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
[ 48, 43, 35, 31 ]
39
[ "43-31=12", "48/12=4", "35+4=39" ]
Current State: 39:[48, 43, 35, 31], Operations: [] Exploring Operation: 43-31=12, Resulting Numbers: [48, 35, 12] Generated Node #2: [48, 35, 12] from Operation: 43-31=12 Current State: 39:[48, 35, 12], Operations: ['43-31=12'] Exploring Operation: 48/12=4, Resulting Numbers: [35, 4] Generated Node #3: [35, 4] from Operation: 48/12=4 Current State: 39:[35, 4], Operations: ['43-31=12', '48/12=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[48, 43, 35, 31], Operations: [] Exploring Operation: 48-43=5, Resulting Numbers: [35, 31, 5] Generated Node #0,0: 39:[35, 31, 5] Operation: 48-43=5 Exploring Operation: 48-35=13, Resulting Numbers: [43, 31, 13] Generated Node #0,1: 39:[43, 31, 13] Operation: 48-35=13 Exploring Operation: 48-31=17, Resulting Numbers: [43, 35, 17] Generated Node #0,2: 39:[43, 35, 17] Operation: 48-31=17 Moving to Node #0,1 Current State: 39:[43, 31, 13], Operations: ['48-35=13'] Exploring Operation: 31+13=44, Resulting Numbers: [43, 44] Generated Node #0,1,0: 39:[43, 44] Operation: 31+13=44 Exploring Operation: 43-31=12, Resulting Numbers: [13, 12] Generated Node #0,1,1: 39:[13, 12] Operation: 43-31=12 Exploring Operation: 31-13=18, Resulting Numbers: [43, 18] Generated Node #0,1,2: 39:[43, 18] Operation: 31-13=18 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[13, 12], Operations: ['48-35=13', '43-31=12'] Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 13*12=156, Resulting Numbers: [156] 156,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[43, 44], Operations: ['48-35=13', '31+13=44'] Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,39 unequal: No Solution Exploring Operation: 43*44=1892, Resulting Numbers: [1892] 1892,39 unequal: No Solution Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 39:[43, 18], Operations: ['48-35=13', '31-13=18'] Exploring Operation: 43*18=774, Resulting Numbers: [774] 774,39 unequal: No Solution Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,39 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: 39:[43, 35, 17], Operations: ['48-31=17'] Exploring Operation: 35-17=18, Resulting Numbers: [43, 18] Generated Node #0,2,0: 39:[43, 18] Operation: 35-17=18 Exploring Operation: 43-35=8, Resulting Numbers: [17, 8] Generated Node #0,2,1: 39:[17, 8] Operation: 43-35=8 Exploring Operation: 43-17=26, Resulting Numbers: [35, 26] Generated Node #0,2,2: 39:[35, 26] Operation: 43-17=26 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[43, 18], Operations: ['48-31=17', '35-17=18'] Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,39 unequal: No Solution Exploring Operation: 43*18=774, Resulting Numbers: [774] 774,39 unequal: No Solution Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,39 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 #0,2,1 Current State: 39:[17, 8], Operations: ['48-31=17', '43-35=8'] Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,39 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,39 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 #0,2,2 Current State: 39:[35, 26], Operations: ['48-31=17', '43-17=26'] Exploring Operation: 35+26=61, Resulting Numbers: [61] 61,39 unequal: No Solution Exploring Operation: 35*26=910, Resulting Numbers: [910] 910,39 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 39:[35, 31, 5], Operations: ['48-43=5'] Exploring Operation: 35+5=40, Resulting Numbers: [31, 40] Generated Node #0,0,0: 39:[31, 40] Operation: 35+5=40 Exploring Operation: 35-31=4, Resulting Numbers: [5, 4] Generated Node #0,0,1: 39:[5, 4] Operation: 35-31=4 Exploring Operation: 31+5=36, Resulting Numbers: [35, 36] Generated Node #0,0,2: 39:[35, 36] Operation: 31+5=36 Moving to Node #0,0,1 Current State: 39:[5, 4], Operations: ['48-43=5', '35-31=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[35, 36], Operations: ['48-43=5', '31+5=36'] Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[31, 40], Operations: ['48-43=5', '35+5=40'] Exploring Operation: 31*40=1240, Resulting Numbers: [1240] 1240,39 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,39 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 40, 11, 6, 35 ]
27
[ "11-6=5", "40/5=8", "35-8=27" ]
Current State: 27:[40, 11, 6, 35], Operations: [] Exploring Operation: 11-6=5, Resulting Numbers: [40, 35, 5] Generated Node #2: [40, 35, 5] from Operation: 11-6=5 Current State: 27:[40, 35, 5], Operations: ['11-6=5'] Exploring Operation: 40/5=8, Resulting Numbers: [35, 8] Generated Node #3: [35, 8] from Operation: 40/5=8 Current State: 27:[35, 8], Operations: ['11-6=5', '40/5=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[40, 11, 6, 35], Operations: [] Exploring Operation: 40-11=29, Resulting Numbers: [6, 35, 29] Generated Node #0,0: 27:[6, 35, 29] Operation: 40-11=29 Exploring Operation: 35-11=24, Resulting Numbers: [40, 6, 24] Generated Node #0,1: 27:[40, 6, 24] Operation: 35-11=24 Exploring Operation: 40-35=5, Resulting Numbers: [11, 6, 5] Generated Node #0,2: 27:[11, 6, 5] Operation: 40-35=5 Exploring Operation: 35-6=29, Resulting Numbers: [40, 11, 29] Generated Node #0,3: 27:[40, 11, 29] Operation: 35-6=29 Exploring Operation: 40-6=34, Resulting Numbers: [11, 35, 34] Generated Node #0,4: 27:[11, 35, 34] Operation: 40-6=34 Moving to Node #0,2 Current State: 27:[11, 6, 5], Operations: ['40-35=5'] Exploring Operation: 11-5=6, Resulting Numbers: [6, 6] Generated Node #0,2,0: 27:[6, 6] Operation: 11-5=6 Exploring Operation: 6-5=1, Resulting Numbers: [11, 1] Generated Node #0,2,1: 27:[11, 1] Operation: 6-5=1 Exploring Operation: 11-6=5, Resulting Numbers: [5, 5] Generated Node #0,2,2: 27:[5, 5] Operation: 11-6=5 Exploring Operation: 6+5=11, Resulting Numbers: [11, 11] Generated Node #0,2,3: 27:[11, 11] Operation: 6+5=11 Exploring Operation: 6*5=30, Resulting Numbers: [11, 30] Generated Node #0,2,4: 27:[11, 30] Operation: 6*5=30 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[11, 1], Operations: ['40-35=5', '6-5=1'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,27 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,27 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:[5, 5], Operations: ['40-35=5', '11-6=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,27 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 #0,2,3 Current State: 27:[11, 11], Operations: ['40-35=5', '6+5=11'] Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,27 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 #0,2,4 Current State: 27:[11, 30], Operations: ['40-35=5', '6*5=30'] Exploring Operation: 11*30=330, Resulting Numbers: [330] 330,27 unequal: No Solution Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,27 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 #0,2,0 Current State: 27:[6, 6], Operations: ['40-35=5', '11-5=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,27 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: 27:[6, 35, 29], Operations: ['40-11=29'] Exploring Operation: 35-29=6, Resulting Numbers: [6, 6] Generated Node #0,0,0: 27:[6, 6] Operation: 35-29=6 Exploring Operation: 6+35=41, Resulting Numbers: [29, 41] Generated Node #0,0,1: 27:[29, 41] Operation: 6+35=41 Exploring Operation: 6+29=35, Resulting Numbers: [35, 35] Generated Node #0,0,2: 27:[35, 35] Operation: 6+29=35 Exploring Operation: 35-6=29, Resulting Numbers: [29, 29] Generated Node #0,0,3: 27:[29, 29] Operation: 35-6=29 Exploring Operation: 29-6=23, Resulting Numbers: [35, 23] Generated Node #0,0,4: 27:[35, 23] Operation: 29-6=23 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 27:[29, 29], Operations: ['40-11=29', '35-6=29'] Exploring Operation: 29*29=841, Resulting Numbers: [841] 841,27 unequal: No Solution Exploring Operation: 29-29=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 29/29=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 29+29=58, Resulting Numbers: [58] 58,27 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 #0,0,0 Current State: 27:[6, 6], Operations: ['40-11=29', '35-29=6'] Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,27 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 #0,0,4 Current State: 27:[35, 23], Operations: ['40-11=29', '29-6=23'] Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,27 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,27 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:[29, 41], Operations: ['40-11=29', '6+35=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,27 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,27 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,27 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:[35, 35], Operations: ['40-11=29', '6+29=35'] Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,27 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,27 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: 27:[40, 11, 29], Operations: ['35-6=29'] Exploring Operation: 11+29=40, Resulting Numbers: [40, 40] Generated Node #0,3,0: 