['52-14=38', '38-21=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,26 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[21, 35], Operations: ['52-14=38', '38-3=35'] Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,26 unequal: No Solution Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,26 unequal: No Solution Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[38, 24], Operations: ['52-14=38', '21+3=24'] Exploring Operation: 38*24=912, Resulting Numbers: [912] 912,26 unequal: No Solution Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,26 unequal: No Solution Exploring Operation: 38+24=62, Resulting Numbers: [62] 62,26 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: 26:[21, 14, 49], Operations: ['52-3=49'] Exploring Operation: 21-14=7, Resulting Numbers: [49, 7] Generated Node #0,1,0: 26:[49, 7] Operation: 21-14=7 Exploring Operation: 49-21=28, Resulting Numbers: [14, 28] Generated Node #0,1,1: 26:[14, 28] Operation: 49-21=28 Exploring Operation: 49-14=35, Resulting Numbers: [21, 35] Generated Node #0,1,2: 26:[21, 35] Operation: 49-14=35 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[14, 28], Operations: ['52-3=49', '49-21=28'] Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,26 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[21, 35], Operations: ['52-3=49', '49-14=35'] Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,26 unequal: No Solution Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[49, 7], Operations: ['52-3=49', '21-14=7'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,26 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
[ 56, 2, 37, 29 ]
47
[ "56-29=27", "2*37=74", "74-27=47" ]
Current State: 47:[56, 2, 37, 29], Operations: [] Exploring Operation: 56-29=27, Resulting Numbers: [2, 37, 27] Generated Node #2: [2, 37, 27] from Operation: 56-29=27 Current State: 47:[2, 37, 27], Operations: ['56-29=27'] Exploring Operation: 2*37=74, Resulting Numbers: [27, 74] Generated Node #3: [27, 74] from Operation: 2*37=74 Current State: 47:[27, 74], Operations: ['56-29=27', '2*37=74'] Exploring Operation: 74-27=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[56, 2, 37, 29], Operations: [] Exploring Operation: 56-2=54, Resulting Numbers: [37, 29, 54] Generated Node #0,0: 47:[37, 29, 54] Operation: 56-2=54 Exploring Operation: 2*29=58, Resulting Numbers: [56, 37, 58] Generated Node #0,1: 47:[56, 37, 58] Operation: 2*29=58 Exploring Operation: 2+37=39, Resulting Numbers: [56, 29, 39] Generated Node #0,2: 47:[56, 29, 39] Operation: 2+37=39 Moving to Node #0,1 Current State: 47:[56, 37, 58], Operations: ['2*29=58'] Exploring Operation: 56-37=19, Resulting Numbers: [58, 19] Generated Node #0,1,0: 47:[58, 19] Operation: 56-37=19 Exploring Operation: 58-56=2, Resulting Numbers: [37, 2] Generated Node #0,1,1: 47:[37, 2] Operation: 58-56=2 Exploring Operation: 58-37=21, Resulting Numbers: [56, 21] Generated Node #0,1,2: 47:[56, 21] Operation: 58-37=21 Moving to Node #0,0 Current State: 47:[37, 29, 54], Operations: ['56-2=54'] Exploring Operation: 54-29=25, Resulting Numbers: [37, 25] Generated Node #0,0,0: 47:[37, 25] Operation: 54-29=25 Exploring Operation: 37+29=66, Resulting Numbers: [54, 66] Generated Node #0,0,1: 47:[54, 66] Operation: 37+29=66 Exploring Operation: 37-29=8, Resulting Numbers: [54, 8] Generated Node #0,0,2: 47:[54, 8] Operation: 37-29=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[54, 66], Operations: ['56-2=54', '37+29=66'] Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,47 unequal: No Solution Exploring Operation: 54*66=3564, Resulting Numbers: [3564] 3564,47 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 #0,0,0 Current State: 47:[37, 25], Operations: ['56-2=54', '54-29=25'] Exploring Operation: 37*25=925, Resulting Numbers: [925] 925,47 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,47 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 #0,0,2 Current State: 47:[54, 8], Operations: ['56-2=54', '37-29=8'] Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,47 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 54*8=432, Resulting Numbers: [432] 432,47 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: 47:[56, 29, 39], Operations: ['2+37=39'] Exploring Operation: 56-29=27, Resulting Numbers: [39, 27] Generated Node #0,2,0: 47:[39, 27] Operation: 56-29=27 Exploring Operation: 56+29=85, Resulting Numbers: [39, 85] Generated Node #0,2,1: 47:[39, 85] Operation: 56+29=85 Exploring Operation: 29+39=68, Resulting Numbers: [56, 68] Generated Node #0,2,2: 47:[56, 68] Operation: 29+39=68 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[39, 27], Operations: ['2+37=39', '56-29=27'] Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,47 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[56, 68], Operations: ['2+37=39', '29+39=68'] Exploring Operation: 56*68=3808, Resulting Numbers: [3808] 3808,47 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 56+68=124, Resulting Numbers: [124] 124,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[39, 85], Operations: ['2+37=39', '56+29=85'] Exploring Operation: 85-39=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 39+85=124, Resulting Numbers: [124] 124,47 unequal: No Solution Exploring Operation: 39*85=3315, Resulting Numbers: [3315] 3315,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 47:[56, 21], Operations: ['2*29=58', '58-37=21'] Exploring Operation: 56+21=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 56*21=1176, Resulting Numbers: [1176] 1176,47 unequal: No Solution Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[58, 19], Operations: ['2*29=58', '56-37=19'] Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 58*19=1102, Resulting Numbers: [1102] 1102,47 unequal: No Solution Exploring Operation: 58+19=77, Resulting Numbers: [77] 77,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[37, 2], Operations: ['2*29=58', '58-56=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,47 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 83, 74, 94, 86 ]
23
[ "83+74=157", "94+86=180", "180-157=23" ]
Current State: 23:[83, 74, 94, 86], Operations: [] Exploring Operation: 83+74=157, Resulting Numbers: [94, 86, 157] Generated Node #2: [94, 86, 157] from Operation: 83+74=157 Current State: 23:[94, 86, 157], Operations: ['83+74=157'] Exploring Operation: 94+86=180, Resulting Numbers: [157, 180] Generated Node #3: [157, 180] from Operation: 94+86=180 Current State: 23:[157, 180], Operations: ['83+74=157', '94+86=180'] Exploring Operation: 180-157=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[83, 74, 94, 86], Operations: [] Exploring Operation: 94-83=11, Resulting Numbers: [74, 86, 11] Generated Node #0,0: 23:[74, 86, 11] Operation: 94-83=11 Exploring Operation: 94-74=20, Resulting Numbers: [83, 86, 20] Generated Node #0,1: 23:[83, 86, 20] Operation: 94-74=20 Exploring Operation: 94-86=8, Resulting Numbers: [83, 74, 8] Generated Node #0,2: 23:[83, 74, 8] Operation: 94-86=8 Exploring Operation: 86-83=3, Resulting Numbers: [74, 94, 3] Generated Node #0,3: 23:[74, 94, 3] Operation: 86-83=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[74, 86, 11], Operations: ['94-83=11'] Exploring Operation: 86-11=75, Resulting Numbers: [74, 75] Generated Node #0,0,0: 23:[74, 75] Operation: 86-11=75 Exploring Operation: 74-11=63, Resulting Numbers: [86, 63] Generated Node #0,0,1: 23:[86, 63] Operation: 74-11=63 Exploring Operation: 86-74=12, Resulting Numbers: [11, 12] Generated Node #0,0,2: 23:[11, 12] Operation: 86-74=12 Exploring Operation: 74+11=85, Resulting Numbers: [86, 85] Generated Node #0,0,3: 23:[86, 85] Operation: 74+11=85 Moving to Node #0,0,2 Current State: 23:[11, 12], Operations: ['94-83=11', '86-74=12'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[83, 74, 94, 86], Operations: [] Exploring Operation: 94-83=11, Resulting Numbers: [74, 86, 11] Generated Node #0,0: 23:[74, 86, 11] Operation: 94-83=11 Moving to Node #0,0 Current State: 23:[74, 86, 11], Operations: ['94-83=11'] Exploring Operation: 86-74=12, Resulting Numbers: [11, 12] Generated Node #0,0,2: 23:[11, 12] Operation: 86-74=12 Moving to Node #0,0,2 Current State: 23:[11, 12], Operations: ['94-83=11', '86-74=12'] Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 15, 12, 86, 86 ]
28
[ "15+12=27", "86/86=1", "27+1=28" ]
Current State: 28:[15, 12, 86, 86], Operations: [] Exploring Operation: 15+12=27, Resulting Numbers: [86, 86, 27] Generated Node #2: [86, 86, 27] from Operation: 15+12=27 Current State: 28:[86, 86, 27], Operations: ['15+12=27'] Exploring Operation: 86/86=1, Resulting Numbers: [27, 1] Generated Node #3: [27, 1] from Operation: 86/86=1 Current State: 28:[27, 1], Operations: ['15+12=27', '86/86=1'] Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[15, 12, 86, 86], Operations: [] Exploring Operation: 86/86=1, Resulting Numbers: [15, 12, 1] Generated Node #0,0: 28:[15, 12, 1] Operation: 86/86=1 Exploring Operation: 86-15=71, Resulting Numbers: [12, 86, 71] Generated Node #0,1: 28:[12, 86, 71] Operation: 86-15=71 Exploring Operation: 86-86=0, Resulting Numbers: [15, 12, 0] Generated Node #0,2: 28:[15, 12, 0] Operation: 86-86=0 Moving to Node #0,0 Current State: 28:[15, 12, 1], Operations: ['86/86=1'] Exploring Operation: 15-12=3, Resulting Numbers: [1, 3] Generated Node #0,0,0: 28:[1, 3] Operation: 15-12=3 Exploring Operation: 15+12=27, Resulting Numbers: [1, 27] Generated Node #0,0,1: 28:[1, 27] Operation: 15+12=27 Exploring Operation: 15-1=14, Resulting Numbers: [12, 14] Generated Node #0,0,2: 28:[12, 14] Operation: 15-1=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[1, 3], Operations: ['86/86=1', '15-12=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,28 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 28:[1, 27], Operations: ['86/86=1', '15+12=27'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,28 unequal: No Solution Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[15, 12, 86, 86], Operations: [] Exploring Operation: 86/86=1, Resulting Numbers: [15, 12, 1] Generated Node #0,0: 28:[15, 12, 1] Operation: 86/86=1 Moving to Node #0,0 Current State: 28:[15, 12, 1], Operations: ['86/86=1'] Exploring Operation: 15+12=27, Resulting Numbers: [1, 27] Generated Node #0,0,1: 28:[1, 27] Operation: 15+12=27 Moving to Node #0,0,1 Current State: 28:[1, 27], Operations: ['86/86=1', '15+12=27'] Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 64, 12, 69, 57 ]
74
[ "64-12=52", "69+57=126", "126-52=74" ]
Current State: 74:[64, 12, 69, 57], Operations: [] Exploring Operation: 64-12=52, Resulting Numbers: [69, 57, 52] Generated Node #2: [69, 57, 52] from Operation: 64-12=52 Current State: 74:[69, 57, 52], Operations: ['64-12=52'] Exploring Operation: 69+57=126, Resulting Numbers: [52, 126] Generated Node #3: [52, 126] from Operation: 69+57=126 Current State: 74:[52, 126], Operations: ['64-12=52', '69+57=126'] Exploring Operation: 126-52=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[64, 12, 69, 57], Operations: [] Exploring Operation: 64-57=7, Resulting Numbers: [12, 69, 7] Generated Node #0,0: 74:[12, 69, 7] Operation: 64-57=7 Moving to Node #0,0 Current State: 74:[12, 69, 7], Operations: ['64-57=7'] Exploring Operation: 12-7=5, Resulting Numbers: [69, 5] Generated Node #0,0,0: 74:[69, 5] Operation: 12-7=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[69, 5], Operations: ['64-57=7', '12-7=5'] Exploring Operation: 69+5=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[64, 12, 69, 57], Operations: [] Exploring Operation: 64-57=7, Resulting Numbers: [12, 69, 7] Generated Node #0,0: 74:[12, 69, 7] Operation: 64-57=7 Moving to Node #0,0 Current State: 74:[12, 69, 7], Operations: ['64-57=7'] Exploring Operation: 12-7=5, Resulting Numbers: [69, 5] Generated Node #0,0,0: 74:[69, 5] Operation: 12-7=5 Moving to Node #0,0,0 Current State: 74:[69, 5], Operations: ['64-57=7', '12-7=5'] Exploring Operation: 69+5=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 84, 88, 51, 48 ]
39
[ "88-84=4", "48/4=12", "51-12=39" ]
Current State: 39:[84, 88, 51, 48], Operations: [] Exploring Operation: 88-84=4, Resulting Numbers: [51, 48, 4] Generated Node #2: [51, 48, 4] from Operation: 88-84=4 Current State: 39:[51, 48, 4], Operations: ['88-84=4'] Exploring Operation: 48/4=12, Resulting Numbers: [51, 12] Generated Node #3: [51, 12] from Operation: 48/4=12 Current State: 39:[51, 12], Operations: ['88-84=4', '48/4=12'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[84, 88, 51, 48], Operations: [] Exploring Operation: 88-84=4, Resulting Numbers: [51, 48, 4] Generated Node #0,0: 39:[51, 48, 4] Operation: 88-84=4 Exploring Operation: 88-51=37, Resulting Numbers: [84, 48, 37] Generated Node #0,1: 39:[84, 48, 37] Operation: 88-51=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[51, 48, 4], Operations: ['88-84=4'] Exploring Operation: 51-48=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 39:[4, 3] Operation: 51-48=3 Exploring Operation: 48/4=12, Resulting Numbers: [51, 12] Generated Node #0,0,1: 39:[51, 12] Operation: 48/4=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[4, 3], Operations: ['88-84=4', '51-48=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[51, 12], Operations: ['88-84=4', '48/4=12'] Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,39 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[84, 88, 51, 48], Operations: [] Exploring Operation: 88-84=4, Resulting Numbers: [51, 48, 4] Generated Node #0,0: 39:[51, 48, 4] Operation: 88-84=4 Moving to Node #0,0 Current State: 39:[51, 48, 4], Operations: ['88-84=4'] Exploring Operation: 48/4=12, Resulting Numbers: [51, 12] Generated Node #0,0,1: 39:[51, 12] Operation: 48/4=12 Moving to Node #0,0,1 Current State: 39:[51, 12], Operations: ['88-84=4', '48/4=12'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 22, 65, 84, 48 ]
51
[ "22+65=87", "84-48=36", "87-36=51" ]
Current State: 51:[22, 65, 84, 48], Operations: [] Exploring Operation: 22+65=87, Resulting Numbers: [84, 48, 87] Generated Node #2: [84, 48, 87] from Operation: 22+65=87 Current State: 51:[84, 48, 87], Operations: ['22+65=87'] Exploring Operation: 84-48=36, Resulting Numbers: [87, 36] Generated Node #3: [87, 36] from Operation: 84-48=36 Current State: 51:[87, 36], Operations: ['22+65=87', '84-48=36'] Exploring Operation: 87-36=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[22, 65, 84, 48], Operations: [] Exploring Operation: 84-22=62, Resulting Numbers: [65, 48, 62] Generated Node #0,0: 51:[65, 48, 62] Operation: 84-22=62 Exploring Operation: 65-48=17, Resulting Numbers: [22, 84, 17] Generated Node #0,1: 51:[22, 84, 17] Operation: 65-48=17 Exploring Operation: 84-65=19, Resulting Numbers: [22, 48, 19] Generated Node #0,2: 51:[22, 48, 19] Operation: 84-65=19 Exploring Operation: 84-48=36, Resulting Numbers: [22, 65, 36] Generated Node #0,3: 51:[22, 65, 36] Operation: 84-48=36 Moving to Node #0,2 Current State: 51:[22, 48, 19], Operations: ['84-65=19'] Exploring Operation: 48-22=26, Resulting Numbers: [19, 26] Generated Node #0,2,0: 51:[19, 26] Operation: 48-22=26 Exploring Operation: 22-19=3, Resulting Numbers: [48, 3] Generated Node #0,2,1: 51:[48, 3] Operation: 22-19=3 Exploring Operation: 22+19=41, Resulting Numbers: [48, 41] Generated Node #0,2,2: 51:[48, 41] Operation: 22+19=41 Exploring Operation: 48-19=29, Resulting Numbers: [22, 29] Generated Node #0,2,3: 51:[22, 29] Operation: 48-19=29 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[48, 3], Operations: ['84-65=19', '22-19=3'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,51 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[22, 65, 84, 48], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [22, 48, 19] Generated Node #0,2: 51:[22, 48, 19] Operation: 84-65=19 Moving to Node #0,2 Current State: 51:[22, 48, 19], Operations: ['84-65=19'] Exploring Operation: 22-19=3, Resulting Numbers: [48, 3] Generated Node #0,2,1: 51:[48, 3] Operation: 22-19=3 Moving to Node #0,2,1 Current State: 51:[48, 3], Operations: ['84-65=19', '22-19=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 74, 52, 96, 54 ]
85
[ "74+96=170", "54-52=2", "170/2=85" ]
Current State: 85:[74, 52, 96, 54], Operations: [] Exploring Operation: 74+96=170, Resulting Numbers: [52, 54, 170] Generated Node #2: [52, 54, 170] from Operation: 74+96=170 Current State: 85:[52, 54, 170], Operations: ['74+96=170'] Exploring Operation: 54-52=2, Resulting Numbers: [170, 2] Generated Node #3: [170, 2] from Operation: 54-52=2 Current State: 85:[170, 2], Operations: ['74+96=170', '54-52=2'] Exploring Operation: 170/2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[74, 52, 96, 54], Operations: [] Exploring Operation: 52+54=106, Resulting Numbers: [74, 96, 106] Generated Node #0,0: 85:[74, 96, 106] Operation: 52+54=106 Exploring Operation: 54-52=2, Resulting Numbers: [74, 96, 2] Generated Node #0,1: 85:[74, 96, 2] Operation: 54-52=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[74, 96, 2], Operations: ['54-52=2'] Exploring Operation: 74+2=76, Resulting Numbers: [96, 76] Generated Node #0,1,0: 85:[96, 76] Operation: 74+2=76 Exploring Operation: 96-74=22, Resulting Numbers: [2, 22] Generated Node #0,1,1: 85:[2, 22] Operation: 96-74=22 Moving to Node #0,1,1 Current State: 85:[2, 22], Operations: ['54-52=2', '96-74=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[96, 76], Operations: ['54-52=2', '74+2=76'] Exploring Operation: 96+76=172, Resulting Numbers: [172] 172,85 unequal: No Solution Exploring Operation: 96-76=20, Resulting Numbers: [20] 20,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[74, 96, 106], Operations: ['52+54=106'] Exploring Operation: 106-96=10, Resulting Numbers: [74, 10] Generated Node #0,0,0: 85:[74, 10] Operation: 106-96=10 Exploring Operation: 96-74=22, Resulting Numbers: [106, 22] Generated Node #0,0,1: 85:[106, 22] Operation: 96-74=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[74, 10], Operations: ['52+54=106', '106-96=10'] Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[106, 22], Operations: ['52+54=106', '96-74=22'] Exploring Operation: 106-22=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 106+22=128, Resulting Numbers: [128] 128,85 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_2
mult_heuristic
[ 85, 10, 7, 34 ]
83
[ "10+7=17", "34/17=2", "85-2=83" ]
Current State: 83:[85, 10, 7, 34], Operations: [] Exploring Operation: 10+7=17, Resulting Numbers: [85, 34, 17] Generated Node #2: [85, 34, 17] from Operation: 10+7=17 Current State: 83:[85, 34, 17], Operations: ['10+7=17'] Exploring Operation: 34/17=2, Resulting Numbers: [85, 2] Generated Node #3: [85, 2] from Operation: 34/17=2 Current State: 83:[85, 2], Operations: ['10+7=17', '34/17=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[85, 10, 7, 34], Operations: [] Exploring Operation: 85-7=78, Resulting Numbers: [10, 34, 78] Generated Node #0,0: 83:[10, 34, 78] Operation: 85-7=78 Exploring Operation: 7+34=41, Resulting Numbers: [85, 10, 41] Generated Node #0,1: 83:[85, 10, 41] Operation: 7+34=41 Exploring Operation: 10+34=44, Resulting Numbers: [85, 7, 44] Generated Node #0,2: 83:[85, 7, 44] Operation: 10+34=44 Exploring Operation: 10*7=70, Resulting Numbers: [85, 34, 70] Generated Node #0,3: 83:[85, 34, 70] Operation: 10*7=70 Exploring Operation: 10+7=17, Resulting Numbers: [85, 34, 17] Generated Node #0,4: 83:[85, 34, 17] Operation: 10+7=17 Moving to Node #0,3 Current State: 83:[85, 34, 70], Operations: ['10*7=70'] Exploring Operation: 85+34=119, Resulting Numbers: [70, 119] Generated Node #0,3,0: 83:[70, 119] Operation: 85+34=119 Exploring Operation: 85-34=51, Resulting Numbers: [70, 51] Generated Node #0,3,1: 83:[70, 51] Operation: 85-34=51 Exploring Operation: 34+70=104, Resulting Numbers: [85, 104] Generated Node #0,3,2: 83:[85, 104] Operation: 34+70=104 Exploring Operation: 85-70=15, Resulting Numbers: [34, 15] Generated Node #0,3,3: 83:[34, 15] Operation: 85-70=15 Exploring Operation: 70-34=36, Resulting Numbers: [85, 36] Generated Node #0,3,4: 83:[85, 36] Operation: 70-34=36 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 83:[85, 104], Operations: ['10*7=70', '34+70=104'] Exploring Operation: 85*104=8840, Resulting Numbers: [8840] 8840,83 unequal: No Solution Exploring Operation: 85+104=189, Resulting Numbers: [189] 189,83 unequal: No Solution Exploring Operation: 104-85=19, Resulting Numbers: [19] 19,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 83:[70, 51], Operations: ['10*7=70', '85-34=51'] Exploring Operation: 70+51=121, Resulting Numbers: [121] 121,83 unequal: No Solution Exploring Operation: 70*51=3570, Resulting Numbers: [3570] 3570,83 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 83:[70, 119], Operations: ['10*7=70', '85+34=119'] Exploring Operation: 119-70=49, Resulting Numbers: [49] 49,83 unequal: No Solution Exploring Operation: 70+119=189, Resulting Numbers: [189] 189,83 unequal: No Solution Exploring Operation: 70*119=8330, Resulting Numbers: [8330] 8330,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 83:[85, 36], Operations: ['10*7=70', '70-34=36'] Exploring Operation: 85-36=49, Resulting Numbers: [49] 49,83 unequal: No Solution Exploring Operation: 85+36=121, Resulting Numbers: [121] 121,83 unequal: No Solution Exploring Operation: 85*36=3060, Resulting Numbers: [3060] 3060,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 83:[34, 15], Operations: ['10*7=70', '85-70=15'] Exploring Operation: 34*15=510, Resulting Numbers: [510] 510,83 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,83 unequal: No Solution Exploring Operation: 34+15=49, Resulting Numbers: [49] 49,83 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:[85, 7, 44], Operations: ['10+34=44'] Exploring Operation: 85-7=78, Resulting Numbers: [44, 78] Generated Node #0,2,0: 83:[44, 78] Operation: 85-7=78 Exploring Operation: 7+44=51, Resulting Numbers: [85, 51] Generated Node #0,2,1: 83:[85, 51] Operation: 7+44=51 Exploring Operation: 85+7=92, Resulting Numbers: [44, 92] Generated Node #0,2,2: 83:[44, 92] Operation: 85+7=92 Exploring Operation: 44-7=37, Resulting Numbers: [85, 37] Generated Node #0,2,3: 83:[85, 37] Operation: 44-7=37 Exploring Operation: 85-44=41, Resulting Numbers: [7, 41] Generated Node #0,2,4: 83:[7, 41] Operation: 85-44=41 Moving to Node #0,1 Current State: 83:[85, 10, 41], Operations: ['7+34=41'] Exploring Operation: 85+10=95, Resulting Numbers: [41, 95] Generated Node #0,1,0: 83:[41, 95] Operation: 85+10=95 Exploring Operation: 85-41=44, Resulting Numbers: [10, 44] Generated Node #0,1,1: 83:[10, 44] Operation: 85-41=44 Exploring Operation: 85-10=75, Resulting Numbers: [41, 75] Generated Node #0,1,2: 83:[41, 75] Operation: 85-10=75 Exploring Operation: 41-10=31, Resulting Numbers: [85, 31] Generated Node #0,1,3: 83:[85, 31] Operation: 41-10=31 Exploring Operation: 10+41=51, Resulting Numbers: [85, 51] Generated Node #0,1,4: 83:[85, 51] Operation: 10+41=51 Moving to Node #0,4 Current State: 83:[85, 34, 17], Operations: ['10+7=17'] Exploring Operation: 34+17=51, Resulting Numbers: [85, 51] Generated Node #0,4,0: 83:[85, 51] Operation: 34+17=51 Exploring Operation: 85+17=102, Resulting Numbers: [34, 102] Generated Node #0,4,1: 83:[34, 102] Operation: 85+17=102 Exploring Operation: 34/17=2, Resulting Numbers: [85, 2] Generated Node #0,4,2: 83:[85, 2] Operation: 34/17=2 Exploring Operation: 34-17=17, Resulting Numbers: [85, 17] Generated Node #0,4,3: 83:[85, 17] Operation: 34-17=17 Exploring Operation: 85-17=68, Resulting Numbers: [34, 68] Generated Node #0,4,4: 83:[34, 68] Operation: 85-17=68 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 83:[85, 51], Operations: ['10+7=17', '34+17=51'] Exploring Operation: 85*51=4335, Resulting Numbers: [4335] 4335,83 unequal: No Solution Exploring Operation: 85+51=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 85-51=34, Resulting Numbers: [34] 34,83 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 #0,4,4 Current State: 83:[34, 68], Operations: ['10+7=17', '85-17=68'] Exploring Operation: 34*68=2312, Resulting Numbers: [2312] 2312,83 unequal: No Solution Exploring Operation: 68-34=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 34+68=102, Resulting Numbers: [102] 102,83 unequal: No Solution Exploring Operation: 68/34=2, Resulting Numbers: [2] 2,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 83:[34, 102], Operations: ['10+7=17', '85+17=102'] Exploring Operation: 102/34=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 102-34=68, Resulting Numbers: [68] 68,83 unequal: No Solution Exploring Operation: 34*102=3468, Resulting Numbers: [3468] 3468,83 unequal: No Solution Exploring Operation: 34+102=136, Resulting Numbers: [136] 136,83 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 #0,4,3 Current State: 83:[85, 17], Operations: ['10+7=17', '34-17=17'] Exploring Operation: 85*17=1445, Resulting Numbers: [1445] 1445,83 unequal: No Solution Exploring Operation: 85-17=68, Resulting Numbers: [68] 68,83 unequal: No Solution Exploring Operation: 85+17=102, Resulting Numbers: [102] 102,83 unequal: No Solution Exploring Operation: 85/17=5, Resulting Numbers: [5] 5,83 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 #0,4,2 Current State: 83:[85, 2], Operations: ['10+7=17', '34/17=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[85, 10, 7, 34], Operations: [] Exploring Operation: 10+7=17, Resulting Numbers: [85, 34, 17] Generated Node #0,4: 83:[85, 34, 17] Operation: 10+7=17 Moving to Node #0,4 Current State: 83:[85, 34, 17], Operations: ['10+7=17'] Exploring Operation: 34/17=2, Resulting Numbers: [85, 2] Generated Node #0,4,2: 83:[85, 2] Operation: 34/17=2 Moving to Node #0,4,2 Current State: 83:[85, 2], Operations: ['10+7=17', '34/17=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.947049
hs_5
mult_heuristic
[ 66, 34, 3, 11 ]
47
[ "66-11=55", "34*3=102", "102-55=47" ]
Current State: 47:[66, 34, 3, 11], Operations: [] Exploring Operation: 66-11=55, Resulting Numbers: [34, 3, 55] Generated Node #2: [34, 3, 55] from Operation: 66-11=55 Current State: 47:[34, 3, 55], Operations: ['66-11=55'] Exploring Operation: 34*3=102, Resulting Numbers: [55, 102] Generated Node #3: [55, 102] from Operation: 34*3=102 Current State: 47:[55, 102], Operations: ['66-11=55', '34*3=102'] Exploring Operation: 102-55=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[66, 34, 3, 11], Operations: [] Exploring Operation: 66-3=63, Resulting Numbers: [34, 11, 63] Generated Node #0,0: 47:[34, 11, 63] Operation: 66-3=63 Exploring Operation: 3*11=33, Resulting Numbers: [66, 34, 33] Generated Node #0,1: 47:[66, 34, 33] Operation: 3*11=33 Moving to Node #0,1 Current State: 47:[66, 34, 33], Operations: ['3*11=33'] Exploring Operation: 66-33=33, Resulting Numbers: [34, 33] Generated Node #0,1,0: 47:[34, 33] Operation: 66-33=33 Exploring Operation: 66-34=32, Resulting Numbers: [33, 32] Generated Node #0,1,1: 47:[33, 32] Operation: 66-34=32 Moving to Node #0,0 Current State: 47:[34, 11, 63], Operations: ['66-3=63'] Exploring Operation: 34+11=45, Resulting Numbers: [63, 45] Generated Node #0,0,0: 47:[63, 45] Operation: 34+11=45 Exploring Operation: 63-11=52, Resulting Numbers: [34, 52] Generated Node #0,0,1: 47:[34, 52] Operation: 63-11=52 Moving to Node #0,0,0 Current State: 47:[63, 45], Operations: ['66-3=63', '34+11=45'] Exploring Operation: 63+45=108, Resulting Numbers: [108] 108,47 unequal: No Solution Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[34, 52], Operations: ['66-3=63', '63-11=52'] Exploring Operation: 34+52=86, Resulting Numbers: [86] 86,47 unequal: No Solution Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[34, 33], Operations: ['3*11=33', '66-33=33'] Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[33, 32], Operations: ['3*11=33', '66-34=32'] Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,47 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 24, 37, 4, 7 ]
64
[ "24+37=61", "7-4=3", "61+3=64" ]
Current State: 64:[24, 37, 4, 7], Operations: [] Exploring Operation: 24+37=61, Resulting Numbers: [4, 7, 61] Generated Node #2: [4, 7, 61] from Operation: 24+37=61 Current State: 64:[4, 7, 61], Operations: ['24+37=61'] Exploring Operation: 7-4=3, Resulting Numbers: [61, 3] Generated Node #3: [61, 3] from Operation: 7-4=3 Current State: 64:[61, 3], Operations: ['24+37=61', '7-4=3'] Exploring Operation: 61+3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[24, 37, 4, 7], Operations: [] Exploring Operation: 24-7=17, Resulting Numbers: [37, 4, 17] Generated Node #0,0: 64:[37, 4, 17] Operation: 24-7=17 Exploring Operation: 37-24=13, Resulting Numbers: [4, 7, 13] Generated Node #0,1: 64:[4, 7, 13] Operation: 37-24=13 Exploring Operation: 24+37=61, Resulting Numbers: [4, 7, 61] Generated Node #0,2: 64:[4, 7, 61] Operation: 24+37=61 Exploring Operation: 24+7=31, Resulting Numbers: [37, 4, 31] Generated Node #0,3: 64:[37, 4, 31] Operation: 24+7=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[4, 7, 13], Operations: ['37-24=13'] Exploring Operation: 13-7=6, Resulting Numbers: [4, 6] Generated Node #0,1,0: 64:[4, 6] Operation: 13-7=6 Exploring Operation: 13-4=9, Resulting Numbers: [7, 9] Generated Node #0,1,1: 64:[7, 9] Operation: 13-4=9 Exploring Operation: 7-4=3, Resulting Numbers: [13, 3] Generated Node #0,1,2: 64:[13, 3] Operation: 7-4=3 Exploring Operation: 4+13=17, Resulting Numbers: [7, 17] Generated Node #0,1,3: 64:[7, 17] Operation: 4+13=17 Moving to Node #0,1,0 Current State: 64:[4, 6], Operations: ['37-24=13', '13-7=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,64 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,64 unequal: No Solution Moving to Node #0,1,3 Current State: 64:[7, 17], Operations: ['37-24=13', '4+13=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,64 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[7, 9], Operations: ['37-24=13', '13-4=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,64 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,64 unequal: No Solution Moving to Node #0,1,2 Current State: 64:[13, 3], Operations: ['37-24=13', '7-4=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[4, 7, 61], Operations: ['24+37=61'] Exploring Operation: 7-4=3, Resulting Numbers: [61, 3] Generated Node #0,2,0: 64:[61, 3] Operation: 7-4=3 Exploring Operation: 4+61=65, Resulting Numbers: [7, 65] Generated Node #0,2,1: 64:[7, 65] Operation: 4+61=65 Exploring Operation: 7+61=68, Resulting Numbers: [4, 68] Generated Node #0,2,2: 64:[4, 68] Operation: 7+61=68 Exploring Operation: 4+7=11, Resulting Numbers: [61, 11] Generated Node #0,2,3: 64:[61, 11] Operation: 4+7=11 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 64:[7, 65], Operations: ['24+37=61', '4+61=65'] Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,64 unequal: No Solution Exploring Operation: 7*65=455, Resulting Numbers: [455] 455,64 unequal: No Solution Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,64 unequal: No Solution No 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: 64:[61, 3], Operations: ['24+37=61', '7-4=3'] Exploring Operation: 61*3=183, Resulting Numbers: [183] 183,64 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,64 unequal: No Solution Exploring Operation: 61+3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[24, 37, 4, 7], Operations: [] Exploring Operation: 24+37=61, Resulting Numbers: [4, 7, 61] Generated Node #0,2: 64:[4, 7, 61] Operation: 24+37=61 Moving to Node #0,2 Current State: 64:[4, 7, 61], Operations: ['24+37=61'] Exploring Operation: 7-4=3, Resulting Numbers: [61, 3] Generated Node #0,2,0: 64:[61, 3] Operation: 7-4=3 Moving to Node #0,2,0 Current State: 64:[61, 3], Operations: ['24+37=61', '7-4=3'] Exploring Operation: 61+3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 18, 51, 52, 76 ]
68
[ "76-52=24", "51*24=1224", "1224/18=68" ]
Current State: 68:[18, 51, 52, 76], Operations: [] Exploring Operation: 76-52=24, Resulting Numbers: [18, 51, 24] Generated Node #2: [18, 51, 24] from Operation: 76-52=24 Current State: 68:[18, 51, 24], Operations: ['76-52=24'] Exploring Operation: 51*24=1224, Resulting Numbers: [18, 1224] Generated Node #3: [18, 1224] from Operation: 51*24=1224 Current State: 68:[18, 1224], Operations: ['76-52=24', '51*24=1224'] Exploring Operation: 1224/18=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[18, 51, 52, 76], Operations: [] Exploring Operation: 52-51=1, Resulting Numbers: [18, 76, 1] Generated Node #0,0: 68:[18, 76, 1] Operation: 52-51=1 Exploring Operation: 18+51=69, Resulting Numbers: [52, 76, 69] Generated Node #0,1: 68:[52, 76, 69] Operation: 18+51=69 Exploring Operation: 51-18=33, Resulting Numbers: [52, 76, 33] Generated Node #0,2: 68:[52, 76, 33] Operation: 51-18=33 Moving to Node #0,0 Current State: 68:[18, 76, 1], Operations: ['52-51=1'] Exploring Operation: 18-1=17, Resulting Numbers: [76, 17] Generated Node #0,0,0: 68:[76, 17] Operation: 18-1=17 Exploring Operation: 76-1=75, Resulting Numbers: [18, 75] Generated Node #0,0,1: 68:[18, 75] Operation: 76-1=75 Exploring Operation: 18*1=18, Resulting Numbers: [76, 18] Generated Node #0,0,2: 68:[76, 18] Operation: 18*1=18 Moving to Node #0,1 Current State: 68:[52, 76, 69], Operations: ['18+51=69'] Exploring Operation: 76-52=24, Resulting Numbers: [69, 24] Generated Node #0,1,0: 68:[69, 24] Operation: 76-52=24 Exploring Operation: 69-52=17, Resulting Numbers: [76, 17] Generated Node #0,1,1: 68:[76, 17] Operation: 69-52=17 Exploring Operation: 76-69=7, Resulting Numbers: [52, 7] Generated Node #0,1,2: 68:[52, 7] Operation: 76-69=7 Moving to Node #0,2 Current State: 68:[52, 76, 33], Operations: ['51-18=33'] Exploring Operation: 76-52=24, Resulting Numbers: [33, 24] Generated Node #0,2,0: 68:[33, 24] Operation: 76-52=24 Exploring Operation: 52+33=85, Resulting Numbers: [76, 85] Generated Node #0,2,1: 68:[76, 85] Operation: 52+33=85 Exploring Operation: 52-33=19, Resulting Numbers: [76, 19] Generated Node #0,2,2: 68:[76, 19] Operation: 52-33=19 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 68:[33, 24], Operations: ['51-18=33', '76-52=24'] Exploring Operation: 33+24=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 33*24=792, Resulting Numbers: [792] 792,68 unequal: No Solution Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 68:[76, 19], Operations: ['51-18=33', '52-33=19'] Exploring Operation: 76/19=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 76+19=95, Resulting Numbers: [95] 95,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[76, 85], Operations: ['51-18=33', '52+33=85'] Exploring Operation: 76*85=6460, Resulting Numbers: [6460] 6460,68 unequal: No Solution Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 76+85=161, Resulting Numbers: [161] 161,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 68:[76, 17], Operations: ['52-51=1', '18-1=17'] Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 76*17=1292, Resulting Numbers: [1292] 1292,68 unequal: No Solution Exploring Operation: 76+17=93, Resulting Numbers: [93] 93,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[18, 75], Operations: ['52-51=1', '76-1=75'] Exploring Operation: 18+75=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 18*75=1350, Resulting Numbers: [1350] 1350,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[76, 17], Operations: ['18+51=69', '69-52=17'] Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 76+17=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 76*17=1292, Resulting Numbers: [1292] 1292,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[69, 24], Operations: ['18+51=69', '76-52=24'] Exploring Operation: 69+24=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 69*24=1656, Resulting Numbers: [1656] 1656,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[76, 18], Operations: ['52-51=1', '18*1=18'] Exploring Operation: 76*18=1368, Resulting Numbers: [1368] 1368,68 unequal: No Solution Exploring Operation: 76+18=94, Resulting Numbers: [94] 94,68 unequal: No Solution Exploring Operation: 76-18=58, Resulting Numbers: [58] 58,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[52, 7], Operations: ['18+51=69', '76-69=7'] Exploring Operation: 52+7=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 52*7=364, Resulting Numbers: [364] 364,68 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 14, 94, 6, 56 ]
92
[ "56/14=4", "94-6=88", "4+88=92" ]
Current State: 92:[14, 94, 6, 56], Operations: [] Exploring Operation: 56/14=4, Resulting Numbers: [94, 6, 4] Generated Node #2: [94, 6, 4] from Operation: 56/14=4 Current State: 92:[94, 6, 4], Operations: ['56/14=4'] Exploring Operation: 94-6=88, Resulting Numbers: [4, 88] Generated Node #3: [4, 88] from Operation: 94-6=88 Current State: 92:[4, 88], Operations: ['56/14=4', '94-6=88'] Exploring Operation: 4+88=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[14, 94, 6, 56], Operations: [] Exploring Operation: 56-14=42, Resulting Numbers: [94, 6, 42] Generated Node #0,0: 92:[94, 6, 42] Operation: 56-14=42 Exploring Operation: 56/14=4, Resulting Numbers: [94, 6, 4] Generated Node #0,1: 92:[94, 6, 4] Operation: 56/14=4 Moving to Node #0,1 Current State: 92:[94, 6, 4], Operations: ['56/14=4'] Exploring Operation: 6-4=2, Resulting Numbers: [94, 2] Generated Node #0,1,0: 92:[94, 2] Operation: 6-4=2 Exploring Operation: 6*4=24, Resulting Numbers: [94, 24] Generated Node #0,1,1: 92:[94, 24] Operation: 6*4=24 Moving to Node #0,0 Current State: 92:[94, 6, 42], Operations: ['56-14=42'] Exploring Operation: 6+42=48, Resulting Numbers: [94, 48] Generated Node #0,0,0: 92:[94, 48] Operation: 6+42=48 Exploring Operation: 42/6=7, Resulting Numbers: [94, 7] Generated Node #0,0,1: 92:[94, 7] Operation: 42/6=7 Moving to Node #0,1,0 Current State: 92:[94, 2], Operations: ['56/14=4', '6-4=2'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,92 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[14, 94, 6, 56], Operations: [] Exploring Operation: 56/14=4, Resulting Numbers: [94, 6, 4] Generated Node #0,1: 92:[94, 6, 4] Operation: 56/14=4 Moving to Node #0,1 Current State: 92:[94, 6, 4], Operations: ['56/14=4'] Exploring Operation: 6-4=2, Resulting Numbers: [94, 2] Generated Node #0,1,0: 92:[94, 2] Operation: 6-4=2 Moving to Node #0,1,0 Current State: 92:[94, 2], Operations: ['56/14=4', '6-4=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 65, 94, 38, 48 ]
57
[ "94-65=29", "38+48=86", "86-29=57" ]
Current State: 57:[65, 94, 38, 48], Operations: [] Exploring Operation: 94-65=29, Resulting Numbers: [38, 48, 29] Generated Node #2: [38, 48, 29] from Operation: 94-65=29 Current State: 57:[38, 48, 29], Operations: ['94-65=29'] Exploring Operation: 38+48=86, Resulting Numbers: [29, 86] Generated Node #3: [29, 86] from Operation: 38+48=86 Current State: 57:[29, 86], Operations: ['94-65=29', '38+48=86'] Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[65, 94, 38, 48], Operations: [] Exploring Operation: 94-65=29, Resulting Numbers: [38, 48, 29] Generated Node #0,0: 57:[38, 48, 29] Operation: 94-65=29 Exploring Operation: 94-48=46, Resulting Numbers: [65, 38, 46] Generated Node #0,1: 57:[65, 38, 46] Operation: 94-48=46 Exploring Operation: 94-38=56, Resulting Numbers: [65, 48, 56] Generated Node #0,2: 57:[65, 48, 56] Operation: 94-38=56 Moving to Node #0,2 Current State: 57:[65, 48, 56], Operations: ['94-38=56'] Exploring Operation: 65-48=17, Resulting Numbers: [56, 17] Generated Node #0,2,0: 57:[56, 17] Operation: 65-48=17 Exploring Operation: 56-48=8, Resulting Numbers: [65, 8] Generated Node #0,2,1: 57:[65, 8] Operation: 56-48=8 Exploring Operation: 65-56=9, Resulting Numbers: [48, 9] Generated Node #0,2,2: 57:[48, 9] Operation: 65-56=9 Moving to Node #0,0 Current State: 57:[38, 48, 29], Operations: ['94-65=29'] Exploring Operation: 48-38=10, Resulting Numbers: [29, 10] Generated Node #0,0,0: 57:[29, 10] Operation: 48-38=10 Exploring Operation: 38-29=9, Resulting Numbers: [48, 9] Generated Node #0,0,1: 57:[48, 9] Operation: 38-29=9 Exploring Operation: 38+29=67, Resulting Numbers: [48, 67] Generated Node #0,0,2: 57:[48, 67] Operation: 38+29=67 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[48, 9], Operations: ['94-65=29', '38-29=9'] Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,57 unequal: No Solution Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,57 unequal: No Solution Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[65, 94, 38, 48], Operations: [] Exploring Operation: 94-65=29, Resulting Numbers: [38, 48, 29] Generated Node #0,0: 57:[38, 48, 29] Operation: 94-65=29 Moving to Node #0,0 Current State: 57:[38, 48, 29], Operations: ['94-65=29'] Exploring Operation: 38-29=9, Resulting Numbers: [48, 9] Generated Node #0,0,1: 57:[48, 9] Operation: 38-29=9 Moving to Node #0,0,1 Current State: 57:[48, 9], Operations: ['94-65=29', '38-29=9'] Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 20, 41, 12, 22 ]
71
[ "20+41=61", "22-12=10", "61+10=71" ]
Current State: 71:[20, 41, 12, 22], Operations: [] Exploring Operation: 20+41=61, Resulting Numbers: [12, 22, 61] Generated Node #2: [12, 22, 61] from Operation: 20+41=61 Current State: 71:[12, 22, 61], Operations: ['20+41=61'] Exploring Operation: 22-12=10, Resulting Numbers: [61, 10] Generated Node #3: [61, 10] from Operation: 22-12=10 Current State: 71:[61, 10], Operations: ['20+41=61', '22-12=10'] Exploring Operation: 61+10=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[20, 41, 12, 22], Operations: [] Exploring Operation: 41+22=63, Resulting Numbers: [20, 12, 63] Generated Node #0,0: 71:[20, 12, 63] Operation: 41+22=63 Exploring Operation: 20+41=61, Resulting Numbers: [12, 22, 61] Generated Node #0,1: 71:[12, 22, 61] Operation: 20+41=61 Exploring Operation: 20+12=32, Resulting Numbers: [41, 22, 32] Generated Node #0,2: 71:[41, 22, 32] Operation: 20+12=32 Exploring Operation: 41+12=53, Resulting Numbers: [20, 22, 53] Generated Node #0,3: 71:[20, 22, 53] Operation: 41+12=53 Exploring Operation: 20+22=42, Resulting Numbers: [41, 12, 42] Generated Node #0,4: 71:[41, 12, 42] Operation: 20+22=42 Moving to Node #0,0 Current State: 71:[20, 12, 63], Operations: ['41+22=63'] Exploring Operation: 20+12=32, Resulting Numbers: [63, 32] Generated Node #0,0,0: 71:[63, 32] Operation: 20+12=32 Exploring Operation: 20+63=83, Resulting Numbers: [12, 83] Generated Node #0,0,1: 71:[12, 83] Operation: 20+63=83 Exploring Operation: 20-12=8, Resulting Numbers: [63, 8] Generated Node #0,0,2: 71:[63, 8] Operation: 20-12=8 Exploring Operation: 63-12=51, Resulting Numbers: [20, 51] Generated Node #0,0,3: 71:[20, 51] Operation: 63-12=51 Exploring Operation: 12+63=75, Resulting Numbers: [20, 75] Generated Node #0,0,4: 71:[20, 75] Operation: 12+63=75 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[63, 32], Operations: ['41+22=63', '20+12=32'] Exploring Operation: 63*32=2016, Resulting Numbers: [2016] 2016,71 unequal: No Solution Exploring Operation: 63+32=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 71:[20, 75], Operations: ['41+22=63', '12+63=75'] Exploring Operation: 20+75=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 20*75=1500, Resulting Numbers: [1500] 1500,71 unequal: No Solution Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[12, 83], Operations: ['41+22=63', '20+63=83'] Exploring Operation: 12*83=996, Resulting Numbers: [996] 996,71 unequal: No Solution Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[20, 41, 12, 22], Operations: [] Exploring Operation: 41+22=63, Resulting Numbers: [20, 12, 63] Generated Node #0,0: 71:[20, 12, 63] Operation: 41+22=63 Moving to Node #0,0 Current State: 71:[20, 12, 63], Operations: ['41+22=63'] Exploring Operation: 20+63=83, Resulting Numbers: [12, 83] Generated Node #0,0,1: 71:[12, 83] Operation: 20+63=83 Moving to Node #0,0,1 Current State: 71:[12, 83], Operations: ['41+22=63', '20+63=83'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 6, 4, 91, 10 ]
86
[ "6-4=2", "10/2=5", "91-5=86" ]
Current State: 86:[6, 4, 91, 10], Operations: [] Exploring Operation: 6-4=2, Resulting Numbers: [91, 10, 2] Generated Node #2: [91, 10, 2] from Operation: 6-4=2 Current State: 86:[91, 10, 2], Operations: ['6-4=2'] Exploring Operation: 10/2=5, Resulting Numbers: [91, 5] Generated Node #3: [91, 5] from Operation: 10/2=5 Current State: 86:[91, 5], Operations: ['6-4=2', '10/2=5'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[6, 4, 91, 10], Operations: [] Exploring Operation: 10-6=4, Resulting Numbers: [4, 91, 4] Generated Node #0,0: 86:[4, 91, 4] Operation: 10-6=4 Exploring Operation: 91-6=85, Resulting Numbers: [4, 10, 85] Generated Node #0,1: 86:[4, 10, 85] Operation: 91-6=85 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[4, 91, 4], Operations: ['10-6=4'] Exploring Operation: 91-4=87, Resulting Numbers: [4, 87] Generated Node #0,0,0: 86:[4, 87] Operation: 91-4=87 Exploring Operation: 91-4=87, Resulting Numbers: [4, 87] Generated Node #0,0,1: 86:[4, 87] Operation: 91-4=87 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[4, 87], Operations: ['10-6=4', '91-4=87'] Exploring Operation: 4+87=91, Resulting Numbers: [91] 91,86 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[4, 87], Operations: ['10-6=4', '91-4=87'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 4+87=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 #0,1 Current State: 86:[4, 10, 85], Operations: ['91-6=85'] Exploring Operation: 4*10=40, Resulting Numbers: [85, 40] Generated Node #0,1,0: 86:[85, 40] Operation: 4*10=40 Exploring Operation: 10-4=6, Resulting Numbers: [85, 6] Generated Node #0,1,1: 86:[85, 6] Operation: 10-4=6 Moving to Node #0,1,0 Current State: 86:[85, 40], Operations: ['91-6=85', '4*10=40'] Exploring Operation: 85-40=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 85+40=125, Resulting Numbers: [125] 125,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[85, 6], Operations: ['91-6=85', '10-4=6'] Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,86 unequal: No Solution Exploring Operation: 85+6=91, Resulting Numbers: [91] 91,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 62, 16, 85, 98 ]
14
[ "62+16=78", "85-78=7", "98/7=14" ]
Current State: 14:[62, 16, 85, 98], Operations: [] Exploring Operation: 62+16=78, Resulting Numbers: [85, 98, 78] Generated Node #2: [85, 98, 78] from Operation: 62+16=78 Current State: 14:[85, 98, 78], Operations: ['62+16=78'] Exploring Operation: 85-78=7, Resulting Numbers: [98, 7] Generated Node #3: [98, 7] from Operation: 85-78=7 Current State: 14:[98, 7], Operations: ['62+16=78', '85-78=7'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[62, 16, 85, 98], Operations: [] Exploring Operation: 98-85=13, Resulting Numbers: [62, 16, 13] Generated Node #0,0: 14:[62, 16, 13] Operation: 98-85=13 Exploring Operation: 85-62=23, Resulting Numbers: [16, 98, 23] Generated Node #0,1: 14:[16, 98, 23] Operation: 85-62=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[62, 16, 13], Operations: ['98-85=13'] Exploring Operation: 62-16=46, Resulting Numbers: [13, 46] Generated Node #0,0,0: 14:[13, 46] Operation: 62-16=46 Exploring Operation: 62-13=49, Resulting Numbers: [16, 49] Generated Node #0,0,1: 14:[16, 49] Operation: 62-13=49 Moving to Node #0,0,0 Current State: 14:[13, 46], Operations: ['98-85=13', '62-16=46'] Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,14 unequal: No Solution Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[16, 49], Operations: ['98-85=13', '62-13=49'] Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 16+49=65, Resulting Numbers: [65] 65,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[16, 98, 23], Operations: ['85-62=23'] Exploring Operation: 98-16=82, Resulting Numbers: [23, 82] Generated Node #0,1,0: 14:[23, 82] Operation: 98-16=82 Exploring Operation: 98-23=75, Resulting Numbers: [16, 75] Generated Node #0,1,1: 14:[16, 75] Operation: 98-23=75 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[16, 75], Operations: ['85-62=23', '98-23=75'] Exploring Operation: 16+75=91, Resulting Numbers: [91] 91,14 unequal: No Solution Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[23, 82], Operations: ['85-62=23', '98-16=82'] Exploring Operation: 23+82=105, Resulting Numbers: [105] 105,14 unequal: No Solution Exploring Operation: 82-23=59, Resulting Numbers: [59] 59,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 22, 66, 37, 98 ]
14
[ "66-22=44", "44-37=7", "98/7=14" ]
Current State: 14:[22, 66, 37, 98], Operations: [] Exploring Operation: 66-22=44, Resulting Numbers: [37, 98, 44] Generated Node #2: [37, 98, 44] from Operation: 66-22=44 Current State: 14:[37, 98, 44], Operations: ['66-22=44'] Exploring Operation: 44-37=7, Resulting Numbers: [98, 7] Generated Node #3: [98, 7] from Operation: 44-37=7 Current State: 14:[98, 7], Operations: ['66-22=44', '44-37=7'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[22, 66, 37, 98], Operations: [] Exploring Operation: 98-66=32, Resulting Numbers: [22, 37, 32] Generated Node #0,0: 14:[22, 37, 32] Operation: 98-66=32 Moving to Node #0,0 Current State: 14:[22, 37, 32], Operations: ['98-66=32'] Exploring Operation: 37-32=5, Resulting Numbers: [22, 5] Generated Node #0,0,0: 14:[22, 5] Operation: 37-32=5 Moving to Node #0,0,0 Current State: 14:[22, 5], Operations: ['98-66=32', '37-32=5'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,14 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 88, 56, 65, 7 ]
25
[ "65-56=9", "7*9=63", "88-63=25" ]
Current State: 25:[88, 56, 65, 7], Operations: [] Exploring Operation: 65-56=9, Resulting Numbers: [88, 7, 9] Generated Node #2: [88, 7, 9] from Operation: 65-56=9 Current State: 25:[88, 7, 9], Operations: ['65-56=9'] Exploring Operation: 7*9=63, Resulting Numbers: [88, 63] Generated Node #3: [88, 63] from Operation: 7*9=63 Current State: 25:[88, 63], Operations: ['65-56=9', '7*9=63'] Exploring Operation: 88-63=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[88, 56, 65, 7], Operations: [] Exploring Operation: 88-65=23, Resulting Numbers: [56, 7, 23] Generated Node #0,0: 25:[56, 7, 23] Operation: 88-65=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[56, 7, 23], Operations: ['88-65=23'] Exploring Operation: 56/7=8, Resulting Numbers: [23, 8] Generated Node #0,0,0: 25:[23, 8] Operation: 56/7=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[23, 8], Operations: ['88-65=23', '56/7=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,25 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
[ 25, 22, 4, 41 ]
42
[ "25-22=3", "4+41=45", "45-3=42" ]
Current State: 42:[25, 22, 4, 41], Operations: [] Exploring Operation: 25-22=3, Resulting Numbers: [4, 41, 3] Generated Node #2: [4, 41, 3] from Operation: 25-22=3 Current State: 42:[4, 41, 3], Operations: ['25-22=3'] Exploring Operation: 4+41=45, Resulting Numbers: [3, 45] Generated Node #3: [3, 45] from Operation: 4+41=45 Current State: 42:[3, 45], Operations: ['25-22=3', '4+41=45'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[25, 22, 4, 41], Operations: [] Exploring Operation: 25-22=3, Resulting Numbers: [4, 41, 3] Generated Node #0,0: 42:[4, 41, 3] Operation: 25-22=3 Exploring Operation: 25-4=21, Resulting Numbers: [22, 41, 21] Generated Node #0,1: 42:[22, 41, 21] Operation: 25-4=21 Moving to Node #0,0 Current State: 42:[4, 41, 3], Operations: ['25-22=3'] Exploring Operation: 4+3=7, Resulting Numbers: [41, 7] Generated Node #0,0,0: 42:[41, 7] Operation: 4+3=7 Exploring Operation: 4-3=1, Resulting Numbers: [41, 1] Generated Node #0,0,1: 42:[41, 1] Operation: 4-3=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[41, 7], Operations: ['25-22=3', '4+3=7'] Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,42 unequal: No Solution No 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: 42:[41, 1], Operations: ['25-22=3', '4-3=1'] Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[25, 22, 4, 41], Operations: [] Exploring Operation: 25-22=3, Resulting Numbers: [4, 41, 3] Generated Node #0,0: 42:[4, 41, 3] Operation: 25-22=3 Moving to Node #0,0 Current State: 42:[4, 41, 3], Operations: ['25-22=3'] Exploring Operation: 4-3=1, Resulting Numbers: [41, 1] Generated Node #0,0,1: 42:[41, 1] Operation: 4-3=1 Moving to Node #0,0,1 Current State: 42:[41, 1], Operations: ['25-22=3', '4-3=1'] Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 70, 76, 12, 74 ]
76
[ "76-70=6", "12/6=2", "74+2=76" ]
Current State: 76:[70, 76, 12, 74], Operations: [] Exploring Operation: 76-70=6, Resulting Numbers: [12, 74, 6] Generated Node #2: [12, 74, 6] from Operation: 76-70=6 Current State: 76:[12, 74, 6], Operations: ['76-70=6'] Exploring Operation: 12/6=2, Resulting Numbers: [74, 2] Generated Node #3: [74, 2] from Operation: 12/6=2 Current State: 76:[74, 2], Operations: ['76-70=6', '12/6=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[70, 76, 12, 74], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [70, 12, 2] Generated Node #0,0: 76:[70, 12, 2] Operation: 76-74=2 Exploring Operation: 76-70=6, Resulting Numbers: [12, 74, 6] Generated Node #0,1: 76:[12, 74, 6] Operation: 76-70=6 Exploring Operation: 70+12=82, Resulting Numbers: [76, 74, 82] Generated Node #0,2: 76:[76, 74, 82] Operation: 70+12=82 Exploring Operation: 74-70=4, Resulting Numbers: [76, 12, 4] Generated Node #0,3: 76:[76, 12, 4] Operation: 74-70=4 Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[76, 12, 4], Operations: ['74-70=4'] Exploring Operation: 12-4=8, Resulting Numbers: [76, 8] Generated Node #0,3,0: 76:[76, 8] Operation: 12-4=8 Exploring Operation: 12+4=16, Resulting Numbers: [76, 16] Generated Node #0,3,1: 76:[76, 16] Operation: 12+4=16 Exploring Operation: 76/4=19, Resulting Numbers: [12, 19] Generated Node #0,3,2: 76:[12, 19] Operation: 76/4=19 Exploring Operation: 12/4=3, Resulting Numbers: [76, 3] Generated Node #0,3,3: 76:[76, 3] Operation: 12/4=3 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 76:[76, 3], Operations: ['74-70=4', '12/4=3'] Exploring Operation: 76*3=228, Resulting Numbers: [228] 228,76 unequal: No Solution Exploring Operation: 76+3=79, Resulting Numbers: [79] 79,76 unequal: No Solution Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,76 unequal: No Solution No 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: 76:[76, 16], Operations: ['74-70=4', '12+4=16'] Exploring Operation: 76+16=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 76-16=60, Resulting Numbers: [60] 60,76 unequal: No Solution Exploring Operation: 76*16=1216, Resulting Numbers: [1216] 1216,76 unequal: No Solution No 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: 76:[76, 8], Operations: ['74-70=4', '12-4=8'] Exploring Operation: 76*8=608, Resulting Numbers: [608] 608,76 unequal: No Solution Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,76 unequal: No Solution No 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: 76:[12, 19], Operations: ['74-70=4', '76/4=19'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,76 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,76 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: 76:[76, 74, 82], Operations: ['70+12=82'] Exploring Operation: 82-74=8, Resulting Numbers: [76, 8] Generated Node #0,2,0: 76:[76, 8] Operation: 82-74=8 Exploring Operation: 76+74=150, Resulting Numbers: [82, 150] Generated Node #0,2,1: 76:[82, 150] Operation: 76+74=150 Exploring Operation: 82-76=6, Resulting Numbers: [74, 6] Generated Node #0,2,2: 76:[74, 6] Operation: 82-76=6 Exploring Operation: 76-74=2, Resulting Numbers: [82, 2] Generated Node #0,2,3: 76:[82, 2] Operation: 76-74=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[76, 8], Operations: ['70+12=82', '82-74=8'] Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,76 unequal: No Solution Exploring Operation: 76*8=608, Resulting Numbers: [608] 608,76 unequal: No Solution No 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: 76:[74, 6], Operations: ['70+12=82', '82-76=6'] Exploring Operation: 74*6=444, Resulting Numbers: [444] 444,76 unequal: No Solution Exploring Operation: 74+6=80, Resulting Numbers: [80] 80,76 unequal: No Solution Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,76 unequal: No Solution No 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: 76:[82, 2], Operations: ['70+12=82', '76-74=2'] Exploring Operation: 82*2=164, Resulting Numbers: [164] 164,76 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,76 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,76 unequal: No Solution Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,76 unequal: No Solution No 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: 76:[82, 150], Operations: ['70+12=82', '76+74=150'] Exploring Operation: 150-82=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 82*150=12300, Resulting Numbers: [12300] 12300,76 unequal: No Solution Exploring Operation: 82+150=232, Resulting Numbers: [232] 232,76 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: 76:[12, 74, 6], Operations: ['76-70=6'] Exploring Operation: 12*6=72, Resulting Numbers: [74, 72] Generated Node #0,1,0: 76:[74, 72] Operation: 12*6=72 Exploring Operation: 12/6=2, Resulting Numbers: [74, 2] Generated Node #0,1,1: 76:[74, 2] Operation: 12/6=2 Exploring Operation: 12-6=6, Resulting Numbers: [74, 6] Generated Node #0,1,2: 76:[74, 6] Operation: 12-6=6 Exploring Operation: 12+6=18, Resulting Numbers: [74, 18] Generated Node #0,1,3: 76:[74, 18] Operation: 12+6=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 76:[74, 2], Operations: ['76-70=6', '12/6=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[70, 76, 12, 74], Operations: [] Exploring Operation: 76-70=6, Resulting Numbers: [12, 74, 6] Generated Node #0,1: 76:[12, 74, 6] Operation: 76-70=6 Moving to Node #0,1 Current State: 76:[12, 74, 6], Operations: ['76-70=6'] Exploring Operation: 12/6=2, Resulting Numbers: [74, 2] Generated Node #0,1,1: 76:[74, 2] Operation: 12/6=2 Moving to Node #0,1,1 Current State: 76:[74, 2], Operations: ['76-70=6', '12/6=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_4
mult_heuristic
[ 29, 97, 8, 90 ]
45
[ "29*8=232", "97+90=187", "232-187=45" ]
Current State: 45:[29, 97, 8, 90], Operations: [] Exploring Operation: 29*8=232, Resulting Numbers: [97, 90, 232] Generated Node #2: [97, 90, 232] from Operation: 29*8=232 Current State: 45:[97, 90, 232], Operations: ['29*8=232'] Exploring Operation: 97+90=187, Resulting Numbers: [232, 187] Generated Node #3: [232, 187] from Operation: 97+90=187 Current State: 45:[232, 187], Operations: ['29*8=232', '97+90=187'] Exploring Operation: 232-187=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[29, 97, 8, 90], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [29, 8, 7] Generated Node #0,0: 45:[29, 8, 7] Operation: 97-90=7 Moving to Node #0,0 Current State: 45:[29, 8, 7], Operations: ['97-90=7'] Exploring Operation: 29-8=21, Resulting Numbers: [7, 21] Generated Node #0,0,0: 45:[7, 21] Operation: 29-8=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[7, 21], Operations: ['97-90=7', '29-8=21'] Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,45 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
[ 67, 15, 49, 33 ]
67
[ "49-15=34", "34-33=1", "67*1=67" ]
Current State: 67:[67, 15, 49, 33], Operations: [] Exploring Operation: 49-15=34, Resulting Numbers: [67, 33, 34] Generated Node #2: [67, 33, 34] from Operation: 49-15=34 Current State: 67:[67, 33, 34], Operations: ['49-15=34'] Exploring Operation: 34-33=1, Resulting Numbers: [67, 1] Generated Node #3: [67, 1] from Operation: 34-33=1 Current State: 67:[67, 1], Operations: ['49-15=34', '34-33=1'] Exploring Operation: 67*1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[67, 15, 49, 33], Operations: [] Exploring Operation: 15+33=48, Resulting Numbers: [67, 49, 48] Generated Node #0,0: 67:[67, 49, 48] Operation: 15+33=48 Exploring Operation: 15+49=64, Resulting Numbers: [67, 33, 64] Generated Node #0,1: 67:[67, 33, 64] Operation: 15+49=64 Moving to Node #0,0 Current State: 67:[67, 49, 48], Operations: ['15+33=48'] Exploring Operation: 67+48=115, Resulting Numbers: [49, 115] Generated Node #0,0,0: 67:[49, 115] Operation: 67+48=115 Exploring Operation: 49+48=97, Resulting Numbers: [67, 97] Generated Node #0,0,1: 67:[67, 97] Operation: 49+48=97 Moving to Node #0,1 Current State: 67:[67, 33, 64], Operations: ['15+49=64'] Exploring Operation: 67+33=100, Resulting Numbers: [64, 100] Generated Node #0,1,0: 67:[64, 100] Operation: 67+33=100 Exploring Operation: 33+64=97, Resulting Numbers: [67, 97] Generated Node #0,1,1: 67:[67, 97] Operation: 33+64=97 Moving to Node #0,0,1 Current State: 67:[67, 97], Operations: ['15+33=48', '49+48=97'] Exploring Operation: 97-67=30, Resulting Numbers: [30] 30,67 unequal: No Solution Exploring Operation: 67+97=164, Resulting Numbers: [164] 164,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[67, 97], Operations: ['15+49=64', '33+64=97'] Exploring Operation: 67+97=164, Resulting Numbers: [164] 164,67 unequal: No Solution Exploring Operation: 97-67=30, Resulting Numbers: [30] 30,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[64, 100], Operations: ['15+49=64', '67+33=100'] Exploring Operation: 100-64=36, Resulting Numbers: [36] 36,67 unequal: No Solution Exploring Operation: 64+100=164, Resulting Numbers: [164] 164,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[49, 115], Operations: ['15+33=48', '67+48=115'] Exploring Operation: 115-49=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 49+115=164, Resulting Numbers: [164] 164,67 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 59, 31, 37, 81 ]
33
[ "37+81=118", "118/59=2", "31+2=33" ]
Current State: 33:[59, 31, 37, 81], Operations: [] Exploring Operation: 37+81=118, Resulting Numbers: [59, 31, 118] Generated Node #2: [59, 31, 118] from Operation: 37+81=118 Current State: 33:[59, 31, 118], Operations: ['37+81=118'] Exploring Operation: 118/59=2, Resulting Numbers: [31, 2] Generated Node #3: [31, 2] from Operation: 118/59=2 Current State: 33:[31, 2], Operations: ['37+81=118', '118/59=2'] Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[59, 31, 37, 81], Operations: [] Exploring Operation: 81-37=44, Resulting Numbers: [59, 31, 44] Generated Node #0,0: 33:[59, 31, 44] Operation: 81-37=44 Exploring Operation: 81-31=50, Resulting Numbers: [59, 37, 50] Generated Node #0,1: 33:[59, 37, 50] Operation: 81-31=50 Exploring Operation: 81-59=22, Resulting Numbers: [31, 37, 22] Generated Node #0,2: 33:[31, 37, 22] Operation: 81-59=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[31, 37, 22], Operations: ['81-59=22'] Exploring Operation: 31-22=9, Resulting Numbers: [37, 9] Generated Node #0,2,0: 33:[37, 9] Operation: 31-22=9 Exploring Operation: 37-22=15, Resulting Numbers: [31, 15] Generated Node #0,2,1: 33:[31, 15] Operation: 37-22=15 Exploring Operation: 37-31=6, Resulting Numbers: [22, 6] Generated Node #0,2,2: 33:[22, 6] Operation: 37-31=6 Moving to Node #0,2,0 Current State: 33:[37, 9], Operations: ['81-59=22', '31-22=9'] Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 37*9=333, Resulting Numbers: [333] 333,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[31, 15], Operations: ['81-59=22', '37-22=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,33 unequal: No Solution Moving to Node #0,2,2 Current State: 33:[22, 6], Operations: ['81-59=22', '37-31=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,33 unequal: No Solution Exploring Operation: 22-6=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 #0,0 Current State: 33:[59, 31, 44], Operations: ['81-37=44'] Exploring Operation: 59-31=28, Resulting Numbers: [44, 28] Generated Node #0,0,0: 33:[44, 28] Operation: 59-31=28 Exploring Operation: 59-44=15, Resulting Numbers: [31, 15] Generated Node #0,0,1: 33:[31, 15] Operation: 59-44=15 Exploring Operation: 44-31=13, Resulting Numbers: [59, 13] Generated Node #0,0,2: 33:[59, 13] Operation: 44-31=13 Moving to Node #0,0,1 Current State: 33:[31, 15], Operations: ['81-37=44', '59-44=15'] Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[44, 28], Operations: ['81-37=44', '59-31=28'] Exploring Operation: 44*28=1232, Resulting Numbers: [1232] 1232,33 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,33 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,33 unequal: No Solution Moving to Node #0,0,2 Current State: 33:[59, 13], Operations: ['81-37=44', '44-31=13'] Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,33 unequal: No Solution Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,33 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 Current State: 33:[59, 37, 50], Operations: ['81-31=50'] Exploring Operation: 59-37=22, Resulting Numbers: [50, 22] Generated Node #0,1,0: 33:[50, 22] Operation: 59-37=22 Exploring Operation: 50-37=13, Resulting Numbers: [59, 13] Generated Node #0,1,1: 33:[59, 13] Operation: 50-37=13 Exploring Operation: 59-50=9, Resulting Numbers: [37, 9] Generated Node #0,1,2: 33:[37, 9] Operation: 59-50=9 Moving to Node #0,1,2 Current State: 33:[37, 9], Operations: ['81-31=50', '59-50=9'] Exploring Operation: 37*9=333, Resulting Numbers: [333] 333,33 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[50, 22], Operations: ['81-31=50', '59-37=22'] Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,33 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,33 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[59, 13], Operations: ['81-31=50', '50-37=13'] Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,33 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,33 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
[ 5, 74, 28, 24 ]
83
[ "5+74=79", "28-24=4", "79+4=83" ]
Current State: 83:[5, 74, 28, 24], Operations: [] Exploring Operation: 5+74=79, Resulting Numbers: [28, 24, 79] Generated Node #2: [28, 24, 79] from Operation: 5+74=79 Current State: 83:[28, 24, 79], Operations: ['5+74=79'] Exploring Operation: 28-24=4, Resulting Numbers: [79, 4] Generated Node #3: [79, 4] from Operation: 28-24=4 Current State: 83:[79, 4], Operations: ['5+74=79', '28-24=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[5, 74, 28, 24], Operations: [] Exploring Operation: 5+24=29, Resulting Numbers: [74, 28, 29] Generated Node #0,0: 83:[74, 28, 29] Operation: 5+24=29 Exploring Operation: 5+28=33, Resulting Numbers: [74, 24, 33] Generated Node #0,1: 83:[74, 24, 33] Operation: 5+28=33 Exploring Operation: 5+74=79, Resulting Numbers: [28, 24, 79] Generated Node #0,2: 83:[28, 24, 79] Operation: 5+74=79 Exploring Operation: 28+24=52, Resulting Numbers: [5, 74, 52] Generated Node #0,3: 83:[5, 74, 52] Operation: 28+24=52 Exploring Operation: 5*24=120, Resulting Numbers: [74, 28, 120] Generated Node #0,4: 83:[74, 28, 120] Operation: 5*24=120 Start Sub Search at level 1: Moving to Node #0,4 Current State: 83:[74, 28, 120], Operations: ['5*24=120'] Exploring Operation: 74-28=46, Resulting Numbers: [120, 46] Generated Node #0,4,0: 83:[120, 46] Operation: 74-28=46 Exploring Operation: 120-28=92, Resulting Numbers: [74, 92] Generated Node #0,4,1: 83:[74, 92] Operation: 120-28=92 Exploring Operation: 28+120=148, Resulting Numbers: [74, 148] Generated Node #0,4,2: 83:[74, 148] Operation: 28+120=148 Exploring Operation: 74+28=102, Resulting Numbers: [120, 102] Generated Node #0,4,3: 83:[120, 102] Operation: 74+28=102 Exploring Operation: 120-74=46, Resulting Numbers: [28, 46] Generated Node #0,4,4: 83:[28, 46] Operation: 120-74=46 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 83:[74, 92], Operations: ['5*24=120', '120-28=92'] Exploring Operation: 74+92=166, Resulting Numbers: [166] 166,83 unequal: No Solution Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,83 unequal: No Solution Exploring Operation: 74*92=6808, Resulting Numbers: [6808] 6808,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 83:[120, 102], Operations: ['5*24=120', '74+28=102'] Exploring Operation: 120+102=222, Resulting Numbers: [222] 222,83 unequal: No Solution Exploring Operation: 120*102=12240, Resulting Numbers: [12240] 12240,83 unequal: No Solution Exploring Operation: 120-102=18, Resulting Numbers: [18] 18,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 83:[120, 46], Operations: ['5*24=120', '74-28=46'] Exploring Operation: 120*46=5520, Resulting Numbers: [5520] 5520,83 unequal: No Solution Exploring Operation: 120-46=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 120+46=166, Resulting Numbers: [166] 166,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 83:[74, 148], Operations: ['5*24=120', '28+120=148'] Exploring Operation: 74+148=222, Resulting Numbers: [222] 222,83 unequal: No Solution Exploring Operation: 148/74=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 74*148=10952, Resulting Numbers: [10952] 10952,83 unequal: No Solution Exploring Operation: 148-74=74, Resulting Numbers: [74] 74,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 83:[28, 46], Operations: ['5*24=120', '120-74=46'] Exploring Operation: 28+46=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,83 unequal: No Solution Exploring Operation: 28*46=1288, Resulting Numbers: [1288] 1288,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[74, 28, 29], Operations: ['5+24=29'] Exploring Operation: 74+29=103, Resulting Numbers: [28, 103] Generated Node #0,0,0: 83:[28, 103] Operation: 74+29=103 Exploring Operation: 74-28=46, Resulting Numbers: [29, 46] Generated Node #0,0,1: 83:[29, 46] Operation: 74-28=46 Exploring Operation: 28+29=57, Resulting Numbers: [74, 57] Generated Node #0,0,2: 83:[74, 57] Operation: 28+29=57 Exploring Operation: 29-28=1, Resulting Numbers: [74, 1] Generated Node #0,0,3: 83:[74, 1] Operation: 29-28=1 Exploring Operation: 74+28=102, Resulting Numbers: [29, 102] Generated Node #0,0,4: 83:[29, 102] Operation: 74+28=102 Moving to Node #0,0,2 Current State: 83:[74, 57], Operations: ['5+24=29', '28+29=57'] Exploring Operation: 74*57=4218, Resulting Numbers: [4218] 4218,83 unequal: No Solution Exploring Operation: 74+57=131, Resulting Numbers: [131] 131,83 unequal: No Solution Exploring Operation: 74-57=17, Resulting Numbers: [17] 17,83 unequal: No Solution Moving to Node #0,0,4 Current State: 83:[29, 102], Operations: ['5+24=29', '74+28=102'] Exploring Operation: 29*102=2958, Resulting Numbers: [2958] 2958,83 unequal: No Solution Exploring Operation: 29+102=131, Resulting Numbers: [131] 131,83 unequal: No Solution Exploring Operation: 102-29=73, Resulting Numbers: [73] 73,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[28, 103], Operations: ['5+24=29', '74+29=103'] Exploring Operation: 28*103=2884, Resulting Numbers: [2884] 2884,83 unequal: No Solution Exploring Operation: 28+103=131, Resulting Numbers: [131] 131,83 unequal: No Solution Exploring Operation: 103-28=75, Resulting Numbers: [75] 75,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[29, 46], Operations: ['5+24=29', '74-28=46'] Exploring Operation: 29+46=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 29*46=1334, Resulting Numbers: [1334] 1334,83 unequal: No Solution Exploring Operation: 46-29=17, Resulting Numbers: [17] 17,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[74, 1], Operations: ['5+24=29', '29-28=1'] Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,83 unequal: No Solution Exploring Operation: 74+1=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 74/1=74, Resulting Numbers: [74] 74,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[74, 24, 33], Operations: ['5+28=33'] Exploring Operation: 74+24=98, Resulting Numbers: [33, 98] Generated Node #0,1,0: 83:[33, 98] Operation: 74+24=98 Exploring Operation: 74-24=50, Resulting Numbers: [33, 50] Generated Node #0,1,1: 83:[33, 50] Operation: 74-24=50 Exploring Operation: 33-24=9, Resulting Numbers: [74, 9] Generated Node #0,1,2: 83:[74, 9] Operation: 33-24=9 Exploring Operation: 74+33=107, Resulting Numbers: [24, 107] Generated Node #0,1,3: 83:[24, 107] Operation: 74+33=107 Exploring Operation: 24+33=57, Resulting Numbers: [74, 57] Generated Node #0,1,4: 83:[74, 57] Operation: 24+33=57 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 83:[74, 57], Operations: ['5+28=33', '24+33=57'] Exploring Operation: 74*57=4218, Resulting Numbers: [4218] 4218,83 unequal: No Solution Exploring Operation: 74+57=131, Resulting Numbers: [131] 131,83 unequal: No Solution Exploring Operation: 74-57=17, Resulting Numbers: [17] 17,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[33, 98], Operations: ['5+28=33', '74+24=98'] Exploring Operation: 98-33=65, Resulting Numbers: [65] 65,83 unequal: No Solution Exploring Operation: 33+98=131, Resulting Numbers: [131] 131,83 unequal: No Solution Exploring Operation: 33*98=3234, Resulting Numbers: [3234] 3234,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[33, 50], Operations: ['5+28=33', '74-24=50'] Exploring Operation: 50-33=17, Resulting Numbers: [17] 17,83 unequal: No Solution Exploring Operation: 33*50=1650, Resulting Numbers: [1650] 1650,83 unequal: No Solution Exploring Operation: 33+50=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[5, 74, 28, 24], Operations: [] Exploring Operation: 5+28=33, Resulting Numbers: [74, 24, 33] Generated Node #0,1: 83:[74, 24, 33] Operation: 5+28=33 Moving to Node #0,1 Current State: 83:[74, 24, 33], Operations: ['5+28=33'] Exploring Operation: 74-24=50, Resulting Numbers: [33, 50] Generated Node #0,1,1: 83:[33, 50] Operation: 74-24=50 Moving to Node #0,1,1 Current State: 83:[33, 50], Operations: ['5+28=33', '74-24=50'] Exploring Operation: 33+50=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.943576
hs_5
mult_heuristic
[ 92, 46, 3, 26 ]
69
[ "92-46=46", "26-3=23", "46+23=69" ]
Current State: 69:[92, 46, 3, 26], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [3, 26, 46] Generated Node #2: [3, 26, 46] from Operation: 92-46=46 Current State: 69:[3, 26, 46], Operations: ['92-46=46'] Exploring Operation: 26-3=23, Resulting Numbers: [46, 23] Generated Node #3: [46, 23] from Operation: 26-3=23 Current State: 69:[46, 23], Operations: ['92-46=46', '26-3=23'] Exploring Operation: 46+23=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[92, 46, 3, 26], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [3, 26, 2] Generated Node #0,0: 69:[3, 26, 2] Operation: 92/46=2 Exploring Operation: 46+26=72, Resulting Numbers: [92, 3, 72] Generated Node #0,1: 69:[92, 3, 72] Operation: 46+26=72 Exploring Operation: 46-26=20, Resulting Numbers: [92, 3, 20] Generated Node #0,2: 69:[92, 3, 20] Operation: 46-26=20 Exploring Operation: 92-26=66, Resulting Numbers: [46, 3, 66] Generated Node #0,3: 69:[46, 3, 66] Operation: 92-26=66 Exploring Operation: 92-46=46, Resulting Numbers: [3, 26, 46] Generated Node #0,4: 69:[3, 26, 46] Operation: 92-46=46 Moving to Node #0,0 Current State: 69:[3, 26, 2], Operations: ['92/46=2'] Exploring Operation: 26-2=24, Resulting Numbers: [3, 24] Generated Node #0,0,0: 69:[3, 24] Operation: 26-2=24 Exploring Operation: 26-3=23, Resulting Numbers: [2, 23] Generated Node #0,0,1: 69:[2, 23] Operation: 26-3=23 Exploring Operation: 3+2=5, Resulting Numbers: [26, 5] Generated Node #0,0,2: 69:[26, 5] Operation: 3+2=5 Exploring Operation: 26+2=28, Resulting Numbers: [3, 28] Generated Node #0,0,3: 69:[3, 28] Operation: 26+2=28 Exploring Operation: 3-2=1, Resulting Numbers: [26, 1] Generated Node #0,0,4: 69:[26, 1] Operation: 3-2=1 Moving to Node #0,2 Current State: 69:[92, 3, 20], Operations: ['46-26=20'] Exploring Operation: 92-3=89, Resulting Numbers: [20, 89] Generated Node #0,2,0: 69:[20, 89] Operation: 92-3=89 Exploring Operation: 92+3=95, Resulting Numbers: [20, 95] Generated Node #0,2,1: 69:[20, 95] Operation: 92+3=95 Exploring Operation: 3+20=23, Resulting Numbers: [92, 23] Generated Node #0,2,2: 69:[92, 23] Operation: 3+20=23 Exploring Operation: 92-20=72, Resulting Numbers: [3, 72] Generated Node #0,2,3: 69:[3, 72] Operation: 92-20=72 Exploring Operation: 20-3=17, Resulting Numbers: [92, 17] Generated Node #0,2,4: 69:[92, 17] Operation: 20-3=17 Moving to Node #0,4 Current State: 69:[3, 26, 46], Operations: ['92-46=46'] Exploring Operation: 26+46=72, Resulting Numbers: [3, 72] Generated Node #0,4,0: 69:[3, 72] Operation: 26+46=72 Exploring Operation: 46-26=20, Resulting Numbers: [3, 20] Generated Node #0,4,1: 69:[3, 20] Operation: 46-26=20 Exploring Operation: 26-3=23, Resulting Numbers: [46, 23] Generated Node #0,4,2: 69:[46, 23] Operation: 26-3=23 Exploring Operation: 46-3=43, Resulting Numbers: [26, 43] Generated Node #0,4,3: 69:[26, 43] Operation: 46-3=43 Exploring Operation: 3+46=49, Resulting Numbers: [26, 49] Generated Node #0,4,4: 69:[26, 49] Operation: 3+46=49 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 69:[3, 72], Operations: ['92-46=46', '26+46=72'] Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[92, 46, 3, 26], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [3, 26, 46] Generated Node #0,4: 69:[3, 26, 46] Operation: 92-46=46 Moving to Node #0,4 Current State: 69:[3, 26, 46], Operations: ['92-46=46'] Exploring Operation: 26+46=72, Resulting Numbers: [3, 72] Generated Node #0,4,0: 69:[3, 72] Operation: 26+46=72 Moving to Node #0,4,0 Current State: 69:[3, 72], Operations: ['92-46=46', '26+46=72'] Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 95, 15, 1, 10 ]
65
[ "15+1=16", "10*16=160", "160-95=65" ]
Current State: 65:[95, 15, 1, 10], Operations: [] Exploring Operation: 15+1=16, Resulting Numbers: [95, 10, 16] Generated Node #2: [95, 10, 16] from Operation: 15+1=16 Current State: 65:[95, 10, 16], Operations: ['15+1=16'] Exploring Operation: 10*16=160, Resulting Numbers: [95, 160] Generated Node #3: [95, 160] from Operation: 10*16=160 Current State: 65:[95, 160], Operations: ['15+1=16', '10*16=160'] Exploring Operation: 160-95=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[95, 15, 1, 10], Operations: [] Exploring Operation: 95-15=80, Resulting Numbers: [1, 10, 80] Generated Node #0,0: 65:[1, 10, 80] Operation: 95-15=80 Moving to Node #0,0 Current State: 65:[1, 10, 80], Operations: ['95-15=80'] Exploring Operation: 80/10=8, Resulting Numbers: [1, 8] Generated Node #0,0,0: 65:[1, 8] Operation: 80/10=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[1, 8], Operations: ['95-15=80', '80/10=8'] Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 69, 92, 25, 2 ]
50
[ "92-69=23", "25+2=27", "23+27=50" ]
Current State: 50:[69, 92, 25, 2], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [25, 2, 23] Generated Node #2: [25, 2, 23] from Operation: 92-69=23 Current State: 50:[25, 2, 23], Operations: ['92-69=23'] Exploring Operation: 25+2=27, Resulting Numbers: [23, 27] Generated Node #3: [23, 27] from Operation: 25+2=27 Current State: 50:[23, 27], Operations: ['92-69=23', '25+2=27'] Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[69, 92, 25, 2], Operations: [] Exploring Operation: 92/2=46, Resulting Numbers: [69, 25, 46] Generated Node #0,0: 50:[69, 25, 46] Operation: 92/2=46 Exploring Operation: 69-2=67, Resulting Numbers: [92, 25, 67] Generated Node #0,1: 50:[92, 25, 67] Operation: 69-2=67 Exploring Operation: 92-69=23, Resulting Numbers: [25, 2, 23] Generated Node #0,2: 50:[25, 2, 23] Operation: 92-69=23 Exploring Operation: 69-25=44, Resulting Numbers: [92, 2, 44] Generated Node #0,3: 50:[92, 2, 44] Operation: 69-25=44 Exploring Operation: 92-25=67, Resulting Numbers: [69, 2, 67] Generated Node #0,4: 50:[69, 2, 67] Operation: 92-25=67 Moving to Node #0,2 Current State: 50:[25, 2, 23], Operations: ['92-69=23'] Exploring Operation: 25+2=27, Resulting Numbers: [23, 27] Generated Node #0,2,0: 50:[23, 27] Operation: 25+2=27 Exploring Operation: 25+23=48, Resulting Numbers: [2, 48] Generated Node #0,2,1: 50:[2, 48] Operation: 25+23=48 Exploring Operation: 25*2=50, Resulting Numbers: [23, 50] Generated Node #0,2,2: 50:[23, 50] Operation: 25*2=50 Exploring Operation: 2+23=25, Resulting Numbers: [25, 25] Generated Node #0,2,3: 50:[25, 25] Operation: 2+23=25 Exploring Operation: 25-23=2, Resulting Numbers: [2, 2] Generated Node #0,2,4: 50:[2, 2] Operation: 25-23=2 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 50:[25, 25], Operations: ['92-69=23', '2+23=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[69, 92, 25, 2], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [25, 2, 23] Generated Node #0,2: 50:[25, 2, 23] Operation: 92-69=23 Moving to Node #0,2 Current State: 50:[25, 2, 23], Operations: ['92-69=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25, 25] Generated Node #0,2,3: 50:[25, 25] Operation: 2+23=25 Moving to Node #0,2,3 Current State: 50:[25, 25], Operations: ['92-69=23', '2+23=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 76, 44, 71, 77 ]
27
[ "77-76=1", "71-44=27", "1*27=27" ]