27:[40, 40] Operation: 11+29=40 Exploring Operation: 40-11=29, Resulting Numbers: [29, 29] Generated Node #0,3,1: 27:[29, 29] Operation: 40-11=29 Exploring Operation: 40-29=11, Resulting Numbers: [11, 11] Generated Node #0,3,2: 27:[11, 11] Operation: 40-29=11 Exploring Operation: 40+11=51, Resulting Numbers: [29, 51] Generated Node #0,3,3: 27:[29, 51] Operation: 40+11=51 Exploring Operation: 29-11=18, Resulting Numbers: [40, 18] Generated Node #0,3,4: 27:[40, 18] Operation: 29-11=18 Moving to Node #0,4 Current State: 27:[11, 35, 34], Operations: ['40-6=34'] Exploring Operation: 35-11=24, Resulting Numbers: [34, 24] Generated Node #0,4,0: 27:[34, 24] Operation: 35-11=24 Exploring Operation: 34-11=23, Resulting Numbers: [35, 23] Generated Node #0,4,1: 27:[35, 23] Operation: 34-11=23 Exploring Operation: 11+34=45, Resulting Numbers: [35, 45] Generated Node #0,4,2: 27:[35, 45] Operation: 11+34=45 Exploring Operation: 35-34=1, Resulting Numbers: [11, 1] Generated Node #0,4,3: 27:[11, 1] Operation: 35-34=1 Exploring Operation: 11+35=46, Resulting Numbers: [34, 46] Generated Node #0,4,4: 27:[34, 46] Operation: 11+35=46 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 27:[11, 1], Operations: ['40-6=34', '35-34=1'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,27 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,27 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 #0,4,0 Current State: 27:[34, 24], Operations: ['40-6=34', '35-11=24'] Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,27 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,27 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 #0,4,1 Current State: 27:[35, 23], Operations: ['40-6=34', '34-11=23'] Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,27 unequal: No Solution Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,27 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 #0,4,2 Current State: 27:[35, 45], Operations: ['40-6=34', '11+34=45'] Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,27 unequal: No Solution Exploring Operation: 35*45=1575, Resulting Numbers: [1575] 1575,27 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 #0,4,4 Current State: 27:[34, 46], Operations: ['40-6=34', '11+35=46'] Exploring Operation: 34+46=80, Resulting Numbers: [80] 80,27 unequal: No Solution Exploring Operation: 34*46=1564, Resulting Numbers: [1564] 1564,27 unequal: No Solution Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,27 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: 27:[40, 6, 24], Operations: ['35-11=24'] Exploring Operation: 24/6=4, Resulting Numbers: [40, 4] Generated Node #0,1,0: 27:[40, 4] Operation: 24/6=4 Exploring Operation: 6+24=30, Resulting Numbers: [40, 30] Generated Node #0,1,1: 27:[40, 30] Operation: 6+24=30 Exploring Operation: 40+6=46, Resulting Numbers: [24, 46] Generated Node #0,1,2: 27:[24, 46] Operation: 40+6=46 Exploring Operation: 40-24=16, Resulting Numbers: [6, 16] Generated Node #0,1,3: 27:[6, 16] Operation: 40-24=16 Exploring Operation: 40-6=34, Resulting Numbers: [24, 34] Generated Node #0,1,4: 27:[24, 34] Operation: 40-6=34 Moving to Node #0,3,1 Current State: 27:[29, 29], Operations: ['35-6=29', '40-11=29'] Exploring Operation: 29/29=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 29-29=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 29*29=841, Resulting Numbers: [841] 841,27 unequal: No Solution Exploring Operation: 29+29=58, Resulting Numbers: [58] 58,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[11, 11], Operations: ['35-6=29', '40-29=11'] Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,27 unequal: No Solution Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,27 unequal: No Solution Moving to Node #0,1,3 Current State: 27:[6, 16], Operations: ['35-11=24', '40-24=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,27 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,27 unequal: No Solution Moving to Node #0,1,4 Current State: 27:[24, 34], Operations: ['35-11=24', '40-6=34'] Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 24*34=816, Resulting Numbers: [816] 816,27 unequal: No Solution Exploring Operation: 24+34=58, Resulting Numbers: [58] 58,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[40, 4], Operations: ['35-11=24', '24/6=4'] Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,27 unequal: No Solution Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[40, 30], Operations: ['35-11=24', '6+24=30'] Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,27 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,27 unequal: No Solution Moving to Node #0,3,4 Current State: 27:[40, 18], Operations: ['35-6=29', '29-11=18'] Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,27 unequal: No Solution Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[24, 46], Operations: ['35-11=24', '40+6=46'] Exploring Operation: 24+46=70, Resulting Numbers: [70] 70,27 unequal: No Solution Exploring Operation: 46-24=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 24*46=1104, Resulting Numbers: [1104] 1104,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[29, 51], Operations: ['35-6=29', '40+11=51'] Exploring Operation: 29+51=80, Resulting Numbers: [80] 80,27 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 29*51=1479, Resulting Numbers: [1479] 1479,27 unequal: No Solution Moving to Node #0,3,0 Current State: 27:[40, 40], Operations: ['35-6=29', '11+29=40'] Exploring Operation: 40+40=80, Resulting Numbers: [80] 80,27 unequal: No Solution Exploring Operation: 40/40=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 40-40=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 40*40=1600, Resulting Numbers: [1600] 1600,27 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 49, 65, 23, 74 ]
35
[ "65-49=16", "74-23=51", "51-16=35" ]
Current State: 35:[49, 65, 23, 74], Operations: [] Exploring Operation: 65-49=16, Resulting Numbers: [23, 74, 16] Generated Node #2: [23, 74, 16] from Operation: 65-49=16 Current State: 35:[23, 74, 16], Operations: ['65-49=16'] Exploring Operation: 74-23=51, Resulting Numbers: [16, 51] Generated Node #3: [16, 51] from Operation: 74-23=51 Current State: 35:[16, 51], Operations: ['65-49=16', '74-23=51'] Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[49, 65, 23, 74], Operations: [] Exploring Operation: 74-49=25, Resulting Numbers: [65, 23, 25] Generated Node #0,0: 35:[65, 23, 25] Operation: 74-49=25 Exploring Operation: 65-49=16, Resulting Numbers: [23, 74, 16] Generated Node #0,1: 35:[23, 74, 16] Operation: 65-49=16 Exploring Operation: 74-65=9, Resulting Numbers: [49, 23, 9] Generated Node #0,2: 35:[49, 23, 9] Operation: 74-65=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[49, 23, 9], Operations: ['74-65=9'] Exploring Operation: 49-23=26, Resulting Numbers: [9, 26] Generated Node #0,2,0: 35:[9, 26] Operation: 49-23=26 Exploring Operation: 23+9=32, Resulting Numbers: [49, 32] Generated Node #0,2,1: 35:[49, 32] Operation: 23+9=32 Exploring Operation: 49-9=40, Resulting Numbers: [23, 40] Generated Node #0,2,2: 35:[23, 40] Operation: 49-9=40 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 35:[9, 26], Operations: ['74-65=9', '49-23=26'] Exploring Operation: 9*26=234, Resulting Numbers: [234] 234,35 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,35 unequal: No Solution Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[49, 65, 23, 74], Operations: [] Exploring Operation: 74-65=9, Resulting Numbers: [49, 23, 9] Generated Node #0,2: 35:[49, 23, 9] Operation: 74-65=9 Moving to Node #0,2 Current State: 35:[49, 23, 9], Operations: ['74-65=9'] Exploring Operation: 49-23=26, Resulting Numbers: [9, 26] Generated Node #0,2,0: 35:[9, 26] Operation: 49-23=26 Moving to Node #0,2,0 Current State: 35:[9, 26], Operations: ['74-65=9', '49-23=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 32, 58, 54, 13 ]
67
[ "58-32=26", "54-13=41", "26+41=67" ]