Current State: 27:[76, 44, 71, 77], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [44, 71, 1] Generated Node #2: [44, 71, 1] from Operation: 77-76=1 Current State: 27:[44, 71, 1], Operations: ['77-76=1'] Exploring Operation: 71-44=27, Resulting Numbers: [1, 27] Generated Node #3: [1, 27] from Operation: 71-44=27 Current State: 27:[1, 27], Operations: ['77-76=1', '71-44=27'] Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[76, 44, 71, 77], Operations: [] Exploring Operation: 76-71=5, Resulting Numbers: [44, 77, 5] Generated Node #0,0: 27:[44, 77, 5] Operation: 76-71=5 Exploring Operation: 77-76=1, Resulting Numbers: [44, 71, 1] Generated Node #0,1: 27:[44, 71, 1] Operation: 77-76=1 Exploring Operation: 77-71=6, Resulting Numbers: [76, 44, 6] Generated Node #0,2: 27:[76, 44, 6] Operation: 77-71=6 Moving to Node #0,1 Current State: 27:[44, 71, 1], Operations: ['77-76=1'] Exploring Operation: 44-1=43, Resulting Numbers: [71, 43] Generated Node #0,1,0: 27:[71, 43] Operation: 44-1=43 Exploring Operation: 71-1=70, Resulting Numbers: [44, 70] Generated Node #0,1,1: 27:[44, 70] Operation: 71-1=70 Exploring Operation: 71-44=27, Resulting Numbers: [1, 27] Generated Node #0,1,2: 27:[1, 27] Operation: 71-44=27 Moving to Node #0,0 Current State: 27:[44, 77, 5], Operations: ['76-71=5'] Exploring Operation: 77-44=33, Resulting Numbers: [5, 33] Generated Node #0,0,0: 27:[5, 33] Operation: 77-44=33 Exploring Operation: 44-5=39, Resulting Numbers: [77, 39] Generated Node #0,0,1: 27:[77, 39] Operation: 44-5=39 Exploring Operation: 77-5=72, Resulting Numbers: [44, 72] Generated Node #0,0,2: 27:[44, 72] Operation: 77-5=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[5, 33], Operations: ['76-71=5', '77-44=33'] Exploring Operation: 5*33=165, Resulting Numbers: [165] 165,27 unequal: No Solution Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,27 unequal: No Solution No 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: 27:[77, 39], Operations: ['76-71=5', '44-5=39'] Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 77*39=3003, Resulting Numbers: [3003] 3003,27 unequal: No Solution Exploring Operation: 77+39=116, Resulting Numbers: [116] 116,27 unequal: No Solution No 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: 27:[44, 72], Operations: ['76-71=5', '77-5=72'] Exploring Operation: 44*72=3168, Resulting Numbers: [3168] 3168,27 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,27 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: 27:[76, 44, 6], Operations: ['77-71=6'] Exploring Operation: 76-44=32, Resulting Numbers: [6, 32] Generated Node #0,2,0: 27:[6, 32] Operation: 76-44=32 Exploring Operation: 76-6=70, Resulting Numbers: [44, 70] Generated Node #0,2,1: 27:[44, 70] Operation: 76-6=70 Exploring Operation: 44-6=38, Resulting Numbers: [76, 38] Generated Node #0,2,2: 27:[76, 38] Operation: 44-6=38 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[6, 32], Operations: ['77-71=6', '76-44=32'] Exploring Operation: 6*32=192, Resulting Numbers: [192] 192,27 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 6+32=38, Resulting Numbers: [38] 38,27 unequal: No Solution No 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: 27:[44, 70], Operations: ['77-71=6', '76-6=70'] Exploring Operation: 44+70=114, Resulting Numbers: [114] 114,27 unequal: No Solution Exploring Operation: 44*70=3080, Resulting Numbers: [3080] 3080,27 unequal: No Solution Exploring Operation: 70-44=26, Resulting Numbers: [26] 26,27 unequal: No Solution No 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: 27:[76, 38], Operations: ['77-71=6', '44-6=38'] Exploring Operation: 76/38=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 76+38=114, Resulting Numbers: [114] 114,27 unequal: No Solution Exploring Operation: 76-38=38, Resulting Numbers: [38] 38,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 27:[1, 27], Operations: ['77-76=1', '71-44=27'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[76, 44, 71, 77], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [44, 71, 1] Generated Node #0,1: 27:[44, 71, 1] Operation: 77-76=1 Moving to Node #0,1 Current State: 27:[44, 71, 1], Operations: ['77-76=1'] Exploring Operation: 71-44=27, Resulting Numbers: [1, 27] Generated Node #0,1,2: 27:[1, 27] Operation: 71-44=27 Moving to Node #0,1,2 Current State: 27:[1, 27], Operations: ['77-76=1', '71-44=27'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.969618
hs_3
sum_heuristic
[ 38, 5, 36, 97 ]
94
[ "38-5=33", "97-36=61", "33+61=94" ]
Current State: 94:[38, 5, 36, 97], Operations: [] Exploring Operation: 38-5=33, Resulting Numbers: [36, 97, 33] Generated Node #2: [36, 97, 33] from Operation: 38-5=33 Current State: 94:[36, 97, 33], Operations: ['38-5=33'] Exploring Operation: 97-36=61, Resulting Numbers: [33, 61] Generated Node #3: [33, 61] from Operation: 97-36=61 Current State: 94:[33, 61], Operations: ['38-5=33', '97-36=61'] Exploring Operation: 33+61=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[38, 5, 36, 97], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [5, 97, 2] Generated Node #0,0: 94:[5, 97, 2] Operation: 38-36=2 Exploring Operation: 38+5=43, Resulting Numbers: [36, 97, 43] Generated Node #0,1: 94:[36, 97, 43] Operation: 38+5=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[5, 97, 2], Operations: ['38-36=2'] Exploring Operation: 97-5=92, Resulting Numbers: [2, 92] Generated Node #0,0,0: 94:[2, 92] Operation: 97-5=92 Exploring Operation: 5-2=3, Resulting Numbers: [97, 3] Generated Node #0,0,1: 94:[97, 3] Operation: 5-2=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[2, 92], Operations: ['38-36=2', '97-5=92'] Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[38, 5, 36, 97], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [5, 97, 2] Generated Node #0,0: 94:[5, 97, 2] Operation: 38-36=2 Moving to Node #0,0 Current State: 94:[5, 97, 2], Operations: ['38-36=2'] Exploring Operation: 97-5=92, Resulting Numbers: [2, 92] Generated Node #0,0,0: 94:[2, 92] Operation: 97-5=92 Moving to Node #0,0,0 Current State: 94:[2, 92], Operations: ['38-36=2', '97-5=92'] Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 10, 47, 39, 70 ]
93
[ "70/10=7", "47+39=86", "7+86=93" ]
Current State: 93:[10, 47, 39, 70], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [47, 39, 7] Generated Node #2: [47, 39, 7] from Operation: 70/10=7 Current State: 93:[47, 39, 7], Operations: ['70/10=7'] Exploring Operation: 47+39=86, Resulting Numbers: [7, 86] Generated Node #3: [7, 86] from Operation: 47+39=86 Current State: 93:[7, 86], Operations: ['70/10=7', '47+39=86'] Exploring Operation: 7+86=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[10, 47, 39, 70], Operations: [] Exploring Operation: 47-39=8, Resulting Numbers: [10, 70, 8] Generated Node #0,0: 93:[10, 70, 8] Operation: 47-39=8 Exploring Operation: 47-10=37, Resulting Numbers: [39, 70, 37] Generated Node #0,1: 93:[39, 70, 37] Operation: 47-10=37 Exploring Operation: 70-39=31, Resulting Numbers: [10, 47, 31] Generated Node #0,2: 93:[10, 47, 31] Operation: 70-39=31 Exploring Operation: 70/10=7, Resulting Numbers: [47, 39, 7] Generated Node #0,3: 93:[47, 39, 7] Operation: 70/10=7 Exploring Operation: 70-47=23, Resulting Numbers: [10, 39, 23] Generated Node #0,4: 93:[10, 39, 23] Operation: 70-47=23 Moving to Node #0,2 Current State: 93:[10, 47, 31], Operations: ['70-39=31'] Exploring Operation: 47-31=16, Resulting Numbers: [10, 16] Generated Node #0,2,0: 93:[10, 16] Operation: 47-31=16 Exploring Operation: 10+47=57, Resulting Numbers: [31, 57] Generated Node #0,2,1: 93:[31, 57] Operation: 10+47=57 Exploring Operation: 47+31=78, Resulting Numbers: [10, 78] Generated Node #0,2,2: 93:[10, 78] Operation: 47+31=78 Exploring Operation: 47-10=37, Resulting Numbers: [31, 37] Generated Node #0,2,3: 93:[31, 37] Operation: 47-10=37 Exploring Operation: 10+31=41, Resulting Numbers: [47, 41] Generated Node #0,2,4: 93:[47, 41] Operation: 10+31=41 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 93:[31, 37], Operations: ['70-39=31', '47-10=37'] Exploring Operation: 31+37=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 31*37=1147, Resulting Numbers: [1147] 1147,93 unequal: No Solution Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 93:[10, 16], Operations: ['70-39=31', '47-31=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,93 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 93:[10, 78], Operations: ['70-39=31', '47+31=78'] Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 10+78=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 10*78=780, Resulting Numbers: [780] 780,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 93:[31, 57], Operations: ['70-39=31', '10+47=57'] Exploring Operation: 31*57=1767, Resulting Numbers: [1767] 1767,93 unequal: No Solution Exploring Operation: 57-31=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 31+57=88, Resulting Numbers: [88] 88,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 93:[47, 41], Operations: ['70-39=31', '10+31=41'] Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 93:[10, 39, 23], Operations: ['70-47=23'] Exploring Operation: 39-23=16, Resulting Numbers: [10, 16] Generated Node #0,4,0: 93:[10, 16] Operation: 39-23=16 Exploring Operation: 10+23=33, Resulting Numbers: [39, 33] Generated Node #0,4,1: 93:[39, 33] Operation: 10+23=33 Exploring Operation: 39-10=29, Resulting Numbers: [23, 29] Generated Node #0,4,2: 93:[23, 29] Operation: 39-10=29 Exploring Operation: 23-10=13, Resulting Numbers: [39, 13] Generated Node #0,4,3: 93:[39, 13] Operation: 23-10=13 Exploring Operation: 10+39=49, Resulting Numbers: [23, 49] Generated Node #0,4,4: 93:[23, 49] Operation: 10+39=49 Moving to Node #0,3 Current State: 93:[47, 39, 7], Operations: ['70/10=7'] Exploring Operation: 47-7=40, Resulting Numbers: [39, 40] Generated Node #0,3,0: 93:[39, 40] Operation: 47-7=40 Exploring Operation: 47+39=86, Resulting Numbers: [7, 86] Generated Node #0,3,1: 93:[7, 86] Operation: 47+39=86 Exploring Operation: 39-7=32, Resulting Numbers: [47, 32] Generated Node #0,3,2: 93:[47, 32] Operation: 39-7=32 Exploring Operation: 47+7=54, Resulting Numbers: [39, 54] Generated Node #0,3,3: 93:[39, 54] Operation: 47+7=54 Exploring Operation: 47-39=8, Resulting Numbers: [7, 8] Generated Node #0,3,4: 93:[7, 8] Operation: 47-39=8 Moving to Node #0,0 Current State: 93:[10, 70, 8], Operations: ['47-39=8'] Exploring Operation: 10+70=80, Resulting Numbers: [8, 80] Generated Node #0,0,0: 93:[8, 80] Operation: 10+70=80 Exploring Operation: 70/10=7, Resulting Numbers: [8, 7] Generated Node #0,0,1: 93:[8, 7] Operation: 70/10=7 Exploring Operation: 70-10=60, Resulting Numbers: [8, 60] Generated Node #0,0,2: 93:[8, 60] Operation: 70-10=60 Exploring Operation: 70+8=78, Resulting Numbers: [10, 78] Generated Node #0,0,3: 93:[10, 78] Operation: 70+8=78 Exploring Operation: 10-8=2, Resulting Numbers: [70, 2] Generated Node #0,0,4: 93:[70, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[8, 7], Operations: ['47-39=8', '70/10=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,93 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[8, 80], Operations: ['47-39=8', '10+70=80'] Exploring Operation: 8+80=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,93 unequal: No Solution Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,93 unequal: No Solution Exploring Operation: 8*80=640, Resulting Numbers: [640] 640,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 93:[10, 78], Operations: ['47-39=8', '70+8=78'] Exploring Operation: 10*78=780, Resulting Numbers: [780] 780,93 unequal: No Solution Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 10+78=88, Resulting Numbers: [88] 88,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 93:[70, 2], Operations: ['47-39=8', '10-8=2'] Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,93 unequal: No Solution Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,93 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 93:[8, 60], Operations: ['47-39=8', '70-10=60'] Exploring Operation: 8+60=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 8*60=480, Resulting Numbers: [480] 480,93 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,93 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: 93:[39, 70, 37], Operations: ['47-10=37'] Exploring Operation: 70+37=107, Resulting Numbers: [39, 107] Generated Node #0,1,0: 93:[39, 107] Operation: 70+37=107 Exploring Operation: 39-37=2, Resulting Numbers: [70, 2] Generated Node #0,1,1: 93:[70, 2] Operation: 39-37=2 Exploring Operation: 70-39=31, Resulting Numbers: [37, 31] Generated Node #0,1,2: 93:[37, 31] Operation: 70-39=31 Exploring Operation: 39+70=109, Resulting Numbers: [37, 109] Generated Node #0,1,3: 93:[37, 109] Operation: 39+70=109 Exploring Operation: 70-37=33, Resulting Numbers: [39, 33] Generated Node #0,1,4: 93:[39, 33] Operation: 70-37=33 Moving to Node #0,1,2 Current State: 93:[37, 31], Operations: ['47-10=37', '70-39=31'] Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,93 unequal: No Solution Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,93 unequal: No Solution Moving to Node #0,3,4 Current State: 93:[7, 8], Operations: ['70/10=7', '47-39=8'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,93 unequal: No Solution Moving to Node #0,4,1 Current State: 93:[39, 33], Operations: ['70-47=23', '10+23=33'] Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 39*33=1287, Resulting Numbers: [1287] 1287,93 unequal: No Solution Exploring Operation: 39+33=72, Resulting Numbers: [72] 72,93 unequal: No Solution Moving to Node #0,1,4 Current State: 93:[39, 33], Operations: ['47-10=37', '70-37=33'] Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 39*33=1287, Resulting Numbers: [1287] 1287,93 unequal: No Solution Exploring Operation: 39+33=72, Resulting Numbers: [72] 72,93 unequal: No Solution Moving to Node #0,4,2 Current State: 93:[23, 29], Operations: ['70-47=23', '39-10=29'] Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,93 unequal: No Solution Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,93 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,93 unequal: No Solution Moving to Node #0,3,1 Current State: 93:[7, 86], Operations: ['70/10=7', '47+39=86'] Exploring Operation: 7*86=602, Resulting Numbers: [602] 602,93 unequal: No Solution Exploring Operation: 7+86=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[10, 47, 39, 70], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [47, 39, 7] Generated Node #0,3: 93:[47, 39, 7] Operation: 70/10=7 Moving to Node #0,3 Current State: 93:[47, 39, 7], Operations: ['70/10=7'] Exploring Operation: 47+39=86, Resulting Numbers: [7, 86] Generated Node #0,3,1: 93:[7, 86] Operation: 47+39=86 Moving to Node #0,3,1 Current State: 93:[7, 86], Operations: ['70/10=7', '47+39=86'] Exploring Operation: 7+86=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.927951
hs_5
sum_heuristic
[ 2, 11, 37, 83 ]
20
[ "2*37=74", "11+83=94", "94-74=20" ]
Current State: 20:[2, 11, 37, 83], Operations: [] Exploring Operation: 2*37=74, Resulting Numbers: [11, 83, 74] Generated Node #2: [11, 83, 74] from Operation: 2*37=74 Current State: 20:[11, 83, 74], Operations: ['2*37=74'] Exploring Operation: 11+83=94, Resulting Numbers: [74, 94] Generated Node #3: [74, 94] from Operation: 11+83=94 Current State: 20:[74, 94], Operations: ['2*37=74', '11+83=94'] Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[2, 11, 37, 83], Operations: [] Exploring Operation: 83-37=46, Resulting Numbers: [2, 11, 46] Generated Node #0,0: 20:[2, 11, 46] Operation: 83-37=46 Moving to Node #0,0 Current State: 20:[2, 11, 46], Operations: ['83-37=46'] Exploring Operation: 46/2=23, Resulting Numbers: [11, 23] Generated Node #0,0,0: 20:[11, 23] Operation: 46/2=23 Moving to Node #0,0,0 Current State: 20:[11, 23], Operations: ['83-37=46', '46/2=23'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,20 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 28, 64, 65, 21 ]
80
[ "64-28=36", "65-21=44", "36+44=80" ]
Current State: 80:[28, 64, 65, 21], Operations: [] Exploring Operation: 64-28=36, Resulting Numbers: [65, 21, 36] Generated Node #2: [65, 21, 36] from Operation: 64-28=36 Current State: 80:[65, 21, 36], Operations: ['64-28=36'] Exploring Operation: 65-21=44, Resulting Numbers: [36, 44] Generated Node #3: [36, 44] from Operation: 65-21=44 Current State: 80:[36, 44], Operations: ['64-28=36', '65-21=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[28, 64, 65, 21], Operations: [] Exploring Operation: 65-64=1, Resulting Numbers: [28, 21, 1] Generated Node #0,0: 80:[28, 21, 1] Operation: 65-64=1 Exploring Operation: 64-28=36, Resulting Numbers: [65, 21, 36] Generated Node #0,1: 80:[65, 21, 36] Operation: 64-28=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[28, 21, 1], Operations: ['65-64=1'] Exploring Operation: 28-1=27, Resulting Numbers: [21, 27] Generated Node #0,0,0: 80:[21, 27] Operation: 28-1=27 Exploring Operation: 28-21=7, Resulting Numbers: [1, 7] Generated Node #0,0,1: 80:[1, 7] Operation: 28-21=7 Moving to Node #0,0,1 Current State: 80:[1, 7], Operations: ['65-64=1', '28-21=7'] Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[21, 27], Operations: ['65-64=1', '28-1=27'] Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[65, 21, 36], Operations: ['64-28=36'] Exploring Operation: 65-21=44, Resulting Numbers: [36, 44] Generated Node #0,1,0: 80:[36, 44] Operation: 65-21=44 Exploring Operation: 65+21=86, Resulting Numbers: [36, 86] Generated Node #0,1,1: 80:[36, 86] Operation: 65+21=86 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[36, 44], Operations: ['64-28=36', '65-21=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[28, 64, 65, 21], Operations: [] Exploring Operation: 64-28=36, Resulting Numbers: [65, 21, 36] Generated Node #0,1: 80:[65, 21, 36] Operation: 64-28=36 Moving to Node #0,1 Current State: 80:[65, 21, 36], Operations: ['64-28=36'] Exploring Operation: 65-21=44, Resulting Numbers: [36, 44] Generated Node #0,1,0: 80:[36, 44] Operation: 65-21=44 Moving to Node #0,1,0 Current State: 80:[36, 44], Operations: ['64-28=36', '65-21=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 24, 46, 91, 86 ]
65
[ "24+46=70", "91-86=5", "70-5=65" ]
Current State: 65:[24, 46, 91, 86], Operations: [] Exploring Operation: 24+46=70, Resulting Numbers: [91, 86, 70] Generated Node #2: [91, 86, 70] from Operation: 24+46=70 Current State: 65:[91, 86, 70], Operations: ['24+46=70'] Exploring Operation: 91-86=5, Resulting Numbers: [70, 5] Generated Node #3: [70, 5] from Operation: 91-86=5 Current State: 65:[70, 5], Operations: ['24+46=70', '91-86=5'] Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[24, 46, 91, 86], Operations: [] Exploring Operation: 24+46=70, Resulting Numbers: [91, 86, 70] Generated Node #0,0: 65:[91, 86, 70] Operation: 24+46=70 Exploring Operation: 91-86=5, Resulting Numbers: [24, 46, 5] Generated Node #0,1: 65:[24, 46, 5] Operation: 91-86=5 Exploring Operation: 86-24=62, Resulting Numbers: [46, 91, 62] Generated Node #0,2: 65:[46, 91, 62] Operation: 86-24=62 Exploring Operation: 91-46=45, Resulting Numbers: [24, 86, 45] Generated Node #0,3: 65:[24, 86, 45] Operation: 91-46=45 Exploring Operation: 91-24=67, Resulting Numbers: [46, 86, 67] Generated Node #0,4: 65:[46, 86, 67] Operation: 91-24=67 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[24, 46, 5], Operations: ['91-86=5'] Exploring Operation: 24-5=19, Resulting Numbers: [46, 19] Generated Node #0,1,0: 65:[46, 19] Operation: 24-5=19 Exploring Operation: 24+46=70, Resulting Numbers: [5, 70] Generated Node #0,1,1: 65:[5, 70] Operation: 24+46=70 Exploring Operation: 24+5=29, Resulting Numbers: [46, 29] Generated Node #0,1,2: 65:[46, 29] Operation: 24+5=29 Exploring Operation: 46-24=22, Resulting Numbers: [5, 22] Generated Node #0,1,3: 65:[5, 22] Operation: 46-24=22 Exploring Operation: 46+5=51, Resulting Numbers: [24, 51] Generated Node #0,1,4: 65:[24, 51] Operation: 46+5=51 Moving to Node #0,1,1 Current State: 65:[5, 70], Operations: ['91-86=5', '24+46=70'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 5*70=350, Resulting Numbers: [350] 350,65 unequal: No Solution Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,65 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[24, 46, 91, 86], Operations: [] Exploring Operation: 91-86=5, Resulting Numbers: [24, 46, 5] Generated Node #0,1: 65:[24, 46, 5] Operation: 91-86=5 Moving to Node #0,1 Current State: 65:[24, 46, 5], Operations: ['91-86=5'] Exploring Operation: 24+46=70, Resulting Numbers: [5, 70] Generated Node #0,1,1: 65:[5, 70] Operation: 24+46=70 Moving to Node #0,1,1 Current State: 65:[5, 70], Operations: ['91-86=5', '24+46=70'] Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 55, 64, 58, 53 ]
35
[ "55-53=2", "58/2=29", "64-29=35" ]
Current State: 35:[55, 64, 58, 53], Operations: [] Exploring Operation: 55-53=2, Resulting Numbers: [64, 58, 2] Generated Node #2: [64, 58, 2] from Operation: 55-53=2 Current State: 35:[64, 58, 2], Operations: ['55-53=2'] Exploring Operation: 58/2=29, Resulting Numbers: [64, 29] Generated Node #3: [64, 29] from Operation: 58/2=29 Current State: 35:[64, 29], Operations: ['55-53=2', '58/2=29'] Exploring Operation: 64-29=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[55, 64, 58, 53], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [55, 53, 6] Generated Node #0,0: 35:[55, 53, 6] Operation: 64-58=6 Exploring Operation: 64-55=9, Resulting Numbers: [58, 53, 9] Generated Node #0,1: 35:[58, 53, 9] Operation: 64-55=9 Exploring Operation: 64-53=11, Resulting Numbers: [55, 58, 11] Generated Node #0,2: 35:[55, 58, 11] Operation: 64-53=11 Moving to Node #0,0 Current State: 35:[55, 53, 6], Operations: ['64-58=6'] Exploring Operation: 55-53=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 35:[6, 2] Operation: 55-53=2 Exploring Operation: 53-6=47, Resulting Numbers: [55, 47] Generated Node #0,0,1: 35:[55, 47] Operation: 53-6=47 Exploring Operation: 55-6=49, Resulting Numbers: [53, 49] Generated Node #0,0,2: 35:[53, 49] Operation: 55-6=49 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[6, 2], Operations: ['64-58=6', '55-53=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,35 unequal: No Solution No 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: 35:[55, 47], Operations: ['64-58=6', '53-6=47'] Exploring Operation: 55+47=102, Resulting Numbers: [102] 102,35 unequal: No Solution Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 55*47=2585, Resulting Numbers: [2585] 2585,35 unequal: No Solution No 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: 35:[53, 49], Operations: ['64-58=6', '55-6=49'] Exploring Operation: 53-49=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 53*49=2597, Resulting Numbers: [2597] 2597,35 unequal: No Solution Exploring Operation: 53+49=102, Resulting Numbers: [102] 102,35 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: 35:[58, 53, 9], Operations: ['64-55=9'] Exploring Operation: 53-9=44, Resulting Numbers: [58, 44] Generated Node #0,1,0: 35:[58, 44] Operation: 53-9=44 Exploring Operation: 58-53=5, Resulting Numbers: [9, 5] Generated Node #0,1,1: 35:[9, 5] Operation: 58-53=5 Exploring Operation: 58-9=49, Resulting Numbers: [53, 49] Generated Node #0,1,2: 35:[53, 49] Operation: 58-9=49 Moving to Node #0,2 Current State: 35:[55, 58, 11], Operations: ['64-53=11'] Exploring Operation: 55/11=5, Resulting Numbers: [58, 5] Generated Node #0,2,0: 35:[58, 5] Operation: 55/11=5 Exploring Operation: 58-55=3, Resulting Numbers: [11, 3] Generated Node #0,2,1: 35:[11, 3] Operation: 58-55=3 Exploring Operation: 55-11=44, Resulting Numbers: [58, 44] Generated Node #0,2,2: 35:[58, 44] Operation: 55-11=44 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 35:[11, 3], Operations: ['64-53=11', '58-55=3'] Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,35 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,35 unequal: No Solution No 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: 35:[58, 5], Operations: ['64-53=11', '55/11=5'] Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,35 unequal: No Solution Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,35 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,35 unequal: No Solution No 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: 35:[58, 44], Operations: ['64-53=11', '55-11=44'] Exploring Operation: 58*44=2552, Resulting Numbers: [2552] 2552,35 unequal: No Solution Exploring Operation: 58+44=102, Resulting Numbers: [102] 102,35 unequal: No Solution Exploring Operation: 58-44=14, Resulting Numbers: [14] 14,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 35:[9, 5], Operations: ['64-55=9', '58-53=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[58, 44], Operations: ['64-55=9', '53-9=44'] Exploring Operation: 58-44=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 58*44=2552, Resulting Numbers: [2552] 2552,35 unequal: No Solution Exploring Operation: 58+44=102, Resulting Numbers: [102] 102,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[53, 49], Operations: ['64-55=9', '58-9=49'] Exploring Operation: 53-49=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 53*49=2597, Resulting Numbers: [2597] 2597,35 unequal: No Solution Exploring Operation: 53+49=102, Resulting Numbers: [102] 102,35 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 86, 3, 70, 84 ]
36
[ "86-70=16", "3*16=48", "84-48=36" ]
Current State: 36:[86, 3, 70, 84], Operations: [] Exploring Operation: 86-70=16, Resulting Numbers: [3, 84, 16] Generated Node #2: [3, 84, 16] from Operation: 86-70=16 Current State: 36:[3, 84, 16], Operations: ['86-70=16'] Exploring Operation: 3*16=48, Resulting Numbers: [84, 48] Generated Node #3: [84, 48] from Operation: 3*16=48 Current State: 36:[84, 48], Operations: ['86-70=16', '3*16=48'] Exploring Operation: 84-48=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[86, 3, 70, 84], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [86, 3, 14] Generated Node #0,0: 36:[86, 3, 14] Operation: 84-70=14 Exploring Operation: 86-3=83, Resulting Numbers: [70, 84, 83] Generated Node #0,1: 36:[70, 84, 83] Operation: 86-3=83 Exploring Operation: 86-70=16, Resulting Numbers: [3, 84, 16] Generated Node #0,2: 36:[3, 84, 16] Operation: 86-70=16 Exploring Operation: 86-84=2, Resulting Numbers: [3, 70, 2] Generated Node #0,3: 36:[3, 70, 2] Operation: 86-84=2 Exploring Operation: 84/3=28, Resulting Numbers: [86, 70, 28] Generated Node #0,4: 36:[86, 70, 28] Operation: 84/3=28 Moving to Node #0,3 Current State: 36:[3, 70, 2], Operations: ['86-84=2'] Exploring Operation: 70-2=68, Resulting Numbers: [3, 68] Generated Node #0,3,0: 36:[3, 68] Operation: 70-2=68 Exploring Operation: 3*2=6, Resulting Numbers: [70, 6] Generated Node #0,3,1: 36:[70, 6] Operation: 3*2=6 Exploring Operation: 70-3=67, Resulting Numbers: [2, 67] Generated Node #0,3,2: 36:[2, 67] Operation: 70-3=67 Exploring Operation: 70/2=35, Resulting Numbers: [3, 35] Generated Node #0,3,3: 36:[3, 35] Operation: 70/2=35 Exploring Operation: 3+2=5, Resulting Numbers: [70, 5] Generated Node #0,3,4: 36:[70, 5] Operation: 3+2=5 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 36:[3, 35], Operations: ['86-84=2', '70/2=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,36 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 36:[2, 67], Operations: ['86-84=2', '70-3=67'] Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,36 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[3, 68], Operations: ['86-84=2', '70-2=68'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,36 unequal: No Solution Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,36 unequal: No Solution Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 36:[70, 6], Operations: ['86-84=2', '3*2=6'] Exploring Operation: 70*6=420, Resulting Numbers: [420] 420,36 unequal: No Solution Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,36 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 36:[70, 5], Operations: ['86-84=2', '3+2=5'] Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,36 unequal: No Solution Exploring Operation: 70*5=350, Resulting Numbers: [350] 350,36 unequal: No Solution Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,36 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 36:[3, 84, 16], Operations: ['86-70=16'] Exploring Operation: 84-16=68, Resulting Numbers: [3, 68] Generated Node #0,2,0: 36:[3, 68] Operation: 84-16=68 Exploring Operation: 84/3=28, Resulting Numbers: [16, 28] Generated Node #0,2,1: 36:[16, 28] Operation: 84/3=28 Exploring Operation: 16-3=13, Resulting Numbers: [84, 13] Generated Node #0,2,2: 36:[84, 13] Operation: 16-3=13 Exploring Operation: 3+16=19, Resulting Numbers: [84, 19] Generated Node #0,2,3: 36:[84, 19] Operation: 3+16=19 Exploring Operation: 84-3=81, Resulting Numbers: [16, 81] Generated Node #0,2,4: 36:[16, 81] Operation: 84-3=81 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 36:[16, 28], Operations: ['86-70=16', '84/3=28'] Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,36 unequal: No Solution Exploring Operation: 16*28=448, Resulting Numbers: [448] 448,36 unequal: No Solution Exploring Operation: 16+28=44, Resulting Numbers: [44] 44,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 36:[3, 68], Operations: ['86-70=16', '84-16=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,36 unequal: No Solution Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,36 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 36:[16, 81], Operations: ['86-70=16', '84-3=81'] Exploring Operation: 16+81=97, Resulting Numbers: [97] 97,36 unequal: No Solution Exploring Operation: 16*81=1296, Resulting Numbers: [1296] 1296,36 unequal: No Solution Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 36:[84, 13], Operations: ['86-70=16', '16-3=13'] Exploring Operation: 84*13=1092, Resulting Numbers: [1092] 1092,36 unequal: No Solution Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,36 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 36:[84, 19], Operations: ['86-70=16', '3+16=19'] Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,36 unequal: No Solution Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,36 unequal: No Solution Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 36:[86, 3, 14], Operations: ['84-70=14'] Exploring Operation: 14-3=11, Resulting Numbers: [86, 11] Generated Node #0,0,0: 36:[86, 11] Operation: 14-3=11 Exploring Operation: 86-3=83, Resulting Numbers: [14, 83] Generated Node #0,0,1: 36:[14, 83] Operation: 86-3=83 Exploring Operation: 86-14=72, Resulting Numbers: [3, 72] Generated Node #0,0,2: 36:[3, 72] Operation: 86-14=72 Exploring Operation: 3+14=17, Resulting Numbers: [86, 17] Generated Node #0,0,3: 36:[86, 17] Operation: 3+14=17 Exploring Operation: 86+3=89, Resulting Numbers: [14, 89] Generated Node #0,0,4: 36:[14, 89] Operation: 86+3=89 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 36:[3, 72], Operations: ['84-70=14', '86-14=72'] Exploring Operation: 3*72=216, Resulting Numbers: [216] 216,36 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,36 unequal: No Solution Exploring Operation: 3+72=75, Resulting Numbers: [75] 75,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[14, 83], Operations: ['84-70=14', '86-3=83'] Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 14*83=1162, Resulting Numbers: [1162] 1162,36 unequal: No Solution Exploring Operation: 14+83=97, Resulting Numbers: [97] 97,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[86, 11], Operations: ['84-70=14', '14-3=11'] Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,36 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,36 unequal: No Solution Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 36:[86, 17], Operations: ['84-70=14', '3+14=17'] Exploring Operation: 86+17=103, Resulting Numbers: [103] 103,36 unequal: No Solution Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 86*17=1462, Resulting Numbers: [1462] 1462,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 36:[14, 89], Operations: ['84-70=14', '86+3=89'] Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,36 unequal: No Solution Exploring Operation: 14+89=103, Resulting Numbers: [103] 103,36 unequal: No Solution Exploring Operation: 14*89=1246, Resulting Numbers: [1246] 1246,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 36:[86, 70, 28], Operations: ['84/3=28'] Exploring Operation: 70-28=42, Resulting Numbers: [86, 42] Generated Node #0,4,0: 36:[86, 42] Operation: 70-28=42 Exploring Operation: 86-70=16, Resulting Numbers: [28, 16] Generated Node #0,4,1: 36:[28, 16] Operation: 86-70=16 Exploring Operation: 70+28=98, Resulting Numbers: [86, 98] Generated Node #0,4,2: 36:[86, 98] Operation: 70+28=98 Exploring Operation: 86-28=58, Resulting Numbers: [70, 58] Generated Node #0,4,3: 36:[70, 58] Operation: 86-28=58 Exploring Operation: 86+28=114, Resulting Numbers: [70, 114] Generated Node #0,4,4: 36:[70, 114] Operation: 86+28=114 Moving to Node #0,1 Current State: 36:[70, 84, 83], Operations: ['86-3=83'] Exploring Operation: 70+83=153, Resulting Numbers: [84, 153] Generated Node #0,1,0: 36:[84, 153] Operation: 70+83=153 Exploring Operation: 84-83=1, Resulting Numbers: [70, 1] Generated Node #0,1,1: 36:[70, 1] Operation: 84-83=1 Exploring Operation: 83-70=13, Resulting Numbers: [84, 13] Generated Node #0,1,2: 36:[84, 13] Operation: 83-70=13 Exploring Operation: 70+84=154, Resulting Numbers: [83, 154] Generated Node #0,1,3: 36:[83, 154] Operation: 70+84=154 Exploring Operation: 84-70=14, Resulting Numbers: [83, 14] Generated Node #0,1,4: 36:[83, 14] Operation: 84-70=14 Moving to Node #0,4,1 Current State: 36:[28, 16], Operations: ['84/3=28', '86-70=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,36 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,36 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[70, 1], Operations: ['86-3=83', '84-83=1'] Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,36 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,36 unequal: No Solution Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[84, 13], Operations: ['86-3=83', '83-70=13'] Exploring Operation: 84*13=1092, Resulting Numbers: [1092] 1092,36 unequal: No Solution Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,36 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,36 unequal: No Solution Moving to Node #0,1,4 Current State: 36:[83, 14], Operations: ['86-3=83', '84-70=14'] Exploring Operation: 83+14=97, Resulting Numbers: [97] 97,36 unequal: No Solution Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 83*14=1162, Resulting Numbers: [1162] 1162,36 unequal: No Solution Moving to Node #0,4,3 Current State: 36:[70, 58], Operations: ['84/3=28', '86-28=58'] Exploring Operation: 70+58=128, Resulting Numbers: [128] 128,36 unequal: No Solution Exploring Operation: 70*58=4060, Resulting Numbers: [4060] 4060,36 unequal: No Solution Exploring Operation: 70-58=12, Resulting Numbers: [12] 12,36 unequal: No Solution Moving to Node #0,4,0 Current State: 36:[86, 42], Operations: ['84/3=28', '70-28=42'] Exploring Operation: 86-42=44, Resulting Numbers: [44] 44,36 unequal: No Solution Exploring Operation: 86+42=128, Resulting Numbers: [128] 128,36 unequal: No Solution Exploring Operation: 86*42=3612, Resulting Numbers: [3612] 3612,36 unequal: No Solution Moving to Node #0,4,4 Current State: 36:[70, 114], Operations: ['84/3=28', '86+28=114'] Exploring Operation: 114-70=44, Resulting Numbers: [44] 44,36 unequal: No Solution Exploring Operation: 70*114=7980, Resulting Numbers: [7980] 7980,36 unequal: No Solution Exploring Operation: 70+114=184, Resulting Numbers: [184] 184,36 unequal: No Solution Moving to Node #0,4,2 Current State: 36:[86, 98], Operations: ['84/3=28', '70+28=98'] Exploring Operation: 86*98=8428, Resulting Numbers: [8428] 8428,36 unequal: No Solution Exploring Operation: 86+98=184, Resulting Numbers: [184] 184,36 unequal: No Solution Exploring Operation: 98-86=12, Resulting Numbers: [12] 12,36 unequal: No Solution Moving to Node #0,1,3 Current State: 36:[83, 154], Operations: ['86-3=83', '70+84=154'] Exploring Operation: 83*154=12782, Resulting Numbers: [12782] 12782,36 unequal: No Solution Exploring Operation: 154-83=71, Resulting Numbers: [71] 71,36 unequal: No Solution Exploring Operation: 83+154=237, Resulting Numbers: [237] 237,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[84, 153], Operations: ['86-3=83', '70+83=153'] Exploring Operation: 153-84=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 84+153=237, Resulting Numbers: [237] 237,36 unequal: No Solution Exploring Operation: 84*153=12852, Resulting Numbers: [12852] 12852,36 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 95, 54, 55, 16 ]
30
[ "95-54=41", "55+16=71", "71-41=30" ]
Current State: 30:[95, 54, 55, 16], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [55, 16, 41] Generated Node #2: [55, 16, 41] from Operation: 95-54=41 Current State: 30:[55, 16, 41], Operations: ['95-54=41'] Exploring Operation: 55+16=71, Resulting Numbers: [41, 71] Generated Node #3: [41, 71] from Operation: 55+16=71 Current State: 30:[41, 71], Operations: ['95-54=41', '55+16=71'] Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[95, 54, 55, 16], Operations: [] Exploring Operation: 95-55=40, Resulting Numbers: [54, 16, 40] Generated Node #0,0: 30:[54, 16, 40] Operation: 95-55=40 Moving to Node #0,0 Current State: 30:[54, 16, 40], Operations: ['95-55=40'] Exploring Operation: 54-40=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 30:[16, 14] Operation: 54-40=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[16, 14], Operations: ['95-55=40', '54-40=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[95, 54, 55, 16], Operations: [] Exploring Operation: 95-55=40, Resulting Numbers: [54, 16, 40] Generated Node #0,0: 30:[54, 16, 40] Operation: 95-55=40 Moving to Node #0,0 Current State: 30:[54, 16, 40], Operations: ['95-55=40'] Exploring Operation: 54-40=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 30:[16, 14] Operation: 54-40=14 Moving to Node #0,0,0 Current State: 30:[16, 14], Operations: ['95-55=40', '54-40=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 14, 13, 45, 37 ]
70
[ "45-13=32", "37-32=5", "14*5=70" ]
Current State: 70:[14, 13, 45, 37], Operations: [] Exploring Operation: 45-13=32, Resulting Numbers: [14, 37, 32] Generated Node #2: [14, 37, 32] from Operation: 45-13=32 Current State: 70:[14, 37, 32], Operations: ['45-13=32'] Exploring Operation: 37-32=5, Resulting Numbers: [14, 5] Generated Node #3: [14, 5] from Operation: 37-32=5 Current State: 70:[14, 5], Operations: ['45-13=32', '37-32=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[14, 13, 45, 37], Operations: [] Exploring Operation: 45-13=32, Resulting Numbers: [14, 37, 32] Generated Node #0,0: 70:[14, 37, 32] Operation: 45-13=32 Exploring Operation: 45+37=82, Resulting Numbers: [14, 13, 82] Generated Node #0,1: 70:[14, 13, 82] Operation: 45+37=82 Exploring Operation: 45-37=8, Resulting Numbers: [14, 13, 8] Generated Node #0,2: 70:[14, 13, 8] Operation: 45-37=8 Exploring Operation: 14-13=1, Resulting Numbers: [45, 37, 1] Generated Node #0,3: 70:[45, 37, 1] Operation: 14-13=1 Exploring Operation: 45-14=31, Resulting Numbers: [13, 37, 31] Generated Node #0,4: 70:[13, 37, 31] Operation: 45-14=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[14, 13, 8], Operations: ['45-37=8'] Exploring Operation: 14-8=6, Resulting Numbers: [13, 6] Generated Node #0,2,0: 70:[13, 6] Operation: 14-8=6 Exploring Operation: 13+8=21, Resulting Numbers: [14, 21] Generated Node #0,2,1: 70:[14, 21] Operation: 13+8=21 Exploring Operation: 13-8=5, Resulting Numbers: [14, 5] Generated Node #0,2,2: 70:[14, 5] Operation: 13-8=5 Exploring Operation: 14+13=27, Resulting Numbers: [8, 27] Generated Node #0,2,3: 70:[8, 27] Operation: 14+13=27 Exploring Operation: 14-13=1, Resulting Numbers: [8, 1] Generated Node #0,2,4: 70:[8, 1] Operation: 14-13=1 Moving to Node #0,2,2 Current State: 70:[14, 5], Operations: ['45-37=8', '13-8=5'] Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[14, 13, 45, 37], Operations: [] Exploring Operation: 45-37=8, Resulting Numbers: [14, 13, 8] Generated Node #0,2: 70:[14, 13, 8] Operation: 45-37=8 Moving to Node #0,2 Current State: 70:[14, 13, 8], Operations: ['45-37=8'] Exploring Operation: 13-8=5, Resulting Numbers: [14, 5] Generated Node #0,2,2: 70:[14, 5] Operation: 13-8=5 Moving to Node #0,2,2 Current State: 70:[14, 5], Operations: ['45-37=8', '13-8=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 2, 63, 53, 79 ]
91
[ "2+63=65", "79-53=26", "65+26=91" ]
Current State: 91:[2, 63, 53, 79], Operations: [] Exploring Operation: 2+63=65, Resulting Numbers: [53, 79, 65] Generated Node #2: [53, 79, 65] from Operation: 2+63=65 Current State: 91:[53, 79, 65], Operations: ['2+63=65'] Exploring Operation: 79-53=26, Resulting Numbers: [65, 26] Generated Node #3: [65, 26] from Operation: 79-53=26 Current State: 91:[65, 26], Operations: ['2+63=65', '79-53=26'] Exploring Operation: 65+26=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[2, 63, 53, 79], Operations: [] Exploring Operation: 63-53=10, Resulting Numbers: [2, 79, 10] Generated Node #0,0: 91:[2, 79, 10] Operation: 63-53=10 Exploring Operation: 79-63=16, Resulting Numbers: [2, 53, 16] Generated Node #0,1: 91:[2, 53, 16] Operation: 79-63=16 Exploring Operation: 63+53=116, Resulting Numbers: [2, 79, 116] Generated Node #0,2: 91:[2, 79, 116] Operation: 63+53=116 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[2, 79, 10], Operations: ['63-53=10'] Exploring Operation: 79+10=89, Resulting Numbers: [2, 89] Generated Node #0,0,0: 91:[2, 89] Operation: 79+10=89 Exploring Operation: 2+10=12, Resulting Numbers: [79, 12] Generated Node #0,0,1: 91:[79, 12] Operation: 2+10=12 Exploring Operation: 2+79=81, Resulting Numbers: [10, 81] Generated Node #0,0,2: 91:[10, 81] Operation: 2+79=81 Moving to Node #0,0,0 Current State: 91:[2, 89], Operations: ['63-53=10', '79+10=89'] Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,91 unequal: No Solution Exploring Operation: 2*89=178, Resulting Numbers: [178] 178,91 unequal: No Solution Exploring Operation: 2+89=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[2, 63, 53, 79], Operations: [] Exploring Operation: 63-53=10, Resulting Numbers: [2, 79, 10] Generated Node #0,0: 91:[2, 79, 10] Operation: 63-53=10 Moving to Node #0,0 Current State: 91:[2, 79, 10], Operations: ['63-53=10'] Exploring Operation: 79+10=89, Resulting Numbers: [2, 89] Generated Node #0,0,0: 91:[2, 89] Operation: 79+10=89 Moving to Node #0,0,0 Current State: 91:[2, 89], Operations: ['63-53=10', '79+10=89'] Exploring Operation: 2+89=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 99, 16, 53, 21 ]
97
[ "53-21=32", "32/16=2", "99-2=97" ]
Current State: 97:[99, 16, 53, 21], Operations: [] Exploring Operation: 53-21=32, Resulting Numbers: [99, 16, 32] Generated Node #2: [99, 16, 32] from Operation: 53-21=32 Current State: 97:[99, 16, 32], Operations: ['53-21=32'] Exploring Operation: 32/16=2, Resulting Numbers: [99, 2] Generated Node #3: [99, 2] from Operation: 32/16=2 Current State: 97:[99, 2], Operations: ['53-21=32', '32/16=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[99, 16, 53, 21], Operations: [] Exploring Operation: 16+53=69, Resulting Numbers: [99, 21, 69] Generated Node #0,0: 97:[99, 21, 69] Operation: 16+53=69 Exploring Operation: 16+21=37, Resulting Numbers: [99, 53, 37] Generated Node #0,1: 97:[99, 53, 37] Operation: 16+21=37 Exploring Operation: 53+21=74, Resulting Numbers: [99, 16, 74] Generated Node #0,2: 97:[99, 16, 74] Operation: 53+21=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[99, 21, 69], Operations: ['16+53=69'] Exploring Operation: 99+21=120, Resulting Numbers: [69, 120] Generated Node #0,0,0: 97:[69, 120] Operation: 99+21=120 Exploring Operation: 21+69=90, Resulting Numbers: [99, 90] Generated Node #0,0,1: 97:[99, 90] Operation: 21+69=90 Exploring Operation: 99-21=78, Resulting Numbers: [69, 78] Generated Node #0,0,2: 97:[69, 78] Operation: 99-21=78 Moving to Node #0,0,1 Current State: 97:[99, 90], Operations: ['16+53=69', '21+69=90'] Exploring Operation: 99-90=9, Resulting Numbers: [9] 9,97 unequal: No Solution Exploring Operation: 99*90=8910, Resulting Numbers: [8910] 8910,97 unequal: No Solution Exploring Operation: 99+90=189, Resulting Numbers: [189] 189,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[69, 78], Operations: ['16+53=69', '99-21=78'] Exploring Operation: 69*78=5382, Resulting Numbers: [5382] 5382,97 unequal: No Solution Exploring Operation: 78-69=9, Resulting Numbers: [9] 9,97 unequal: No Solution Exploring Operation: 69+78=147, Resulting Numbers: [147] 147,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[69, 120], Operations: ['16+53=69', '99+21=120'] Exploring Operation: 69*120=8280, Resulting Numbers: [8280] 8280,97 unequal: No Solution Exploring Operation: 120-69=51, Resulting Numbers: [51] 51,97 unequal: No Solution Exploring Operation: 69+120=189, Resulting Numbers: [189] 189,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[99, 53, 37], Operations: ['16+21=37'] Exploring Operation: 53+37=90, Resulting Numbers: [99, 90] Generated Node #0,1,0: 97:[99, 90] Operation: 53+37=90 Exploring Operation: 99-37=62, Resulting Numbers: [53, 62] Generated Node #0,1,1: 97:[53, 62] Operation: 99-37=62 Exploring Operation: 99+37=136, Resulting Numbers: [53, 136] Generated Node #0,1,2: 97:[53, 136] Operation: 99+37=136 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[99, 90], Operations: ['16+21=37', '53+37=90'] Exploring Operation: 99+90=189, Resulting Numbers: [189] 189,97 unequal: No Solution Exploring Operation: 99*90=8910, Resulting Numbers: [8910] 8910,97 unequal: No Solution Exploring Operation: 99-90=9, Resulting Numbers: [9] 9,97 unequal: No Solution No 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: 97:[53, 62], Operations: ['16+21=37', '99-37=62'] Exploring Operation: 53+62=115, Resulting Numbers: [115] 115,97 unequal: No Solution Exploring Operation: 53*62=3286, Resulting Numbers: [3286] 3286,97 unequal: No Solution Exploring Operation: 62-53=9, Resulting Numbers: [9] 9,97 unequal: No Solution No 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: 97:[53, 136], Operations: ['16+21=37', '99+37=136'] Exploring Operation: 136-53=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 53*136=7208, Resulting Numbers: [7208] 7208,97 unequal: No Solution Exploring Operation: 53+136=189, Resulting Numbers: [189] 189,97 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: 97:[99, 16, 74], Operations: ['53+21=74'] Exploring Operation: 99+16=115, Resulting Numbers: [74, 115] Generated Node #0,2,0: 97:[74, 115] Operation: 99+16=115 Exploring Operation: 16+74=90, Resulting Numbers: [99, 90] Generated Node #0,2,1: 97:[99, 90] Operation: 16+74=90 Exploring Operation: 99-16=83, Resulting Numbers: [74, 83] Generated Node #0,2,2: 97:[74, 83] Operation: 99-16=83 Moving to Node #0,2,1 Current State: 97:[99, 90], Operations: ['53+21=74', '16+74=90'] Exploring Operation: 99-90=9, Resulting Numbers: [9] 9,97 unequal: No Solution Exploring Operation: 99*90=8910, Resulting Numbers: [8910] 8910,97 unequal: No Solution Exploring Operation: 99+90=189, Resulting Numbers: [189] 189,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[74, 83], Operations: ['53+21=74', '99-16=83'] Exploring Operation: 74*83=6142, Resulting Numbers: [6142] 6142,97 unequal: No Solution Exploring Operation: 83-74=9, Resulting Numbers: [9] 9,97 unequal: No Solution Exploring Operation: 74+83=157, Resulting Numbers: [157] 157,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[74, 115], Operations: ['53+21=74', '99+16=115'] Exploring Operation: 115-74=41, Resulting Numbers: [41] 41,97 unequal: No Solution Exploring Operation: 74+115=189, Resulting Numbers: [189] 189,97 unequal: No Solution Exploring Operation: 74*115=8510, Resulting Numbers: [8510] 8510,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 3, 75, 21, 6 ]
15
[ "3*75=225", "21-6=15", "225/15=15" ]
Current State: 15:[3, 75, 21, 6], Operations: [] Exploring Operation: 3*75=225, Resulting Numbers: [21, 6, 225] Generated Node #2: [21, 6, 225] from Operation: 3*75=225 Current State: 15:[21, 6, 225], Operations: ['3*75=225'] Exploring Operation: 21-6=15, Resulting Numbers: [225, 15] Generated Node #3: [225, 15] from Operation: 21-6=15 Current State: 15:[225, 15], Operations: ['3*75=225', '21-6=15'] Exploring Operation: 225/15=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[3, 75, 21, 6], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [21, 6, 25] Generated Node #0,0: 15:[21, 6, 25] Operation: 75/3=25 Exploring Operation: 75-21=54, Resulting Numbers: [3, 6, 54] Generated Node #0,1: 15:[3, 6, 54] Operation: 75-21=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[21, 6, 25], Operations: ['75/3=25'] Exploring Operation: 25-21=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 15:[6, 4] Operation: 25-21=4 Exploring Operation: 21-6=15, Resulting Numbers: [25, 15] Generated Node #0,0,1: 15:[25, 15] Operation: 21-6=15 Moving to Node #0,0,0 Current State: 15:[6, 4], Operations: ['75/3=25', '25-21=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[25, 15], Operations: ['75/3=25', '21-6=15'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[3, 6, 54], Operations: ['75-21=54'] Exploring Operation: 54/3=18, Resulting Numbers: [6, 18] Generated Node #0,1,0: 15:[6, 18] Operation: 54/3=18 Exploring Operation: 54/6=9, Resulting Numbers: [3, 9] Generated Node #0,1,1: 15:[3, 9] Operation: 54/6=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 15:[6, 18], Operations: ['75-21=54', '54/3=18'] Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 15:[3, 9], Operations: ['75-21=54', '54/6=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 77, 16, 15, 72 ]
48
[ "77-72=5", "16*15=240", "240/5=48" ]
Current State: 48:[77, 16, 15, 72], Operations: [] Exploring Operation: 77-72=5, Resulting Numbers: [16, 15, 5] Generated Node #2: [16, 15, 5] from Operation: 77-72=5 Current State: 48:[16, 15, 5], Operations: ['77-72=5'] Exploring Operation: 16*15=240, Resulting Numbers: [5, 240] Generated Node #3: [5, 240] from Operation: 16*15=240 Current State: 48:[5, 240], Operations: ['77-72=5', '16*15=240'] Exploring Operation: 240/5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[77, 16, 15, 72], Operations: [] Exploring Operation: 77-15=62, Resulting Numbers: [16, 72, 62] Generated Node #0,0: 48:[16, 72, 62] Operation: 77-15=62 Exploring Operation: 77-16=61, Resulting Numbers: [15, 72, 61] Generated Node #0,1: 48:[15, 72, 61] Operation: 77-16=61 Exploring Operation: 77-72=5, Resulting Numbers: [16, 15, 5] Generated Node #0,2: 48:[16, 15, 5] Operation: 77-72=5 Moving to Node #0,2 Current State: 48:[16, 15, 5], Operations: ['77-72=5'] Exploring Operation: 16-15=1, Resulting Numbers: [5, 1] Generated Node #0,2,0: 48:[5, 1] Operation: 16-15=1 Exploring Operation: 16-5=11, Resulting Numbers: [15, 11] Generated Node #0,2,1: 48:[15, 11] Operation: 16-5=11 Exploring Operation: 15/5=3, Resulting Numbers: [16, 3] Generated Node #0,2,2: 48:[16, 3] Operation: 15/5=3 Moving to Node #0,0 Current State: 48:[16, 72, 62], Operations: ['77-15=62'] Exploring Operation: 72-16=56, Resulting Numbers: [62, 56] Generated Node #0,0,0: 48:[62, 56] Operation: 72-16=56 Exploring Operation: 62-16=46, Resulting Numbers: [72, 46] Generated Node #0,0,1: 48:[72, 46] Operation: 62-16=46 Exploring Operation: 72-62=10, Resulting Numbers: [16, 10] Generated Node #0,0,2: 48:[16, 10] Operation: 72-62=10 Moving to Node #0,1 Current State: 48:[15, 72, 61], Operations: ['77-16=61'] Exploring Operation: 61-15=46, Resulting Numbers: [72, 46] Generated Node #0,1,0: 48:[72, 46] Operation: 61-15=46 Exploring Operation: 72-61=11, Resulting Numbers: [15, 11] Generated Node #0,1,1: 48:[15, 11] Operation: 72-61=11 Exploring Operation: 72-15=57, Resulting Numbers: [61, 57] Generated Node #0,1,2: 48:[61, 57] Operation: 72-15=57 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 48:[15, 11], Operations: ['77-16=61', '72-61=11'] Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,48 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 48:[61, 57], Operations: ['77-16=61', '72-15=57'] Exploring Operation: 61*57=3477, Resulting Numbers: [3477] 3477,48 unequal: No Solution Exploring Operation: 61+57=118, Resulting Numbers: [118] 118,48 unequal: No Solution Exploring Operation: 61-57=4, Resulting Numbers: [4] 4,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[72, 46], Operations: ['77-16=61', '61-15=46'] Exploring Operation: 72+46=118, Resulting Numbers: [118] 118,48 unequal: No Solution Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 72*46=3312, Resulting Numbers: [3312] 3312,48 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: 48:[16, 3], Operations: ['77-72=5', '15/5=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,48 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[77, 16, 15, 72], Operations: [] Exploring Operation: 77-72=5, Resulting Numbers: [16, 15, 5] Generated Node #0,2: 48:[16, 15, 5] Operation: 77-72=5 Moving to Node #0,2 Current State: 48:[16, 15, 5], Operations: ['77-72=5'] Exploring Operation: 15/5=3, Resulting Numbers: [16, 3] Generated Node #0,2,2: 48:[16, 3] Operation: 15/5=3 Moving to Node #0,2,2 Current State: 48:[16, 3], Operations: ['77-72=5', '15/5=3'] Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 75, 24, 53, 15 ]
61
[ "75+24=99", "53-15=38", "99-38=61" ]
Current State: 61:[75, 24, 53, 15], Operations: [] Exploring Operation: 75+24=99, Resulting Numbers: [53, 15, 99] Generated Node #2: [53, 15, 99] from Operation: 75+24=99 Current State: 61:[53, 15, 99], Operations: ['75+24=99'] Exploring Operation: 53-15=38, Resulting Numbers: [99, 38] Generated Node #3: [99, 38] from Operation: 53-15=38 Current State: 61:[99, 38], Operations: ['75+24=99', '53-15=38'] Exploring Operation: 99-38=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[75, 24, 53, 15], Operations: [] Exploring Operation: 75-15=60, Resulting Numbers: [24, 53, 60] Generated Node #0,0: 61:[24, 53, 60] Operation: 75-15=60 Exploring Operation: 24+15=39, Resulting Numbers: [75, 53, 39] Generated Node #0,1: 61:[75, 53, 39] Operation: 24+15=39 Exploring Operation: 75-24=51, Resulting Numbers: [53, 15, 51] Generated Node #0,2: 61:[53, 15, 51] Operation: 75-24=51 Exploring Operation: 53+15=68, Resulting Numbers: [75, 24, 68] Generated Node #0,3: 61:[75, 24, 68] Operation: 53+15=68 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[75, 53, 39], Operations: ['24+15=39'] Exploring Operation: 75-53=22, Resulting Numbers: [39, 22] Generated Node #0,1,0: 61:[39, 22] Operation: 75-53=22 Exploring Operation: 53+39=92, Resulting Numbers: [75, 92] Generated Node #0,1,1: 61:[75, 92] Operation: 53+39=92 Exploring Operation: 75+39=114, Resulting Numbers: [53, 114] Generated Node #0,1,2: 61:[53, 114] Operation: 75+39=114 Exploring Operation: 75-39=36, Resulting Numbers: [53, 36] Generated Node #0,1,3: 61:[53, 36] Operation: 75-39=36 Moving to Node #0,1,3 Current State: 61:[53, 36], Operations: ['24+15=39', '75-39=36'] Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 53+36=89, Resulting Numbers: [89] 89,61 unequal: No Solution Exploring Operation: 53*36=1908, Resulting Numbers: [1908] 1908,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[75, 92], Operations: ['24+15=39', '53+39=92'] Exploring Operation: 75+92=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 75*92=6900, Resulting Numbers: [6900] 6900,61 unequal: No Solution Exploring Operation: 92-75=17, Resulting Numbers: [17] 17,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[53, 114], Operations: ['24+15=39', '75+39=114'] Exploring Operation: 53*114=6042, Resulting Numbers: [6042] 6042,61 unequal: No Solution Exploring Operation: 53+114=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 114-53=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[75, 24, 53, 15], Operations: [] Exploring Operation: 24+15=39, Resulting Numbers: [75, 53, 39] Generated Node #0,1: 61:[75, 53, 39] Operation: 24+15=39 Moving to Node #0,1 Current State: 61:[75, 53, 39], Operations: ['24+15=39'] Exploring Operation: 75+39=114, Resulting Numbers: [53, 114] Generated Node #0,1,2: 61:[53, 114] Operation: 75+39=114 Moving to Node #0,1,2 Current State: 61:[53, 114], Operations: ['24+15=39', '75+39=114'] Exploring Operation: 114-53=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 94, 96, 31, 61 ]
98
[ "94+96=190", "31+61=92", "190-92=98" ]
Current State: 98:[94, 96, 31, 61], Operations: [] Exploring Operation: 94+96=190, Resulting Numbers: [31, 61, 190] Generated Node #2: [31, 61, 190] from Operation: 94+96=190 Current State: 98:[31, 61, 190], Operations: ['94+96=190'] Exploring Operation: 31+61=92, Resulting Numbers: [190, 92] Generated Node #3: [190, 92] from Operation: 31+61=92 Current State: 98:[190, 92], Operations: ['94+96=190', '31+61=92'] Exploring Operation: 190-92=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[94, 96, 31, 61], Operations: [] Exploring Operation: 94-31=63, Resulting Numbers: [96, 61, 63] Generated Node #0,0: 98:[96, 61, 63] Operation: 94-31=63 Exploring Operation: 96-94=2, Resulting Numbers: [31, 61, 2] Generated Node #0,1: 98:[31, 61, 2] Operation: 96-94=2 Exploring Operation: 96-31=65, Resulting Numbers: [94, 61, 65] Generated Node #0,2: 98:[94, 61, 65] Operation: 96-31=65 Exploring Operation: 31+61=92, Resulting Numbers: [94, 96, 92] Generated Node #0,3: 98:[94, 96, 92] Operation: 31+61=92 Exploring Operation: 61-31=30, Resulting Numbers: [94, 96, 30] Generated Node #0,4: 98:[94, 96, 30] Operation: 61-31=30 Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[94, 96, 92], Operations: ['31+61=92'] Exploring Operation: 96-92=4, Resulting Numbers: [94, 4] Generated Node #0,3,0: 98:[94, 4] Operation: 96-92=4 Exploring Operation: 96+92=188, Resulting Numbers: [94, 188] Generated Node #0,3,1: 98:[94, 188] Operation: 96+92=188 Exploring Operation: 94+92=186, Resulting Numbers: [96, 186] Generated Node #0,3,2: 98:[96, 186] Operation: 94+92=186 Exploring Operation: 96-94=2, Resulting Numbers: [92, 2] Generated Node #0,3,3: 98:[92, 2] Operation: 96-94=2 Exploring Operation: 94-92=2, Resulting Numbers: [96, 2] Generated Node #0,3,4: 98:[96, 2] Operation: 94-92=2 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 98:[96, 2], Operations: ['31+61=92', '94-92=2'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,98 unequal: No Solution Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,98 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[94, 96, 31, 61], Operations: [] Exploring Operation: 31+61=92, Resulting Numbers: [94, 96, 92] Generated Node #0,3: 98:[94, 96, 92] Operation: 31+61=92 Moving to Node #0,3 Current State: 98:[94, 96, 92], Operations: ['31+61=92'] Exploring Operation: 94-92=2, Resulting Numbers: [96, 2] Generated Node #0,3,4: 98:[96, 2] Operation: 94-92=2 Moving to Node #0,3,4 Current State: 98:[96, 2], Operations: ['31+61=92', '94-92=2'] Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 67, 36, 71, 93 ]
84
[ "71-67=4", "36/4=9", "93-9=84" ]
Current State: 84:[67, 36, 71, 93], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [36, 93, 4] Generated Node #2: [36, 93, 4] from Operation: 71-67=4 Current State: 84:[36, 93, 4], Operations: ['71-67=4'] Exploring Operation: 36/4=9, Resulting Numbers: [93, 9] Generated Node #3: [93, 9] from Operation: 36/4=9 Current State: 84:[93, 9], Operations: ['71-67=4', '36/4=9'] Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[67, 36, 71, 93], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [36, 93, 4] Generated Node #0,0: 84:[36, 93, 4] Operation: 71-67=4 Exploring Operation: 93-67=26, Resulting Numbers: [36, 71, 26] Generated Node #0,1: 84:[36, 71, 26] Operation: 93-67=26 Exploring Operation: 93-71=22, Resulting Numbers: [67, 36, 22] Generated Node #0,2: 84:[67, 36, 22] Operation: 93-71=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[36, 93, 4], Operations: ['71-67=4'] Exploring Operation: 36+4=40, Resulting Numbers: [93, 40] Generated Node #0,0,0: 84:[93, 40] Operation: 36+4=40 Exploring Operation: 93-4=89, Resulting Numbers: [36, 89] Generated Node #0,0,1: 84:[36, 89] Operation: 93-4=89 Exploring Operation: 36/4=9, Resulting Numbers: [93, 9] Generated Node #0,0,2: 84:[93, 9] Operation: 36/4=9 Moving to Node #0,0,0 Current State: 84:[93, 40], Operations: ['71-67=4', '36+4=40'] Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 93*40=3720, Resulting Numbers: [3720] 3720,84 unequal: No Solution Exploring Operation: 93+40=133, Resulting Numbers: [133] 133,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[36, 89], Operations: ['71-67=4', '93-4=89'] Exploring Operation: 36+89=125, Resulting Numbers: [125] 125,84 unequal: No Solution Exploring Operation: 89-36=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 36*89=3204, Resulting Numbers: [3204] 3204,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[93, 9], Operations: ['71-67=4', '36/4=9'] Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[67, 36, 71, 93], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [36, 93, 4] Generated Node #0,0: 84:[36, 93, 4] Operation: 71-67=4 Moving to Node #0,0 Current State: 84:[36, 93, 4], Operations: ['71-67=4'] Exploring Operation: 36/4=9, Resulting Numbers: [93, 9] Generated Node #0,0,2: 84:[93, 9] Operation: 36/4=9 Moving to Node #0,0,2 Current State: 84:[93, 9], Operations: ['71-67=4', '36/4=9'] Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 75, 99, 68, 66 ]
12
[ "99-75=24", "68-66=2", "24/2=12" ]
Current State: 12:[75, 99, 68, 66], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [68, 66, 24] Generated Node #2: [68, 66, 24] from Operation: 99-75=24 Current State: 12:[68, 66, 24], Operations: ['99-75=24'] Exploring Operation: 68-66=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 68-66=2 Current State: 12:[24, 2], Operations: ['99-75=24', '68-66=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[75, 99, 68, 66], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [68, 66, 24] Generated Node #0,0: 12:[68, 66, 24] Operation: 99-75=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[68, 66, 24], Operations: ['99-75=24'] Exploring Operation: 68-66=2, Resulting Numbers: [24, 2] Generated Node #0,0,0: 12:[24, 2] Operation: 68-66=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[24, 2], Operations: ['99-75=24', '68-66=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[75, 99, 68, 66], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [68, 66, 24] Generated Node #0,0: 12:[68, 66, 24] Operation: 99-75=24 Moving to Node #0,0 Current State: 12:[68, 66, 24], Operations: ['99-75=24'] Exploring Operation: 68-66=2, Resulting Numbers: [24, 2] Generated Node #0,0,0: 12:[24, 2] Operation: 68-66=2 Moving to Node #0,0,0 Current State: 12:[24, 2], Operations: ['99-75=24', '68-66=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 77, 3, 79, 14 ]
100
[ "77-14=63", "63/3=21", "79+21=100" ]
Current State: 100:[77, 3, 79, 14], Operations: [] Exploring Operation: 77-14=63, Resulting Numbers: [3, 79, 63] Generated Node #2: [3, 79, 63] from Operation: 77-14=63 Current State: 100:[3, 79, 63], Operations: ['77-14=63'] Exploring Operation: 63/3=21, Resulting Numbers: [79, 21] Generated Node #3: [79, 21] from Operation: 63/3=21 Current State: 100:[79, 21], Operations: ['77-14=63', '63/3=21'] Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[77, 3, 79, 14], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [3, 14, 2] Generated Node #0,0: 100:[3, 14, 2] Operation: 79-77=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[3, 14, 2], Operations: ['79-77=2'] Exploring Operation: 14-3=11, Resulting Numbers: [2, 11] Generated Node #0,0,0: 100:[2, 11] Operation: 14-3=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 100:[2, 11], Operations: ['79-77=2', '14-3=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 22, 70, 37, 54 ]
34
[ "22*54=1188", "70+1188=1258", "1258/37=34" ]
Current State: 34:[22, 70, 37, 54], Operations: [] Exploring Operation: 22*54=1188, Resulting Numbers: [70, 37, 1188] Generated Node #2: [70, 37, 1188] from Operation: 22*54=1188 Current State: 34:[70, 37, 1188], Operations: ['22*54=1188'] Exploring Operation: 70+1188=1258, Resulting Numbers: [37, 1258] Generated Node #3: [37, 1258] from Operation: 70+1188=1258 Current State: 34:[37, 1258], Operations: ['22*54=1188', '70+1188=1258'] Exploring Operation: 1258/37=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[22, 70, 37, 54], Operations: [] Exploring Operation: 70-37=33, Resulting Numbers: [22, 54, 33] Generated Node #0,0: 34:[22, 54, 33] Operation: 70-37=33 Exploring Operation: 70-54=16, Resulting Numbers: [22, 37, 16] Generated Node #0,1: 34:[22, 37, 16] Operation: 70-54=16 Moving to Node #0,1 Current State: 34:[22, 37, 16], Operations: ['70-54=16'] Exploring Operation: 22+16=38, Resulting Numbers: [37, 38] Generated Node #0,1,0: 34:[37, 38] Operation: 22+16=38 Exploring Operation: 37-22=15, Resulting Numbers: [16, 15] Generated Node #0,1,1: 34:[16, 15] Operation: 37-22=15 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[16, 15], Operations: ['70-54=16', '37-22=15'] Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,34 unequal: No Solution No solution 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: 34:[37, 38], Operations: ['70-54=16', '22+16=38'] Exploring Operation: 37+38=75, Resulting Numbers: [75] 75,34 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,34 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: 34:[22, 54, 33], Operations: ['70-37=33'] Exploring Operation: 54-22=32, Resulting Numbers: [33, 32] Generated Node #0,0,0: 34:[33, 32] Operation: 54-22=32 Exploring Operation: 54-33=21, Resulting Numbers: [22, 21] Generated Node #0,0,1: 34:[22, 21] Operation: 54-33=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[33, 32], Operations: ['70-37=33', '54-22=32'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,34 unequal: No Solution No 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: 34:[22, 21], Operations: ['70-37=33', '54-33=21'] Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,34 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
[ 85, 35, 8, 81 ]
47
[ "85+35=120", "81-8=73", "120-73=47" ]
Current State: 47:[85, 35, 8, 81], Operations: [] Exploring Operation: 85+35=120, Resulting Numbers: [8, 81, 120] Generated Node #2: [8, 81, 120] from Operation: 85+35=120 Current State: 47:[8, 81, 120], Operations: ['85+35=120'] Exploring Operation: 81-8=73, Resulting Numbers: [120, 73] Generated Node #3: [120, 73] from Operation: 81-8=73 Current State: 47:[120, 73], Operations: ['85+35=120', '81-8=73'] Exploring Operation: 120-73=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[85, 35, 8, 81], Operations: [] Exploring Operation: 85-8=77, Resulting Numbers: [35, 81, 77] Generated Node #0,0: 47:[35, 81, 77] Operation: 85-8=77 Exploring Operation: 35+8=43, Resulting Numbers: [85, 81, 43] Generated Node #0,1: 47:[85, 81, 43] Operation: 35+8=43 Exploring Operation: 85-35=50, Resulting Numbers: [8, 81, 50] Generated Node #0,2: 47:[8, 81, 50] Operation: 85-35=50 Moving to Node #0,0 Current State: 47:[35, 81, 77], Operations: ['85-8=77'] Exploring Operation: 81-35=46, Resulting Numbers: [77, 46] Generated Node #0,0,0: 47:[77, 46] Operation: 81-35=46 Exploring Operation: 77-35=42, Resulting Numbers: [81, 42] Generated Node #0,0,1: 47:[81, 42] Operation: 77-35=42 Exploring Operation: 81-77=4, Resulting Numbers: [35, 4] Generated Node #0,0,2: 47:[35, 4] Operation: 81-77=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[77, 46], Operations: ['85-8=77', '81-35=46'] Exploring Operation: 77*46=3542, Resulting Numbers: [3542] 3542,47 unequal: No Solution Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,47 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 #0,0,1 Current State: 47:[81, 42], Operations: ['85-8=77', '77-35=42'] Exploring Operation: 81*42=3402, Resulting Numbers: [3402] 3402,47 unequal: No Solution Exploring Operation: 81+42=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,47 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 #0,0,2 Current State: 47:[35, 4], Operations: ['85-8=77', '81-77=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,47 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,47 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: 47:[85, 81, 43], Operations: ['35+8=43'] Exploring Operation: 81-43=38, Resulting Numbers: [85, 38] Generated Node #0,1,0: 47:[85, 38] Operation: 81-43=38 Exploring Operation: 85-43=42, Resulting Numbers: [81, 42] Generated Node #0,1,1: 47:[81, 42] Operation: 85-43=42 Exploring Operation: 85-81=4, Resulting Numbers: [43, 4] Generated Node #0,1,2: 47:[43, 4] Operation: 85-81=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[81, 42], Operations: ['35+8=43', '85-43=42'] Exploring Operation: 81+42=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 81*42=3402, Resulting Numbers: [3402] 3402,47 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,47 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 #0,1,0 Current State: 47:[85, 38], Operations: ['35+8=43', '81-43=38'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[85, 35, 8, 81], Operations: [] Exploring Operation: 35+8=43, Resulting Numbers: [85, 81, 43] Generated Node #0,1: 47:[85, 81, 43] Operation: 35+8=43 Moving to Node #0,1 Current State: 47:[85, 81, 43], Operations: ['35+8=43'] Exploring Operation: 81-43=38, Resulting Numbers: [85, 38] Generated Node #0,1,0: 47:[85, 38] Operation: 81-43=38 Moving to Node #0,1,0 Current State: 47:[85, 38], Operations: ['35+8=43', '81-43=38'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
sum_heuristic
[ 9, 1, 76, 2 ]
83
[ "9*1=9", "76-2=74", "9+74=83" ]
Current State: 83:[9, 1, 76, 2], Operations: [] Exploring Operation: 9*1=9, Resulting Numbers: [76, 2, 9] Generated Node #2: [76, 2, 9] from Operation: 9*1=9 Current State: 83:[76, 2, 9], Operations: ['9*1=9'] Exploring Operation: 76-2=74, Resulting Numbers: [9, 74] Generated Node #3: [9, 74] from Operation: 76-2=74 Current State: 83:[9, 74], Operations: ['9*1=9', '76-2=74'] Exploring Operation: 9+74=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[9, 1, 76, 2], Operations: [] Exploring Operation: 9+1=10, Resulting Numbers: [76, 2, 10] Generated Node #0,0: 83:[76, 2, 10] Operation: 9+1=10 Exploring Operation: 9*2=18, Resulting Numbers: [1, 76, 18] Generated Node #0,1: 83:[1, 76, 18] Operation: 9*2=18 Exploring Operation: 9+2=11, Resulting Numbers: [1, 76, 11] Generated Node #0,2: 83:[1, 76, 11] Operation: 9+2=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[1, 76, 18], Operations: ['9*2=18'] Exploring Operation: 1*76=76, Resulting Numbers: [18, 76] Generated Node #0,1,0: 83:[18, 76] Operation: 1*76=76 Exploring Operation: 1+76=77, Resulting Numbers: [18, 77] Generated Node #0,1,1: 83:[18, 77] Operation: 1+76=77 Exploring Operation: 1+18=19, Resulting Numbers: [76, 19] Generated Node #0,1,2: 83:[76, 19] Operation: 1+18=19 Moving to Node #0,1,1 Current State: 83:[18, 77], Operations: ['9*2=18', '1+76=77'] Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,83 unequal: No Solution Exploring Operation: 18+77=95, Resulting Numbers: [95] 95,83 unequal: No Solution Exploring Operation: 18*77=1386, Resulting Numbers: [1386] 1386,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[76, 19], Operations: ['9*2=18', '1+18=19'] Exploring Operation: 76/19=4, Resulting Numbers: [4] 4,83 unequal: No Solution Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,83 unequal: No Solution Exploring Operation: 76+19=95, Resulting Numbers: [95] 95,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[18, 76], Operations: ['9*2=18', '1*76=76'] Exploring Operation: 76-18=58, Resulting Numbers: [58] 58,83 unequal: No Solution Exploring Operation: 18+76=94, Resulting Numbers: [94] 94,83 unequal: No Solution Exploring Operation: 18*76=1368, Resulting Numbers: [1368] 1368,83 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 Current State: 83:[76, 2, 10], Operations: ['9+1=10'] Exploring Operation: 2+10=12, Resulting Numbers: [76, 12] Generated Node #0,0,0: 83:[76, 12] Operation: 2+10=12 Exploring Operation: 2*10=20, Resulting Numbers: [76, 20] Generated Node #0,0,1: 83:[76, 20] Operation: 2*10=20 Exploring Operation: 76+2=78, Resulting Numbers: [10, 78] Generated Node #0,0,2: 83:[10, 78] Operation: 76+2=78 Moving to Node #0,0,1 Current State: 83:[76, 20], Operations: ['9+1=10', '2*10=20'] Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 76+20=96, Resulting Numbers: [96] 96,83 unequal: No Solution Exploring Operation: 76*20=1520, Resulting Numbers: [1520] 1520,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[76, 12], Operations: ['9+1=10', '2+10=12'] Exploring Operation: 76*12=912, Resulting Numbers: [912] 912,83 unequal: No Solution Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,83 unequal: No Solution Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[10, 78], Operations: ['9+1=10', '76+2=78'] Exploring Operation: 10*78=780, Resulting Numbers: [780] 780,83 unequal: No Solution Exploring Operation: 10+78=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,83 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 Current State: 83:[1, 76, 11], Operations: ['9+2=11'] Exploring Operation: 1*76=76, Resulting Numbers: [11, 76] Generated Node #0,2,0: 83:[11, 76] Operation: 1*76=76 Exploring Operation: 1+11=12, Resulting Numbers: [76, 12] Generated Node #0,2,1: 83:[76, 12] Operation: 1+11=12 Exploring Operation: 1+76=77, Resulting Numbers: [11, 77] Generated Node #0,2,2: 83:[11, 77] Operation: 1+76=77 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[76, 12], Operations: ['9+2=11', '1+11=12'] Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,83 unequal: No Solution Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 76*12=912, Resulting Numbers: [912] 912,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[11, 77], Operations: ['9+2=11', '1+76=77'] Exploring Operation: 11+77=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[11, 76], Operations: ['9+2=11', '1*76=76'] Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,83 unequal: No Solution Exploring Operation: 11*76=836, Resulting Numbers: [836] 836,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 9, 58, 71, 58 ]
81
[ "9+71=80", "58/58=1", "80+1=81" ]
Current State: 81:[9, 58, 71, 58], Operations: [] Exploring Operation: 9+71=80, Resulting Numbers: [58, 58, 80] Generated Node #2: [58, 58, 80] from Operation: 9+71=80 Current State: 81:[58, 58, 80], Operations: ['9+71=80'] Exploring Operation: 58/58=1, Resulting Numbers: [80, 1] Generated Node #3: [80, 1] from Operation: 58/58=1 Current State: 81:[80, 1], Operations: ['9+71=80', '58/58=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[9, 58, 71, 58], Operations: [] Exploring Operation: 71-58=13, Resulting Numbers: [9, 58, 13] Generated Node #0,0: 81:[9, 58, 13] Operation: 71-58=13 Exploring Operation: 58-58=0, Resulting Numbers: [9, 71, 0] Generated Node #0,1: 81:[9, 71, 0] Operation: 58-58=0 Exploring Operation: 58/58=1, Resulting Numbers: [9, 71, 1] Generated Node #0,2: 81:[9, 71, 1] Operation: 58/58=1 Exploring Operation: 71-58=13, Resulting Numbers: [9, 58, 13] Generated Node #0,3: 81:[9, 58, 13] Operation: 71-58=13 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[9, 71, 1], Operations: ['58/58=1'] Exploring Operation: 9+71=80, Resulting Numbers: [1, 80] Generated Node #0,2,0: 81:[1, 80] Operation: 9+71=80 Exploring Operation: 9*1=9, Resulting Numbers: [71, 9] Generated Node #0,2,1: 81:[71, 9] Operation: 9*1=9 Exploring Operation: 9/1=9, Resulting Numbers: [71, 9] Generated Node #0,2,2: 81:[71, 9] Operation: 9/1=9 Exploring Operation: 71+1=72, Resulting Numbers: [9, 72] Generated Node #0,2,3: 81:[9, 72] Operation: 71+1=72 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[1, 80], Operations: ['58/58=1', '9+71=80'] Exploring Operation: 1+80=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[9, 58, 71, 58], Operations: [] Exploring Operation: 58/58=1, Resulting Numbers: [9, 71, 1] Generated Node #0,2: 81:[9, 71, 1] Operation: 58/58=1 Moving to Node #0,2 Current State: 81:[9, 71, 1], Operations: ['58/58=1'] Exploring Operation: 9+71=80, Resulting Numbers: [1, 80] Generated Node #0,2,0: 81:[1, 80] Operation: 9+71=80 Moving to Node #0,2,0 Current State: 81:[1, 80], Operations: ['58/58=1', '9+71=80'] Exploring Operation: 1+80=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 38, 36, 7, 20 ]
16
[ "38+7=45", "36*20=720", "720/45=16" ]
Current State: 16:[38, 36, 7, 20], Operations: [] Exploring Operation: 38+7=45, Resulting Numbers: [36, 20, 45] Generated Node #2: [36, 20, 45] from Operation: 38+7=45 Current State: 16:[36, 20, 45], Operations: ['38+7=45'] Exploring Operation: 36*20=720, Resulting Numbers: [45, 720] Generated Node #3: [45, 720] from Operation: 36*20=720 Current State: 16:[45, 720], Operations: ['38+7=45', '36*20=720'] Exploring Operation: 720/45=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[38, 36, 7, 20], Operations: [] Exploring Operation: 38-20=18, Resulting Numbers: [36, 7, 18] Generated Node #0,0: 16:[36, 7, 18] Operation: 38-20=18 Exploring Operation: 38-36=2, Resulting Numbers: [7, 20, 2] Generated Node #0,1: 16:[7, 20, 2] Operation: 38-36=2 Moving to Node #0,1 Current State: 16:[7, 20, 2], Operations: ['38-36=2'] Exploring Operation: 20-7=13, Resulting Numbers: [2, 13] Generated Node #0,1,0: 16:[2, 13] Operation: 20-7=13 Exploring Operation: 20-2=18, Resulting Numbers: [7, 18] Generated Node #0,1,1: 16:[7, 18] Operation: 20-2=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[2, 13], Operations: ['38-36=2', '20-7=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[7, 18], Operations: ['38-36=2', '20-2=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,16 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: 16:[36, 7, 18], Operations: ['38-20=18'] Exploring Operation: 36-18=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 16:[7, 18] Operation: 36-18=18 Exploring Operation: 36/18=2, Resulting Numbers: [7, 2] Generated Node #0,0,1: 16:[7, 2] Operation: 36/18=2 Moving to Node #0,0,1 Current State: 16:[7, 2], Operations: ['38-20=18', '36/18=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[7, 18], Operations: ['38-20=18', '36-18=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,16 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 44, 47, 3, 39 ]
39
[ "47-44=3", "3+39=42", "42-3=39" ]
Current State: 39:[44, 47, 3, 39], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [3, 39, 3] Generated Node #2: [3, 39, 3] from Operation: 47-44=3 Current State: 39:[3, 39, 3], Operations: ['47-44=3'] Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,39 equal: Goal Reached Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[44, 47, 3, 39], Operations: [] Exploring Operation: 44-3=41, Resulting Numbers: [47, 39, 41] Generated Node #0,0: 39:[47, 39, 41] Operation: 44-3=41 Exploring Operation: 47-44=3, Resulting Numbers: [3, 39, 3] Generated Node #0,1: 39:[3, 39, 3] Operation: 47-44=3 Moving to Node #0,1 Current State: 39:[3, 39, 3], Operations: ['47-44=3'] Exploring Operation: 39/3=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 39:[3, 13] Operation: 39/3=13 Exploring Operation: 39/3=13, Resulting Numbers: [3, 13] Generated Node #0,1,1: 39:[3, 13] Operation: 39/3=13 Moving to Node #0,0 Current State: 39:[47, 39, 41], Operations: ['44-3=41'] Exploring Operation: 47-39=8, Resulting Numbers: [41, 8] Generated Node #0,0,0: 39:[41, 8] Operation: 47-39=8 Exploring Operation: 47-41=6, Resulting Numbers: [39, 6] Generated Node #0,0,1: 39:[39, 6] Operation: 47-41=6 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[39, 6], Operations: ['44-3=41', '47-41=6'] Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,39 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[41, 8], Operations: ['44-3=41', '47-39=8'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,39 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: 39:[3, 13], Operations: ['47-44=3', '39/3=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[44, 47, 3, 39], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [3, 39, 3] Generated Node #0,1: 39:[3, 39, 3] Operation: 47-44=3 Moving to Node #0,1 Current State: 39:[3, 39, 3], Operations: ['47-44=3'] Exploring Operation: 39/3=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 39:[3, 13] Operation: 39/3=13 Moving to Node #0,1,0 Current State: 39:[3, 13], Operations: ['47-44=3', '39/3=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 3, 74, 10, 33 ]
94
[ "74-3=71", "33-10=23", "71+23=94" ]