Current State: 67:[32, 58, 54, 13], Operations: [] Exploring Operation: 58-32=26, Resulting Numbers: [54, 13, 26] Generated Node #2: [54, 13, 26] from Operation: 58-32=26 Current State: 67:[54, 13, 26], Operations: ['58-32=26'] Exploring Operation: 54-13=41, Resulting Numbers: [26, 41] Generated Node #3: [26, 41] from Operation: 54-13=41 Current State: 67:[26, 41], Operations: ['58-32=26', '54-13=41'] Exploring Operation: 26+41=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[32, 58, 54, 13], Operations: [] Exploring Operation: 32+13=45, Resulting Numbers: [58, 54, 45] Generated Node #0,0: 67:[58, 54, 45] Operation: 32+13=45 Exploring Operation: 54+13=67, Resulting Numbers: [32, 58, 67] Generated Node #0,1: 67:[32, 58, 67] Operation: 54+13=67 Exploring Operation: 58+13=71, Resulting Numbers: [32, 54, 71] Generated Node #0,2: 67:[32, 54, 71] Operation: 58+13=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[58, 54, 45], Operations: ['32+13=45'] Exploring Operation: 58+54=112, Resulting Numbers: [45, 112] Generated Node #0,0,0: 67:[45, 112] Operation: 58+54=112 Exploring Operation: 54+45=99, Resulting Numbers: [58, 99] Generated Node #0,0,1: 67:[58, 99] Operation: 54+45=99 Exploring Operation: 58+45=103, Resulting Numbers: [54, 103] Generated Node #0,0,2: 67:[54, 103] Operation: 58+45=103 Moving to Node #0,0,1 Current State: 67:[58, 99], Operations: ['32+13=45', '54+45=99'] Exploring Operation: 58*99=5742, Resulting Numbers: [5742] 5742,67 unequal: No Solution Exploring Operation: 58+99=157, Resulting Numbers: [157] 157,67 unequal: No Solution Exploring Operation: 99-58=41, Resulting Numbers: [41] 41,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[54, 103], Operations: ['32+13=45', '58+45=103'] Exploring Operation: 54*103=5562, Resulting Numbers: [5562] 5562,67 unequal: No Solution Exploring Operation: 103-54=49, Resulting Numbers: [49] 49,67 unequal: No Solution Exploring Operation: 54+103=157, Resulting Numbers: [157] 157,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[45, 112], Operations: ['32+13=45', '58+54=112'] Exploring Operation: 45+112=157, Resulting Numbers: [157] 157,67 unequal: No Solution Exploring Operation: 112-45=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[32, 58, 54, 13], Operations: [] Exploring Operation: 32+13=45, Resulting Numbers: [58, 54, 45] Generated Node #0,0: 67:[58, 54, 45] Operation: 32+13=45 Moving to Node #0,0 Current State: 67:[58, 54, 45], Operations: ['32+13=45'] Exploring Operation: 58+54=112, Resulting Numbers: [45, 112] Generated Node #0,0,0: 67:[45, 112] Operation: 58+54=112 Moving to Node #0,0,0 Current State: 67:[45, 112], Operations: ['32+13=45', '58+54=112'] Exploring Operation: 112-45=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 73, 3, 58, 35 ]
26
[ "73+58=131", "3*35=105", "131-105=26" ]
Current State: 26:[73, 3, 58, 35], Operations: [] Exploring Operation: 73+58=131, Resulting Numbers: [3, 35, 131] Generated Node #2: [3, 35, 131] from Operation: 73+58=131 Current State: 26:[3, 35, 131], Operations: ['73+58=131'] Exploring Operation: 3*35=105, Resulting Numbers: [131, 105] Generated Node #3: [131, 105] from Operation: 3*35=105 Current State: 26:[131, 105], Operations: ['73+58=131', '3*35=105'] Exploring Operation: 131-105=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[73, 3, 58, 35], Operations: [] Exploring Operation: 73-35=38, Resulting Numbers: [3, 58, 38] Generated Node #0,0: 26:[3, 58, 38] Operation: 73-35=38 Exploring Operation: 58-35=23, Resulting Numbers: [73, 3, 23] Generated Node #0,1: 26:[73, 3, 23] Operation: 58-35=23 Exploring Operation: 73-58=15, Resulting Numbers: [3, 35, 15] Generated Node #0,2: 26:[3, 35, 15] Operation: 73-58=15 Moving to Node #0,2 Current State: 26:[3, 35, 15], Operations: ['73-58=15'] Exploring Operation: 35-3=32, Resulting Numbers: [15, 32] Generated Node #0,2,0: 26:[15, 32] Operation: 35-3=32 Exploring Operation: 15-3=12, Resulting Numbers: [35, 12] Generated Node #0,2,1: 26:[35, 12] Operation: 15-3=12 Exploring Operation: 35-15=20, Resulting Numbers: [3, 20] Generated Node #0,2,2: 26:[3, 20] Operation: 35-15=20 Moving to Node #0,0 Current State: 26:[3, 58, 38], Operations: ['73-35=38'] Exploring Operation: 58-3=55, Resulting Numbers: [38, 55] Generated Node #0,0,0: 26:[38, 55] Operation: 58-3=55 Exploring Operation: 38-3=35, Resulting Numbers: [58, 35] Generated Node #0,0,1: 26:[58, 35] Operation: 38-3=35 Exploring Operation: 58-38=20, Resulting Numbers: [3, 20] Generated Node #0,0,2: 26:[3, 20] Operation: 58-38=20 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[3, 20], Operations: ['73-35=38', '58-38=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,26 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,26 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 #0,0,0 Current State: 26:[38, 55], Operations: ['73-35=38', '58-3=55'] Exploring Operation: 38*55=2090, Resulting Numbers: [2090] 2090,26 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,26 unequal: No Solution Exploring Operation: 38+55=93, Resulting Numbers: [93] 93,26 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:[58, 35], Operations: ['73-35=38', '38-3=35'] Exploring Operation: 58+35=93, Resulting Numbers: [93] 93,26 unequal: No Solution Exploring Operation: 58-35=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 58*35=2030, Resulting Numbers: [2030] 2030,26 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:[73, 3, 23], Operations: ['58-35=23'] Exploring Operation: 3+23=26, Resulting Numbers: [73, 26] Generated Node #0,1,0: 26:[73, 26] Operation: 3+23=26 Exploring Operation: 73-3=70, Resulting Numbers: [23, 70] Generated Node #0,1,1: 26:[23, 70] Operation: 73-3=70 Exploring Operation: 73-23=50, Resulting Numbers: [3, 50] Generated Node #0,1,2: 26:[3, 50] Operation: 73-23=50 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[3, 50], Operations: ['58-35=23', '73-23=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,26 unequal: No Solution Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,26 unequal: No Solution Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,26 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:[73, 26], Operations: ['58-35=23', '3+23=26'] Exploring Operation: 73+26=99, Resulting Numbers: [99] 99,26 unequal: No Solution Exploring Operation: 73*26=1898, Resulting Numbers: [1898] 1898,26 unequal: No Solution Exploring Operation: 73-26=47, Resulting Numbers: [47] 47,26 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 #0,1,1 Current State: 26:[23, 70], Operations: ['58-35=23', '73-3=70'] Exploring Operation: 23+70=93, Resulting Numbers: [93] 93,26 unequal: No Solution Exploring Operation: 23*70=1610, Resulting Numbers: [1610] 1610,26 unequal: No Solution Exploring Operation: 70-23=47, Resulting Numbers: [47] 47,26 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: 26:[3, 20], Operations: ['73-58=15', '35-15=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,26 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,26 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[15, 32], Operations: ['73-58=15', '35-3=32'] Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,26 unequal: No Solution Exploring Operation: 15*32=480, Resulting Numbers: [480] 480,26 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[35, 12], Operations: ['73-58=15', '15-3=12'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,26 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,26 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 42, 12, 72, 30 ]
72
[ "42-12=30", "72+30=102", "102-30=72" ]
Current State: 72:[42, 12, 72, 30], Operations: [] Exploring Operation: 42-12=30, Resulting Numbers: [72, 30, 30] Generated Node #2: [72, 30, 30] from Operation: 42-12=30 Current State: 72:[72, 30, 30], Operations: ['42-12=30'] Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,72 equal: Goal Reached Exploring Operation: 102-30=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[42, 12, 72, 30], Operations: [] Exploring Operation: 42+30=72, Resulting Numbers: [12, 72, 72] Generated Node #0,0: 72:[12, 72, 72] Operation: 42+30=72 Moving to Node #0,0 Current State: 72:[12, 72, 72], Operations: ['42+30=72'] Exploring Operation: 72/12=6, Resulting Numbers: [72, 6] Generated Node #0,0,0: 72:[72, 6] Operation: 72/12=6 Moving to Node #0,0,0 Current State: 72:[72, 6], Operations: ['42+30=72', '72/12=6'] Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,72 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 95, 67, 8, 39 ]
88
[ "95-67=28", "39-28=11", "8*11=88" ]
Current State: 88:[95, 67, 8, 39], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [8, 39, 28] Generated Node #2: [8, 39, 28] from Operation: 95-67=28 Current State: 88:[8, 39, 28], Operations: ['95-67=28'] Exploring Operation: 39-28=11, Resulting Numbers: [8, 11] Generated Node #3: [8, 11] from Operation: 39-28=11 Current State: 88:[8, 11], Operations: ['95-67=28', '39-28=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[95, 67, 8, 39], Operations: [] Exploring Operation: 67+8=75, Resulting Numbers: [95, 39, 75] Generated Node #0,0: 88:[95, 39, 75] Operation: 67+8=75 Exploring Operation: 67+39=106, Resulting Numbers: [95, 8, 106] Generated Node #0,1: 88:[95, 8, 106] Operation: 67+39=106 Exploring Operation: 95-8=87, Resulting Numbers: [67, 39, 87] Generated Node #0,2: 88:[67, 39, 87] Operation: 95-8=87 Exploring Operation: 95-67=28, Resulting Numbers: [8, 39, 28] Generated Node #0,3: 88:[8, 39, 28] Operation: 95-67=28 Exploring Operation: 67-39=28, Resulting Numbers: [95, 8, 28] Generated Node #0,4: 88:[95, 8, 28] Operation: 67-39=28 Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[8, 39, 28], Operations: ['95-67=28'] Exploring Operation: 8+28=36, Resulting Numbers: [39, 36] Generated Node #0,3,0: 88:[39, 36] Operation: 8+28=36 Exploring Operation: 28-8=20, Resulting Numbers: [39, 20] Generated Node #0,3,1: 88:[39, 20] Operation: 28-8=20 Exploring Operation: 39-8=31, Resulting Numbers: [28, 31] Generated Node #0,3,2: 88:[28, 31] Operation: 39-8=31 Exploring Operation: 8+39=47, Resulting Numbers: [28, 47] Generated Node #0,3,3: 88:[28, 47] Operation: 8+39=47 Exploring Operation: 39-28=11, Resulting Numbers: [8, 11] Generated Node #0,3,4: 88:[8, 11] Operation: 39-28=11 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 88:[8, 11], Operations: ['95-67=28', '39-28=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[95, 67, 8, 39], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [8, 39, 28] Generated Node #0,3: 88:[8, 39, 28] Operation: 95-67=28 Moving to Node #0,3 Current State: 88:[8, 39, 28], Operations: ['95-67=28'] Exploring Operation: 39-28=11, Resulting Numbers: [8, 11] Generated Node #0,3,4: 88:[8, 11] Operation: 39-28=11 Moving to Node #0,3,4 Current State: 88:[8, 11], Operations: ['95-67=28', '39-28=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 17, 65, 8, 9 ]