Current State: 94:[3, 74, 10, 33], Operations: [] Exploring Operation: 74-3=71, Resulting Numbers: [10, 33, 71] Generated Node #2: [10, 33, 71] from Operation: 74-3=71 Current State: 94:[10, 33, 71], Operations: ['74-3=71'] Exploring Operation: 33-10=23, Resulting Numbers: [71, 23] Generated Node #3: [71, 23] from Operation: 33-10=23 Current State: 94:[71, 23], Operations: ['74-3=71', '33-10=23'] Exploring Operation: 71+23=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[3, 74, 10, 33], Operations: [] Exploring Operation: 10+33=43, Resulting Numbers: [3, 74, 43] Generated Node #0,0: 94:[3, 74, 43] Operation: 10+33=43 Exploring Operation: 74+10=84, Resulting Numbers: [3, 33, 84] Generated Node #0,1: 94:[3, 33, 84] Operation: 74+10=84 Exploring Operation: 74+33=107, Resulting Numbers: [3, 10, 107] Generated Node #0,2: 94:[3, 10, 107] Operation: 74+33=107 Exploring Operation: 74-10=64, Resulting Numbers: [3, 33, 64] Generated Node #0,3: 94:[3, 33, 64] Operation: 74-10=64 Exploring Operation: 74-33=41, Resulting Numbers: [3, 10, 41] Generated Node #0,4: 94:[3, 10, 41] Operation: 74-33=41 Moving to Node #0,4 Current State: 94:[3, 10, 41], Operations: ['74-33=41'] Exploring Operation: 10-3=7, Resulting Numbers: [41, 7] Generated Node #0,4,0: 94:[41, 7] Operation: 10-3=7 Exploring Operation: 3+10=13, Resulting Numbers: [41, 13] Generated Node #0,4,1: 94:[41, 13] Operation: 3+10=13 Exploring Operation: 10+41=51, Resulting Numbers: [3, 51] Generated Node #0,4,2: 94:[3, 51] Operation: 10+41=51 Exploring Operation: 3+41=44, Resulting Numbers: [10, 44] Generated Node #0,4,3: 94:[10, 44] Operation: 3+41=44 Exploring Operation: 41-3=38, Resulting Numbers: [10, 38] Generated Node #0,4,4: 94:[10, 38] Operation: 41-3=38 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 94:[3, 51], Operations: ['74-33=41', '10+41=51'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,94 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,94 unequal: No Solution Exploring Operation: 3*51=153, Resulting Numbers: [153] 153,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 94:[41, 7], Operations: ['74-33=41', '10-3=7'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,94 unequal: No Solution Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,94 unequal: No Solution Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 94:[10, 44], Operations: ['74-33=41', '3+41=44'] Exploring Operation: 10+44=54, Resulting Numbers: [54] 54,94 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,94 unequal: No Solution Exploring Operation: 10*44=440, Resulting Numbers: [440] 440,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 94:[41, 13], Operations: ['74-33=41', '3+10=13'] Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,94 unequal: No Solution Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,94 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 94:[10, 38], Operations: ['74-33=41', '41-3=38'] Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,94 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,94 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: 94:[3, 10, 107], Operations: ['74+33=107'] Exploring Operation: 107-3=104, Resulting Numbers: [10, 104] Generated Node #0,2,0: 94:[10, 104] Operation: 107-3=104 Exploring Operation: 3+107=110, Resulting Numbers: [10, 110] Generated Node #0,2,1: 94:[10, 110] Operation: 3+107=110 Exploring Operation: 107-10=97, Resulting Numbers: [3, 97] Generated Node #0,2,2: 94:[3, 97] Operation: 107-10=97 Exploring Operation: 10-3=7, Resulting Numbers: [107, 7] Generated Node #0,2,3: 94:[107, 7] Operation: 10-3=7 Exploring Operation: 3+10=13, Resulting Numbers: [107, 13] Generated Node #0,2,4: 94:[107, 13] Operation: 3+10=13 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 94:[3, 97], Operations: ['74+33=107', '107-10=97'] Exploring Operation: 3*97=291, Resulting Numbers: [291] 291,94 unequal: No Solution Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[3, 74, 10, 33], Operations: [] Exploring Operation: 74+33=107, Resulting Numbers: [3, 10, 107] Generated Node #0,2: 94:[3, 10, 107] Operation: 74+33=107 Moving to Node #0,2 Current State: 94:[3, 10, 107], Operations: ['74+33=107'] Exploring Operation: 107-10=97, Resulting Numbers: [3, 97] Generated Node #0,2,2: 94:[3, 97] Operation: 107-10=97 Moving to Node #0,2,2 Current State: 94:[3, 97], Operations: ['74+33=107', '107-10=97'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 88, 3, 45, 68 ]
67
[ "88+45=133", "68+133=201", "201/3=67" ]
Current State: 67:[88, 3, 45, 68], Operations: [] Exploring Operation: 88+45=133, Resulting Numbers: [3, 68, 133] Generated Node #2: [3, 68, 133] from Operation: 88+45=133 Current State: 67:[3, 68, 133], Operations: ['88+45=133'] Exploring Operation: 68+133=201, Resulting Numbers: [3, 201] Generated Node #3: [3, 201] from Operation: 68+133=201 Current State: 67:[3, 201], Operations: ['88+45=133', '68+133=201'] Exploring Operation: 201/3=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[88, 3, 45, 68], Operations: [] Exploring Operation: 45-3=42, Resulting Numbers: [88, 68, 42] Generated Node #0,0: 67:[88, 68, 42] Operation: 45-3=42 Exploring Operation: 3+45=48, Resulting Numbers: [88, 68, 48] Generated Node #0,1: 67:[88, 68, 48] Operation: 3+45=48 Exploring Operation: 68-3=65, Resulting Numbers: [88, 45, 65] Generated Node #0,2: 67:[88, 45, 65] Operation: 68-3=65 Exploring Operation: 88+3=91, Resulting Numbers: [45, 68, 91] Generated Node #0,3: 67:[45, 68, 91] Operation: 88+3=91 Exploring Operation: 88-3=85, Resulting Numbers: [45, 68, 85] Generated Node #0,4: 67:[45, 68, 85] Operation: 88-3=85 Moving to Node #0,1 Current State: 67:[88, 68, 48], Operations: ['3+45=48'] Exploring Operation: 68-48=20, Resulting Numbers: [88, 20] Generated Node #0,1,0: 67:[88, 20] Operation: 68-48=20 Exploring Operation: 88-68=20, Resulting Numbers: [48, 20] Generated Node #0,1,1: 67:[48, 20] Operation: 88-68=20 Exploring Operation: 88-48=40, Resulting Numbers: [68, 40] Generated Node #0,1,2: 67:[68, 40] Operation: 88-48=40 Exploring Operation: 88+48=136, Resulting Numbers: [68, 136] Generated Node #0,1,3: 67:[68, 136] Operation: 88+48=136 Exploring Operation: 68+48=116, Resulting Numbers: [88, 116] Generated Node #0,1,4: 67:[88, 116] Operation: 68+48=116 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[68, 40], Operations: ['3+45=48', '88-48=40'] Exploring Operation: 68*40=2720, Resulting Numbers: [2720] 2720,67 unequal: No Solution Exploring Operation: 68+40=108, Resulting Numbers: [108] 108,67 unequal: No Solution Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,67 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:[48, 20], Operations: ['3+45=48', '88-68=20'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,67 unequal: No Solution Exploring Operation: 48*20=960, Resulting Numbers: [960] 960,67 unequal: No Solution Exploring Operation: 48+20=68, Resulting Numbers: [68] 68,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[88, 20], Operations: ['3+45=48', '68-48=20'] Exploring Operation: 88+20=108, Resulting Numbers: [108] 108,67 unequal: No Solution Exploring Operation: 88*20=1760, Resulting Numbers: [1760] 1760,67 unequal: No Solution Exploring Operation: 88-20=68, Resulting Numbers: [68] 68,67 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:[68, 136], Operations: ['3+45=48', '88+48=136'] Exploring Operation: 68*136=9248, Resulting Numbers: [9248] 9248,67 unequal: No Solution Exploring Operation: 136-68=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 68+136=204, Resulting Numbers: [204] 204,67 unequal: No Solution Exploring Operation: 136/68=2, Resulting Numbers: [2] 2,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 67:[88, 116], Operations: ['3+45=48', '68+48=116'] Exploring Operation: 88*116=10208, Resulting Numbers: [10208] 10208,67 unequal: No Solution Exploring Operation: 116-88=28, Resulting Numbers: [28] 28,67 unequal: No Solution Exploring Operation: 88+116=204, Resulting Numbers: [204] 204,67 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: 67:[45, 68, 85], Operations: ['88-3=85'] Exploring Operation: 85-68=17, Resulting Numbers: [45, 17] Generated Node #0,4,0: 67:[45, 17] Operation: 85-68=17 Exploring Operation: 85-45=40, Resulting Numbers: [68, 40] Generated Node #0,4,1: 67:[68, 40] Operation: 85-45=40 Exploring Operation: 45+85=130, Resulting Numbers: [68, 130] Generated Node #0,4,2: 67:[68, 130] Operation: 45+85=130 Exploring Operation: 45+68=113, Resulting Numbers: [85, 113] Generated Node #0,4,3: 67:[85, 113] Operation: 45+68=113 Exploring Operation: 68-45=23, Resulting Numbers: [85, 23] Generated Node #0,4,4: 67:[85, 23] Operation: 68-45=23 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 67:[68, 40], Operations: ['88-3=85', '85-45=40'] Exploring Operation: 68+40=108, Resulting Numbers: [108] 108,67 unequal: No Solution Exploring Operation: 68*40=2720, Resulting Numbers: [2720] 2720,67 unequal: No Solution Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 67:[85, 23], Operations: ['88-3=85', '68-45=23'] Exploring Operation: 85+23=108, Resulting Numbers: [108] 108,67 unequal: No Solution Exploring Operation: 85-23=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 85*23=1955, Resulting Numbers: [1955] 1955,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 67:[68, 130], Operations: ['88-3=85', '45+85=130'] Exploring Operation: 68*130=8840, Resulting Numbers: [8840] 8840,67 unequal: No Solution Exploring Operation: 130-68=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 68+130=198, Resulting Numbers: [198] 198,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 67:[85, 113], Operations: ['88-3=85', '45+68=113'] Exploring Operation: 85+113=198, Resulting Numbers: [198] 198,67 unequal: No Solution Exploring Operation: 113-85=28, Resulting Numbers: [28] 28,67 unequal: No Solution Exploring Operation: 85*113=9605, Resulting Numbers: [9605] 9605,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 67:[45, 17], Operations: ['88-3=85', '85-68=17'] Exploring Operation: 45*17=765, Resulting Numbers: [765] 765,67 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,67 unequal: No Solution Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,67 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:[88, 45, 65], Operations: ['68-3=65'] Exploring Operation: 65-45=20, Resulting Numbers: [88, 20] Generated Node #0,2,0: 67:[88, 20] Operation: 65-45=20 Exploring Operation: 88-45=43, Resulting Numbers: [65, 43] Generated Node #0,2,1: 67:[65, 43] Operation: 88-45=43 Exploring Operation: 45+65=110, Resulting Numbers: [88, 110] Generated Node #0,2,2: 67:[88, 110] Operation: 45+65=110 Exploring Operation: 88-65=23, Resulting Numbers: [45, 23] Generated Node #0,2,3: 67:[45, 23] Operation: 88-65=23 Exploring Operation: 88+45=133, Resulting Numbers: [65, 133] Generated Node #0,2,4: 67:[65, 133] Operation: 88+45=133 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[65, 43], Operations: ['68-3=65', '88-45=43'] Exploring Operation: 65*43=2795, Resulting Numbers: [2795] 2795,67 unequal: No Solution Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 65+43=108, Resulting Numbers: [108] 108,67 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:[88, 110], Operations: ['68-3=65', '45+65=110'] Exploring Operation: 88+110=198, Resulting Numbers: [198] 198,67 unequal: No Solution Exploring Operation: 110-88=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 88*110=9680, Resulting Numbers: [9680] 9680,67 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:[45, 23], Operations: ['68-3=65', '88-65=23'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,67 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:[88, 20], Operations: ['68-3=65', '65-45=20'] Exploring Operation: 88+20=108, Resulting Numbers: [108] 108,67 unequal: No Solution Exploring Operation: 88*20=1760, Resulting Numbers: [1760] 1760,67 unequal: No Solution Exploring Operation: 88-20=68, Resulting Numbers: [68] 68,67 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 #0,2,4 Current State: 67:[65, 133], Operations: ['68-3=65', '88+45=133'] Exploring Operation: 65+133=198, Resulting Numbers: [198] 198,67 unequal: No Solution Exploring Operation: 133-65=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 65*133=8645, Resulting Numbers: [8645] 8645,67 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:[88, 68, 42], Operations: ['45-3=42'] Exploring Operation: 68+42=110, Resulting Numbers: [88, 110] Generated Node #0,0,0: 67:[88, 110] Operation: 68+42=110 Exploring Operation: 88-68=20, Resulting Numbers: [42, 20] Generated Node #0,0,1: 67:[42, 20] Operation: 88-68=20 Exploring Operation: 68-42=26, Resulting Numbers: [88, 26] Generated Node #0,0,2: 67:[88, 26] Operation: 68-42=26 Exploring Operation: 88+42=130, Resulting Numbers: [68, 130] Generated Node #0,0,3: 67:[68, 130] Operation: 88+42=130 Exploring Operation: 88-42=46, Resulting Numbers: [68, 46] Generated Node #0,0,4: 67:[68, 46] Operation: 88-42=46 Moving to Node #0,3 Current State: 67:[45, 68, 91], Operations: ['88+3=91'] Exploring Operation: 45+68=113, Resulting Numbers: [91, 113] Generated Node #0,3,0: 67:[91, 113] Operation: 45+68=113 Exploring Operation: 91-68=23, Resulting Numbers: [45, 23] Generated Node #0,3,1: 67:[45, 23] Operation: 91-68=23 Exploring Operation: 45+91=136, Resulting Numbers: [68, 136] Generated Node #0,3,2: 67:[68, 136] Operation: 45+91=136 Exploring Operation: 68-45=23, Resulting Numbers: [91, 23] Generated Node #0,3,3: 67:[91, 23] Operation: 68-45=23 Exploring Operation: 91-45=46, Resulting Numbers: [68, 46] Generated Node #0,3,4: 67:[68, 46] Operation: 91-45=46 Moving to Node #0,0,4 Current State: 67:[68, 46], Operations: ['45-3=42', '88-42=46'] Exploring Operation: 68+46=114, Resulting Numbers: [114] 114,67 unequal: No Solution Exploring Operation: 68-46=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 68*46=3128, Resulting Numbers: [3128] 3128,67 unequal: No Solution Moving to Node #0,3,4 Current State: 67:[68, 46], Operations: ['88+3=91', '91-45=46'] Exploring Operation: 68+46=114, Resulting Numbers: [114] 114,67 unequal: No Solution Exploring Operation: 68*46=3128, Resulting Numbers: [3128] 3128,67 unequal: No Solution Exploring Operation: 68-46=22, Resulting Numbers: [22] 22,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[88, 26], Operations: ['45-3=42', '68-42=26'] Exploring Operation: 88*26=2288, Resulting Numbers: [2288] 2288,67 unequal: No Solution Exploring Operation: 88+26=114, Resulting Numbers: [114] 114,67 unequal: No Solution Exploring Operation: 88-26=62, Resulting Numbers: [62] 62,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[88, 110], Operations: ['45-3=42', '68+42=110'] Exploring Operation: 88+110=198, Resulting Numbers: [198] 198,67 unequal: No Solution Exploring Operation: 110-88=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 88*110=9680, Resulting Numbers: [9680] 9680,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[68, 130], Operations: ['45-3=42', '88+42=130'] Exploring Operation: 68+130=198, Resulting Numbers: [198] 198,67 unequal: No Solution Exploring Operation: 68*130=8840, Resulting Numbers: [8840] 8840,67 unequal: No Solution Exploring Operation: 130-68=62, Resulting Numbers: [62] 62,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[45, 23], Operations: ['88+3=91', '91-68=23'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[91, 23], Operations: ['88+3=91', '68-45=23'] Exploring Operation: 91*23=2093, Resulting Numbers: [2093] 2093,67 unequal: No Solution Exploring Operation: 91+23=114, Resulting Numbers: [114] 114,67 unequal: No Solution Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[91, 113], Operations: ['88+3=91', '45+68=113'] Exploring Operation: 91*113=10283, Resulting Numbers: [10283] 10283,67 unequal: No Solution Exploring Operation: 113-91=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 91+113=204, Resulting Numbers: [204] 204,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[68, 136], Operations: ['88+3=91', '45+91=136'] Exploring Operation: 68+136=204, Resulting Numbers: [204] 204,67 unequal: No Solution Exploring Operation: 136/68=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 136-68=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 68*136=9248, Resulting Numbers: [9248] 9248,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[42, 20], Operations: ['45-3=42', '88-68=20'] Exploring Operation: 42+20=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 42*20=840, Resulting Numbers: [840] 840,67 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,67 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 81, 75, 12, 27 ]
13
[ "81/27=3", "75/3=25", "25-12=13" ]
Current State: 13:[81, 75, 12, 27], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [75, 12, 3] Generated Node #2: [75, 12, 3] from Operation: 81/27=3 Current State: 13:[75, 12, 3], Operations: ['81/27=3'] Exploring Operation: 75/3=25, Resulting Numbers: [12, 25] Generated Node #3: [12, 25] from Operation: 75/3=25 Current State: 13:[12, 25], Operations: ['81/27=3', '75/3=25'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[81, 75, 12, 27], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [12, 27, 6] Generated Node #0,0: 13:[12, 27, 6] Operation: 81-75=6 Exploring Operation: 81/27=3, Resulting Numbers: [75, 12, 3] Generated Node #0,1: 13:[75, 12, 3] Operation: 81/27=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[12, 27, 6], Operations: ['81-75=6'] Exploring Operation: 27-6=21, Resulting Numbers: [12, 21] Generated Node #0,0,0: 13:[12, 21] Operation: 27-6=21 Exploring Operation: 27-12=15, Resulting Numbers: [6, 15] Generated Node #0,0,1: 13:[6, 15] Operation: 27-12=15 Moving to Node #0,0,0 Current State: 13:[12, 21], Operations: ['81-75=6', '27-6=21'] Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[6, 15], Operations: ['81-75=6', '27-12=15'] Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,13 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[75, 12, 3], Operations: ['81/27=3'] Exploring Operation: 75-12=63, Resulting Numbers: [3, 63] Generated Node #0,1,0: 13:[3, 63] Operation: 75-12=63 Exploring Operation: 75/3=25, Resulting Numbers: [12, 25] Generated Node #0,1,1: 13:[12, 25] Operation: 75/3=25 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[12, 25], Operations: ['81/27=3', '75/3=25'] Exploring Operation: 12+25=37, Resulting Numbers: [37] 37,13 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[81, 75, 12, 27], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [75, 12, 3] Generated Node #0,1: 13:[75, 12, 3] Operation: 81/27=3 Moving to Node #0,1 Current State: 13:[75, 12, 3], Operations: ['81/27=3'] Exploring Operation: 75/3=25, Resulting Numbers: [12, 25] Generated Node #0,1,1: 13:[12, 25] Operation: 75/3=25 Moving to Node #0,1,1 Current State: 13:[12, 25], Operations: ['81/27=3', '75/3=25'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 36, 96, 51, 4 ]
63
[ "36+51=87", "96/4=24", "87-24=63" ]
Current State: 63:[36, 96, 51, 4], Operations: [] Exploring Operation: 36+51=87, Resulting Numbers: [96, 4, 87] Generated Node #2: [96, 4, 87] from Operation: 36+51=87 Current State: 63:[96, 4, 87], Operations: ['36+51=87'] Exploring Operation: 96/4=24, Resulting Numbers: [87, 24] Generated Node #3: [87, 24] from Operation: 96/4=24 Current State: 63:[87, 24], Operations: ['36+51=87', '96/4=24'] Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[36, 96, 51, 4], Operations: [] Exploring Operation: 96-36=60, Resulting Numbers: [51, 4, 60] Generated Node #0,0: 63:[51, 4, 60] Operation: 96-36=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[51, 4, 60], Operations: ['96-36=60'] Exploring Operation: 60-51=9, Resulting Numbers: [4, 9] Generated Node #0,0,0: 63:[4, 9] Operation: 60-51=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[4, 9], Operations: ['96-36=60', '60-51=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 38, 64, 30, 80 ]
74
[ "38-30=8", "80/8=10", "64+10=74" ]
Current State: 74:[38, 64, 30, 80], Operations: [] Exploring Operation: 38-30=8, Resulting Numbers: [64, 80, 8] Generated Node #2: [64, 80, 8] from Operation: 38-30=8 Current State: 74:[64, 80, 8], Operations: ['38-30=8'] Exploring Operation: 80/8=10, Resulting Numbers: [64, 10] Generated Node #3: [64, 10] from Operation: 80/8=10 Current State: 74:[64, 10], Operations: ['38-30=8', '80/8=10'] Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[38, 64, 30, 80], Operations: [] Exploring Operation: 38+30=68, Resulting Numbers: [64, 80, 68] Generated Node #0,0: 74:[64, 80, 68] Operation: 38+30=68 Exploring Operation: 80-38=42, Resulting Numbers: [64, 30, 42] Generated Node #0,1: 74:[64, 30, 42] Operation: 80-38=42 Exploring Operation: 64-30=34, Resulting Numbers: [38, 80, 34] Generated Node #0,2: 74:[38, 80, 34] Operation: 64-30=34 Exploring Operation: 80-64=16, Resulting Numbers: [38, 30, 16] Generated Node #0,3: 74:[38, 30, 16] Operation: 80-64=16 Exploring Operation: 38-30=8, Resulting Numbers: [64, 80, 8] Generated Node #0,4: 74:[64, 80, 8] Operation: 38-30=8 Moving to Node #0,2 Current State: 74:[38, 80, 34], Operations: ['64-30=34'] Exploring Operation: 80-34=46, Resulting Numbers: [38, 46] Generated Node #0,2,0: 74:[38, 46] Operation: 80-34=46 Exploring Operation: 80-38=42, Resulting Numbers: [34, 42] Generated Node #0,2,1: 74:[34, 42] Operation: 80-38=42 Exploring Operation: 38-34=4, Resulting Numbers: [80, 4] Generated Node #0,2,2: 74:[80, 4] Operation: 38-34=4 Exploring Operation: 80+34=114, Resulting Numbers: [38, 114] Generated Node #0,2,3: 74:[38, 114] Operation: 80+34=114 Exploring Operation: 38+34=72, Resulting Numbers: [80, 72] Generated Node #0,2,4: 74:[80, 72] Operation: 38+34=72 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 74:[34, 42], Operations: ['64-30=34', '80-38=42'] Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,74 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 #0,2,2 Current State: 74:[80, 4], Operations: ['64-30=34', '38-34=4'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,74 unequal: No Solution Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,74 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,74 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 #0,2,4 Current State: 74:[80, 72], Operations: ['64-30=34', '38+34=72'] Exploring Operation: 80+72=152, Resulting Numbers: [152] 152,74 unequal: No Solution Exploring Operation: 80*72=5760, Resulting Numbers: [5760] 5760,74 unequal: No Solution Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,74 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 #0,2,0 Current State: 74:[38, 46], Operations: ['64-30=34', '80-34=46'] Exploring Operation: 38*46=1748, Resulting Numbers: [1748] 1748,74 unequal: No Solution Exploring Operation: 38+46=84, Resulting Numbers: [84] 84,74 unequal: No Solution Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,74 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 #0,2,3 Current State: 74:[38, 114], Operations: ['64-30=34', '80+34=114'] Exploring Operation: 114/38=3, Resulting Numbers: [3] 3,74 unequal: No Solution Exploring Operation: 38*114=4332, Resulting Numbers: [4332] 4332,74 unequal: No Solution Exploring Operation: 38+114=152, Resulting Numbers: [152] 152,74 unequal: No Solution Exploring Operation: 114-38=76, Resulting Numbers: [76] 76,74 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: 74:[64, 30, 42], Operations: ['80-38=42'] Exploring Operation: 30+42=72, Resulting Numbers: [64, 72] Generated Node #0,1,0: 74:[64, 72] Operation: 30+42=72 Exploring Operation: 64+30=94, Resulting Numbers: [42, 94] Generated Node #0,1,1: 74:[42, 94] Operation: 64+30=94 Exploring Operation: 64-42=22, Resulting Numbers: [30, 22] Generated Node #0,1,2: 74:[30, 22] Operation: 64-42=22 Exploring Operation: 64-30=34, Resulting Numbers: [42, 34] Generated Node #0,1,3: 74:[42, 34] Operation: 64-30=34 Exploring Operation: 42-30=12, Resulting Numbers: [64, 12] Generated Node #0,1,4: 74:[64, 12] Operation: 42-30=12 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 74:[42, 34], Operations: ['80-38=42', '64-30=34'] Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,74 unequal: No Solution 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 No solution 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:[64, 72], Operations: ['80-38=42', '30+42=72'] Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 64*72=4608, Resulting Numbers: [4608] 4608,74 unequal: No Solution Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,74 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 #0,1,4 Current State: 74:[64, 12], Operations: ['80-38=42', '42-30=12'] Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,74 unequal: No Solution Exploring Operation: 64+12=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 64*12=768, Resulting Numbers: [768] 768,74 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:[30, 22], Operations: ['80-38=42', '64-42=22'] Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 30*22=660, Resulting Numbers: [660] 660,74 unequal: No Solution Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 74:[42, 94], Operations: ['80-38=42', '64+30=94'] Exploring Operation: 42+94=136, Resulting Numbers: [136] 136,74 unequal: No Solution Exploring Operation: 42*94=3948, Resulting Numbers: [3948] 3948,74 unequal: No Solution Exploring Operation: 94-42=52, Resulting Numbers: [52] 52,74 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: 74:[64, 80, 8], Operations: ['38-30=8'] Exploring Operation: 80/8=10, Resulting Numbers: [64, 10] Generated Node #0,4,0: 74:[64, 10] Operation: 80/8=10 Exploring Operation: 80-64=16, Resulting Numbers: [8, 16] Generated Node #0,4,1: 74:[8, 16] Operation: 80-64=16 Exploring Operation: 80-8=72, Resulting Numbers: [64, 72] Generated Node #0,4,2: 74:[64, 72] Operation: 80-8=72 Exploring Operation: 64+8=72, Resulting Numbers: [80, 72] Generated Node #0,4,3: 74:[80, 72] Operation: 64+8=72 Exploring Operation: 64/8=8, Resulting Numbers: [80, 8] Generated Node #0,4,4: 74:[80, 8] Operation: 64/8=8 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 74:[80, 72], Operations: ['38-30=8', '64+8=72'] Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 80*72=5760, Resulting Numbers: [5760] 5760,74 unequal: No Solution Exploring Operation: 80+72=152, Resulting Numbers: [152] 152,74 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 #0,4,2 Current State: 74:[64, 72], Operations: ['38-30=8', '80-8=72'] Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,74 unequal: No Solution Exploring Operation: 64*72=4608, Resulting Numbers: [4608] 4608,74 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 #0,4,4 Current State: 74:[80, 8], Operations: ['38-30=8', '64/8=8'] Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,74 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,74 unequal: No Solution Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 80*8=640, Resulting Numbers: [640] 640,74 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 #0,4,0 Current State: 74:[64, 10], Operations: ['38-30=8', '80/8=10'] Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[38, 64, 30, 80], Operations: [] Exploring Operation: 38-30=8, Resulting Numbers: [64, 80, 8] Generated Node #0,4: 74:[64, 80, 8] Operation: 38-30=8 Moving to Node #0,4 Current State: 74:[64, 80, 8], Operations: ['38-30=8'] Exploring Operation: 80/8=10, Resulting Numbers: [64, 10] Generated Node #0,4,0: 74:[64, 10] Operation: 80/8=10 Moving to Node #0,4,0 Current State: 74:[64, 10], Operations: ['38-30=8', '80/8=10'] Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.94184
hs_5
mult_heuristic
[ 65, 38, 20, 30 ]
50
[ "65+30=95", "20*95=1900", "1900/38=50" ]
Current State: 50:[65, 38, 20, 30], Operations: [] Exploring Operation: 65+30=95, Resulting Numbers: [38, 20, 95] Generated Node #2: [38, 20, 95] from Operation: 65+30=95 Current State: 50:[38, 20, 95], Operations: ['65+30=95'] Exploring Operation: 20*95=1900, Resulting Numbers: [38, 1900] Generated Node #3: [38, 1900] from Operation: 20*95=1900 Current State: 50:[38, 1900], Operations: ['65+30=95', '20*95=1900'] Exploring Operation: 1900/38=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[65, 38, 20, 30], Operations: [] Exploring Operation: 65-20=45, Resulting Numbers: [38, 30, 45] Generated Node #0,0: 50:[38, 30, 45] Operation: 65-20=45 Exploring Operation: 38-20=18, Resulting Numbers: [65, 30, 18] Generated Node #0,1: 50:[65, 30, 18] Operation: 38-20=18 Exploring Operation: 65-30=35, Resulting Numbers: [38, 20, 35] Generated Node #0,2: 50:[38, 20, 35] Operation: 65-30=35 Exploring Operation: 65-38=27, Resulting Numbers: [20, 30, 27] Generated Node #0,3: 50:[20, 30, 27] Operation: 65-38=27 Exploring Operation: 38-30=8, Resulting Numbers: [65, 20, 8] Generated Node #0,4: 50:[65, 20, 8] Operation: 38-30=8 Moving to Node #0,3 Current State: 50:[20, 30, 27], Operations: ['65-38=27'] Exploring Operation: 27-20=7, Resulting Numbers: [30, 7] Generated Node #0,3,0: 50:[30, 7] Operation: 27-20=7 Exploring Operation: 20+27=47, Resulting Numbers: [30, 47] Generated Node #0,3,1: 50:[30, 47] Operation: 20+27=47 Exploring Operation: 20+30=50, Resulting Numbers: [27, 50] Generated Node #0,3,2: 50:[27, 50] Operation: 20+30=50 Exploring Operation: 30-20=10, Resulting Numbers: [27, 10] Generated Node #0,3,3: 50:[27, 10] Operation: 30-20=10 Exploring Operation: 30-27=3, Resulting Numbers: [20, 3] Generated Node #0,3,4: 50:[20, 3] Operation: 30-27=3 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 50:[27, 50], Operations: ['65-38=27', '20+30=50'] Exploring Operation: 50-27=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 27*50=1350, Resulting Numbers: [1350] 1350,50 unequal: No Solution Exploring Operation: 27+50=77, Resulting Numbers: [77] 77,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 50:[27, 10], Operations: ['65-38=27', '30-20=10'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,50 unequal: No Solution Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 50:[20, 3], Operations: ['65-38=27', '30-27=3'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 50:[30, 7], Operations: ['65-38=27', '27-20=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,50 unequal: No Solution Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,50 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 50:[30, 47], Operations: ['65-38=27', '20+27=47'] Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,50 unequal: No Solution Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,50 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,50 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: 50:[65, 20, 8], Operations: ['38-30=8'] Exploring Operation: 65+8=73, Resulting Numbers: [20, 73] Generated Node #0,4,0: 50:[20, 73] Operation: 65+8=73 Exploring Operation: 20-8=12, Resulting Numbers: [65, 12] Generated Node #0,4,1: 50:[65, 12] Operation: 20-8=12 Exploring Operation: 65-20=45, Resulting Numbers: [8, 45] Generated Node #0,4,2: 50:[8, 45] Operation: 65-20=45 Exploring Operation: 20+8=28, Resulting Numbers: [65, 28] Generated Node #0,4,3: 50:[65, 28] Operation: 20+8=28 Exploring Operation: 65-8=57, Resulting Numbers: [20, 57] Generated Node #0,4,4: 50:[20, 57] Operation: 65-8=57 Moving to Node #0,0 Current State: 50:[38, 30, 45], Operations: ['65-20=45'] Exploring Operation: 30+45=75, Resulting Numbers: [38, 75] Generated Node #0,0,0: 50:[38, 75] Operation: 30+45=75 Exploring Operation: 38+30=68, Resulting Numbers: [45, 68] Generated Node #0,0,1: 50:[45, 68] Operation: 38+30=68 Exploring Operation: 38-30=8, Resulting Numbers: [45, 8] Generated Node #0,0,2: 50:[45, 8] Operation: 38-30=8 Exploring Operation: 45-38=7, Resulting Numbers: [30, 7] Generated Node #0,0,3: 50:[30, 7] Operation: 45-38=7 Exploring Operation: 45-30=15, Resulting Numbers: [38, 15] Generated Node #0,0,4: 50:[38, 15] Operation: 45-30=15 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 50:[45, 8], Operations: ['65-20=45', '38-30=8'] Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,50 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,50 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 50:[30, 7], Operations: ['65-20=45', '45-38=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,50 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 50:[38, 15], Operations: ['65-20=45', '45-30=15'] Exploring Operation: 38*15=570, Resulting Numbers: [570] 570,50 unequal: No Solution Exploring Operation: 38+15=53, Resulting Numbers: [53] 53,50 unequal: No Solution Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[45, 68], Operations: ['65-20=45', '38+30=68'] Exploring Operation: 45*68=3060, Resulting Numbers: [3060] 3060,50 unequal: No Solution Exploring Operation: 68-45=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 45+68=113, Resulting Numbers: [113] 113,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[38, 75], Operations: ['65-20=45', '30+45=75'] Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,50 unequal: No Solution Exploring Operation: 38+75=113, Resulting Numbers: [113] 113,50 unequal: No Solution Exploring Operation: 38*75=2850, Resulting Numbers: [2850] 2850,50 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: 50:[65, 30, 18], Operations: ['38-20=18'] Exploring Operation: 30-18=12, Resulting Numbers: [65, 12] Generated Node #0,1,0: 50:[65, 12] Operation: 30-18=12 Exploring Operation: 65-30=35, Resulting Numbers: [18, 35] Generated Node #0,1,1: 50:[18, 35] Operation: 65-30=35 Exploring Operation: 30+18=48, Resulting Numbers: [65, 48] Generated Node #0,1,2: 50:[65, 48] Operation: 30+18=48 Exploring Operation: 65-18=47, Resulting Numbers: [30, 47] Generated Node #0,1,3: 50:[30, 47] Operation: 65-18=47 Exploring Operation: 65+18=83, Resulting Numbers: [30, 83] Generated Node #0,1,4: 50:[30, 83] Operation: 65+18=83 Moving to Node #0,2 Current State: 50:[38, 20, 35], Operations: ['65-30=35'] Exploring Operation: 20+35=55, Resulting Numbers: [38, 55] Generated Node #0,2,0: 50:[38, 55] Operation: 20+35=55 Exploring Operation: 38+20=58, Resulting Numbers: [35, 58] Generated Node #0,2,1: 50:[35, 58] Operation: 38+20=58 Exploring Operation: 35-20=15, Resulting Numbers: [38, 15] Generated Node #0,2,2: 50:[38, 15] Operation: 35-20=15 Exploring Operation: 38-20=18, Resulting Numbers: [35, 18] Generated Node #0,2,3: 50:[35, 18] Operation: 38-20=18 Exploring Operation: 38-35=3, Resulting Numbers: [20, 3] Generated Node #0,2,4: 50:[20, 3] Operation: 38-35=3 Moving to Node #0,2,4 Current State: 50:[20, 3], Operations: ['65-30=35', '38-35=3'] Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,50 unequal: No Solution Moving to Node #0,4,2 Current State: 50:[8, 45], Operations: ['38-30=8', '65-20=45'] Exploring Operation: 8*45=360, Resulting Numbers: [360] 360,50 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,50 unequal: No Solution Exploring Operation: 8+45=53, Resulting Numbers: [53] 53,50 unequal: No Solution Moving to Node #0,1,3 Current State: 50:[30, 47], Operations: ['38-20=18', '65-18=47'] Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,50 unequal: No Solution Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,50 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,50 unequal: No Solution Moving to Node #0,4,4 Current State: 50:[20, 57], Operations: ['38-30=8', '65-8=57'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,50 unequal: No Solution Exploring Operation: 20*57=1140, Resulting Numbers: [1140] 1140,50 unequal: No Solution Exploring Operation: 20+57=77, Resulting Numbers: [77] 77,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[65, 12], Operations: ['38-20=18', '30-18=12'] Exploring Operation: 65*12=780, Resulting Numbers: [780] 780,50 unequal: No Solution Exploring Operation: 65+12=77, Resulting Numbers: [77] 77,50 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,50 unequal: No Solution Moving to Node #0,2,3 Current State: 50:[35, 18], Operations: ['65-30=35', '38-20=18'] Exploring Operation: 35+18=53, Resulting Numbers: [53] 53,50 unequal: No Solution Exploring Operation: 35*18=630, Resulting Numbers: [630] 630,50 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[38, 55], Operations: ['65-30=35', '20+35=55'] Exploring Operation: 38*55=2090, Resulting Numbers: [2090] 2090,50 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 38+55=93, Resulting Numbers: [93] 93,50 unequal: No Solution Moving to Node #0,4,1 Current State: 50:[65, 12], Operations: ['38-30=8', '20-8=12'] Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,50 unequal: No Solution Exploring Operation: 65+12=77, Resulting Numbers: [77] 77,50 unequal: No Solution Exploring Operation: 65*12=780, Resulting Numbers: [780] 780,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[38, 15], Operations: ['65-30=35', '35-20=15'] Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 38*15=570, Resulting Numbers: [570] 570,50 unequal: No Solution Exploring Operation: 38+15=53, Resulting Numbers: [53] 53,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[18, 35], Operations: ['38-20=18', '65-30=35'] Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,50 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[65, 48], Operations: ['38-20=18', '30+18=48'] Exploring Operation: 65*48=3120, Resulting Numbers: [3120] 3120,50 unequal: No Solution Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 65+48=113, Resulting Numbers: [113] 113,50 unequal: No Solution Moving to Node #0,4,3 Current State: 50:[65, 28], Operations: ['38-30=8', '20+8=28'] Exploring Operation: 65+28=93, Resulting Numbers: [93] 93,50 unequal: No Solution Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,50 unequal: No Solution Exploring Operation: 65*28=1820, Resulting Numbers: [1820] 1820,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[35, 58], Operations: ['65-30=35', '38+20=58'] Exploring Operation: 58-35=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 35+58=93, Resulting Numbers: [93] 93,50 unequal: No Solution Exploring Operation: 35*58=2030, Resulting Numbers: [2030] 2030,50 unequal: No Solution Moving to Node #0,4,0 Current State: 50:[20, 73], Operations: ['38-30=8', '65+8=73'] Exploring Operation: 20*73=1460, Resulting Numbers: [1460] 1460,50 unequal: No Solution Exploring Operation: 20+73=93, Resulting Numbers: [93] 93,50 unequal: No Solution Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,50 unequal: No Solution Moving to Node #0,1,4 Current State: 50:[30, 83], Operations: ['38-20=18', '65+18=83'] Exploring Operation: 30*83=2490, Resulting Numbers: [2490] 2490,50 unequal: No Solution Exploring Operation: 30+83=113, Resulting Numbers: [113] 113,50 unequal: No Solution Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,50 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 13, 50, 70, 92 ]
15
[ "50-13=37", "92-70=22", "37-22=15" ]
Current State: 15:[13, 50, 70, 92], Operations: [] Exploring Operation: 50-13=37, Resulting Numbers: [70, 92, 37] Generated Node #2: [70, 92, 37] from Operation: 50-13=37 Current State: 15:[70, 92, 37], Operations: ['50-13=37'] Exploring Operation: 92-70=22, Resulting Numbers: [37, 22] Generated Node #3: [37, 22] from Operation: 92-70=22 Current State: 15:[37, 22], Operations: ['50-13=37', '92-70=22'] Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[13, 50, 70, 92], Operations: [] Exploring Operation: 70-50=20, Resulting Numbers: [13, 92, 20] Generated Node #0,0: 15:[13, 92, 20] Operation: 70-50=20 Exploring Operation: 92-70=22, Resulting Numbers: [13, 50, 22] Generated Node #0,1: 15:[13, 50, 22] Operation: 92-70=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[13, 50, 22], Operations: ['92-70=22'] Exploring Operation: 50-22=28, Resulting Numbers: [13, 28] Generated Node #0,1,0: 15:[13, 28] Operation: 50-22=28 Exploring Operation: 50-13=37, Resulting Numbers: [22, 37] Generated Node #0,1,1: 15:[22, 37] Operation: 50-13=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 15:[13, 28], Operations: ['92-70=22', '50-22=28'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[13, 50, 70, 92], Operations: [] Exploring Operation: 92-70=22, Resulting Numbers: [13, 50, 22] Generated Node #0,1: 15:[13, 50, 22] Operation: 92-70=22 Moving to Node #0,1 Current State: 15:[13, 50, 22], Operations: ['92-70=22'] Exploring Operation: 50-22=28, Resulting Numbers: [13, 28] Generated Node #0,1,0: 15:[13, 28] Operation: 50-22=28 Moving to Node #0,1,0 Current State: 15:[13, 28], Operations: ['92-70=22', '50-22=28'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 57, 3, 86, 80 ]
25
[ "57/3=19", "86-80=6", "19+6=25" ]
Current State: 25:[57, 3, 86, 80], Operations: [] Exploring Operation: 57/3=19, Resulting Numbers: [86, 80, 19] Generated Node #2: [86, 80, 19] from Operation: 57/3=19 Current State: 25:[86, 80, 19], Operations: ['57/3=19'] Exploring Operation: 86-80=6, Resulting Numbers: [19, 6] Generated Node #3: [19, 6] from Operation: 86-80=6 Current State: 25:[19, 6], Operations: ['57/3=19', '86-80=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[57, 3, 86, 80], Operations: [] Exploring Operation: 86-57=29, Resulting Numbers: [3, 80, 29] Generated Node #0,0: 25:[3, 80, 29] Operation: 86-57=29 Exploring Operation: 86-80=6, Resulting Numbers: [57, 3, 6] Generated Node #0,1: 25:[57, 3, 6] Operation: 86-80=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[57, 3, 6], Operations: ['86-80=6'] Exploring Operation: 57-6=51, Resulting Numbers: [3, 51] Generated Node #0,1,0: 25:[3, 51] Operation: 57-6=51 Exploring Operation: 57/3=19, Resulting Numbers: [6, 19] Generated Node #0,1,1: 25:[6, 19] Operation: 57/3=19 Moving to Node #0,1,1 Current State: 25:[6, 19], Operations: ['86-80=6', '57/3=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[57, 3, 86, 80], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [57, 3, 6] Generated Node #0,1: 25:[57, 3, 6] Operation: 86-80=6 Moving to Node #0,1 Current State: 25:[57, 3, 6], Operations: ['86-80=6'] Exploring Operation: 57/3=19, Resulting Numbers: [6, 19] Generated Node #0,1,1: 25:[6, 19] Operation: 57/3=19 Moving to Node #0,1,1 Current State: 25:[6, 19], Operations: ['86-80=6', '57/3=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 66, 62, 92, 30 ]
67
[ "92-62=30", "30/30=1", "66+1=67" ]
Current State: 67:[66, 62, 92, 30], Operations: [] Exploring Operation: 92-62=30, Resulting Numbers: [66, 30, 30] Generated Node #2: [66, 30, 30] from Operation: 92-62=30 Current State: 67:[66, 30, 30], Operations: ['92-62=30'] Exploring Operation: 30/30=1, Resulting Numbers: [66, 1] Generated Node #3: [66, 1] from Operation: 30/30=1 Current State: 67:[66, 1], Operations: ['92-62=30', '30/30=1'] Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[66, 62, 92, 30], Operations: [] Exploring Operation: 62+30=92, Resulting Numbers: [66, 92, 92] Generated Node #0,0: 67:[66, 92, 92] Operation: 62+30=92 Exploring Operation: 66+30=96, Resulting Numbers: [62, 92, 96] Generated Node #0,1: 67:[62, 92, 96] Operation: 66+30=96 Exploring Operation: 66-30=36, Resulting Numbers: [62, 92, 36] Generated Node #0,2: 67:[62, 92, 36] Operation: 66-30=36 Exploring Operation: 92-30=62, Resulting Numbers: [66, 62, 62] Generated Node #0,3: 67:[66, 62, 62] Operation: 92-30=62 Moving to Node #0,3 Current State: 67:[66, 62, 62], Operations: ['92-30=62'] Exploring Operation: 62/62=1, Resulting Numbers: [66, 1] Generated Node #0,3,0: 67:[66, 1] Operation: 62/62=1 Exploring Operation: 66+62=128, Resulting Numbers: [62, 128] Generated Node #0,3,1: 67:[62, 128] Operation: 66+62=128 Exploring Operation: 62+62=124, Resulting Numbers: [66, 124] Generated Node #0,3,2: 67:[66, 124] Operation: 62+62=124 Exploring Operation: 66+62=128, Resulting Numbers: [62, 128] Generated Node #0,3,3: 67:[62, 128] Operation: 66+62=128 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 67:[66, 124], Operations: ['92-30=62', '62+62=124'] Exploring Operation: 66*124=8184, Resulting Numbers: [8184] 8184,67 unequal: No Solution Exploring Operation: 124-66=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 66+124=190, Resulting Numbers: [190] 190,67 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:[62, 128], Operations: ['92-30=62', '66+62=128'] Exploring Operation: 128-62=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 62+128=190, Resulting Numbers: [190] 190,67 unequal: No Solution Exploring Operation: 62*128=7936, Resulting Numbers: [7936] 7936,67 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:[62, 128], Operations: ['92-30=62', '66+62=128'] Exploring Operation: 128-62=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 62*128=7936, Resulting Numbers: [7936] 7936,67 unequal: No Solution Exploring Operation: 62+128=190, Resulting Numbers: [190] 190,67 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 #0,3,0 Current State: 67:[66, 1], Operations: ['92-30=62', '62/62=1'] Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[66, 62, 92, 30], Operations: [] Exploring Operation: 92-30=62, Resulting Numbers: [66, 62, 62] Generated Node #0,3: 67:[66, 62, 62] Operation: 92-30=62 Moving to Node #0,3 Current State: 67:[66, 62, 62], Operations: ['92-30=62'] Exploring Operation: 62/62=1, Resulting Numbers: [66, 1] Generated Node #0,3,0: 67:[66, 1] Operation: 62/62=1 Moving to Node #0,3,0 Current State: 67:[66, 1], Operations: ['92-30=62', '62/62=1'] Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
sum_heuristic
[ 90, 83, 53, 28 ]
18
[ "90-83=7", "53-28=25", "25-7=18" ]
Current State: 18:[90, 83, 53, 28], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [53, 28, 7] Generated Node #2: [53, 28, 7] from Operation: 90-83=7 Current State: 18:[53, 28, 7], Operations: ['90-83=7'] Exploring Operation: 53-28=25, Resulting Numbers: [7, 25] Generated Node #3: [7, 25] from Operation: 53-28=25 Current State: 18:[7, 25], Operations: ['90-83=7', '53-28=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[90, 83, 53, 28], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [53, 28, 7] Generated Node #0,0: 18:[53, 28, 7] Operation: 90-83=7 Exploring Operation: 90-28=62, Resulting Numbers: [83, 53, 62] Generated Node #0,1: 18:[83, 53, 62] Operation: 90-28=62 Exploring Operation: 90-53=37, Resulting Numbers: [83, 28, 37] Generated Node #0,2: 18:[83, 28, 37] Operation: 90-53=37 Exploring Operation: 83-53=30, Resulting Numbers: [90, 28, 30] Generated Node #0,3: 18:[90, 28, 30] Operation: 83-53=30 Moving to Node #0,0 Current State: 18:[53, 28, 7], Operations: ['90-83=7'] Exploring Operation: 53-28=25, Resulting Numbers: [7, 25] Generated Node #0,0,0: 18:[7, 25] Operation: 53-28=25 Exploring Operation: 53-7=46, Resulting Numbers: [28, 46] Generated Node #0,0,1: 18:[28, 46] Operation: 53-7=46 Exploring Operation: 28/7=4, Resulting Numbers: [53, 4] Generated Node #0,0,2: 18:[53, 4] Operation: 28/7=4 Exploring Operation: 28-7=21, Resulting Numbers: [53, 21] Generated Node #0,0,3: 18:[53, 21] Operation: 28-7=21 Moving to Node #0,3 Current State: 18:[90, 28, 30], Operations: ['83-53=30'] Exploring Operation: 90-28=62, Resulting Numbers: [30, 62] Generated Node #0,3,0: 18:[30, 62] Operation: 90-28=62 Exploring Operation: 90-30=60, Resulting Numbers: [28, 60] Generated Node #0,3,1: 18:[28, 60] Operation: 90-30=60 Exploring Operation: 90/30=3, Resulting Numbers: [28, 3] Generated Node #0,3,2: 18:[28, 3] Operation: 90/30=3 Exploring Operation: 30-28=2, Resulting Numbers: [90, 2] Generated Node #0,3,3: 18:[90, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[28, 3], Operations: ['83-53=30', '90/30=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[28, 60], Operations: ['83-53=30', '90-30=60'] Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 28*60=1680, Resulting Numbers: [1680] 1680,18 unequal: No Solution Exploring Operation: 28+60=88, Resulting Numbers: [88] 88,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[30, 62], Operations: ['83-53=30', '90-28=62'] Exploring Operation: 30+62=92, Resulting Numbers: [92] 92,18 unequal: No Solution Exploring Operation: 30*62=1860, Resulting Numbers: [1860] 1860,18 unequal: No Solution Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 18:[90, 2], Operations: ['83-53=30', '30-28=2'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 90*2=180, Resulting Numbers: [180] 180,18 unequal: No Solution Exploring Operation: 90+2=92, Resulting Numbers: [92] 92,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[83, 28, 37], Operations: ['90-53=37'] Exploring Operation: 83-37=46, Resulting Numbers: [28, 46] Generated Node #0,2,0: 18:[28, 46] Operation: 83-37=46 Exploring Operation: 83+28=111, Resulting Numbers: [37, 111] Generated Node #0,2,1: 18:[37, 111] Operation: 83+28=111 Exploring Operation: 37-28=9, Resulting Numbers: [83, 9] Generated Node #0,2,2: 18:[83, 9] Operation: 37-28=9 Exploring Operation: 83-28=55, Resulting Numbers: [37, 55] Generated Node #0,2,3: 18:[37, 55] Operation: 83-28=55 Moving to Node #0,1 Current State: 18:[83, 53, 62], Operations: ['90-28=62'] Exploring Operation: 62-53=9, Resulting Numbers: [83, 9] Generated Node #0,1,0: 18:[83, 9] Operation: 62-53=9 Exploring Operation: 83-53=30, Resulting Numbers: [62, 30] Generated Node #0,1,1: 18:[62, 30] Operation: 83-53=30 Exploring Operation: 83+53=136, Resulting Numbers: [62, 136] Generated Node #0,1,2: 18:[62, 136] Operation: 83+53=136 Exploring Operation: 83-62=21, Resulting Numbers: [53, 21] Generated Node #0,1,3: 18:[53, 21] Operation: 83-62=21 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[53, 21], Operations: ['90-28=62', '83-62=21'] Exploring Operation: 53*21=1113, Resulting Numbers: [1113] 1113,18 unequal: No Solution Exploring Operation: 53+21=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[62, 30], Operations: ['90-28=62', '83-53=30'] Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,18 unequal: No Solution Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,18 unequal: No Solution Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[83, 9], Operations: ['90-28=62', '62-53=9'] Exploring Operation: 83+9=92, Resulting Numbers: [92] 92,18 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 83*9=747, Resulting Numbers: [747] 747,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[62, 136], Operations: ['90-28=62', '83+53=136'] Exploring Operation: 62+136=198, Resulting Numbers: [198] 198,18 unequal: No Solution Exploring Operation: 136-62=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 62*136=8432, Resulting Numbers: [8432] 8432,18 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: 18:[7, 25], Operations: ['90-83=7', '53-28=25'] Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,18 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[90, 83, 53, 28], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [53, 28, 7] Generated Node #0,0: 18:[53, 28, 7] Operation: 90-83=7 Moving to Node #0,0 Current State: 18:[53, 28, 7], Operations: ['90-83=7'] Exploring Operation: 53-28=25, Resulting Numbers: [7, 25] Generated Node #0,0,0: 18:[7, 25] Operation: 53-28=25 Moving to Node #0,0,0 Current State: 18:[7, 25], Operations: ['90-83=7', '53-28=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.954861
hs_4
mult_heuristic
[ 21, 47, 75, 5 ]
17
[ "21*5=105", "47+75=122", "122-105=17" ]
Current State: 17:[21, 47, 75, 5], Operations: [] Exploring Operation: 21*5=105, Resulting Numbers: [47, 75, 105] Generated Node #2: [47, 75, 105] from Operation: 21*5=105 Current State: 17:[47, 75, 105], Operations: ['21*5=105'] Exploring Operation: 47+75=122, Resulting Numbers: [105, 122] Generated Node #3: [105, 122] from Operation: 47+75=122 Current State: 17:[105, 122], Operations: ['21*5=105', '47+75=122'] Exploring Operation: 122-105=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[21, 47, 75, 5], Operations: [] Exploring Operation: 47-5=42, Resulting Numbers: [21, 75, 42] Generated Node #0,0: 17:[21, 75, 42] Operation: 47-5=42 Exploring Operation: 75-47=28, Resulting Numbers: [21, 5, 28] Generated Node #0,1: 17:[21, 5, 28] Operation: 75-47=28 Exploring Operation: 75-21=54, Resulting Numbers: [47, 5, 54] Generated Node #0,2: 17:[47, 5, 54] Operation: 75-21=54 Exploring Operation: 75/5=15, Resulting Numbers: [21, 47, 15] Generated Node #0,3: 17:[21, 47, 15] Operation: 75/5=15 Exploring Operation: 47-21=26, Resulting Numbers: [75, 5, 26] Generated Node #0,4: 17:[75, 5, 26] Operation: 47-21=26 Moving to Node #0,1 Current State: 17:[21, 5, 28], Operations: ['75-47=28'] Exploring Operation: 5+28=33, Resulting Numbers: [21, 33] Generated Node #0,1,0: 17:[21, 33] Operation: 5+28=33 Exploring Operation: 28-21=7, Resulting Numbers: [5, 7] Generated Node #0,1,1: 17:[5, 7] Operation: 28-21=7 Exploring Operation: 21-5=16, Resulting Numbers: [28, 16] Generated Node #0,1,2: 17:[28, 16] Operation: 21-5=16 Exploring Operation: 28-5=23, Resulting Numbers: [21, 23] Generated Node #0,1,3: 17:[21, 23] Operation: 28-5=23 Exploring Operation: 21+5=26, Resulting Numbers: [28, 26] Generated Node #0,1,4: 17:[28, 26] Operation: 21+5=26 Moving to Node #0,3 Current State: 17:[21, 47, 15], Operations: ['75/5=15'] Exploring Operation: 47+15=62, Resulting Numbers: [21, 62] Generated Node #0,3,0: 17:[21, 62] Operation: 47+15=62 Exploring Operation: 47-15=32, Resulting Numbers: [21, 32] Generated Node #0,3,1: 17:[21, 32] Operation: 47-15=32 Exploring Operation: 21+15=36, Resulting Numbers: [47, 36] Generated Node #0,3,2: 17:[47, 36] Operation: 21+15=36 Exploring Operation: 47-21=26, Resulting Numbers: [15, 26] Generated Node #0,3,3: 17:[15, 26] Operation: 47-21=26 Exploring Operation: 21-15=6, Resulting Numbers: [47, 6] Generated Node #0,3,4: 17:[47, 6] Operation: 21-15=6 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 17:[15, 26], Operations: ['75/5=15', '47-21=26'] Exploring Operation: 15+26=41, Resulting Numbers: [41] 41,17 unequal: No Solution Exploring Operation: 15*26=390, Resulting Numbers: [390] 390,17 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 17:[21, 32], Operations: ['75/5=15', '47-15=32'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 17:[47, 6], Operations: ['75/5=15', '21-15=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,17 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 17:[21, 62], Operations: ['75/5=15', '47+15=62'] Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,17 unequal: No Solution Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 17:[47, 36], Operations: ['75/5=15', '21+15=36'] Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 47*36=1692, Resulting Numbers: [1692] 1692,17 unequal: No Solution Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,17 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: 17:[47, 5, 54], Operations: ['75-21=54'] Exploring Operation: 47+5=52, Resulting Numbers: [54, 52] Generated Node #0,2,0: 17:[54, 52] Operation: 47+5=52 Exploring Operation: 54-47=7, Resulting Numbers: [5, 7] Generated Node #0,2,1: 17:[5, 7] Operation: 54-47=7 Exploring Operation: 54-5=49, Resulting Numbers: [47, 49] Generated Node #0,2,2: 17:[47, 49] Operation: 54-5=49 Exploring Operation: 5+54=59, Resulting Numbers: [47, 59] Generated Node #0,2,3: 17:[47, 59] Operation: 5+54=59 Exploring Operation: 47-5=42, Resulting Numbers: [54, 42] Generated Node #0,2,4: 17:[54, 42] Operation: 47-5=42 Moving to Node #0,4 Current State: 17:[75, 5, 26], Operations: ['47-21=26'] Exploring Operation: 26-5=21, Resulting Numbers: [75, 21] Generated Node #0,4,0: 17:[75, 21] Operation: 26-5=21 Exploring Operation: 75+5=80, Resulting Numbers: [26, 80] Generated Node #0,4,1: 17:[26, 80] Operation: 75+5=80 Exploring Operation: 75-26=49, Resulting Numbers: [5, 49] Generated Node #0,4,2: 17:[5, 49] Operation: 75-26=49 Exploring Operation: 75/5=15, Resulting Numbers: [26, 15] Generated Node #0,4,3: 17:[26, 15] Operation: 75/5=15 Exploring Operation: 75-5=70, Resulting Numbers: [26, 70] Generated Node #0,4,4: 17:[26, 70] Operation: 75-5=70 Moving to Node #0,0 Current State: 17:[21, 75, 42], Operations: ['47-5=42'] Exploring Operation: 42-21=21, Resulting Numbers: [75, 21] Generated Node #0,0,0: 17:[75, 21] Operation: 42-21=21 Exploring Operation: 75-42=33, Resulting Numbers: [21, 33] Generated Node #0,0,1: 17:[21, 33] Operation: 75-42=33 Exploring Operation: 75-21=54, Resulting Numbers: [42, 54] Generated Node #0,0,2: 17:[42, 54] Operation: 75-21=54 Exploring Operation: 21+75=96, Resulting Numbers: [42, 96] Generated Node #0,0,3: 17:[42, 96] Operation: 21+75=96 Exploring Operation: 42/21=2, Resulting Numbers: [75, 2] Generated Node #0,0,4: 17:[75, 2] Operation: 42/21=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 17:[21, 33], Operations: ['47-5=42', '75-42=33'] Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 21+33=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 21*33=693, Resulting Numbers: [693] 693,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[75, 21], Operations: ['47-5=42', '42-21=21'] Exploring Operation: 75+21=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 75*21=1575, Resulting Numbers: [1575] 1575,17 unequal: No Solution Exploring Operation: 75-21=54, Resulting Numbers: [54] 54,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 17:[42, 54], Operations: ['47-5=42', '75-21=54'] Exploring Operation: 42+54=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 42*54=2268, Resulting Numbers: [2268] 2268,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 17:[75, 2], Operations: ['47-5=42', '42/21=2'] Exploring Operation: 75*2=150, Resulting Numbers: [150] 150,17 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,17 unequal: No Solution Exploring Operation: 75+2=77, Resulting Numbers: [77] 77,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 17:[42, 96], Operations: ['47-5=42', '21+75=96'] Exploring Operation: 42*96=4032, Resulting Numbers: [4032] 4032,17 unequal: No Solution Exploring Operation: 42+96=138, Resulting Numbers: [138] 138,17 unequal: No Solution Exploring Operation: 96-42=54, Resulting Numbers: [54] 54,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 17:[21, 23], Operations: ['75-47=28', '28-5=23'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 21*23=483, Resulting Numbers: [483] 483,17 unequal: No Solution Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,17 unequal: No Solution Moving to Node #0,4,3 Current State: 17:[26, 15], Operations: ['47-21=26', '75/5=15'] Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,17 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,17 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[28, 16], Operations: ['75-47=28', '21-5=16'] Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,17 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[21, 33], Operations: ['75-47=28', '5+28=33'] Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 21+33=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 21*33=693, Resulting Numbers: [693] 693,17 unequal: No Solution Moving to Node #0,1,4 Current State: 17:[28, 26], Operations: ['75-47=28', '21+5=26'] Exploring Operation: 28*26=728, Resulting Numbers: [728] 728,17 unequal: No Solution Exploring Operation: 28+26=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[5, 7], Operations: ['75-21=54', '54-47=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,17 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[5, 7], Operations: ['75-47=28', '28-21=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,17 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,17 unequal: No Solution Moving to Node #0,4,2 Current State: 17:[5, 49], Operations: ['47-21=26', '75-26=49'] Exploring Operation: 5+49=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 5*49=245, Resulting Numbers: [245] 245,17 unequal: No Solution Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[47, 49], Operations: ['75-21=54', '54-5=49'] Exploring Operation: 47*49=2303, Resulting Numbers: [2303] 2303,17 unequal: No Solution Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,17 unequal: No Solution Moving to Node #0,4,4 Current State: 17:[26, 70], Operations: ['47-21=26', '75-5=70'] Exploring Operation: 26+70=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 26*70=1820, Resulting Numbers: [1820] 1820,17 unequal: No Solution Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,17 unequal: No Solution Moving to Node #0,4,0 Current State: 17:[75, 21], Operations: ['47-21=26', '26-5=21'] Exploring Operation: 75*21=1575, Resulting Numbers: [1575] 1575,17 unequal: No Solution Exploring Operation: 75+21=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 75-21=54, Resulting Numbers: [54] 54,17 unequal: No Solution Moving to Node #0,2,4 Current State: 17:[54, 42], Operations: ['75-21=54', '47-5=42'] Exploring Operation: 54*42=2268, Resulting Numbers: [2268] 2268,17 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 54+42=96, Resulting Numbers: [96] 96,17 unequal: No Solution Moving to Node #0,4,1 Current State: 17:[26, 80], Operations: ['47-21=26', '75+5=80'] Exploring Operation: 26*80=2080, Resulting Numbers: [2080] 2080,17 unequal: No Solution Exploring Operation: 26+80=106, Resulting Numbers: [106] 106,17 unequal: No Solution Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[54, 52], Operations: ['75-21=54', '47+5=52'] Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 54*52=2808, Resulting Numbers: [2808] 2808,17 unequal: No Solution Exploring Operation: 54+52=106, Resulting Numbers: [106] 106,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[47, 59], Operations: ['75-21=54', '5+54=59'] Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 47*59=2773, Resulting Numbers: [2773] 2773,17 unequal: No Solution Exploring Operation: 47+59=106, Resulting Numbers: [106] 106,17 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 38, 30, 22, 6 ]
40
[ "38+30=68", "22+6=28", "68-28=40" ]
Current State: 40:[38, 30, 22, 6], Operations: [] Exploring Operation: 38+30=68, Resulting Numbers: [22, 6, 68] Generated Node #2: [22, 6, 68] from Operation: 38+30=68 Current State: 40:[22, 6, 68], Operations: ['38+30=68'] Exploring Operation: 22+6=28, Resulting Numbers: [68, 28] Generated Node #3: [68, 28] from Operation: 22+6=28 Current State: 40:[68, 28], Operations: ['38+30=68', '22+6=28'] Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[38, 30, 22, 6], Operations: [] Exploring Operation: 38-30=8, Resulting Numbers: [22, 6, 8] Generated Node #0,0: 40:[22, 6, 8] Operation: 38-30=8 Exploring Operation: 30/6=5, Resulting Numbers: [38, 22, 5] Generated Node #0,1: 40:[38, 22, 5] Operation: 30/6=5 Exploring Operation: 30-22=8, Resulting Numbers: [38, 6, 8] Generated Node #0,2: 40:[38, 6, 8] Operation: 30-22=8 Moving to Node #0,0 Current State: 40:[22, 6, 8], Operations: ['38-30=8'] Exploring Operation: 22-8=14, Resulting Numbers: [6, 14] Generated Node #0,0,0: 40:[6, 14] Operation: 22-8=14 Exploring Operation: 8-6=2, Resulting Numbers: [22, 2] Generated Node #0,0,1: 40:[22, 2] Operation: 8-6=2 Exploring Operation: 22-6=16, Resulting Numbers: [8, 16] Generated Node #0,0,2: 40:[8, 16] Operation: 22-6=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[22, 2], Operations: ['38-30=8', '8-6=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,40 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 40:[8, 16], Operations: ['38-30=8', '22-6=16'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,40 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,40 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[6, 14], Operations: ['38-30=8', '22-8=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,40 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,40 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: 40:[38, 6, 8], Operations: ['30-22=8'] Exploring Operation: 8-6=2, Resulting Numbers: [38, 2] Generated Node #0,2,0: 40:[38, 2] Operation: 8-6=2 Exploring Operation: 6+8=14, Resulting Numbers: [38, 14] Generated Node #0,2,1: 40:[38, 14] Operation: 6+8=14 Exploring Operation: 38+6=44, Resulting Numbers: [8, 44] Generated Node #0,2,2: 40:[8, 44] Operation: 38+6=44 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[38, 2], Operations: ['30-22=8', '8-6=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[38, 30, 22, 6], Operations: [] Exploring Operation: 30-22=8, Resulting Numbers: [38, 6, 8] Generated Node #0,2: 40:[38, 6, 8] Operation: 30-22=8 Moving to Node #0,2 Current State: 40:[38, 6, 8], Operations: ['30-22=8'] Exploring Operation: 8-6=2, Resulting Numbers: [38, 2] Generated Node #0,2,0: 40:[38, 2] Operation: 8-6=2 Moving to Node #0,2,0 Current State: 40:[38, 2], Operations: ['30-22=8', '8-6=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 43, 83, 73, 83 ]
30
[ "43+83=126", "73+83=156", "156-126=30" ]
Current State: 30:[43, 83, 73, 83], Operations: [] Exploring Operation: 43+83=126, Resulting Numbers: [73, 126] Generated Node #2: [73, 126] from Operation: 43+83=126 Current State: 30:[73, 126], Operations: ['43+83=126'] Exploring Operation: 73+83=156, Resulting Numbers: [126, 156] Generated Node #3: [126, 156] from Operation: 73+83=156 Current State: 30:[126, 156], Operations: ['43+83=126', '73+83=156'] Exploring Operation: 156-126=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[43, 83, 73, 83], Operations: [] Exploring Operation: 83-73=10, Resulting Numbers: [43, 83, 10] Generated Node #0,0: 30:[43, 83, 10] Operation: 83-73=10 Exploring Operation: 83-83=0, Resulting Numbers: [43, 73, 0] Generated Node #0,1: 30:[43, 73, 0] Operation: 83-83=0 Exploring Operation: 83-73=10, Resulting Numbers: [43, 83, 10] Generated Node #0,2: 30:[43, 83, 10] Operation: 83-73=10 Exploring Operation: 83/83=1, Resulting Numbers: [43, 73, 1] Generated Node #0,3: 30:[43, 73, 1] Operation: 83/83=1 Moving to Node #0,3 Current State: 30:[43, 73, 1], Operations: ['83/83=1'] Exploring Operation: 43-1=42, Resulting Numbers: [73, 42] Generated Node #0,3,0: 30:[73, 42] Operation: 43-1=42 Exploring Operation: 43*1=43, Resulting Numbers: [73, 43] Generated Node #0,3,1: 30:[73, 43] Operation: 43*1=43 Exploring Operation: 73-1=72, Resulting Numbers: [43, 72] Generated Node #0,3,2: 30:[43, 72] Operation: 73-1=72 Exploring Operation: 73-43=30, Resulting Numbers: [1, 30] Generated Node #0,3,3: 30:[1, 30] Operation: 73-43=30 Moving to Node #0,1 Current State: 30:[43, 73, 0], Operations: ['83-83=0'] Exploring Operation: 73-43=30, Resulting Numbers: [0, 30] Generated Node #0,1,0: 30:[0, 30] Operation: 73-43=30 Exploring Operation: 43+0=43, Resulting Numbers: [73, 43] Generated Node #0,1,1: 30:[73, 43] Operation: 43+0=43 Exploring Operation: 43*0=0, Resulting Numbers: [73, 0] Generated Node #0,1,2: 30:[73, 0] Operation: 43*0=0 Exploring Operation: 73*0=0, Resulting Numbers: [43, 0] Generated Node #0,1,3: 30:[43, 0] Operation: 73*0=0 Moving to Node #0,2 Current State: 30:[43, 83, 10], Operations: ['83-73=10'] Exploring Operation: 43+10=53, Resulting Numbers: [83, 53] Generated Node #0,2,0: 30:[83, 53] Operation: 43+10=53 Exploring Operation: 83-10=73, Resulting Numbers: [43, 73] Generated Node #0,2,1: 30:[43, 73] Operation: 83-10=73 Exploring Operation: 43-10=33, Resulting Numbers: [83, 33] Generated Node #0,2,2: 30:[83, 33] Operation: 43-10=33 Exploring Operation: 83-43=40, Resulting Numbers: [10, 40] Generated Node #0,2,3: 30:[10, 40] Operation: 83-43=40 Moving to Node #0,0 Current State: 30:[43, 83, 10], Operations: ['83-73=10'] Exploring Operation: 83-10=73, Resulting Numbers: [43, 73] Generated Node #0,0,0: 30:[43, 73] Operation: 83-10=73 Exploring Operation: 43+10=53, Resulting Numbers: [83, 53] Generated Node #0,0,1: 30:[83, 53] Operation: 43+10=53 Exploring Operation: 43-10=33, Resulting Numbers: [83, 33] Generated Node #0,0,2: 30:[83, 33] Operation: 43-10=33 Exploring Operation: 83-43=40, Resulting Numbers: [10, 40] Generated Node #0,0,3: 30:[10, 40] Operation: 83-43=40 Moving to Node #0,3,3 Current State: 30:[1, 30], Operations: ['83/83=1', '73-43=30'] Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[43, 83, 73, 83], Operations: [] Exploring Operation: 83/83=1, Resulting Numbers: [43, 73, 1] Generated Node #0,3: 30:[43, 73, 1] Operation: 83/83=1 Moving to Node #0,3 Current State: 30:[43, 73, 1], Operations: ['83/83=1'] Exploring Operation: 73-43=30, Resulting Numbers: [1, 30] Generated Node #0,3,3: 30:[1, 30] Operation: 73-43=30 Moving to Node #0,3,3 Current State: 30:[1, 30], Operations: ['83/83=1', '73-43=30'] Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.978299
hs_4
mult_heuristic
[ 39, 32, 92, 45 ]
95
[ "45-32=13", "39/13=3", "92+3=95" ]
Current State: 95:[39, 32, 92, 45], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [39, 92, 13] Generated Node #2: [39, 92, 13] from Operation: 45-32=13 Current State: 95:[39, 92, 13], Operations: ['45-32=13'] Exploring Operation: 39/13=3, Resulting Numbers: [92, 3] Generated Node #3: [92, 3] from Operation: 39/13=3 Current State: 95:[92, 3], Operations: ['45-32=13', '39/13=3'] Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[39, 32, 92, 45], Operations: [] Exploring Operation: 45-39=6, Resulting Numbers: [32, 92, 6] Generated Node #0,0: 95:[32, 92, 6] Operation: 45-39=6 Exploring Operation: 39+45=84, Resulting Numbers: [32, 92, 84] Generated Node #0,1: 95:[32, 92, 84] Operation: 39+45=84 Exploring Operation: 45-32=13, Resulting Numbers: [39, 92, 13] Generated Node #0,2: 95:[39, 92, 13] Operation: 45-32=13 Exploring Operation: 32+45=77, Resulting Numbers: [39, 92, 77] Generated Node #0,3: 95:[39, 92, 77] Operation: 32+45=77 Exploring Operation: 39-32=7, Resulting Numbers: [92, 45, 7] Generated Node #0,4: 95:[92, 45, 7] Operation: 39-32=7 Moving to Node #0,0 Current State: 95:[32, 92, 6], Operations: ['45-39=6'] Exploring Operation: 32+92=124, Resulting Numbers: [6, 124] Generated Node #0,0,0: 95:[6, 124] Operation: 32+92=124 Exploring Operation: 92-6=86, Resulting Numbers: [32, 86] Generated Node #0,0,1: 95:[32, 86] Operation: 92-6=86 Exploring Operation: 32-6=26, Resulting Numbers: [92, 26] Generated Node #0,0,2: 95:[92, 26] Operation: 32-6=26 Exploring Operation: 92+6=98, Resulting Numbers: [32, 98] Generated Node #0,0,3: 95:[32, 98] Operation: 92+6=98 Exploring Operation: 32+6=38, Resulting Numbers: [92, 38] Generated Node #0,0,4: 95:[92, 38] Operation: 32+6=38 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[92, 26], Operations: ['45-39=6', '32-6=26'] Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,95 unequal: No Solution Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,95 unequal: No Solution Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 95:[32, 98], Operations: ['45-39=6', '92+6=98'] Exploring Operation: 98-32=66, Resulting Numbers: [66] 66,95 unequal: No Solution Exploring Operation: 32*98=3136, Resulting Numbers: [3136] 3136,95 unequal: No Solution Exploring Operation: 32+98=130, Resulting Numbers: [130] 130,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[32, 86], Operations: ['45-39=6', '92-6=86'] Exploring Operation: 32+86=118, Resulting Numbers: [118] 118,95 unequal: No Solution Exploring Operation: 86-32=54, Resulting Numbers: [54] 54,95 unequal: No Solution Exploring Operation: 32*86=2752, Resulting Numbers: [2752] 2752,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 95:[92, 38], Operations: ['45-39=6', '32+6=38'] Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,95 unequal: No Solution Exploring Operation: 92+38=130, Resulting Numbers: [130] 130,95 unequal: No Solution Exploring Operation: 92*38=3496, Resulting Numbers: [3496] 3496,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[6, 124], Operations: ['45-39=6', '32+92=124'] Exploring Operation: 124-6=118, Resulting Numbers: [118] 118,95 unequal: No Solution Exploring Operation: 6*124=744, Resulting Numbers: [744] 744,95 unequal: No Solution Exploring Operation: 6+124=130, Resulting Numbers: [130] 130,95 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: 95:[32, 92, 84], Operations: ['39+45=84'] Exploring Operation: 32+84=116, Resulting Numbers: [92, 116] Generated Node #0,1,0: 95:[92, 116] Operation: 32+84=116 Exploring Operation: 92-32=60, Resulting Numbers: [84, 60] Generated Node #0,1,1: 95:[84, 60] Operation: 92-32=60 Exploring Operation: 92-84=8, Resulting Numbers: [32, 8] Generated Node #0,1,2: 95:[32, 8] Operation: 92-84=8 Exploring Operation: 32+92=124, Resulting Numbers: [84, 124] Generated Node #0,1,3: 95:[84, 124] Operation: 32+92=124 Exploring Operation: 84-32=52, Resulting Numbers: [92, 52] Generated Node #0,1,4: 95:[92, 52] Operation: 84-32=52 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 95:[32, 8], Operations: ['39+45=84', '92-84=8'] Exploring Operation: 32*8=256, Resulting Numbers: [256] 256,95 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,95 unequal: No Solution Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[92, 116], Operations: ['39+45=84', '32+84=116'] Exploring Operation: 92+116=208, Resulting Numbers: [208] 208,95 unequal: No Solution Exploring Operation: 116-92=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 92*116=10672, Resulting Numbers: [10672] 10672,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 95:[92, 52], Operations: ['39+45=84', '84-32=52'] Exploring Operation: 92+52=144, Resulting Numbers: [144] 144,95 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 92*52=4784, Resulting Numbers: [4784] 4784,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 95:[84, 124], Operations: ['39+45=84', '32+92=124'] Exploring Operation: 124-84=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 84*124=10416, Resulting Numbers: [10416] 10416,95 unequal: No Solution Exploring Operation: 84+124=208, Resulting Numbers: [208] 208,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[84, 60], Operations: ['39+45=84', '92-32=60'] Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,95 unequal: No Solution Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,95 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: 95:[39, 92, 13], Operations: ['45-32=13'] Exploring Operation: 92-13=79, Resulting Numbers: [39, 79] Generated Node #0,2,0: 95:[39, 79] Operation: 92-13=79 Exploring Operation: 92+13=105, Resulting Numbers: [39, 105] Generated Node #0,2,1: 95:[39, 105] Operation: 92+13=105 Exploring Operation: 39/13=3, Resulting Numbers: [92, 3] Generated Node #0,2,2: 95:[92, 3] Operation: 39/13=3 Exploring Operation: 39-13=26, Resulting Numbers: [92, 26] Generated Node #0,2,3: 95:[92, 26] Operation: 39-13=26 Exploring Operation: 39+13=52, Resulting Numbers: [92, 52] Generated Node #0,2,4: 95:[92, 52] Operation: 39+13=52 Moving to Node #0,4 Current State: 95:[92, 45, 7], Operations: ['39-32=7'] Exploring Operation: 92-7=85, Resulting Numbers: [45, 85] Generated Node #0,4,0: 95:[45, 85] Operation: 92-7=85 Exploring Operation: 92+7=99, Resulting Numbers: [45, 99] Generated Node #0,4,1: 95:[45, 99] Operation: 92+7=99 Exploring Operation: 45-7=38, Resulting Numbers: [92, 38] Generated Node #0,4,2: 95:[92, 38] Operation: 45-7=38 Exploring Operation: 45+7=52, Resulting Numbers: [92, 52] Generated Node #0,4,3: 95:[92, 52] Operation: 45+7=52 Exploring Operation: 92-45=47, Resulting Numbers: [7, 47] Generated Node #0,4,4: 95:[7, 47] Operation: 92-45=47 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 95:[92, 38], Operations: ['39-32=7', '45-7=38'] Exploring Operation: 92+38=130, Resulting Numbers: [130] 130,95 unequal: No Solution Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,95 unequal: No Solution Exploring Operation: 92*38=3496, Resulting Numbers: [3496] 3496,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 95:[45, 99], Operations: ['39-32=7', '92+7=99'] Exploring Operation: 45+99=144, Resulting Numbers: [144] 144,95 unequal: No Solution Exploring Operation: 45*99=4455, Resulting Numbers: [4455] 4455,95 unequal: No Solution Exploring Operation: 99-45=54, Resulting Numbers: [54] 54,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 95:[7, 47], Operations: ['39-32=7', '92-45=47'] Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 7*47=329, Resulting Numbers: [329] 329,95 unequal: No Solution Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 95:[45, 85], Operations: ['39-32=7', '92-7=85'] Exploring Operation: 45+85=130, Resulting Numbers: [130] 130,95 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 45*85=3825, Resulting Numbers: [3825] 3825,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 95:[92, 52], Operations: ['39-32=7', '45+7=52'] Exploring Operation: 92+52=144, Resulting Numbers: [144] 144,95 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 92*52=4784, Resulting Numbers: [4784] 4784,95 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: 95:[39, 92, 77], Operations: ['32+45=77'] Exploring Operation: 39+77=116, Resulting Numbers: [92, 116] Generated Node #0,3,0: 95:[92, 116] Operation: 39+77=116 Exploring Operation: 92-39=53, Resulting Numbers: [77, 53] Generated Node #0,3,1: 95:[77, 53] Operation: 92-39=53 Exploring Operation: 92-77=15, Resulting Numbers: [39, 15] Generated Node #0,3,2: 95:[39, 15] Operation: 92-77=15 Exploring Operation: 77-39=38, Resulting Numbers: [92, 38] Generated Node #0,3,3: 95:[92, 38] Operation: 77-39=38 Exploring Operation: 39+92=131, Resulting Numbers: [77, 131] Generated Node #0,3,4: 95:[77, 131] Operation: 39+92=131 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 95:[92, 38], Operations: ['32+45=77', '77-39=38'] Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,95 unequal: No Solution Exploring Operation: 92*38=3496, Resulting Numbers: [3496] 3496,95 unequal: No Solution Exploring Operation: 92+38=130, Resulting Numbers: [130] 130,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 95:[92, 116], Operations: ['32+45=77', '39+77=116'] Exploring Operation: 92*116=10672, Resulting Numbers: [10672] 10672,95 unequal: No Solution Exploring Operation: 92+116=208, Resulting Numbers: [208] 208,95 unequal: No Solution Exploring Operation: 116-92=24, Resulting Numbers: [24] 24,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 95:[39, 15], Operations: ['32+45=77', '92-77=15'] Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,95 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 95:[77, 53], Operations: ['32+45=77', '92-39=53'] Exploring Operation: 77*53=4081, Resulting Numbers: [4081] 4081,95 unequal: No Solution Exploring Operation: 77+53=130, Resulting Numbers: [130] 130,95 unequal: No Solution Exploring Operation: 77-53=24, Resulting Numbers: [24] 24,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 95:[77, 131], Operations: ['32+45=77', '39+92=131'] Exploring Operation: 77+131=208, Resulting Numbers: [208] 208,95 unequal: No Solution Exploring Operation: 77*131=10087, Resulting Numbers: [10087] 10087,95 unequal: No Solution Exploring Operation: 131-77=54, Resulting Numbers: [54] 54,95 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: 95:[92, 3], Operations: ['45-32=13', '39/13=3'] Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,95 unequal: No Solution Exploring Operation: 92*3=276, Resulting Numbers: [276] 276,95 unequal: No Solution Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[39, 32, 92, 45], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [39, 92, 13] Generated Node #0,2: 95:[39, 92, 13] Operation: 45-32=13 Moving to Node #0,2 Current State: 95:[39, 92, 13], Operations: ['45-32=13'] Exploring Operation: 39/13=3, Resulting Numbers: [92, 3] Generated Node #0,2,2: 95:[92, 3] Operation: 39/13=3 Moving to Node #0,2,2 Current State: 95:[92, 3], Operations: ['45-32=13', '39/13=3'] Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.914931
hs_5
sum_heuristic
[ 19, 65, 31, 14 ]
29
[ "65-19=46", "31-14=17", "46-17=29" ]
Current State: 29:[19, 65, 31, 14], Operations: [] Exploring Operation: 65-19=46, Resulting Numbers: [31, 14, 46] Generated Node #2: [31, 14, 46] from Operation: 65-19=46 Current State: 29:[31, 14, 46], Operations: ['65-19=46'] Exploring Operation: 31-14=17, Resulting Numbers: [46, 17] Generated Node #3: [46, 17] from Operation: 31-14=17 Current State: 29:[46, 17], Operations: ['65-19=46', '31-14=17'] Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[19, 65, 31, 14], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [19, 14, 34] Generated Node #0,0: 29:[19, 14, 34] Operation: 65-31=34 Exploring Operation: 65-19=46, Resulting Numbers: [31, 14, 46] Generated Node #0,1: 29:[31, 14, 46] Operation: 65-19=46 Exploring Operation: 65-14=51, Resulting Numbers: [19, 31, 51] Generated Node #0,2: 29:[19, 31, 51] Operation: 65-14=51 Exploring Operation: 31-14=17, Resulting Numbers: [19, 65, 17] Generated Node #0,3: 29:[19, 65, 17] Operation: 31-14=17 Exploring Operation: 19+14=33, Resulting Numbers: [65, 31, 33] Generated Node #0,4: 29:[65, 31, 33] Operation: 19+14=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[19, 14, 34], Operations: ['65-31=34'] Exploring Operation: 34-19=15, Resulting Numbers: [14, 15] Generated Node #0,0,0: 29:[14, 15] Operation: 34-19=15 Exploring Operation: 19+14=33, Resulting Numbers: [34, 33] Generated Node #0,0,1: 29:[34, 33] Operation: 19+14=33 Exploring Operation: 19-14=5, Resulting Numbers: [34, 5] Generated Node #0,0,2: 29:[34, 5] Operation: 19-14=5 Exploring Operation: 14+34=48, Resulting Numbers: [19, 48] Generated Node #0,0,3: 29:[19, 48] Operation: 14+34=48 Exploring Operation: 34-14=20, Resulting Numbers: [19, 20] Generated Node #0,0,4: 29:[19, 20] Operation: 34-14=20 Moving to Node #0,0,1 Current State: 29:[34, 33], Operations: ['65-31=34', '19+14=33'] Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,29 unequal: No Solution Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,29 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,29 unequal: No Solution Moving to Node #0,0,4 Current State: 29:[19, 20], Operations: ['65-31=34', '34-14=20'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,29 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[14, 15], Operations: ['65-31=34', '34-19=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[19, 65, 31, 14], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [19, 14, 34] Generated Node #0,0: 29:[19, 14, 34] Operation: 65-31=34 Moving to Node #0,0 Current State: 29:[19, 14, 34], Operations: ['65-31=34'] Exploring Operation: 34-19=15, Resulting Numbers: [14, 15] Generated Node #0,0,0: 29:[14, 15] Operation: 34-19=15 Moving to Node #0,0,0 Current State: 29:[14, 15], Operations: ['65-31=34', '34-19=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 18, 23, 39, 26 ]
65
[ "23-18=5", "39-26=13", "5*13=65" ]
Current State: 65:[18, 23, 39, 26], Operations: [] Exploring Operation: 23-18=5, Resulting Numbers: [39, 26, 5] Generated Node #2: [39, 26, 5] from Operation: 23-18=5 Current State: 65:[39, 26, 5], Operations: ['23-18=5'] Exploring Operation: 39-26=13, Resulting Numbers: [5, 13] Generated Node #3: [5, 13] from Operation: 39-26=13 Current State: 65:[5, 13], Operations: ['23-18=5', '39-26=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[18, 23, 39, 26], Operations: [] Exploring Operation: 23+39=62, Resulting Numbers: [18, 26, 62] Generated Node #0,0: 65:[18, 26, 62] Operation: 23+39=62 Exploring Operation: 39-26=13, Resulting Numbers: [18, 23, 13] Generated Node #0,1: 65:[18, 23, 13] Operation: 39-26=13 Exploring Operation: 39+26=65, Resulting Numbers: [18, 23, 65] Generated Node #0,2: 65:[18, 23, 65] Operation: 39+26=65 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[18, 23, 13], Operations: ['39-26=13'] Exploring Operation: 23-13=10, Resulting Numbers: [18, 10] Generated Node #0,1,0: 65:[18, 10] Operation: 23-13=10 Exploring Operation: 23-18=5, Resulting Numbers: [13, 5] Generated Node #0,1,1: 65:[13, 5] Operation: 23-18=5 Exploring Operation: 18-13=5, Resulting Numbers: [23, 5] Generated Node #0,1,2: 65:[23, 5] Operation: 18-13=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 65:[13, 5], Operations: ['39-26=13', '23-18=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[18, 23, 39, 26], Operations: [] Exploring Operation: 39-26=13, Resulting Numbers: [18, 23, 13] Generated Node #0,1: 65:[18, 23, 13] Operation: 39-26=13 Moving to Node #0,1 Current State: 65:[18, 23, 13], Operations: ['39-26=13'] Exploring Operation: 23-18=5, Resulting Numbers: [13, 5] Generated Node #0,1,1: 65:[13, 5] Operation: 23-18=5 Moving to Node #0,1,1 Current State: 65:[13, 5], Operations: ['39-26=13', '23-18=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 44, 40, 64, 24 ]