11
[ "17*9=153", "153-65=88", "88/8=11" ]
Current State: 11:[17, 65, 8, 9], Operations: [] Exploring Operation: 17*9=153, Resulting Numbers: [65, 8, 153] Generated Node #2: [65, 8, 153] from Operation: 17*9=153 Current State: 11:[65, 8, 153], Operations: ['17*9=153'] Exploring Operation: 153-65=88, Resulting Numbers: [8, 88] Generated Node #3: [8, 88] from Operation: 153-65=88 Current State: 11:[8, 88], Operations: ['17*9=153', '153-65=88'] Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[17, 65, 8, 9], Operations: [] Exploring Operation: 17-8=9, Resulting Numbers: [65, 9, 9] Generated Node #0,0: 11:[65, 9, 9] Operation: 17-8=9 Exploring Operation: 65-17=48, Resulting Numbers: [8, 9, 48] Generated Node #0,1: 11:[8, 9, 48] Operation: 65-17=48 Exploring Operation: 17-9=8, Resulting Numbers: [65, 8, 8] Generated Node #0,2: 11:[65, 8, 8] Operation: 17-9=8 Exploring Operation: 65-9=56, Resulting Numbers: [17, 8, 56] Generated Node #0,3: 11:[17, 8, 56] Operation: 65-9=56 Exploring Operation: 65-8=57, Resulting Numbers: [17, 9, 57] Generated Node #0,4: 11:[17, 9, 57] Operation: 65-8=57 Moving to Node #0,1 Current State: 11:[8, 9, 48], Operations: ['65-17=48'] Exploring Operation: 8+9=17, Resulting Numbers: [48, 17] Generated Node #0,1,0: 11:[48, 17] Operation: 8+9=17 Exploring Operation: 9-8=1, Resulting Numbers: [48, 1] Generated Node #0,1,1: 11:[48, 1] Operation: 9-8=1 Exploring Operation: 48-8=40, Resulting Numbers: [9, 40] Generated Node #0,1,2: 11:[9, 40] Operation: 48-8=40 Exploring Operation: 48/8=6, Resulting Numbers: [9, 6] Generated Node #0,1,3: 11:[9, 6] Operation: 48/8=6 Exploring Operation: 48-9=39, Resulting Numbers: [8, 39] Generated Node #0,1,4: 11:[8, 39] Operation: 48-9=39 Moving to Node #0,4 Current State: 11:[17, 9, 57], Operations: ['65-8=57'] Exploring Operation: 57-9=48, Resulting Numbers: [17, 48] Generated Node #0,4,0: 11:[17, 48] Operation: 57-9=48 Exploring Operation: 57-17=40, Resulting Numbers: [9, 40] Generated Node #0,4,1: 11:[9, 40] Operation: 57-17=40 Exploring Operation: 17-9=8, Resulting Numbers: [57, 8] Generated Node #0,4,2: 11:[57, 8] Operation: 17-9=8 Exploring Operation: 9+57=66, Resulting Numbers: [17, 66] Generated Node #0,4,3: 11:[17, 66] Operation: 9+57=66 Exploring Operation: 17+9=26, Resulting Numbers: [57, 26] Generated Node #0,4,4: 11:[57, 26] Operation: 17+9=26 Moving to Node #0,3 Current State: 11:[17, 8, 56], Operations: ['65-9=56'] Exploring Operation: 56/8=7, Resulting Numbers: [17, 7] Generated Node #0,3,0: 11:[17, 7] Operation: 56/8=7 Exploring Operation: 56-17=39, Resulting Numbers: [8, 39] Generated Node #0,3,1: 11:[8, 39] Operation: 56-17=39 Exploring Operation: 17+8=25, Resulting Numbers: [56, 25] Generated Node #0,3,2: 11:[56, 25] Operation: 17+8=25 Exploring Operation: 56-8=48, Resulting Numbers: [17, 48] Generated Node #0,3,3: 11:[17, 48] Operation: 56-8=48 Exploring Operation: 17-8=9, Resulting Numbers: [56, 9] Generated Node #0,3,4: 11:[56, 9] Operation: 17-8=9 Moving to Node #0,0 Current State: 11:[65, 9, 9], Operations: ['17-8=9'] Exploring Operation: 65-9=56, Resulting Numbers: [9, 56] Generated Node #0,0,0: 11:[9, 56] Operation: 65-9=56 Exploring Operation: 9/9=1, Resulting Numbers: [65, 1] Generated Node #0,0,1: 11:[65, 1] Operation: 9/9=1 Exploring Operation: 9+9=18, Resulting Numbers: [65, 18] Generated Node #0,0,2: 11:[65, 18] Operation: 9+9=18 Exploring Operation: 65-9=56, Resulting Numbers: [9, 56] Generated Node #0,0,3: 11:[9, 56] Operation: 65-9=56 Exploring Operation: 65+9=74, Resulting Numbers: [9, 74] Generated Node #0,0,4: 11:[9, 74] Operation: 65+9=74 Moving to Node #0,2 Current State: 11:[65, 8, 8], Operations: ['17-9=8'] Exploring Operation: 8+8=16, Resulting Numbers: [65, 16] Generated Node #0,2,0: 11:[65, 16] Operation: 8+8=16 Exploring Operation: 8/8=1, Resulting Numbers: [65, 1] Generated Node #0,2,1: 11:[65, 1] Operation: 8/8=1 Exploring Operation: 65-8=57, Resulting Numbers: [8, 57] Generated Node #0,2,2: 11:[8, 57] Operation: 65-8=57 Exploring Operation: 65-8=57, Resulting Numbers: [8, 57] Generated Node #0,2,3: 11:[8, 57] Operation: 65-8=57 Exploring Operation: 65+8=73, Resulting Numbers: [8, 73] Generated Node #0,2,4: 11:[8, 73] Operation: 65+8=73 Moving to Node #0,1,3 Current State: 11:[9, 6], Operations: ['65-17=48', '48/8=6'] Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,11 unequal: No Solution Moving to Node #0,3,0 Current State: 11:[17, 7], Operations: ['65-9=56', '56/8=7'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 17*7=119, Resulting Numbers: [119] 119,11 unequal: No Solution Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,11 unequal: No Solution Moving to Node #0,1,4 Current State: 11:[8, 39], Operations: ['65-17=48', '48-9=39'] Exploring Operation: 8*39=312, Resulting Numbers: [312] 312,11 unequal: No Solution Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,4,1 Current State: 11:[9, 40], Operations: ['65-8=57', '57-17=40'] Exploring Operation: 9*40=360, Resulting Numbers: [360] 360,11 unequal: No Solution Exploring Operation: 9+40=49, Resulting Numbers: [49] 49,11 unequal: No Solution Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[8, 39], Operations: ['65-9=56', '56-17=39'] Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 8*39=312, Resulting Numbers: [312] 312,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[9, 40], Operations: ['65-17=48', '48-8=40'] Exploring Operation: 9+40=49, Resulting Numbers: [49] 49,11 unequal: No Solution Exploring Operation: 9*40=360, Resulting Numbers: [360] 360,11 unequal: No Solution Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,4,0 Current State: 11:[17, 48], Operations: ['65-8=57', '57-9=48'] Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,11 unequal: No Solution Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[17, 48], Operations: ['65-9=56', '56-8=48'] Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,11 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[48, 17], Operations: ['65-17=48', '8+9=17'] Exploring Operation: 48*17=816, Resulting Numbers: [816] 816,11 unequal: No Solution Exploring Operation: 48+17=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,3,4 Current State: 11:[56, 9], Operations: ['65-9=56', '17-8=9'] Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 56*9=504, Resulting Numbers: [504] 504,11 unequal: No Solution Exploring Operation: 56+9=65, Resulting Numbers: [65] 65,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[48, 1], Operations: ['65-17=48', '9-8=1'] Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[9, 56], Operations: ['17-8=9', '65-9=56'] Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 9+56=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 9*56=504, Resulting Numbers: [504] 504,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[9, 56], Operations: ['17-8=9', '65-9=56'] Exploring Operation: 9+56=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 9*56=504, Resulting Numbers: [504] 504,11 unequal: No Solution Moving to Node #0,2,3 Current State: 11:[8, 57], Operations: ['17-9=8', '65-8=57'] Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,11 unequal: No Solution Exploring Operation: 8*57=456, Resulting Numbers: [456] 456,11 unequal: No Solution Exploring Operation: 8+57=65, Resulting Numbers: [65] 65,11 unequal: No Solution Moving to Node #0,2,2 Current State: 11:[8, 57], Operations: ['17-9=8', '65-8=57'] Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,11 unequal: No Solution Exploring Operation: 8+57=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 8*57=456, Resulting Numbers: [456] 456,11 unequal: No Solution Moving to Node #0,4,2 Current State: 11:[57, 8], Operations: ['65-8=57', '17-9=8'] Exploring Operation: 57+8=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 57*8=456, Resulting Numbers: [456] 456,11 unequal: No Solution Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[56, 25], Operations: ['65-9=56', '17+8=25'] Exploring Operation: 56*25=1400, Resulting Numbers: [1400] 1400,11 unequal: No Solution Exploring Operation: 56+25=81, Resulting Numbers: [81] 81,11 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,2,0 Current State: 11:[65, 16], Operations: ['17-9=8', '8+8=16'] Exploring Operation: 65+16=81, Resulting Numbers: [81] 81,11 unequal: No Solution Exploring Operation: 65*16=1040, Resulting Numbers: [1040] 1040,11 unequal: No Solution Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,11 unequal: No Solution Moving to Node #0,4,4 Current State: 11:[57, 26], Operations: ['65-8=57', '17+9=26'] Exploring Operation: 57*26=1482, Resulting Numbers: [1482] 1482,11 unequal: No Solution Exploring Operation: 57+26=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[65, 18], Operations: ['17-8=9', '9+9=18'] Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 65+18=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 65*18=1170, Resulting Numbers: [1170] 1170,11 unequal: No Solution Moving to Node #0,4,3 Current State: 11:[17, 66], Operations: ['65-8=57', '9+57=66'] Exploring Operation: 17+66=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,11 unequal: No Solution Exploring Operation: 17*66=1122, Resulting Numbers: [1122] 1122,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[65, 1], Operations: ['17-9=8', '8/8=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,11 unequal: No Solution Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,11 unequal: No Solution Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[65, 1], Operations: ['17-8=9', '9/9=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,11 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,11 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,11 unequal: No Solution Moving to Node #0,0,4 Current State: 11:[9, 74], Operations: ['17-8=9', '65+9=74'] Exploring Operation: 9*74=666, Resulting Numbers: [666] 666,11 unequal: No Solution Exploring Operation: 9+74=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,11 unequal: No Solution Moving to Node #0,2,4 Current State: 11:[8, 73], Operations: ['17-9=8', '65+8=73'] Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,11 unequal: No Solution Exploring Operation: 8*73=584, Resulting Numbers: [584] 584,11 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 99, 94, 45, 12 ]
28
[ "99-94=5", "45-12=33", "33-5=28" ]
Current State: 28:[99, 94, 45, 12], Operations: [] Exploring Operation: 99-94=5, Resulting Numbers: [45, 12, 5] Generated Node #2: [45, 12, 5] from Operation: 99-94=5 Current State: 28:[45, 12, 5], Operations: ['99-94=5'] Exploring Operation: 45-12=33, Resulting Numbers: [5, 33] Generated Node #3: [5, 33] from Operation: 45-12=33 Current State: 28:[5, 33], Operations: ['99-94=5', '45-12=33'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[99, 94, 45, 12], Operations: [] Exploring Operation: 99-45=54, Resulting Numbers: [94, 12, 54] Generated Node #0,0: 28:[94, 12, 54] Operation: 99-45=54 Exploring Operation: 99-94=5, Resulting Numbers: [45, 12, 5] Generated Node #0,1: 28:[45, 12, 5] Operation: 99-94=5 Moving to Node #0,1 Current State: 28:[45, 12, 5], Operations: ['99-94=5'] Exploring Operation: 45/5=9, Resulting Numbers: [12, 9] Generated Node #0,1,0: 28:[12, 9] Operation: 45/5=9 Exploring Operation: 45-12=33, Resulting Numbers: [5, 33] Generated Node #0,1,1: 28:[5, 33] Operation: 45-12=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[12, 9], Operations: ['99-94=5', '45/5=9'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,28 unequal: No Solution Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,28 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 #0,1,1 Current State: 28:[5, 33], Operations: ['99-94=5', '45-12=33'] Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[99, 94, 45, 12], Operations: [] Exploring Operation: 99-94=5, Resulting Numbers: [45, 12, 5] Generated Node #0,1: 28:[45, 12, 5] Operation: 99-94=5 Moving to Node #0,1 Current State: 28:[45, 12, 5], Operations: ['99-94=5'] Exploring Operation: 45-12=33, Resulting Numbers: [5, 33] Generated Node #0,1,1: 28:[5, 33] Operation: 45-12=33 Moving to Node #0,1,1 Current State: 28:[5, 33], Operations: ['99-94=5', '45-12=33'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 76, 26, 27, 31 ]
59
[ "31-26=5", "27*5=135", "135-76=59" ]
Current State: 59:[76, 26, 27, 31], Operations: [] Exploring Operation: 31-26=5, Resulting Numbers: [76, 27, 5] Generated Node #2: [76, 27, 5] from Operation: 31-26=5 Current State: 59:[76, 27, 5], Operations: ['31-26=5'] Exploring Operation: 27*5=135, Resulting Numbers: [76, 135] Generated Node #3: [76, 135] from Operation: 27*5=135 Current State: 59:[76, 135], Operations: ['31-26=5', '27*5=135'] Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[76, 26, 27, 31], Operations: [] Exploring Operation: 26+27=53, Resulting Numbers: [76, 31, 53] Generated Node #0,0: 59:[76, 31, 53] Operation: 26+27=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[76, 31, 53], Operations: ['26+27=53'] Exploring Operation: 76-31=45, Resulting Numbers: [53, 45] Generated Node #0,0,0: 59:[53, 45] Operation: 76-31=45 Moving to Node #0,0,0 Current State: 59:[53, 45], Operations: ['26+27=53', '76-31=45'] Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,59 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
[ 3, 59, 83, 34 ]
88
[ "83-34=49", "3*49=147", "147-59=88" ]
Current State: 88:[3, 59, 83, 34], Operations: [] Exploring Operation: 83-34=49, Resulting Numbers: [3, 59, 49] Generated Node #2: [3, 59, 49] from Operation: 83-34=49 Current State: 88:[3, 59, 49], Operations: ['83-34=49'] Exploring Operation: 3*49=147, Resulting Numbers: [59, 147] Generated Node #3: [59, 147] from Operation: 3*49=147 Current State: 88:[59, 147], Operations: ['83-34=49', '3*49=147'] Exploring Operation: 147-59=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[3, 59, 83, 34], Operations: [] Exploring Operation: 59-34=25, Resulting Numbers: [3, 83, 25] Generated Node #0,0: 88:[3, 83, 25] Operation: 59-34=25 Exploring Operation: 59+34=93, Resulting Numbers: [3, 83, 93] Generated Node #0,1: 88:[3, 83, 93] Operation: 59+34=93 Exploring Operation: 83-59=24, Resulting Numbers: [3, 34, 24] Generated Node #0,2: 88:[3, 34, 24] Operation: 83-59=24 Exploring Operation: 83-34=49, Resulting Numbers: [3, 59, 49] Generated Node #0,3: 88:[3, 59, 49] Operation: 83-34=49 Moving to Node #0,0 Current State: 88:[3, 83, 25], Operations: ['59-34=25'] Exploring Operation: 3+83=86, Resulting Numbers: [25, 86] Generated Node #0,0,0: 88:[25, 86] Operation: 3+83=86 Exploring Operation: 3+25=28, Resulting Numbers: [83, 28] Generated Node #0,0,1: 88:[83, 28] Operation: 3+25=28 Exploring Operation: 25-3=22, Resulting Numbers: [83, 22] Generated Node #0,0,2: 88:[83, 22] Operation: 25-3=22 Exploring Operation: 83-3=80, Resulting Numbers: [25, 80] Generated Node #0,0,3: 88:[25, 80] Operation: 83-3=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[25, 86], Operations: ['59-34=25', '3+83=86'] Exploring Operation: 25*86=2150, Resulting Numbers: [2150] 2150,88 unequal: No Solution Exploring Operation: 86-25=61, Resulting Numbers: [61] 61,88 unequal: No Solution Exploring Operation: 25+86=111, Resulting Numbers: [111] 111,88 unequal: No Solution No 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: 88:[83, 22], Operations: ['59-34=25', '25-3=22'] Exploring Operation: 83+22=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 83*22=1826, Resulting Numbers: [1826] 1826,88 unequal: No Solution Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,88 unequal: No Solution No 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: 88:[83, 28], Operations: ['59-34=25', '3+25=28'] Exploring Operation: 83-28=55, Resulting Numbers: [55] 55,88 unequal: No Solution Exploring Operation: 83*28=2324, Resulting Numbers: [2324] 2324,88 unequal: No Solution Exploring Operation: 83+28=111, Resulting Numbers: [111] 111,88 unequal: No Solution No 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: 88:[25, 80], Operations: ['59-34=25', '83-3=80'] Exploring Operation: 25*80=2000, Resulting Numbers: [2000] 2000,88 unequal: No Solution Exploring Operation: 25+80=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,88 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: 88:[3, 83, 93], Operations: ['59+34=93'] Exploring Operation: 83-3=80, Resulting Numbers: [93, 80] Generated Node #0,1,0: 88:[93, 80] Operation: 83-3=80 Exploring Operation: 93-3=90, Resulting Numbers: [83, 90] Generated Node #0,1,1: 88:[83, 90] Operation: 93-3=90 Exploring Operation: 93-83=10, Resulting Numbers: [3, 10] Generated Node #0,1,2: 88:[3, 10] Operation: 93-83=10 Exploring Operation: 3+83=86, Resulting Numbers: [93, 86] Generated Node #0,1,3: 88:[93, 86] Operation: 3+83=86 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[3, 10], Operations: ['59+34=93', '93-83=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,88 unequal: No Solution No 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: 88:[83, 90], Operations: ['59+34=93', '93-3=90'] Exploring Operation: 83+90=173, Resulting Numbers: [173] 173,88 unequal: No Solution Exploring Operation: 90-83=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 83*90=7470, Resulting Numbers: [7470] 7470,88 unequal: No Solution No 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: 88:[93, 86], Operations: ['59+34=93', '3+83=86'] Exploring Operation: 93+86=179, Resulting Numbers: [179] 179,88 unequal: No Solution Exploring Operation: 93-86=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 93*86=7998, Resulting Numbers: [7998] 7998,88 unequal: No Solution No 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: 88:[93, 80], Operations: ['59+34=93', '83-3=80'] Exploring Operation: 93*80=7440, Resulting Numbers: [7440] 7440,88 unequal: No Solution Exploring Operation: 93-80=13, Resulting Numbers: [13] 13,88 unequal: No Solution Exploring Operation: 93+80=173, Resulting Numbers: [173] 173,88 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: 88:[3, 34, 24], Operations: ['83-59=24'] Exploring Operation: 24/3=8, Resulting Numbers: [34, 8] Generated Node #0,2,0: 88:[34, 8] Operation: 24/3=8 Exploring Operation: 3+34=37, Resulting Numbers: [24, 37] Generated Node #0,2,1: 88:[24, 37] Operation: 3+34=37 Exploring Operation: 34-24=10, Resulting Numbers: [3, 10] Generated Node #0,2,2: 88:[3, 10] Operation: 34-24=10 Exploring Operation: 34-3=31, Resulting Numbers: [24, 31] Generated Node #0,2,3: 88:[24, 31] Operation: 34-3=31 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[3, 10], Operations: ['83-59=24', '34-24=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,88 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,88 unequal: No Solution No 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: 88:[24, 37], Operations: ['83-59=24', '3+34=37'] Exploring Operation: 24*37=888, Resulting Numbers: [888] 888,88 unequal: No Solution Exploring Operation: 24+37=61, Resulting Numbers: [61] 61,88 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,88 unequal: No Solution No 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: 88:[34, 8], Operations: ['83-59=24', '24/3=8'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 34+8=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 34*8=272, Resulting Numbers: [272] 272,88 unequal: No Solution No 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: 88:[24, 31], Operations: ['83-59=24', '34-3=31'] Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,88 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,88 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,88 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: 88:[3, 59, 49], Operations: ['83-34=49'] Exploring Operation: 59-3=56, Resulting Numbers: [49, 56] Generated Node #0,3,0: 88:[49, 56] Operation: 59-3=56 Exploring Operation: 59+49=108, Resulting Numbers: [3, 108] Generated Node #0,3,1: 88:[3, 108] Operation: 59+49=108 Exploring Operation: 49-3=46, Resulting Numbers: [59, 46] Generated Node #0,3,2: 88:[59, 46] Operation: 49-3=46 Exploring Operation: 59-49=10, Resulting Numbers: [3, 10] Generated Node #0,3,3: 88:[3, 10] Operation: 59-49=10 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 88:[3, 10], Operations: ['83-34=49', '59-49=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,88 unequal: No Solution No 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: 88:[49, 56], Operations: ['83-34=49', '59-3=56'] Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,88 unequal: No Solution No 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: 88:[59, 46], Operations: ['83-34=49', '49-3=46'] Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,88 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,88 unequal: No Solution No 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: 88:[3, 108], Operations: ['83-34=49', '59+49=108'] Exploring Operation: 108/3=36, Resulting Numbers: [36] 36,88 unequal: No Solution Exploring Operation: 108-3=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 3+108=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 3*108=324, Resulting Numbers: [324] 324,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 47, 15, 72, 17 ]
27
[ "47+15=62", "72+17=89", "89-62=27" ]
Current State: 27:[47, 15, 72, 17], Operations: [] Exploring Operation: 47+15=62, Resulting Numbers: [72, 17, 62] Generated Node #2: [72, 17, 62] from Operation: 47+15=62 Current State: 27:[72, 17, 62], Operations: ['47+15=62'] Exploring Operation: 72+17=89, Resulting Numbers: [62, 89] Generated Node #3: [62, 89] from Operation: 72+17=89 Current State: 27:[62, 89], Operations: ['47+15=62', '72+17=89'] Exploring Operation: 89-62=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[47, 15, 72, 17], Operations: [] Exploring Operation: 72-15=57, Resulting Numbers: [47, 17, 57] Generated Node #0,0: 27:[47, 17, 57] Operation: 72-15=57 Exploring Operation: 47-15=32, Resulting Numbers: [72, 17, 32] Generated Node #0,1: 27:[72, 17, 32] Operation: 47-15=32 Exploring Operation: 72-17=55, Resulting Numbers: [47, 15, 55] Generated Node #0,2: 27:[47, 15, 55] Operation: 72-17=55 Exploring Operation: 47-17=30, Resulting Numbers: [15, 72, 30] Generated Node #0,3: 27:[15, 72, 30] Operation: 47-17=30 Exploring Operation: 72-47=25, Resulting Numbers: [15, 17, 25] Generated Node #0,4: 27:[15, 17, 25] Operation: 72-47=25 Start Sub Search at level 1: Moving to Node #0,4 Current State: 27:[15, 17, 25], Operations: ['72-47=25'] Exploring Operation: 17-15=2, Resulting Numbers: [25, 2] Generated Node #0,4,0: 27:[25, 2] Operation: 17-15=2 Exploring Operation: 25-15=10, Resulting Numbers: [17, 10] Generated Node #0,4,1: 27:[17, 10] Operation: 25-15=10 Exploring Operation: 15+25=40, Resulting Numbers: [17, 40] Generated Node #0,4,2: 27:[17, 40] Operation: 15+25=40 Exploring Operation: 25-17=8, Resulting Numbers: [15, 8] Generated Node #0,4,3: 27:[15, 8] Operation: 25-17=8 Exploring Operation: 15+17=32, Resulting Numbers: [25, 32] Generated Node #0,4,4: 27:[25, 32] Operation: 15+17=32 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 27:[25, 2], Operations: ['72-47=25', '17-15=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,27 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[47, 15, 72, 17], Operations: [] Exploring Operation: 72-47=25, Resulting Numbers: [15, 17, 25] Generated Node #0,4: 27:[15, 17, 25] Operation: 72-47=25 Moving to Node #0,4 Current State: 27:[15, 17, 25], Operations: ['72-47=25'] Exploring Operation: 17-15=2, Resulting Numbers: [25, 2] Generated Node #0,4,0: 27:[25, 2] Operation: 17-15=2 Moving to Node #0,4,0 Current State: 27:[25, 2], Operations: ['72-47=25', '17-15=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 31, 46, 66, 50 ]
39
[ "31+46=77", "66+50=116", "116-77=39" ]
Current State: 39:[31, 46, 66, 50], Operations: [] Exploring Operation: 31+46=77, Resulting Numbers: [66, 50, 77] Generated Node #2: [66, 50, 77] from Operation: 31+46=77 Current State: 39:[66, 50, 77], Operations: ['31+46=77'] Exploring Operation: 66+50=116, Resulting Numbers: [77, 116] Generated Node #3: [77, 116] from Operation: 66+50=116 Current State: 39:[77, 116], Operations: ['31+46=77', '66+50=116'] Exploring Operation: 116-77=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[31, 46, 66, 50], Operations: [] Exploring Operation: 66-50=16, Resulting Numbers: [31, 46, 16] Generated Node #0,0: 39:[31, 46, 16] Operation: 66-50=16 Exploring Operation: 66-31=35, Resulting Numbers: [46, 50, 35] Generated Node #0,1: 39:[46, 50, 35] Operation: 66-31=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[31, 46, 16], Operations: ['66-50=16'] Exploring Operation: 31-16=15, Resulting Numbers: [46, 15] Generated Node #0,0,0: 39:[46, 15] Operation: 31-16=15 Exploring Operation: 46-31=15, Resulting Numbers: [16, 15] Generated Node #0,0,1: 39:[16, 15] Operation: 46-31=15 Moving to Node #0,0,1 Current State: 39:[16, 15], Operations: ['66-50=16', '46-31=15'] Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[46, 15], Operations: ['66-50=16', '31-16=15'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[46, 50, 35], Operations: ['66-31=35'] Exploring Operation: 50-46=4, Resulting Numbers: [35, 4] Generated Node #0,1,0: 39:[35, 4] Operation: 50-46=4 Exploring Operation: 50-35=15, Resulting Numbers: [46, 15] Generated Node #0,1,1: 39:[46, 15] Operation: 50-35=15 Moving to Node #0,1,0 Current State: 39:[35, 4], Operations: ['66-31=35', '50-46=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[31, 46, 66, 50], Operations: [] Exploring Operation: 66-31=35, Resulting Numbers: [46, 50, 35] Generated Node #0,1: 39:[46, 50, 35] Operation: 66-31=35 Moving to Node #0,1 Current State: 39:[46, 50, 35], Operations: ['66-31=35'] Exploring Operation: 50-46=4, Resulting Numbers: [35, 4] Generated Node #0,1,0: 39:[35, 4] Operation: 50-46=4 Moving to Node #0,1,0 Current State: 39:[35, 4], Operations: ['66-31=35', '50-46=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 82, 77, 87, 44 ]
42
[ "77+87=164", "164/82=2", "44-2=42" ]
Current State: 42:[82, 77, 87, 44], Operations: [] Exploring Operation: 77+87=164, Resulting Numbers: [82, 44, 164] Generated Node #2: [82, 44, 164] from Operation: 77+87=164 Current State: 42:[82, 44, 164], Operations: ['77+87=164'] Exploring Operation: 164/82=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 164/82=2 Current State: 42:[44, 2], Operations: ['77+87=164', '164/82=2'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[82, 77, 87, 44], Operations: [] Exploring Operation: 87-77=10, Resulting Numbers: [82, 44, 10] Generated Node #0,0: 42:[82, 44, 10] Operation: 87-77=10 Exploring Operation: 87-82=5, Resulting Numbers: [77, 44, 5] Generated Node #0,1: 42:[77, 44, 5] Operation: 87-82=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[77, 44, 5], Operations: ['87-82=5'] Exploring Operation: 77-44=33, Resulting Numbers: [5, 33] Generated Node #0,1,0: 42:[5, 33] Operation: 77-44=33 Exploring Operation: 77-5=72, Resulting Numbers: [44, 72] Generated Node #0,1,1: 42:[44, 72] Operation: 77-5=72 Moving to Node #0,1,0 Current State: 42:[5, 33], Operations: ['87-82=5', '77-44=33'] Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,42 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[44, 72], Operations: ['87-82=5', '77-5=72'] Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,42 unequal: No Solution Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,42 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 Current State: 42:[82, 44, 10], Operations: ['87-77=10'] Exploring Operation: 82-44=38, Resulting Numbers: [10, 38] Generated Node #0,0,0: 42:[10, 38] Operation: 82-44=38 Exploring Operation: 82-10=72, Resulting Numbers: [44, 72] Generated Node #0,0,1: 42:[44, 72] Operation: 82-10=72 Moving to Node #0,0,0 Current State: 42:[10, 38], Operations: ['87-77=10', '82-44=38'] Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[44, 72], Operations: ['87-77=10', '82-10=72'] Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,42 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,42 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
[ 24, 3, 35, 8 ]
45
[ "24*3=72", "35-8=27", "72-27=45" ]
Current State: 45:[24, 3, 35, 8], Operations: [] Exploring Operation: 24*3=72, Resulting Numbers: [35, 8, 72] Generated Node #2: [35, 8, 72] from Operation: 24*3=72 Current State: 45:[35, 8, 72], Operations: ['24*3=72'] Exploring Operation: 35-8=27, Resulting Numbers: [72, 27] Generated Node #3: [72, 27] from Operation: 35-8=27 Current State: 45:[72, 27], Operations: ['24*3=72', '35-8=27'] Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[24, 3, 35, 8], Operations: [] Exploring Operation: 35+8=43, Resulting Numbers: [24, 3, 43] Generated Node #0,0: 45:[24, 3, 43] Operation: 35+8=43 Exploring Operation: 24-8=16, Resulting Numbers: [3, 35, 16] Generated Node #0,1: 45:[3, 35, 16] Operation: 24-8=16 Exploring Operation: 35-24=11, Resulting Numbers: [3, 8, 11] Generated Node #0,2: 45:[3, 8, 11] Operation: 35-24=11 Exploring Operation: 24/8=3, Resulting Numbers: [3, 35, 3] Generated Node #0,3: 45:[3, 35, 3] Operation: 24/8=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[3, 8, 11], Operations: ['35-24=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3, 3] Generated Node #0,2,0: 45:[3, 3] Operation: 11-8=3 Exploring Operation: 8-3=5, Resulting Numbers: [11, 5] Generated Node #0,2,1: 45:[11, 5] Operation: 8-3=5 Exploring Operation: 11-3=8, Resulting Numbers: [8, 8] Generated Node #0,2,2: 45:[8, 8] Operation: 11-3=8 Exploring Operation: 3+11=14, Resulting Numbers: [8, 14] Generated Node #0,2,3: 45:[8, 14] Operation: 3+11=14 Moving to Node #0,2,0 Current State: 45:[3, 3], Operations: ['35-24=11', '11-8=3'] Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[8, 8], Operations: ['35-24=11', '11-3=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,45 unequal: No Solution Moving to Node #0,2,1 Current State: 45:[11, 5], Operations: ['35-24=11', '8-3=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,45 unequal: No Solution Moving to Node #0,2,3 Current State: 45:[8, 14], Operations: ['35-24=11', '3+11=14'] Exploring Operation: 8*14=112, Resulting Numbers: [112] 112,45 unequal: No Solution Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 45:[3, 35, 3], Operations: ['24/8=3'] Exploring Operation: 3+35=38, Resulting Numbers: [3, 38] Generated Node #0,3,0: 45:[3, 38] Operation: 3+35=38 Exploring Operation: 3+3=6, Resulting Numbers: [35, 6] Generated Node #0,3,1: 45:[35, 6] Operation: 3+3=6 Exploring Operation: 3*3=9, Resulting Numbers: [35, 9] Generated Node #0,3,2: 45:[35, 9] Operation: 3*3=9 Exploring Operation: 35+3=38, Resulting Numbers: [3, 38] Generated Node #0,3,3: 45:[3, 38] Operation: 35+3=38 Moving to Node #0,3,0 Current State: 45:[3, 38], Operations: ['24/8=3', '3+35=38'] Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,45 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,45 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[3, 38], Operations: ['24/8=3', '35+3=38'] Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,45 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,45 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[35, 9], Operations: ['24/8=3', '3*3=9'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,45 unequal: No Solution Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,45 unequal: No Solution Moving to Node #0,3,1 Current State: 45:[35, 6], Operations: ['24/8=3', '3+3=6'] Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,45 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,45 unequal: No Solution Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[24, 3, 43], Operations: ['35+8=43'] Exploring Operation: 24-3=21, Resulting Numbers: [43, 21] Generated Node #0,0,0: 45:[43, 21] Operation: 24-3=21 Exploring Operation: 3+43=46, Resulting Numbers: [24, 46] Generated Node #0,0,1: 45:[24, 46] Operation: 3+43=46 Exploring Operation: 43-24=19, Resulting Numbers: [3, 19] Generated Node #0,0,2: 45:[3, 19] Operation: 43-24=19 Exploring Operation: 24/3=8, Resulting Numbers: [43, 8] Generated Node #0,0,3: 45:[43, 8] Operation: 24/3=8 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 45:[43, 8], Operations: ['35+8=43', '24/3=8'] Exploring Operation: 43+8=51, Resulting Numbers: [51] 51,45 unequal: No Solution Exploring Operation: 43*8=344, Resulting Numbers: [344] 344,45 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 45:[3, 19], Operations: ['35+8=43', '43-24=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[43, 21], Operations: ['35+8=43', '24-3=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,45 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[24, 46], Operations: ['35+8=43', '3+43=46'] Exploring Operation: 24*46=1104, Resulting Numbers: [1104] 1104,45 unequal: No Solution Exploring Operation: 24+46=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 46-24=22, Resulting Numbers: [22] 22,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[3, 35, 16], Operations: ['24-8=16'] Exploring Operation: 35+16=51, Resulting Numbers: [3, 51] Generated Node #0,1,0: 45:[3, 51] Operation: 35+16=51 Exploring Operation: 16-3=13, Resulting Numbers: [35, 13] Generated Node #0,1,1: 45:[35, 13] Operation: 16-3=13 Exploring Operation: 3+35=38, Resulting Numbers: [16, 38] Generated Node #0,1,2: 45:[16, 38] Operation: 3+35=38 Exploring Operation: 35-16=19, Resulting Numbers: [3, 19] Generated Node #0,1,3: 45:[3, 19] Operation: 35-16=19 Moving to Node #0,1,3 Current State: 45:[3, 19], Operations: ['24-8=16', '35-16=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[3, 51], Operations: ['24-8=16', '35+16=51'] Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,45 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,45 unequal: No Solution Exploring Operation: 3*51=153, Resulting Numbers: [153] 153,45 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[16, 38], Operations: ['24-8=16', '3+35=38'] Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,45 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,45 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[35, 13], Operations: ['24-8=16', '16-3=13'] Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,45 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 89, 6, 20, 15 ]
81
[ "6*20=120", "120/15=8", "89-8=81" ]
Current State: 81:[89, 6, 20, 15], Operations: [] Exploring Operation: 6*20=120, Resulting Numbers: [89, 15, 120] Generated Node #2: [89, 15, 120] from Operation: 6*20=120 Current State: 81:[89, 15, 120], Operations: ['6*20=120'] Exploring Operation: 120/15=8, Resulting Numbers: [89, 8] Generated Node #3: [89, 8] from Operation: 120/15=8 Current State: 81:[89, 8], Operations: ['6*20=120', '120/15=8'] Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[89, 6, 20, 15], Operations: [] Exploring Operation: 6+20=26, Resulting Numbers: [89, 15, 26] Generated Node #0,0: 81:[89, 15, 26] Operation: 6+20=26 Exploring Operation: 15-6=9, Resulting Numbers: [89, 20, 9] Generated Node #0,1: 81:[89, 20, 9] Operation: 15-6=9 Exploring Operation: 20-15=5, Resulting Numbers: [89, 6, 5] Generated Node #0,2: 81:[89, 6, 5] Operation: 20-15=5 Exploring Operation: 89-6=83, Resulting Numbers: [20, 15, 83] Generated Node #0,3: 81:[20, 15, 83] Operation: 89-6=83 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[89, 6, 5], Operations: ['20-15=5'] Exploring Operation: 6+5=11, Resulting Numbers: [89, 11] Generated Node #0,2,0: 81:[89, 11] Operation: 6+5=11 Exploring Operation: 6-5=1, Resulting Numbers: [89, 1] Generated Node #0,2,1: 81:[89, 1] Operation: 6-5=1 Exploring Operation: 89-6=83, Resulting Numbers: [5, 83] Generated Node #0,2,2: 81:[5, 83] Operation: 89-6=83 Exploring Operation: 89-5=84, Resulting Numbers: [6, 84] Generated Node #0,2,3: 81:[6, 84] Operation: 89-5=84 Moving to Node #0,2,2 Current State: 81:[5, 83], Operations: ['20-15=5', '89-6=83'] Exploring Operation: 5*83=415, Resulting Numbers: [415] 415,81 unequal: No Solution Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 5+83=88, Resulting Numbers: [88] 88,81 unequal: No Solution Moving to Node #0,2,3 Current State: 81:[6, 84], Operations: ['20-15=5', '89-5=84'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 6*84=504, Resulting Numbers: [504] 504,81 unequal: No Solution Exploring Operation: 6+84=90, Resulting Numbers: [90] 90,81 unequal: No Solution Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[89, 1], Operations: ['20-15=5', '6-5=1'] Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,81 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,81 unequal: No Solution Moving to Node #0,2,0 Current State: 81:[89, 11], Operations: ['20-15=5', '6+5=11'] Exploring Operation: 89+11=100, Resulting Numbers: [100] 100,81 unequal: No Solution Exploring Operation: 89*11=979, Resulting Numbers: [979] 979,81 unequal: No Solution Exploring Operation: 89-11=78, Resulting Numbers: [78] 78,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[89, 15, 26], Operations: ['6+20=26'] Exploring Operation: 15+26=41, Resulting Numbers: [89, 41] Generated Node #0,0,0: 81:[89, 41] Operation: 15+26=41 Exploring Operation: 89-15=74, Resulting Numbers: [26, 74] Generated Node #0,0,1: 81:[26, 74] Operation: 89-15=74 Exploring Operation: 26-15=11, Resulting Numbers: [89, 11] Generated Node #0,0,2: 81:[89, 11] Operation: 26-15=11 Exploring Operation: 89+15=104, Resulting Numbers: [26, 104] Generated Node #0,0,3: 81:[26, 104] Operation: 89+15=104 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 81:[26, 74], Operations: ['6+20=26', '89-15=74'] Exploring Operation: 74-26=48, Resulting Numbers: [48] 48,81 unequal: No Solution Exploring Operation: 26*74=1924, Resulting Numbers: [1924] 1924,81 unequal: No Solution Exploring Operation: 26+74=100, Resulting Numbers: [100] 100,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 81:[89, 11], Operations: ['6+20=26', '26-15=11'] Exploring Operation: 89+11=100, Resulting Numbers: [100] 100,81 unequal: No Solution Exploring Operation: 89-11=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 89*11=979, Resulting Numbers: [979] 979,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[89, 41], Operations: ['6+20=26', '15+26=41'] Exploring Operation: 89+41=130, Resulting Numbers: [130] 130,81 unequal: No Solution Exploring Operation: 89*41=3649, Resulting Numbers: [3649] 3649,81 unequal: No Solution Exploring Operation: 89-41=48, Resulting Numbers: [48] 48,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 81:[26, 104], Operations: ['6+20=26', '89+15=104'] Exploring Operation: 26*104=2704, Resulting Numbers: [2704] 2704,81 unequal: No Solution Exploring Operation: 26+104=130, Resulting Numbers: [130] 130,81 unequal: No Solution Exploring Operation: 104-26=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 104/26=4, Resulting Numbers: [4] 4,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[89, 20, 9], Operations: ['15-6=9'] Exploring Operation: 20+9=29, Resulting Numbers: [89, 29] Generated Node #0,1,0: 81:[89, 29] Operation: 20+9=29 Exploring Operation: 89-20=69, Resulting Numbers: [9, 69] Generated Node #0,1,1: 81:[9, 69] Operation: 89-20=69 Exploring Operation: 89-9=80, Resulting Numbers: [20, 80] Generated Node #0,1,2: 81:[20, 80] Operation: 89-9=80 Exploring Operation: 20-9=11, Resulting Numbers: [89, 11] Generated Node #0,1,3: 81:[89, 11] Operation: 20-9=11 Moving to Node #0,1,2 Current State: 81:[20, 80], Operations: ['15-6=9', '89-9=80'] Exploring Operation: 20+80=100, Resulting Numbers: [100] 100,81 unequal: No Solution Exploring Operation: 80-20=60, Resulting Numbers: [60] 60,81 unequal: No Solution Exploring Operation: 20*80=1600, Resulting Numbers: [1600] 1600,81 unequal: No Solution Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[89, 11], Operations: ['15-6=9', '20-9=11'] Exploring Operation: 89-11=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 89+11=100, Resulting Numbers: [100] 100,81 unequal: No Solution Exploring Operation: 89*11=979, Resulting Numbers: [979] 979,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[89, 29], Operations: ['15-6=9', '20+9=29'] Exploring Operation: 89+29=118, Resulting Numbers: [118] 118,81 unequal: No Solution Exploring Operation: 89*29=2581, Resulting Numbers: [2581] 2581,81 unequal: No Solution Exploring Operation: 89-29=60, Resulting Numbers: [60] 60,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[9, 69], Operations: ['15-6=9', '89-20=69'] Exploring Operation: 69-9=60, Resulting Numbers: [60] 60,81 unequal: No Solution Exploring Operation: 9*69=621, Resulting Numbers: [621] 621,81 unequal: No Solution Exploring Operation: 9+69=78, Resulting Numbers: [78] 78,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[20, 15, 83], Operations: ['89-6=83'] Exploring Operation: 83-15=68, Resulting Numbers: [20, 68] Generated Node #0,3,0: 81:[20, 68] Operation: 83-15=68 Exploring Operation: 20-15=5, Resulting Numbers: [83, 5] Generated Node #0,3,1: 81:[83, 5] Operation: 20-15=5 Exploring Operation: 20+15=35, Resulting Numbers: [83, 35] Generated Node #0,3,2: 81:[83, 35] Operation: 20+15=35 Exploring Operation: 83-20=63, Resulting Numbers: [15, 63] Generated Node #0,3,3: 81:[15, 63] Operation: 83-20=63 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 81:[83, 5], Operations: ['89-6=83', '20-15=5'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 83*5=415, Resulting Numbers: [415] 415,81 unequal: No Solution Exploring Operation: 83+5=88, Resulting Numbers: [88] 88,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 81:[83, 35], Operations: ['89-6=83', '20+15=35'] Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,81 unequal: No Solution Exploring Operation: 83+35=118, Resulting Numbers: [118] 118,81 unequal: No Solution Exploring Operation: 83*35=2905, Resulting Numbers: [2905] 2905,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 81:[20, 68], Operations: ['89-6=83', '83-15=68'] Exploring Operation: 20+68=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 20*68=1360, Resulting Numbers: [1360] 1360,81 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 81:[15, 63], Operations: ['89-6=83', '83-20=63'] Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,81 unequal: No Solution Exploring Operation: 15*63=945, Resulting Numbers: [945] 945,81 unequal: No Solution Exploring Operation: 15+63=78, Resulting Numbers: [78] 78,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 75, 17, 77, 91 ]
72
[ "75-17=58", "91-77=14", "58+14=72" ]
Current State: 72:[75, 17, 77, 91], Operations: [] Exploring Operation: 75-17=58, Resulting Numbers: [77, 91, 58] Generated Node #2: [77, 91, 58] from Operation: 75-17=58 Current State: 72:[77, 91, 58], Operations: ['75-17=58'] Exploring Operation: 91-77=14, Resulting Numbers: [58, 14] Generated Node #3: [58, 14] from Operation: 91-77=14 Current State: 72:[58, 14], Operations: ['75-17=58', '91-77=14'] Exploring Operation: 58+14=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[75, 17, 77, 91], Operations: [] Exploring Operation: 91-75=16, Resulting Numbers: [17, 77, 16] Generated Node #0,0: 72:[17, 77, 16] Operation: 91-75=16 Exploring Operation: 91-77=14, Resulting Numbers: [75, 17, 14] Generated Node #0,1: 72:[75, 17, 14] Operation: 91-77=14 Exploring Operation: 91-17=74, Resulting Numbers: [75, 77, 74] Generated Node #0,2: 72:[75, 77, 74] Operation: 91-17=74 Exploring Operation: 77-75=2, Resulting Numbers: [17, 91, 2] Generated Node #0,3: 72:[17, 91, 2] Operation: 77-75=2 Moving to Node #0,1 Current State: 72:[75, 17, 14], Operations: ['91-77=14'] Exploring Operation: 17-14=3, Resulting Numbers: [75, 3] Generated Node #0,1,0: 72:[75, 3] Operation: 17-14=3 Exploring Operation: 75-17=58, Resulting Numbers: [14, 58] Generated Node #0,1,1: 72:[14, 58] Operation: 75-17=58 Exploring Operation: 17+14=31, Resulting Numbers: [75, 31] Generated Node #0,1,2: 72:[75, 31] Operation: 17+14=31 Exploring Operation: 75-14=61, Resulting Numbers: [17, 61] Generated Node #0,1,3: 72:[17, 61] Operation: 75-14=61 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[75, 3], Operations: ['91-77=14', '17-14=3'] Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[75, 17, 77, 91], Operations: [] Exploring Operation: 91-77=14, Resulting Numbers: [75, 17, 14] Generated Node #0,1: 72:[75, 