66
[ "44-24=20", "40/20=2", "64+2=66" ]
Current State: 66:[44, 40, 64, 24], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [40, 64, 20] Generated Node #2: [40, 64, 20] from Operation: 44-24=20 Current State: 66:[40, 64, 20], Operations: ['44-24=20'] Exploring Operation: 40/20=2, Resulting Numbers: [64, 2] Generated Node #3: [64, 2] from Operation: 40/20=2 Current State: 66:[64, 2], Operations: ['44-24=20', '40/20=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[44, 40, 64, 24], Operations: [] Exploring Operation: 44+24=68, Resulting Numbers: [40, 64, 68] Generated Node #0,0: 66:[40, 64, 68] Operation: 44+24=68 Exploring Operation: 44-40=4, Resulting Numbers: [64, 24, 4] Generated Node #0,1: 66:[64, 24, 4] Operation: 44-40=4 Exploring Operation: 64-44=20, Resulting Numbers: [40, 24, 20] Generated Node #0,2: 66:[40, 24, 20] Operation: 64-44=20 Exploring Operation: 44-24=20, Resulting Numbers: [40, 64, 20] Generated Node #0,3: 66:[40, 64, 20] Operation: 44-24=20 Moving to Node #0,1 Current State: 66:[64, 24, 4], Operations: ['44-40=4'] Exploring Operation: 64+4=68, Resulting Numbers: [24, 68] Generated Node #0,1,0: 66:[24, 68] Operation: 64+4=68 Exploring Operation: 24/4=6, Resulting Numbers: [64, 6] Generated Node #0,1,1: 66:[64, 6] Operation: 24/4=6 Exploring Operation: 24-4=20, Resulting Numbers: [64, 20] Generated Node #0,1,2: 66:[64, 20] Operation: 24-4=20 Exploring Operation: 64/4=16, Resulting Numbers: [24, 16] Generated Node #0,1,3: 66:[24, 16] Operation: 64/4=16 Moving to Node #0,2 Current State: 66:[40, 24, 20], Operations: ['64-44=20'] Exploring Operation: 40/20=2, Resulting Numbers: [24, 2] Generated Node #0,2,0: 66:[24, 2] Operation: 40/20=2 Exploring Operation: 40-24=16, Resulting Numbers: [20, 16] Generated Node #0,2,1: 66:[20, 16] Operation: 40-24=16 Exploring Operation: 40+24=64, Resulting Numbers: [20, 64] Generated Node #0,2,2: 66:[20, 64] Operation: 40+24=64 Exploring Operation: 40-20=20, Resulting Numbers: [24, 20] Generated Node #0,2,3: 66:[24, 20] Operation: 40-20=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[24, 2], Operations: ['64-44=20', '40/20=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[20, 64], Operations: ['64-44=20', '40+24=64'] Exploring Operation: 20*64=1280, Resulting Numbers: [1280] 1280,66 unequal: No Solution Exploring Operation: 20+64=84, Resulting Numbers: [84] 84,66 unequal: No Solution Exploring Operation: 64-20=44, Resulting Numbers: [44] 44,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 66:[24, 20], Operations: ['64-44=20', '40-20=20'] Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 24*20=480, Resulting Numbers: [480] 480,66 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 66:[20, 16], Operations: ['64-44=20', '40-24=16'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,66 unequal: No Solution Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 66:[40, 64, 68], Operations: ['44+24=68'] Exploring Operation: 68-64=4, Resulting Numbers: [40, 4] Generated Node #0,0,0: 66:[40, 4] Operation: 68-64=4 Exploring Operation: 68-40=28, Resulting Numbers: [64, 28] Generated Node #0,0,1: 66:[64, 28] Operation: 68-40=28 Exploring Operation: 64-40=24, Resulting Numbers: [68, 24] Generated Node #0,0,2: 66:[68, 24] Operation: 64-40=24 Exploring Operation: 40+64=104, Resulting Numbers: [68, 104] Generated Node #0,0,3: 66:[68, 104] Operation: 40+64=104 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 66:[68, 24], Operations: ['44+24=68', '64-40=24'] Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,66 unequal: No Solution Exploring Operation: 68*24=1632, Resulting Numbers: [1632] 1632,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 66:[64, 28], Operations: ['44+24=68', '68-40=28'] Exploring Operation: 64-28=36, Resulting Numbers: [36] 36,66 unequal: No Solution Exploring Operation: 64+28=92, Resulting Numbers: [92] 92,66 unequal: No Solution Exploring Operation: 64*28=1792, Resulting Numbers: [1792] 1792,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[40, 4], Operations: ['44+24=68', '68-64=4'] Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,66 unequal: No Solution Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 66:[68, 104], Operations: ['44+24=68', '40+64=104'] Exploring Operation: 104-68=36, Resulting Numbers: [36] 36,66 unequal: No Solution Exploring Operation: 68*104=7072, Resulting Numbers: [7072] 7072,66 unequal: No Solution Exploring Operation: 68+104=172, Resulting Numbers: [172] 172,66 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: 66:[40, 64, 20], Operations: ['44-24=20'] Exploring Operation: 40/20=2, Resulting Numbers: [64, 2] Generated Node #0,3,0: 66:[64, 2] Operation: 40/20=2 Exploring Operation: 64-40=24, Resulting Numbers: [20, 24] Generated Node #0,3,1: 66:[20, 24] Operation: 64-40=24 Exploring Operation: 40-20=20, Resulting Numbers: [64, 20] Generated Node #0,3,2: 66:[64, 20] Operation: 40-20=20 Exploring Operation: 40+20=60, Resulting Numbers: [64, 60] Generated Node #0,3,3: 66:[64, 60] Operation: 40+20=60 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 66:[64, 2], Operations: ['44-24=20', '40/20=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,66 unequal: No Solution Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,66 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[44, 40, 64, 24], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [40, 64, 20] Generated Node #0,3: 66:[40, 64, 20] Operation: 44-24=20 Moving to Node #0,3 Current State: 66:[40, 64, 20], Operations: ['44-24=20'] Exploring Operation: 40/20=2, Resulting Numbers: [64, 2] Generated Node #0,3,0: 66:[64, 2] Operation: 40/20=2 Moving to Node #0,3,0 Current State: 66:[64, 2], Operations: ['44-24=20', '40/20=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_4
sum_heuristic
[ 60, 29, 9, 23 ]
45
[ "60-29=31", "23-9=14", "31+14=45" ]
Current State: 45:[60, 29, 9, 23], Operations: [] Exploring Operation: 60-29=31, Resulting Numbers: [9, 23, 31] Generated Node #2: [9, 23, 31] from Operation: 60-29=31 Current State: 45:[9, 23, 31], Operations: ['60-29=31'] Exploring Operation: 23-9=14, Resulting Numbers: [31, 14] Generated Node #3: [31, 14] from Operation: 23-9=14 Current State: 45:[31, 14], Operations: ['60-29=31', '23-9=14'] Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[60, 29, 9, 23], Operations: [] Exploring Operation: 29-23=6, Resulting Numbers: [60, 9, 6] Generated Node #0,0: 45:[60, 9, 6] Operation: 29-23=6 Moving to Node #0,0 Current State: 45:[60, 9, 6], Operations: ['29-23=6'] Exploring Operation: 60/6=10, Resulting Numbers: [9, 10] Generated Node #0,0,0: 45:[9, 10] Operation: 60/6=10 Moving to Node #0,0,0 Current State: 45:[9, 10], Operations: ['29-23=6', '60/6=10'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,45 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 12, 14, 13, 37 ]
35
[ "12+14=26", "26/13=2", "37-2=35" ]
Current State: 35:[12, 14, 13, 37], Operations: [] Exploring Operation: 12+14=26, Resulting Numbers: [13, 37, 26] Generated Node #2: [13, 37, 26] from Operation: 12+14=26 Current State: 35:[13, 37, 26], Operations: ['12+14=26'] Exploring Operation: 26/13=2, Resulting Numbers: [37, 2] Generated Node #3: [37, 2] from Operation: 26/13=2 Current State: 35:[37, 2], Operations: ['12+14=26', '26/13=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[12, 14, 13, 37], Operations: [] Exploring Operation: 14-13=1, Resulting Numbers: [12, 37, 1] Generated Node #0,0: 35:[12, 37, 1] Operation: 14-13=1 Exploring Operation: 14-12=2, Resulting Numbers: [13, 37, 2] Generated Node #0,1: 35:[13, 37, 2] Operation: 14-12=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[12, 37, 1], Operations: ['14-13=1'] Exploring Operation: 12-1=11, Resulting Numbers: [37, 11] Generated Node #0,0,0: 35:[37, 11] Operation: 12-1=11 Exploring Operation: 37-1=36, Resulting Numbers: [12, 36] Generated Node #0,0,1: 35:[12, 36] Operation: 37-1=36 Moving to Node #0,0,0 Current State: 35:[37, 11], Operations: ['14-13=1', '12-1=11'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[12, 36], Operations: ['14-13=1', '37-1=36'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,35 unequal: No Solution No solution 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: 35:[13, 37, 2], Operations: ['14-12=2'] Exploring Operation: 13-2=11, Resulting Numbers: [37, 11] Generated Node #0,1,0: 35:[37, 11] Operation: 13-2=11 Exploring Operation: 37-2=35, Resulting Numbers: [13, 35] Generated Node #0,1,1: 35:[13, 35] Operation: 37-2=35 Moving to Node #0,1,0 Current State: 35:[37, 11], Operations: ['14-12=2', '13-2=11'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[13, 35], Operations: ['14-12=2', '37-2=35'] Exploring Operation: 13+35=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,35 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
[ 22, 41, 93, 4 ]
17
[ "41-22=19", "4*19=76", "93-76=17" ]
Current State: 17:[22, 41, 93, 4], Operations: [] Exploring Operation: 41-22=19, Resulting Numbers: [93, 4, 19] Generated Node #2: [93, 4, 19] from Operation: 41-22=19 Current State: 17:[93, 4, 19], Operations: ['41-22=19'] Exploring Operation: 4*19=76, Resulting Numbers: [93, 76] Generated Node #3: [93, 76] from Operation: 4*19=76 Current State: 17:[93, 76], Operations: ['41-22=19', '4*19=76'] Exploring Operation: 93-76=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[22, 41, 93, 4], Operations: [] Exploring Operation: 93-41=52, Resulting Numbers: [22, 4, 52] Generated Node #0,0: 17:[22, 4, 52] Operation: 93-41=52 Exploring Operation: 41-22=19, Resulting Numbers: [93, 4, 19] Generated Node #0,1: 17:[93, 4, 19] Operation: 41-22=19 Exploring Operation: 22-4=18, Resulting Numbers: [41, 93, 18] Generated Node #0,2: 17:[41, 93, 18] Operation: 22-4=18 Exploring Operation: 93-22=71, Resulting Numbers: [41, 4, 71] Generated Node #0,3: 17:[41, 4, 71] Operation: 93-22=71 Moving to Node #0,0 Current State: 17:[22, 4, 52], Operations: ['93-41=52'] Exploring Operation: 52-22=30, Resulting Numbers: [4, 30] Generated Node #0,0,0: 17:[4, 30] Operation: 52-22=30 Exploring Operation: 52-4=48, Resulting Numbers: [22, 48] Generated Node #0,0,1: 17:[22, 48] Operation: 52-4=48 Exploring Operation: 22-4=18, Resulting Numbers: [52, 18] Generated Node #0,0,2: 17:[52, 18] Operation: 22-4=18 Exploring Operation: 52/4=13, Resulting Numbers: [22, 13] Generated Node #0,0,3: 17:[22, 13] Operation: 52/4=13 Moving to Node #0,3 Current State: 17:[41, 4, 71], Operations: ['93-22=71'] Exploring Operation: 71-41=30, Resulting Numbers: [4, 30] Generated Node #0,3,0: 17:[4, 30] Operation: 71-41=30 Exploring Operation: 71-4=67, Resulting Numbers: [41, 67] Generated Node #0,3,1: 17:[41, 67] Operation: 71-4=67 Exploring Operation: 41+4=45, Resulting Numbers: [71, 45] Generated Node #0,3,2: 17:[71, 45] Operation: 41+4=45 Exploring Operation: 41-4=37, Resulting Numbers: [71, 37] Generated Node #0,3,3: 17:[71, 37] Operation: 41-4=37 Moving to Node #0,1 Current State: 17:[93, 4, 19], Operations: ['41-22=19'] Exploring Operation: 19-4=15, Resulting Numbers: [93, 15] Generated Node #0,1,0: 17:[93, 15] Operation: 19-4=15 Exploring Operation: 93-19=74, Resulting Numbers: [4, 74] Generated Node #0,1,1: 17:[4, 74] Operation: 93-19=74 Exploring Operation: 93+4=97, Resulting Numbers: [19, 97] Generated Node #0,1,2: 17:[19, 97] Operation: 93+4=97 Exploring Operation: 93-4=89, Resulting Numbers: [19, 89] Generated Node #0,1,3: 17:[19, 89] Operation: 93-4=89 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[4, 74], Operations: ['41-22=19', '93-19=74'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,17 unequal: No Solution Exploring Operation: 4+74=78, Resulting Numbers: [78] 78,17 unequal: No Solution Exploring Operation: 4*74=296, Resulting Numbers: [296] 296,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 17:[19, 89], Operations: ['41-22=19', '93-4=89'] Exploring Operation: 19+89=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 19*89=1691, Resulting Numbers: [1691] 1691,17 unequal: No Solution Exploring Operation: 89-19=70, Resulting Numbers: [70] 70,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[93, 15], Operations: ['41-22=19', '19-4=15'] Exploring Operation: 93+15=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 93*15=1395, Resulting Numbers: [1395] 1395,17 unequal: No Solution Exploring Operation: 93-15=78, Resulting Numbers: [78] 78,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 17:[19, 97], Operations: ['41-22=19', '93+4=97'] Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,17 unequal: No Solution Exploring Operation: 19*97=1843, Resulting Numbers: [1843] 1843,17 unequal: No Solution Exploring Operation: 19+97=116, Resulting Numbers: [116] 116,17 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: 17:[41, 93, 18], Operations: ['22-4=18'] Exploring Operation: 93-18=75, Resulting Numbers: [41, 75] Generated Node #0,2,0: 17:[41, 75] Operation: 93-18=75 Exploring Operation: 41-18=23, Resulting Numbers: [93, 23] Generated Node #0,2,1: 17:[93, 23] Operation: 41-18=23 Exploring Operation: 93-41=52, Resulting Numbers: [18, 52] Generated Node #0,2,2: 17:[18, 52] Operation: 93-41=52 Exploring Operation: 41+93=134, Resulting Numbers: [18, 134] Generated Node #0,2,3: 17:[18, 134] Operation: 41+93=134 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 17:[18, 52], Operations: ['22-4=18', '93-41=52'] Exploring Operation: 18*52=936, Resulting Numbers: [936] 936,17 unequal: No Solution Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 18+52=70, Resulting Numbers: [70] 70,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 17:[41, 75], Operations: ['22-4=18', '93-18=75'] Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,17 unequal: No Solution Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,17 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 17:[93, 23], Operations: ['22-4=18', '41-18=23'] Exploring Operation: 93-23=70, Resulting Numbers: [70] 70,17 unequal: No Solution Exploring Operation: 93+23=116, Resulting Numbers: [116] 116,17 unequal: No Solution Exploring Operation: 93*23=2139, Resulting Numbers: [2139] 2139,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 17:[18, 134], Operations: ['22-4=18', '41+93=134'] Exploring Operation: 18+134=152, Resulting Numbers: [152] 152,17 unequal: No Solution Exploring Operation: 18*134=2412, Resulting Numbers: [2412] 2412,17 unequal: No Solution Exploring Operation: 134-18=116, Resulting Numbers: [116] 116,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 17:[22, 13], Operations: ['93-41=52', '52/4=13'] Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 22+13=35, Resulting Numbers: [35] 35,17 unequal: No Solution Exploring Operation: 22*13=286, Resulting Numbers: [286] 286,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[4, 30], Operations: ['93-41=52', '52-22=30'] Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,17 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,17 unequal: No Solution Moving to Node #0,3,0 Current State: 17:[4, 30], Operations: ['93-22=71', '71-41=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,17 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[22, 48], Operations: ['93-41=52', '52-4=48'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 22*48=1056, Resulting Numbers: [1056] 1056,17 unequal: No Solution Exploring Operation: 22+48=70, Resulting Numbers: [70] 70,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[52, 18], Operations: ['93-41=52', '22-4=18'] Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 52+18=70, Resulting Numbers: [70] 70,17 unequal: No Solution Exploring Operation: 52*18=936, Resulting Numbers: [936] 936,17 unequal: No Solution Moving to Node #0,3,1 Current State: 17:[41, 67], Operations: ['93-22=71', '71-4=67'] Exploring Operation: 41+67=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 41*67=2747, Resulting Numbers: [2747] 2747,17 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,17 unequal: No Solution Moving to Node #0,3,3 Current State: 17:[71, 37], Operations: ['93-22=71', '41-4=37'] Exploring Operation: 71*37=2627, Resulting Numbers: [2627] 2627,17 unequal: No Solution Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 71+37=108, Resulting Numbers: [108] 108,17 unequal: No Solution Moving to Node #0,3,2 Current State: 17:[71, 45], Operations: ['93-22=71', '41+4=45'] Exploring Operation: 71+45=116, Resulting Numbers: [116] 116,17 unequal: No Solution Exploring Operation: 71-45=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 71*45=3195, Resulting Numbers: [3195] 3195,17 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 42, 60, 59, 31 ]
12
[ "42+60=102", "59+31=90", "102-90=12" ]
Current State: 12:[42, 60, 59, 31], Operations: [] Exploring Operation: 42+60=102, Resulting Numbers: [59, 31, 102] Generated Node #2: [59, 31, 102] from Operation: 42+60=102 Current State: 12:[59, 31, 102], Operations: ['42+60=102'] Exploring Operation: 59+31=90, Resulting Numbers: [102, 90] Generated Node #3: [102, 90] from Operation: 59+31=90 Current State: 12:[102, 90], Operations: ['42+60=102', '59+31=90'] Exploring Operation: 102-90=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[42, 60, 59, 31], Operations: [] Exploring Operation: 60-42=18, Resulting Numbers: [59, 31, 18] Generated Node #0,0: 12:[59, 31, 18] Operation: 60-42=18 Exploring Operation: 60-59=1, Resulting Numbers: [42, 31, 1] Generated Node #0,1: 12:[42, 31, 1] Operation: 60-59=1 Moving to Node #0,1 Current State: 12:[42, 31, 1], Operations: ['60-59=1'] Exploring Operation: 42-31=11, Resulting Numbers: [1, 11] Generated Node #0,1,0: 12:[1, 11] Operation: 42-31=11 Exploring Operation: 42-1=41, Resulting Numbers: [31, 41] Generated Node #0,1,1: 12:[31, 41] Operation: 42-1=41 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[1, 11], Operations: ['60-59=1', '42-31=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[42, 60, 59, 31], Operations: [] Exploring Operation: 60-59=1, Resulting Numbers: [42, 31, 1] Generated Node #0,1: 12:[42, 31, 1] Operation: 60-59=1 Moving to Node #0,1 Current State: 12:[42, 31, 1], Operations: ['60-59=1'] Exploring Operation: 42-31=11, Resulting Numbers: [1, 11] Generated Node #0,1,0: 12:[1, 11] Operation: 42-31=11 Moving to Node #0,1,0 Current State: 12:[1, 11], Operations: ['60-59=1', '42-31=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 20, 23, 4, 35 ]
93
[ "23-20=3", "35-4=31", "3*31=93" ]
Current State: 93:[20, 23, 4, 35], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [4, 35, 3] Generated Node #2: [4, 35, 3] from Operation: 23-20=3 Current State: 93:[4, 35, 3], Operations: ['23-20=3'] Exploring Operation: 35-4=31, Resulting Numbers: [3, 31] Generated Node #3: [3, 31] from Operation: 35-4=31 Current State: 93:[3, 31], Operations: ['23-20=3', '35-4=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[20, 23, 4, 35], Operations: [] Exploring Operation: 20/4=5, Resulting Numbers: [23, 35, 5] Generated Node #0,0: 93:[23, 35, 5] Operation: 20/4=5 Exploring Operation: 23-20=3, Resulting Numbers: [4, 35, 3] Generated Node #0,1: 93:[4, 35, 3] Operation: 23-20=3 Exploring Operation: 20+23=43, Resulting Numbers: [4, 35, 43] Generated Node #0,2: 93:[4, 35, 43] Operation: 20+23=43 Exploring Operation: 23*4=92, Resulting Numbers: [20, 35, 92] Generated Node #0,3: 93:[20, 35, 92] Operation: 23*4=92 Moving to Node #0,1 Current State: 93:[4, 35, 3], Operations: ['23-20=3'] Exploring Operation: 4+35=39, Resulting Numbers: [3, 39] Generated Node #0,1,0: 93:[3, 39] Operation: 4+35=39 Exploring Operation: 4-3=1, Resulting Numbers: [35, 1] Generated Node #0,1,1: 93:[35, 1] Operation: 4-3=1 Exploring Operation: 35-4=31, Resulting Numbers: [3, 31] Generated Node #0,1,2: 93:[3, 31] Operation: 35-4=31 Exploring Operation: 35-3=32, Resulting Numbers: [4, 32] Generated Node #0,1,3: 93:[4, 32] Operation: 35-3=32 Moving to Node #0,0 Current State: 93:[23, 35, 5], Operations: ['20/4=5'] Exploring Operation: 35/5=7, Resulting Numbers: [23, 7] Generated Node #0,0,0: 93:[23, 7] Operation: 35/5=7 Exploring Operation: 35-23=12, Resulting Numbers: [5, 12] Generated Node #0,0,1: 93:[5, 12] Operation: 35-23=12 Exploring Operation: 23+5=28, Resulting Numbers: [35, 28] Generated Node #0,0,2: 93:[35, 28] Operation: 23+5=28 Exploring Operation: 35-5=30, Resulting Numbers: [23, 30] Generated Node #0,0,3: 93:[23, 30] Operation: 35-5=30 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 93:[35, 28], Operations: ['20/4=5', '23+5=28'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,93 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 93:[23, 30], Operations: ['20/4=5', '35-5=30'] Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,93 unequal: No Solution Exploring Operation: 23+30=53, Resulting Numbers: [53] 53,93 unequal: No Solution Exploring Operation: 23*30=690, Resulting Numbers: [690] 690,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[5, 12], Operations: ['20/4=5', '35-23=12'] Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,93 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,93 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[23, 7], Operations: ['20/4=5', '35/5=7'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,93 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 93:[20, 35, 92], Operations: ['23*4=92'] Exploring Operation: 20+92=112, Resulting Numbers: [35, 112] Generated Node #0,3,0: 93:[35, 112] Operation: 20+92=112 Exploring Operation: 35-20=15, Resulting Numbers: [92, 15] Generated Node #0,3,1: 93:[92, 15] Operation: 35-20=15 Exploring Operation: 92-20=72, Resulting Numbers: [35, 72] Generated Node #0,3,2: 93:[35, 72] Operation: 92-20=72 Exploring Operation: 20+35=55, Resulting Numbers: [92, 55] Generated Node #0,3,3: 93:[92, 55] Operation: 20+35=55 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 93:[92, 15], Operations: ['23*4=92', '35-20=15'] Exploring Operation: 92+15=107, Resulting Numbers: [107] 107,93 unequal: No Solution Exploring Operation: 92*15=1380, Resulting Numbers: [1380] 1380,93 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 93:[35, 112], Operations: ['23*4=92', '20+92=112'] Exploring Operation: 35*112=3920, Resulting Numbers: [3920] 3920,93 unequal: No Solution Exploring Operation: 112-35=77, Resulting Numbers: [77] 77,93 unequal: No Solution Exploring Operation: 35+112=147, Resulting Numbers: [147] 147,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 93:[35, 72], Operations: ['23*4=92', '92-20=72'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 35*72=2520, Resulting Numbers: [2520] 2520,93 unequal: No Solution Exploring Operation: 35+72=107, Resulting Numbers: [107] 107,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 93:[92, 55], Operations: ['23*4=92', '20+35=55'] Exploring Operation: 92+55=147, Resulting Numbers: [147] 147,93 unequal: No Solution Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 92*55=5060, Resulting Numbers: [5060] 5060,93 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: 93:[4, 35, 43], Operations: ['20+23=43'] Exploring Operation: 35-4=31, Resulting Numbers: [43, 31] Generated Node #0,2,0: 93:[43, 31] Operation: 35-4=31 Exploring Operation: 43-35=8, Resulting Numbers: [4, 8] Generated Node #0,2,1: 93:[4, 8] Operation: 43-35=8 Exploring Operation: 35+43=78, Resulting Numbers: [4, 78] Generated Node #0,2,2: 93:[4, 78] Operation: 35+43=78 Exploring Operation: 43-4=39, Resulting Numbers: [35, 39] Generated Node #0,2,3: 93:[35, 39] Operation: 43-4=39 Moving to Node #0,1,2 Current State: 93:[3, 31], Operations: ['23-20=3', '35-4=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[20, 23, 4, 35], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [4, 35, 3] Generated Node #0,1: 93:[4, 35, 3] Operation: 23-20=3 Moving to Node #0,1 Current State: 93:[4, 35, 3], Operations: ['23-20=3'] Exploring Operation: 35-4=31, Resulting Numbers: [3, 31] Generated Node #0,1,2: 93:[3, 31] Operation: 35-4=31 Moving to Node #0,1,2 Current State: 93:[3, 31], Operations: ['23-20=3', '35-4=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.957465
hs_4
sum_heuristic
[ 85, 72, 90, 82 ]
42
[ "85-82=3", "90/3=30", "72-30=42" ]
Current State: 42:[85, 72, 90, 82], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [72, 90, 3] Generated Node #2: [72, 90, 3] from Operation: 85-82=3 Current State: 42:[72, 90, 3], Operations: ['85-82=3'] Exploring Operation: 90/3=30, Resulting Numbers: [72, 30] Generated Node #3: [72, 30] from Operation: 90/3=30 Current State: 42:[72, 30], Operations: ['85-82=3', '90/3=30'] Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[85, 72, 90, 82], Operations: [] Exploring Operation: 85-72=13, Resulting Numbers: [90, 82, 13] Generated Node #0,0: 42:[90, 82, 13] Operation: 85-72=13 Exploring Operation: 85-82=3, Resulting Numbers: [72, 90, 3] Generated Node #0,1: 42:[72, 90, 3] Operation: 85-82=3 Exploring Operation: 90-85=5, Resulting Numbers: [72, 82, 5] Generated Node #0,2: 42:[72, 82, 5] Operation: 90-85=5 Exploring Operation: 90-82=8, Resulting Numbers: [85, 72, 8] Generated Node #0,3: 42:[85, 72, 8] Operation: 90-82=8 Exploring Operation: 90-72=18, Resulting Numbers: [85, 82, 18] Generated Node #0,4: 42:[85, 82, 18] Operation: 90-72=18 Moving to Node #0,2 Current State: 42:[72, 82, 5], Operations: ['90-85=5'] Exploring Operation: 82-72=10, Resulting Numbers: [5, 10] Generated Node #0,2,0: 42:[5, 10] Operation: 82-72=10 Exploring Operation: 82+5=87, Resulting Numbers: [72, 87] Generated Node #0,2,1: 42:[72, 87] Operation: 82+5=87 Exploring Operation: 72+5=77, Resulting Numbers: [82, 77] Generated Node #0,2,2: 42:[82, 77] Operation: 72+5=77 Exploring Operation: 82-5=77, Resulting Numbers: [72, 77] Generated Node #0,2,3: 42:[72, 77] Operation: 82-5=77 Exploring Operation: 72-5=67, Resulting Numbers: [82, 67] Generated Node #0,2,4: 42:[82, 67] Operation: 72-5=67 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[5, 10], Operations: ['90-85=5', '82-72=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,42 unequal: No Solution No 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: 42:[72, 77], Operations: ['90-85=5', '82-5=77'] Exploring Operation: 72*77=5544, Resulting Numbers: [5544] 5544,42 unequal: No Solution Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 72+77=149, Resulting Numbers: [149] 149,42 unequal: No Solution No 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: 42:[82, 67], Operations: ['90-85=5', '72-5=67'] Exploring Operation: 82+67=149, Resulting Numbers: [149] 149,42 unequal: No Solution Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 82*67=5494, Resulting Numbers: [5494] 5494,42 unequal: No Solution No 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: 42:[72, 87], Operations: ['90-85=5', '82+5=87'] Exploring Operation: 72*87=6264, Resulting Numbers: [6264] 6264,42 unequal: No Solution Exploring Operation: 87-72=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 72+87=159, Resulting Numbers: [159] 159,42 unequal: No Solution No 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: 42:[82, 77], Operations: ['90-85=5', '72+5=77'] Exploring Operation: 82+77=159, Resulting Numbers: [159] 159,42 unequal: No Solution Exploring Operation: 82*77=6314, Resulting Numbers: [6314] 6314,42 unequal: No Solution Exploring Operation: 82-77=5, Resulting Numbers: [5] 5,42 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: 42:[85, 72, 8], Operations: ['90-82=8'] Exploring Operation: 85-8=77, Resulting Numbers: [72, 77] Generated Node #0,3,0: 42:[72, 77] Operation: 85-8=77 Exploring Operation: 85-72=13, Resulting Numbers: [8, 13] Generated Node #0,3,1: 42:[8, 13] Operation: 85-72=13 Exploring Operation: 72-8=64, Resulting Numbers: [85, 64] Generated Node #0,3,2: 42:[85, 64] Operation: 72-8=64 Exploring Operation: 85+8=93, Resulting Numbers: [72, 93] Generated Node #0,3,3: 42:[72, 93] Operation: 85+8=93 Exploring Operation: 72/8=9, Resulting Numbers: [85, 9] Generated Node #0,3,4: 42:[85, 9] Operation: 72/8=9 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 42:[8, 13], Operations: ['90-82=8', '85-72=13'] Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,42 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,42 unequal: No Solution No 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: 42:[85, 9], Operations: ['90-82=8', '72/8=9'] Exploring Operation: 85+9=94, Resulting Numbers: [94] 94,42 unequal: No Solution Exploring Operation: 85*9=765, Resulting Numbers: [765] 765,42 unequal: No Solution Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,42 unequal: No Solution No 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: 42:[72, 77], Operations: ['90-82=8', '85-8=77'] Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 72*77=5544, Resulting Numbers: [5544] 5544,42 unequal: No Solution Exploring Operation: 72+77=149, Resulting Numbers: [149] 149,42 unequal: No Solution No 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: 42:[85, 64], Operations: ['90-82=8', '72-8=64'] Exploring Operation: 85*64=5440, Resulting Numbers: [5440] 5440,42 unequal: No Solution Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 85+64=149, Resulting Numbers: [149] 149,42 unequal: No Solution No 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: 42:[72, 93], Operations: ['90-82=8', '85+8=93'] Exploring Operation: 72+93=165, Resulting Numbers: [165] 165,42 unequal: No Solution Exploring Operation: 93-72=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 72*93=6696, Resulting Numbers: [6696] 6696,42 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: 42:[72, 90, 3], Operations: ['85-82=3'] Exploring Operation: 72/3=24, Resulting Numbers: [90, 24] Generated Node #0,1,0: 42:[90, 24] Operation: 72/3=24 Exploring Operation: 72-3=69, Resulting Numbers: [90, 69] Generated Node #0,1,1: 42:[90, 69] Operation: 72-3=69 Exploring Operation: 90-72=18, Resulting Numbers: [3, 18] Generated Node #0,1,2: 42:[3, 18] Operation: 90-72=18 Exploring Operation: 90/3=30, Resulting Numbers: [72, 30] Generated Node #0,1,3: 42:[72, 30] Operation: 90/3=30 Exploring Operation: 90-3=87, Resulting Numbers: [72, 87] Generated Node #0,1,4: 42:[72, 87] Operation: 90-3=87 Moving to Node #0,4 Current State: 42:[85, 82, 18], Operations: ['90-72=18'] Exploring Operation: 85-82=3, Resulting Numbers: [18, 3] Generated Node #0,4,0: 42:[18, 3] Operation: 85-82=3 Exploring Operation: 82-18=64, Resulting Numbers: [85, 64] Generated Node #0,4,1: 42:[85, 64] Operation: 82-18=64 Exploring Operation: 82+18=100, Resulting Numbers: [85, 100] Generated Node #0,4,2: 42:[85, 100] Operation: 82+18=100 Exploring Operation: 85+18=103, Resulting Numbers: [82, 103] Generated Node #0,4,3: 42:[82, 103] Operation: 85+18=103 Exploring Operation: 85-18=67, Resulting Numbers: [82, 67] Generated Node #0,4,4: 42:[82, 67] Operation: 85-18=67 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 42:[18, 3], Operations: ['90-72=18', '85-82=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,42 unequal: No Solution No 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: 42:[85, 64], Operations: ['90-72=18', '82-18=64'] Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 85+64=149, Resulting Numbers: [149] 149,42 unequal: No Solution Exploring Operation: 85*64=5440, Resulting Numbers: [5440] 5440,42 unequal: No Solution No 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: 42:[82, 67], Operations: ['90-72=18', '85-18=67'] Exploring Operation: 82+67=149, Resulting Numbers: [149] 149,42 unequal: No Solution Exploring Operation: 82*67=5494, Resulting Numbers: [5494] 5494,42 unequal: No Solution Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,42 unequal: No Solution No 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: 42:[85, 100], Operations: ['90-72=18', '82+18=100'] Exploring Operation: 85+100=185, Resulting Numbers: [185] 185,42 unequal: No Solution Exploring Operation: 85*100=8500, Resulting Numbers: [8500] 8500,42 unequal: No Solution Exploring Operation: 100-85=15, Resulting Numbers: [15] 15,42 unequal: No Solution No 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: 42:[82, 103], Operations: ['90-72=18', '85+18=103'] Exploring Operation: 82+103=185, Resulting Numbers: [185] 185,42 unequal: No Solution Exploring Operation: 103-82=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 82*103=8446, Resulting Numbers: [8446] 8446,42 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: 42:[90, 82, 13], Operations: ['85-72=13'] Exploring Operation: 90-13=77, Resulting Numbers: [82, 77] Generated Node #0,0,0: 42:[82, 77] Operation: 90-13=77 Exploring Operation: 90-82=8, Resulting Numbers: [13, 8] Generated Node #0,0,1: 42:[13, 8] Operation: 90-82=8 Exploring Operation: 82+13=95, Resulting Numbers: [90, 95] Generated Node #0,0,2: 42:[90, 95] Operation: 82+13=95 Exploring Operation: 90+13=103, Resulting Numbers: [82, 103] Generated Node #0,0,3: 42:[82, 103] Operation: 90+13=103 Exploring Operation: 82-13=69, Resulting Numbers: [90, 69] Generated Node #0,0,4: 42:[90, 69] Operation: 82-13=69 Moving to Node #0,0,1 Current State: 42:[13, 8], Operations: ['85-72=13', '90-82=8'] Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,42 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[3, 18], Operations: ['85-82=3', '90-72=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,42 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,1,3 Current State: 42:[72, 30], Operations: ['85-82=3', '90/3=30'] Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[85, 72, 90, 82], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [72, 90, 3] Generated Node #0,1: 42:[72, 90, 3] Operation: 85-82=3 Moving to Node #0,1 Current State: 42:[72, 90, 3], Operations: ['85-82=3'] Exploring Operation: 90/3=30, Resulting Numbers: [72, 30] Generated Node #0,1,3: 42:[72, 30] Operation: 90/3=30 Moving to Node #0,1,3 Current State: 42:[72, 30], Operations: ['85-82=3', '90/3=30'] Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.922743
hs_5
sum_heuristic
[ 3, 20, 43, 95 ]
66
[ "43+95=138", "138/3=46", "20+46=66" ]
Current State: 66:[3, 20, 43, 95], Operations: [] Exploring Operation: 43+95=138, Resulting Numbers: [3, 20, 138] Generated Node #2: [3, 20, 138] from Operation: 43+95=138 Current State: 66:[3, 20, 138], Operations: ['43+95=138'] Exploring Operation: 138/3=46, Resulting Numbers: [20, 46] Generated Node #3: [20, 46] from Operation: 138/3=46 Current State: 66:[20, 46], Operations: ['43+95=138', '138/3=46'] Exploring Operation: 20+46=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[3, 20, 43, 95], Operations: [] Exploring Operation: 95-20=75, Resulting Numbers: [3, 43, 75] Generated Node #0,0: 66:[3, 43, 75] Operation: 95-20=75 Exploring Operation: 43-20=23, Resulting Numbers: [3, 95, 23] Generated Node #0,1: 66:[3, 95, 23] Operation: 43-20=23 Exploring Operation: 95-43=52, Resulting Numbers: [3, 20, 52] Generated Node #0,2: 66:[3, 20, 52] Operation: 95-43=52 Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[3, 20, 52], Operations: ['95-43=52'] Exploring Operation: 20+52=72, Resulting Numbers: [3, 72] Generated Node #0,2,0: 66:[3, 72] Operation: 20+52=72 Exploring Operation: 3+52=55, Resulting Numbers: [20, 55] Generated Node #0,2,1: 66:[20, 55] Operation: 3+52=55 Exploring Operation: 52-20=32, Resulting Numbers: [3, 32] Generated Node #0,2,2: 66:[3, 32] Operation: 52-20=32 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 66:[3, 32], Operations: ['95-43=52', '52-20=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,66 unequal: No Solution Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,66 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,66 unequal: No Solution No 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: 66:[3, 72], Operations: ['95-43=52', '20+52=72'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,66 unequal: No Solution Exploring Operation: 3+72=75, Resulting Numbers: [75] 75,66 unequal: No Solution No 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: 66:[20, 55], Operations: ['95-43=52', '3+52=55'] Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,66 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,66 unequal: No Solution Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,66 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: 66:[3, 43, 75], Operations: ['95-20=75'] Exploring Operation: 43-3=40, Resulting Numbers: [75, 40] Generated Node #0,0,0: 66:[75, 40] Operation: 43-3=40 Exploring Operation: 75-43=32, Resulting Numbers: [3, 32] Generated Node #0,0,1: 66:[3, 32] Operation: 75-43=32 Exploring Operation: 75/3=25, Resulting Numbers: [43, 25] Generated Node #0,0,2: 66:[43, 25] Operation: 75/3=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[3, 32], Operations: ['95-20=75', '75-43=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,66 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,66 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,66 unequal: No Solution No 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: 66:[43, 25], Operations: ['95-20=75', '75/3=25'] Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,66 unequal: No Solution Exploring Operation: 43+25=68, Resulting Numbers: [68] 68,66 unequal: No Solution Exploring Operation: 43*25=1075, Resulting Numbers: [1075] 1075,66 unequal: No Solution No 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: 66:[75, 40], Operations: ['95-20=75', '43-3=40'] Exploring Operation: 75+40=115, Resulting Numbers: [115] 115,66 unequal: No Solution Exploring Operation: 75*40=3000, Resulting Numbers: [3000] 3000,66 unequal: No Solution Exploring Operation: 75-40=35, Resulting Numbers: [35] 35,66 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: 66:[3, 95, 23], Operations: ['43-20=23'] Exploring Operation: 95-3=92, Resulting Numbers: [23, 92] Generated Node #0,1,0: 66:[23, 92] Operation: 95-3=92 Exploring Operation: 95-23=72, Resulting Numbers: [3, 72] Generated Node #0,1,1: 66:[3, 72] Operation: 95-23=72 Exploring Operation: 23-3=20, Resulting Numbers: [95, 20] Generated Node #0,1,2: 66:[95, 20] Operation: 23-3=20 Moving to Node #0,1,1 Current State: 66:[3, 72], Operations: ['43-20=23', '95-23=72'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 3+72=75, Resulting Numbers: [75] 75,66 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,66 unequal: No Solution Moving to Node #0,1,0 Current State: 66:[23, 92], Operations: ['43-20=23', '95-3=92'] Exploring Operation: 92/23=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 92-23=69, Resulting Numbers: [69] 69,66 unequal: No Solution Exploring Operation: 23+92=115, Resulting Numbers: [115] 115,66 unequal: No Solution Moving to Node #0,1,2 Current State: 66:[95, 20], Operations: ['43-20=23', '23-3=20'] Exploring Operation: 95+20=115, Resulting Numbers: [115] 115,66 unequal: No Solution Exploring Operation: 95-20=75, Resulting Numbers: [75] 75,66 unequal: No Solution Exploring Operation: 95*20=1900, Resulting Numbers: [1900] 1900,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 7, 5, 30, 60 ]
65
[ "7*5=35", "60-30=30", "35+30=65" ]
Current State: 65:[7, 5, 30, 60], Operations: [] Exploring Operation: 7*5=35, Resulting Numbers: [30, 60, 35] Generated Node #2: [30, 60, 35] from Operation: 7*5=35 Current State: 65:[30, 60, 35], Operations: ['7*5=35'] Exploring Operation: 60-30=30, Resulting Numbers: [35, 30] Generated Node #3: [35, 30] from Operation: 60-30=30 Current State: 65:[35, 30], Operations: ['7*5=35', '60-30=30'] Exploring Operation: 35+30=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[7, 5, 30, 60], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [7, 5, 2] Generated Node #0,0: 65:[7, 5, 2] Operation: 60/30=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[7, 5, 2], Operations: ['60/30=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 65:[5, 5] Operation: 7-2=5 Moving to Node #0,0,0 Current State: 65:[5, 5], Operations: ['60/30=2', '7-2=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 14, 86, 79, 2 ]
73
[ "86-2=84", "84/14=6", "79-6=73" ]
Current State: 73:[14, 86, 79, 2], Operations: [] Exploring Operation: 86-2=84, Resulting Numbers: [14, 79, 84] Generated Node #2: [14, 79, 84] from Operation: 86-2=84 Current State: 73:[14, 79, 84], Operations: ['86-2=84'] Exploring Operation: 84/14=6, Resulting Numbers: [79, 6] Generated Node #3: [79, 6] from Operation: 84/14=6 Current State: 73:[79, 6], Operations: ['86-2=84', '84/14=6'] Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[14, 86, 79, 2], Operations: [] Exploring Operation: 14*2=28, Resulting Numbers: [86, 79, 28] Generated Node #0,0: 73:[86, 79, 28] Operation: 14*2=28 Exploring Operation: 14+2=16, Resulting Numbers: [86, 79, 16] Generated Node #0,1: 73:[86, 79, 16] Operation: 14+2=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[86, 79, 28], Operations: ['14*2=28'] Exploring Operation: 79-28=51, Resulting Numbers: [86, 51] Generated Node #0,0,0: 73:[86, 51] Operation: 79-28=51 Exploring Operation: 86-28=58, Resulting Numbers: [79, 58] Generated Node #0,0,1: 73:[79, 58] Operation: 86-28=58 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[79, 58], Operations: ['14*2=28', '86-28=58'] Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 79+58=137, Resulting Numbers: [137] 137,73 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 #0,0,0 Current State: 73:[86, 51], Operations: ['14*2=28', '79-28=51'] Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 86+51=137, Resulting Numbers: [137] 137,73 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:[86, 79, 16], Operations: ['14+2=16'] Exploring Operation: 86-16=70, Resulting Numbers: [79, 70] Generated Node #0,1,0: 73:[79, 70] Operation: 86-16=70 Exploring Operation: 79-16=63, Resulting Numbers: [86, 63] Generated Node #0,1,1: 73:[86, 63] Operation: 79-16=63 Moving to Node #0,1,0 Current State: 73:[79, 70], Operations: ['14+2=16', '86-16=70'] Exploring Operation: 79-70=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 79+70=149, Resulting Numbers: [149] 149,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[86, 63], Operations: ['14+2=16', '79-16=63'] Exploring Operation: 86+63=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 86-63=23, Resulting Numbers: [23] 23,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 68, 83, 79, 96 ]
32
[ "83-68=15", "96-79=17", "15+17=32" ]
Current State: 32:[68, 83, 79, 96], Operations: [] Exploring Operation: 83-68=15, Resulting Numbers: [79, 96, 15] Generated Node #2: [79, 96, 15] from Operation: 83-68=15 Current State: 32:[79, 96, 15], Operations: ['83-68=15'] Exploring Operation: 96-79=17, Resulting Numbers: [15, 17] Generated Node #3: [15, 17] from Operation: 96-79=17 Current State: 32:[15, 17], Operations: ['83-68=15', '96-79=17'] Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[68, 83, 79, 96], Operations: [] Exploring Operation: 96-68=28, Resulting Numbers: [83, 79, 28] Generated Node #0,0: 32:[83, 79, 28] Operation: 96-68=28 Exploring Operation: 96-83=13, Resulting Numbers: [68, 79, 13] Generated Node #0,1: 32:[68, 79, 13] Operation: 96-83=13 Exploring Operation: 96-79=17, Resulting Numbers: [68, 83, 17] Generated Node #0,2: 32:[68, 83, 17] Operation: 96-79=17 Exploring Operation: 83-79=4, Resulting Numbers: [68, 96, 4] Generated Node #0,3: 32:[68, 96, 4] Operation: 83-79=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[68, 79, 13], Operations: ['96-83=13'] Exploring Operation: 79-13=66, Resulting Numbers: [68, 66] Generated Node #0,1,0: 32:[68, 66] Operation: 79-13=66 Exploring Operation: 68+13=81, Resulting Numbers: [79, 81] Generated Node #0,1,1: 32:[79, 81] Operation: 68+13=81 Exploring Operation: 68-13=55, Resulting Numbers: [79, 55] Generated Node #0,1,2: 32:[79, 55] Operation: 68-13=55 Exploring Operation: 79-68=11, Resulting Numbers: [13, 11] Generated Node #0,1,3: 32:[13, 11] Operation: 79-68=11 Moving to Node #0,1,3 Current State: 32:[13, 11], Operations: ['96-83=13', '79-68=11'] Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,32 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,32 unequal: No Solution Moving to Node #0,1,2 Current State: 32:[79, 55], Operations: ['96-83=13', '68-13=55'] Exploring Operation: 79*55=4345, Resulting Numbers: [4345] 4345,32 unequal: No Solution Exploring Operation: 79-55=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 79+55=134, Resulting Numbers: [134] 134,32 unequal: No Solution Moving to Node #0,1,0 Current State: 32:[68, 66], Operations: ['96-83=13', '79-13=66'] Exploring Operation: 68*66=4488, Resulting Numbers: [4488] 4488,32 unequal: No Solution Exploring Operation: 68-66=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 68+66=134, Resulting Numbers: [134] 134,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[79, 81], Operations: ['96-83=13', '68+13=81'] Exploring Operation: 79+81=160, Resulting Numbers: [160] 160,32 unequal: No Solution Exploring Operation: 79*81=6399, Resulting Numbers: [6399] 6399,32 unequal: No Solution Exploring Operation: 81-79=2, Resulting Numbers: [2] 2,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[68, 83, 17], Operations: ['96-79=17'] Exploring Operation: 83-17=66, Resulting Numbers: [68, 66] Generated Node #0,2,0: 32:[68, 66] Operation: 83-17=66 Exploring Operation: 68-17=51, Resulting Numbers: [83, 51] Generated Node #0,2,1: 32:[83, 51] Operation: 68-17=51 Exploring Operation: 83-68=15, Resulting Numbers: [17, 15] Generated Node #0,2,2: 32:[17, 15] Operation: 83-68=15 Exploring Operation: 68/17=4, Resulting Numbers: [83, 4] Generated Node #0,2,3: 32:[83, 4] Operation: 68/17=4 Moving to Node #0,2,2 Current State: 32:[17, 15], Operations: ['96-79=17', '83-68=15'] Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[68, 83, 79, 96], Operations: [] Exploring Operation: 96-79=17, Resulting Numbers: [68, 83, 17] Generated Node #0,2: 32:[68, 83, 17] Operation: 96-79=17 Moving to Node #0,2 Current State: 32:[68, 83, 17], Operations: ['96-79=17'] Exploring Operation: 83-68=15, Resulting Numbers: [17, 15] Generated Node #0,2,2: 32:[17, 15] Operation: 83-68=15 Moving to Node #0,2,2 Current State: 32:[17, 15], Operations: ['96-79=17', '83-68=15'] Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 75, 20, 30, 45 ]
12
[ "75+45=120", "30-20=10", "120/10=12" ]
Current State: 12:[75, 20, 30, 45], Operations: [] Exploring Operation: 75+45=120, Resulting Numbers: [20, 30, 120] Generated Node #2: [20, 30, 120] from Operation: 75+45=120 Current State: 12:[20, 30, 120], Operations: ['75+45=120'] Exploring Operation: 30-20=10, Resulting Numbers: [120, 10] Generated Node #3: [120, 10] from Operation: 30-20=10 Current State: 12:[120, 10], Operations: ['75+45=120', '30-20=10'] Exploring Operation: 120/10=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[75, 20, 30, 45], Operations: [] Exploring Operation: 75-20=55, Resulting Numbers: [30, 45, 55] Generated Node #0,0: 12:[30, 45, 55] Operation: 75-20=55 Exploring Operation: 75-30=45, Resulting Numbers: [20, 45, 45] Generated Node #0,1: 12:[20, 45, 45] Operation: 75-30=45 Exploring Operation: 75-45=30, Resulting Numbers: [20, 30, 30] Generated Node #0,2: 12:[20, 30, 30] Operation: 75-45=30 Exploring Operation: 45-30=15, Resulting Numbers: [75, 20, 15] Generated Node #0,3: 12:[75, 20, 15] Operation: 45-30=15 Moving to Node #0,2 Current State: 12:[20, 30, 30], Operations: ['75-45=30'] Exploring Operation: 30/30=1, Resulting Numbers: [20, 1] Generated Node #0,2,0: 12:[20, 1] Operation: 30/30=1 Exploring Operation: 30-30=0, Resulting Numbers: [20, 0] Generated Node #0,2,1: 12:[20, 0] Operation: 30-30=0 Exploring Operation: 30-20=10, Resulting Numbers: [30, 10] Generated Node #0,2,2: 12:[30, 10] Operation: 30-20=10 Exploring Operation: 30-20=10, Resulting Numbers: [30, 10] Generated Node #0,2,3: 12:[30, 10] Operation: 30-20=10 Moving to Node #0,3 Current State: 12:[75, 20, 15], Operations: ['45-30=15'] Exploring Operation: 75-20=55, Resulting Numbers: [15, 55] Generated Node #0,3,0: 12:[15, 55] Operation: 75-20=55 Exploring Operation: 75-15=60, Resulting Numbers: [20, 60] Generated Node #0,3,1: 12:[20, 60] Operation: 75-15=60 Exploring Operation: 20-15=5, Resulting Numbers: [75, 5] Generated Node #0,3,2: 12:[75, 5] Operation: 20-15=5 Exploring Operation: 75/15=5, Resulting Numbers: [20, 5] Generated Node #0,3,3: 12:[20, 5] Operation: 75/15=5 Moving to Node #0,1 Current State: 12:[20, 45, 45], Operations: ['75-30=45'] Exploring Operation: 45-45=0, Resulting Numbers: [20, 0] Generated Node #0,1,0: 12:[20, 0] Operation: 45-45=0 Exploring Operation: 45-20=25, Resulting Numbers: [45, 25] Generated Node #0,1,1: 12:[45, 25] Operation: 45-20=25 Exploring Operation: 45-20=25, Resulting Numbers: [45, 25] Generated Node #0,1,2: 12:[45, 25] Operation: 45-20=25 Exploring Operation: 45/45=1, Resulting Numbers: [20, 1] Generated Node #0,1,3: 12:[20, 1] Operation: 45/45=1 Moving to Node #0,0 Current State: 12:[30, 45, 55], Operations: ['75-20=55'] Exploring Operation: 45-30=15, Resulting Numbers: [55, 15] Generated Node #0,0,0: 12:[55, 15] Operation: 45-30=15 Exploring Operation: 55-45=10, Resulting Numbers: [30, 10] Generated Node #0,0,1: 12:[30, 10] Operation: 55-45=10 Exploring Operation: 55-30=25, Resulting Numbers: [45, 25] Generated Node #0,0,2: 12:[45, 25] Operation: 55-30=25 Exploring Operation: 30+45=75, Resulting Numbers: [55, 75] Generated Node #0,0,3: 12:[55, 75] Operation: 30+45=75 Moving to Node #0,2,0 Current State: 12:[20, 1], Operations: ['75-45=30', '30/30=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,12 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[20, 5], Operations: ['45-30=15', '75/15=5'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,12 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[20, 1], Operations: ['75-30=45', '45/45=1'] Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[20, 0], Operations: ['75-45=30', '30-30=0'] Exploring Operation: 20-0=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 20*0=0, Resulting Numbers: [0] 0,12 unequal: No Solution Exploring Operation: 20+0=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[20, 0], Operations: ['75-30=45', '45-45=0'] Exploring Operation: 20-0=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 20+0=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 20*0=0, Resulting Numbers: [0] 0,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[30, 10], Operations: ['75-45=30', '30-20=10'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,12 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[30, 10], Operations: ['75-20=55', '55-45=10'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[30, 10], Operations: ['75-45=30', '30-20=10'] Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,12 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[55, 15], Operations: ['75-20=55', '45-30=15'] Exploring Operation: 55+15=70, Resulting Numbers: [70] 70,12 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 55*15=825, Resulting Numbers: [825] 825,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[45, 25], Operations: ['75-30=45', '45-20=25'] Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,12 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[45, 25], Operations: ['75-30=45', '45-20=25'] Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,12 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[45, 25], Operations: ['75-20=55', '55-30=25'] Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,12 unequal: No Solution Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[15, 55], Operations: ['45-30=15', '75-20=55'] Exploring Operation: 15*55=825, Resulting Numbers: [825] 825,12 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 15+55=70, Resulting Numbers: [70] 70,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[20, 60], Operations: ['45-30=15', '75-15=60'] Exploring Operation: 20+60=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 60/20=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 20*60=1200, Resulting Numbers: [1200] 1200,12 unequal: No Solution Exploring Operation: 60-20=40, Resulting Numbers: [40] 40,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[75, 5], Operations: ['45-30=15', '20-15=5'] Exploring Operation: 75-5=70, Resulting Numbers: [70] 70,12 unequal: No Solution Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,12 unequal: No Solution Exploring Operation: 75*5=375, Resulting Numbers: [375] 375,12 unequal: No Solution Moving to Node #0,0,3 Current State: 12:[55, 75], Operations: ['75-20=55', '30+45=75'] Exploring Operation: 75-55=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 55*75=4125, Resulting Numbers: [4125] 4125,12 unequal: No Solution Exploring Operation: 55+75=130, Resulting Numbers: [130] 130,12 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 3, 68, 43, 98 ]
33
[ "98-68=30", "30/3=10", "43-10=33" ]
Current State: 33:[3, 68, 43, 98], Operations: [] Exploring Operation: 98-68=30, Resulting Numbers: [3, 43, 30] Generated Node #2: [3, 43, 30] from Operation: 98-68=30 Current State: 33:[3, 43, 30], Operations: ['98-68=30'] Exploring Operation: 30/3=10, Resulting Numbers: [43, 10] Generated Node #3: [43, 10] from Operation: 30/3=10 Current State: 33:[43, 10], Operations: ['98-68=30', '30/3=10'] Exploring Operation: 43-10=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[3, 68, 43, 98], Operations: [] Exploring Operation: 98-43=55, Resulting Numbers: [3, 68, 55] Generated Node #0,0: 33:[3, 68, 55] Operation: 98-43=55 Exploring Operation: 68-43=25, Resulting Numbers: [3, 98, 25] Generated Node #0,1: 33:[3, 98, 25] Operation: 68-43=25 Exploring Operation: 98-68=30, Resulting Numbers: [3, 43, 30] Generated Node #0,2: 33:[3, 43, 30] Operation: 98-68=30 Moving to Node #0,2 Current State: 33:[3, 43, 30], Operations: ['98-68=30'] Exploring Operation: 43-30=13, Resulting Numbers: [3, 13] Generated Node #0,2,0: 33:[3, 13] Operation: 43-30=13 Exploring Operation: 43-3=40, Resulting Numbers: [30, 40] Generated Node #0,2,1: 33:[30, 40] Operation: 43-3=40 Exploring Operation: 3+30=33, Resulting Numbers: [43, 33] Generated Node #0,2,2: 33:[43, 33] Operation: 3+30=33 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 33:[3, 13], Operations: ['98-68=30', '43-30=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,33 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:[30, 40], Operations: ['98-68=30', '43-3=40'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,33 unequal: No Solution Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,33 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:[43, 33], Operations: ['98-68=30', '3+30=33'] Exploring Operation: 43*33=1419, Resulting Numbers: [1419] 1419,33 unequal: No Solution Exploring Operation: 43+33=76, Resulting Numbers: [76] 76,33 unequal: No Solution Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,33 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:[3, 68, 55], Operations: ['98-43=55'] Exploring Operation: 68-3=65, Resulting Numbers: [55, 65] Generated Node #0,0,0: 33:[55, 65] Operation: 68-3=65 Exploring Operation: 55-3=52, Resulting Numbers: [68, 52] Generated Node #0,0,1: 33:[68, 52] Operation: 55-3=52 Exploring Operation: 68-55=13, Resulting Numbers: [3, 13] Generated Node #0,0,2: 33:[3, 13] Operation: 68-55=13 Moving to Node #0,1 Current State: 33:[3, 98, 25], Operations: ['68-43=25'] Exploring Operation: 98-25=73, Resulting Numbers: [3, 73] Generated Node #0,1,0: 33:[3, 73] Operation: 98-25=73 Exploring Operation: 3+25=28, Resulting Numbers: [98, 28] Generated Node #0,1,1: 33:[98, 28] Operation: 3+25=28 Exploring Operation: 98-3=95, Resulting Numbers: [25, 95] Generated Node #0,1,2: 33:[25, 95] Operation: 98-3=95 Moving to Node #0,0,2 Current State: 33:[3, 13], Operations: ['98-43=55', '68-55=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,33 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[3, 73], Operations: ['68-43=25', '98-25=73'] Exploring Operation: 3*73=219, Resulting Numbers: [219] 219,33 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,33 unequal: No Solution Exploring Operation: 3+73=76, Resulting Numbers: [76] 76,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[68, 52], Operations: ['98-43=55', '55-3=52'] Exploring Operation: 68-52=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 68+52=120, Resulting Numbers: [120] 120,33 unequal: No Solution Exploring Operation: 68*52=3536, Resulting Numbers: [3536] 3536,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[55, 65], Operations: ['98-43=55', '68-3=65'] Exploring Operation: 55*65=3575, Resulting Numbers: [3575] 3575,33 unequal: No Solution Exploring Operation: 65-55=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 55+65=120, Resulting Numbers: [120] 120,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[25, 95], Operations: ['68-43=25', '98-3=95'] Exploring Operation: 95-25=70, Resulting Numbers: [70] 70,33 unequal: No Solution Exploring Operation: 25*95=2375, Resulting Numbers: [2375] 2375,33 unequal: No Solution Exploring Operation: 25+95=120, Resulting Numbers: [120] 120,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[98, 28], Operations: ['68-43=25', '3+25=28'] Exploring Operation: 98-28=70, Resulting Numbers: [70] 70,33 unequal: No Solution Exploring Operation: 98+28=126, Resulting Numbers: [126] 126,33 unequal: No Solution Exploring Operation: 98*28=2744, Resulting Numbers: [2744] 2744,33 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 21, 80, 40, 54 ]
48
[ "80/40=2", "54/2=27", "21+27=48" ]
Current State: 48:[21, 80, 40, 54], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [21, 54, 2] Generated Node #2: [21, 54, 2] from Operation: 80/40=2 Current State: 48:[21, 54, 2], Operations: ['80/40=2'] Exploring Operation: 54/2=27, Resulting Numbers: [21, 27] Generated Node #3: [21, 27] from Operation: 54/2=27 Current State: 48:[21, 27], Operations: ['80/40=2', '54/2=27'] Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[21, 80, 40, 54], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [21, 54, 2] Generated Node #0,0: 48:[21, 54, 2] Operation: 80/40=2 Exploring Operation: 80-40=40, Resulting Numbers: [21, 54, 40] Generated Node #0,1: 48:[21, 54, 40] Operation: 80-40=40 Exploring Operation: 80-54=26, Resulting Numbers: [21, 40, 26] Generated Node #0,2: 48:[21, 40, 26] Operation: 80-54=26 Moving to Node #0,0 Current State: 48:[21, 54, 2], Operations: ['80/40=2'] Exploring Operation: 54-2=52, Resulting Numbers: [21, 52] Generated Node #0,0,0: 48:[21, 52] Operation: 54-2=52 Exploring Operation: 54/2=27, Resulting Numbers: [21, 27] Generated Node #0,0,1: 48:[21, 27] Operation: 54/2=27 Exploring Operation: 21+2=23, Resulting Numbers: [54, 23] Generated Node #0,0,2: 48:[54, 23] Operation: 21+2=23 Moving to Node #0,2 Current State: 48:[21, 40, 26], Operations: ['80-54=26'] Exploring Operation: 40-26=14, Resulting Numbers: [21, 14] Generated Node #0,2,0: 48:[21, 14] Operation: 40-26=14 Exploring Operation: 40-21=19, Resulting Numbers: [26, 19] Generated Node #0,2,1: 48:[26, 19] Operation: 40-21=19 Exploring Operation: 21+26=47, Resulting Numbers: [40, 47] Generated Node #0,2,2: 48:[40, 47] Operation: 21+26=47 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[21, 14], Operations: ['80-54=26', '40-26=14'] Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,48 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[26, 19], Operations: ['80-54=26', '40-21=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,48 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[40, 47], Operations: ['80-54=26', '21+26=47'] Exploring Operation: 40+47=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 40*47=1880, Resulting Numbers: [1880] 1880,48 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: 48:[21, 54, 40], Operations: ['80-40=40'] Exploring Operation: 40-21=19, Resulting Numbers: [54, 19] Generated Node #0,1,0: 48:[54, 19] Operation: 40-21=19 Exploring Operation: 54-21=33, Resulting Numbers: [40, 33] Generated Node #0,1,1: 48:[40, 33] Operation: 54-21=33 Exploring Operation: 54-40=14, Resulting Numbers: [21, 14] Generated Node #0,1,2: 48:[21, 14] Operation: 54-40=14 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 48:[21, 14], Operations: ['80-40=40', '54-40=14'] Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,48 unequal: No Solution Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,48 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[54, 19], Operations: ['80-40=40', '40-21=19'] Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,48 unequal: No Solution Exploring Operation: 54*19=1026, Resulting Numbers: [1026] 1026,48 unequal: No Solution Exploring Operation: 54+19=73, Resulting Numbers: [73] 73,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 48:[40, 33], Operations: ['80-40=40', '54-21=33'] Exploring Operation: 40*33=1320, Resulting Numbers: [1320] 1320,48 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 40+33=73, Resulting Numbers: [73] 73,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 48:[21, 27], Operations: ['80/40=2', '54/2=27'] Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,48 unequal: No Solution Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,48 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[21, 80, 40, 54], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [21, 54, 2] Generated Node #0,0: 48:[21, 54, 2] Operation: 80/40=2 Moving to Node #0,0 Current State: 48:[21, 54, 2], Operations: ['80/40=2'] Exploring Operation: 54/2=27, Resulting Numbers: [21, 27] Generated Node #0,0,1: 48:[21, 27] Operation: 54/2=27 Moving to Node #0,0,1 Current State: 48:[21, 27], Operations: ['80/40=2', '54/2=27'] Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.967882
hs_3
mult_heuristic
[ 3, 55, 53, 14 ]
70
[ "3+55=58", "58-53=5", "14*5=70" ]
Current State: 70:[3, 55, 53, 14], Operations: [] Exploring Operation: 3+55=58, Resulting Numbers: [53, 14, 58] Generated Node #2: [53, 14, 58] from Operation: 3+55=58 Current State: 70:[53, 14, 58], Operations: ['3+55=58'] Exploring Operation: 58-53=5, Resulting Numbers: [14, 5] Generated Node #3: [14, 5] from Operation: 58-53=5 Current State: 70:[14, 5], Operations: ['3+55=58', '58-53=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[3, 55, 53, 14], Operations: [] Exploring Operation: 55-53=2, Resulting Numbers: [3, 14, 2] Generated Node #0,0: 70:[3, 14, 2] Operation: 55-53=2 Exploring Operation: 53-14=39, Resulting Numbers: [3, 55, 39] Generated Node #0,1: 70:[3, 55, 39] Operation: 53-14=39 Exploring Operation: 55-14=41, Resulting Numbers: [3, 53, 41] Generated Node #0,2: 70:[3, 53, 41] Operation: 55-14=41 Exploring Operation: 55+14=69, Resulting Numbers: [3, 53, 69] Generated Node #0,3: 70:[3, 53, 69] Operation: 55+14=69 Exploring Operation: 53+14=67, Resulting Numbers: [3, 55, 67] Generated Node #0,4: 70:[3, 55, 67] Operation: 53+14=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[3, 14, 2], Operations: ['55-53=2'] Exploring Operation: 3+2=5, Resulting Numbers: [14, 5] Generated Node #0,0,0: 70:[14, 5] Operation: 3+2=5 Exploring Operation: 14-3=11, Resulting Numbers: [2, 11] Generated Node #0,0,1: 70:[2, 11] Operation: 14-3=11 Exploring Operation: 14/2=7, Resulting Numbers: [3, 7] Generated Node #0,0,2: 70:[3, 7] Operation: 14/2=7 Exploring Operation: 3*2=6, Resulting Numbers: [14, 6] Generated Node #0,0,3: 70:[14, 6] Operation: 3*2=6 Exploring Operation: 3-2=1, Resulting Numbers: [14, 1] Generated Node #0,0,4: 70:[14, 1] Operation: 3-2=1 Moving to Node #0,0,0 Current State: 70:[14, 5], Operations: ['55-53=2', '3+2=5'] Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[3, 55, 53, 14], Operations: [] Exploring Operation: 55-53=2, Resulting Numbers: [3, 14, 2] Generated Node #0,0: 70:[3, 14, 2] Operation: 55-53=2 Moving to Node #0,0 Current State: 70:[3, 14, 2], Operations: ['55-53=2'] Exploring Operation: 3+2=5, Resulting Numbers: [14, 5] Generated Node #0,0,0: 70:[14, 5] Operation: 3+2=5 Moving to Node #0,0,0 Current State: 70:[14, 5], Operations: ['55-53=2', '3+2=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 92, 98, 34, 60 ]
24
[ "98-92=6", "60/6=10", "34-10=24" ]
Current State: 24:[92, 98, 34, 60], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [34, 60, 6] Generated Node #2: [34, 60, 6] from Operation: 98-92=6 Current State: 24:[34, 60, 6], Operations: ['98-92=6'] Exploring Operation: 60/6=10, Resulting Numbers: [34, 10] Generated Node #3: [34, 10] from Operation: 60/6=10 Current State: 24:[34, 10], Operations: ['98-92=6', '60/6=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[92, 98, 34, 60], Operations: [] Exploring Operation: 92-60=32, Resulting Numbers: [98, 34, 32] Generated Node #0,0: 24:[98, 34, 32] Operation: 92-60=32 Exploring Operation: 98-92=6, Resulting Numbers: [34, 60, 6] Generated Node #0,1: 24:[34, 60, 6] Operation: 98-92=6 Moving to Node #0,1 Current State: 24:[34, 60, 6], Operations: ['98-92=6'] Exploring Operation: 60-34=26, Resulting Numbers: [6, 26] Generated Node #0,1,0: 24:[6, 26] Operation: 60-34=26 Exploring Operation: 60/6=10, Resulting Numbers: [34, 10] Generated Node #0,1,1: 24:[34, 10] Operation: 60/6=10 Moving to Node #0,0 Current State: 24:[98, 34, 32], Operations: ['92-60=32'] Exploring Operation: 98-32=66, Resulting Numbers: [34, 66] Generated Node #0,0,0: 24:[34, 66] Operation: 98-32=66 Exploring Operation: 98-34=64, Resulting Numbers: [32, 64] Generated Node #0,0,1: 24:[32, 64] Operation: 98-34=64 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[32, 64], Operations: ['92-60=32', '98-34=64'] Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,24 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 #0,0,0 Current State: 24:[34, 66], Operations: ['92-60=32', '98-32=66'] Exploring Operation: 34+66=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 66-34=32, Resulting Numbers: [32] 32,24 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: 24:[6, 26], Operations: ['98-92=6', '60-34=26'] Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[34, 10], Operations: ['98-92=6', '60/6=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[92, 98, 34, 60], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [34, 60, 6] Generated Node #0,1: 24:[34, 60, 6] Operation: 98-92=6 Moving to Node #0,1 Current State: 24:[34, 60, 6], Operations: ['98-92=6'] Exploring Operation: 60/6=10, Resulting Numbers: [34, 10] Generated Node #0,1,1: 24:[34, 10] Operation: 60/6=10 Moving to Node #0,1,1 Current State: 24:[34, 10], Operations: ['98-92=6', '60/6=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 60, 9, 81, 55 ]
36
[ "60-55=5", "9*5=45", "81-45=36" ]
Current State: 36:[60, 9, 81, 55], Operations: [] Exploring Operation: 60-55=5, Resulting Numbers: [9, 81, 5] Generated Node #2: [9, 81, 5] from Operation: 60-55=5 Current State: 36:[9, 81, 5], Operations: ['60-55=5'] Exploring Operation: 9*5=45, Resulting Numbers: [81, 45] Generated Node #3: [81, 45] from Operation: 9*5=45 Current State: 36:[81, 45], Operations: ['60-55=5', '9*5=45'] Exploring Operation: 81-45=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[60, 9, 81, 55], Operations: [] Exploring Operation: 81-60=21, Resulting Numbers: [9, 55, 21] Generated Node #0,0: 36:[9, 55, 21] Operation: 81-60=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[9, 55, 21], Operations: ['81-60=21'] Exploring Operation: 55-21=34, Resulting Numbers: [9, 34] Generated Node #0,0,0: 36:[9, 34] Operation: 55-21=34 Moving to Node #0,0,0 Current State: 36:[9, 34], Operations: ['81-60=21', '55-21=34'] Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,36 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
[ 58, 38, 69, 14 ]
63
[ "58-38=20", "69+14=83", "83-20=63" ]
Current State: 63:[58, 38, 69, 14], Operations: [] Exploring Operation: 58-38=20, Resulting Numbers: [69, 14, 20] Generated Node #2: [69, 14, 20] from Operation: 58-38=20 Current State: 63:[69, 14, 20], Operations: ['58-38=20'] Exploring Operation: 69+14=83, Resulting Numbers: [20, 83] Generated Node #3: [20, 83] from Operation: 69+14=83 Current State: 63:[20, 83], Operations: ['58-38=20', '69+14=83'] Exploring Operation: 83-20=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[58, 38, 69, 14], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [58, 14, 31] Generated Node #0,0: 63:[58, 14, 31] Operation: 69-38=31 Exploring Operation: 58-38=20, Resulting Numbers: [69, 14, 20] Generated Node #0,1: 63:[69, 14, 20] Operation: 58-38=20 Exploring Operation: 38-14=24, Resulting Numbers: [58, 69, 24] Generated Node #0,2: 63:[58, 69, 24] Operation: 38-14=24 Moving to Node #0,1 Current State: 63:[69, 14, 20], Operations: ['58-38=20'] Exploring Operation: 69-14=55, Resulting Numbers: [20, 55] Generated Node #0,1,0: 63:[20, 55] Operation: 69-14=55 Exploring Operation: 20-14=6, Resulting Numbers: [69, 6] Generated Node #0,1,1: 63:[69, 6] Operation: 20-14=6 Exploring Operation: 69-20=49, Resulting Numbers: [14, 49] Generated Node #0,1,2: 63:[14, 49] Operation: 69-20=49 Moving to Node #0,2 Current State: 63:[58, 69, 24], Operations: ['38-14=24'] Exploring Operation: 69-24=45, Resulting Numbers: [58, 45] Generated Node #0,2,0: 63:[58, 45] Operation: 69-24=45 Exploring Operation: 58-24=34, Resulting Numbers: [69, 34] Generated Node #0,2,1: 63:[69, 34] Operation: 58-24=34 Exploring Operation: 69-58=11, Resulting Numbers: [24, 11] Generated Node #0,2,2: 63:[24, 11] Operation: 69-58=11 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 63:[24, 11], Operations: ['38-14=24', '69-58=11'] Exploring Operation: 24+11=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,63 unequal: No Solution Exploring Operation: 24*11=264, Resulting Numbers: [264] 264,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[69, 34], Operations: ['38-14=24', '58-24=34'] Exploring Operation: 69*34=2346, Resulting Numbers: [2346] 2346,63 unequal: No Solution Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 69+34=103, Resulting Numbers: [103] 103,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[58, 45], Operations: ['38-14=24', '69-24=45'] Exploring Operation: 58*45=2610, Resulting Numbers: [2610] 2610,63 unequal: No Solution Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,63 unequal: No Solution Exploring Operation: 58+45=103, Resulting Numbers: [103] 103,63 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: 63:[58, 14, 31], Operations: ['69-38=31'] Exploring Operation: 31-14=17, Resulting Numbers: [58, 17] Generated Node #0,0,0: 63:[58, 17] Operation: 31-14=17 Exploring Operation: 58+14=72, Resulting Numbers: [31, 72] Generated Node #0,0,1: 63:[31, 72] Operation: 58+14=72 Exploring Operation: 58-31=27, Resulting Numbers: [14, 27] Generated Node #0,0,2: 63:[14, 27] Operation: 58-31=27 Moving to Node #0,1,1 Current State: 63:[69, 6], Operations: ['58-38=20', '20-14=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[58, 38, 69, 14], Operations: [] Exploring Operation: 58-38=20, Resulting Numbers: [69, 14, 20] Generated Node #0,1: 63:[69, 14, 20] Operation: 58-38=20 Moving to Node #0,1 Current State: 63:[69, 14, 20], Operations: ['58-38=20'] Exploring Operation: 20-14=6, Resulting Numbers: [69, 6] Generated Node #0,1,1: 63:[69, 6] Operation: 20-14=6 Moving to Node #0,1,1 Current State: 63:[69, 6], Operations: ['58-38=20', '20-14=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
0.977431
hs_3
mult_heuristic
[ 19, 18, 24, 4 ]
82
[ "19*4=76", "24-18=6", "76+6=82" ]
Current State: 82:[19, 18, 24, 4], Operations: [] Exploring Operation: 19*4=76, Resulting Numbers: [18, 24, 76] Generated Node #2: [18, 24, 76] from Operation: 19*4=76 Current State: 82:[18, 24, 76], Operations: ['19*4=76'] Exploring Operation: 24-18=6, Resulting Numbers: [76, 6] Generated Node #3: [76, 6] from Operation: 24-18=6 Current State: 82:[76, 6], Operations: ['19*4=76', '24-18=6'] Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[19, 18, 24, 4], Operations: [] Exploring Operation: 18+24=42, Resulting Numbers: [19, 4, 42] Generated Node #0,0: 82:[19, 4, 42] Operation: 18+24=42 Exploring Operation: 19+18=37, Resulting Numbers: [24, 4, 37] Generated Node #0,1: 82:[24, 4, 37] Operation: 19+18=37 Exploring Operation: 19-18=1, Resulting Numbers: [24, 4, 1] Generated Node #0,2: 82:[24, 4, 1] Operation: 19-18=1 Exploring Operation: 24-19=5, Resulting Numbers: [18, 4, 5] Generated Node #0,3: 82:[18, 4, 5] Operation: 24-19=5 Exploring Operation: 19+24=43, Resulting Numbers: [18, 4, 43] Generated Node #0,4: 82:[18, 4, 43] Operation: 19+24=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[19, 4, 42], Operations: ['18+24=42'] Exploring Operation: 19+4=23, Resulting Numbers: [42, 23] Generated Node #0,0,0: 82:[42, 23] Operation: 19+4=23 Exploring Operation: 19-4=15, Resulting Numbers: [42, 15] Generated Node #0,0,1: 82:[42, 15] Operation: 19-4=15 Exploring Operation: 42-4=38, Resulting Numbers: [19, 38] Generated Node #0,0,2: 82:[19, 38] Operation: 42-4=38 Exploring Operation: 19*4=76, Resulting Numbers: [42, 76] Generated Node #0,0,3: 82:[42, 76] Operation: 19*4=76 Exploring Operation: 42-19=23, Resulting Numbers: [4, 23] Generated Node #0,0,4: 82:[4, 23] Operation: 42-19=23 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 82:[42, 76], Operations: ['18+24=42', '19*4=76'] Exploring Operation: 42*76=3192, Resulting Numbers: [3192] 3192,82 unequal: No Solution Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 42+76=118, Resulting Numbers: [118] 118,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[42, 15], Operations: ['18+24=42', '19-4=15'] Exploring Operation: 42+15=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 42*15=630, Resulting Numbers: [630] 630,82 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[42, 23], Operations: ['18+24=42', '19+4=23'] Exploring Operation: 42+23=65, Resulting Numbers: [65] 65,82 unequal: No Solution Exploring Operation: 42*23=966, Resulting Numbers: [966] 966,82 unequal: No Solution Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[19, 38], Operations: ['18+24=42', '42-4=38'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,82 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 82:[4, 23], Operations: ['18+24=42', '42-19=23'] Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,82 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[24, 4, 1], Operations: ['19-18=1'] Exploring Operation: 24*4=96, Resulting Numbers: [1, 96] Generated Node #0,2,0: 82:[1, 96] Operation: 24*4=96 Exploring Operation: 4-1=3, Resulting Numbers: [24, 3] Generated Node #0,2,1: 82:[24, 3] Operation: 4-1=3 Exploring Operation: 24/4=6, Resulting Numbers: [1, 6] Generated Node #0,2,2: 82:[1, 6] Operation: 24/4=6 Exploring Operation: 24+4=28, Resulting Numbers: [1, 28] Generated Node #0,2,3: 82:[1, 28] Operation: 24+4=28 Exploring Operation: 24+1=25, Resulting Numbers: [4, 25] Generated Node #0,2,4: 82:[4, 25] Operation: 24+1=25 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[1, 6], Operations: ['19-18=1', '24/4=6'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[1, 28], Operations: ['19-18=1', '24+4=28'] Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,82 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[1, 96], Operations: ['19-18=1', '24*4=96'] Exploring Operation: 1*96=96, Resulting Numbers: [96] 96,82 unequal: No Solution Exploring Operation: 1+96=97, Resulting Numbers: [97] 97,82 unequal: No Solution Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,82 unequal: No Solution Exploring Operation: 96/1=96, Resulting Numbers: [96] 96,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[24, 3], Operations: ['19-18=1', '4-1=3'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,82 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 82:[4, 25], Operations: ['19-18=1', '24+1=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,82 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,82 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 82:[18, 4, 43], Operations: ['19+24=43'] Exploring Operation: 43-4=39, Resulting Numbers: [18, 39] Generated Node #0,4,0: 82:[18, 39] Operation: 43-4=39 Exploring Operation: 18*4=72, Resulting Numbers: [43, 72] Generated Node #0,4,1: 82:[43, 72] Operation: 18*4=72 Exploring Operation: 18+4=22, Resulting Numbers: [43, 22] Generated Node #0,4,2: 82:[43, 22] Operation: 18+4=22 Exploring Operation: 18-4=14, Resulting Numbers: [43, 14] Generated Node #0,4,3: 82:[43, 14] Operation: 18-4=14 Exploring Operation: 43-18=25, Resulting Numbers: [4, 25] Generated Node #0,4,4: 82:[4, 25] Operation: 43-18=25 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 82:[43, 72], Operations: ['19+24=43', '18*4=72'] Exploring Operation: 43+72=115, Resulting Numbers: [115] 115,82 unequal: No Solution Exploring Operation: 43*72=3096, Resulting Numbers: [3096] 3096,82 unequal: No Solution Exploring Operation: 72-43=29, Resulting Numbers: [29] 29,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 82:[43, 14], Operations: ['19+24=43', '18-4=14'] Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 43*14=602, Resulting Numbers: [602] 602,82 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 82:[18, 39], Operations: ['19+24=43', '43-4=39'] Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,82 unequal: No Solution Exploring Operation: 18*39=702, Resulting Numbers: [702] 702,82 unequal: No Solution Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 82:[4, 25], Operations: ['19+24=43', '43-18=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,82 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,82 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 82:[43, 22], Operations: ['19+24=43', '18+4=22'] Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,82 unequal: No Solution Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,82 unequal: No Solution Exploring Operation: 43*22=946, Resulting Numbers: [946] 946,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[18, 4, 5], Operations: ['24-19=5'] Exploring Operation: 18*5=90, Resulting Numbers: [4, 90] Generated Node #0,3,0: 82:[4, 90] Operation: 18*5=90 Exploring Operation: 18-5=13, Resulting Numbers: [4, 13] Generated Node #0,3,1: 82:[4, 13] Operation: 18-5=13 Exploring Operation: 18-4=14, Resulting Numbers: [5, 14] Generated Node #0,3,2: 82:[5, 14] Operation: 18-4=14 Exploring Operation: 18*4=72, Resulting Numbers: [5, 72] Generated Node #0,3,3: 82:[5, 72] Operation: 18*4=72 Exploring Operation: 5-4=1, Resulting Numbers: [18, 1] Generated Node #0,3,4: 82:[18, 1] Operation: 5-4=1 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 82:[4, 90], Operations: ['24-19=5', '18*5=90'] Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,82 unequal: No Solution Exploring Operation: 4+90=94, Resulting Numbers: [94] 94,82 unequal: No Solution Exploring Operation: 4*90=360, Resulting Numbers: [360] 360,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 82:[4, 13], Operations: ['24-19=5', '18-5=13'] Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 82:[5, 72], Operations: ['24-19=5', '18*4=72'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,82 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 82:[5, 14], Operations: ['24-19=5', '18-4=14'] Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 5+14=19, Resulting Numbers: [19] 19,82 unequal: No Solution Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 82:[18, 1], Operations: ['24-19=5', '5-4=1'] Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,82 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[24, 4, 37], Operations: ['19+18=37'] Exploring Operation: 24+4=28, Resulting Numbers: [37, 28] Generated Node #0,1,0: 82:[37, 28] Operation: 24+4=28 Exploring Operation: 4+37=41, Resulting Numbers: [24, 41] Generated Node #0,1,1: 82:[24, 41] Operation: 4+37=41 Exploring Operation: 24*4=96, Resulting Numbers: [37, 96] Generated Node #0,1,2: 82:[37, 96] Operation: 24*4=96 Exploring Operation: 37-24=13, Resulting Numbers: [4, 13] Generated Node #0,1,3: 82:[4, 13] Operation: 37-24=13 Exploring Operation: 24/4=6, Resulting Numbers: [37, 6] Generated Node #0,1,4: 82:[37, 6] Operation: 24/4=6 Moving to Node #0,1,4 Current State: 82:[37, 6], Operations: ['19+18=37', '24/4=6'] Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,82 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[4, 13], Operations: ['19+18=37', '37-24=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[37, 28], Operations: ['19+18=37', '24+4=28'] Exploring Operation: 37*28=1036, Resulting Numbers: [1036] 1036,82 unequal: No Solution Exploring Operation: 37-28=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 37+28=65, Resulting Numbers: [65] 65,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[24, 41], Operations: ['19+18=37', '4+37=41'] Exploring Operation: 24+41=65, Resulting Numbers: [65] 65,82 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 24*41=984, Resulting Numbers: [984] 984,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[37, 96], Operations: ['19+18=37', '24*4=96'] Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,82 unequal: No Solution Exploring Operation: 37+96=133, Resulting Numbers: [133] 133,82 unequal: No Solution Exploring Operation: 37*96=3552, Resulting Numbers: [3552] 3552,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic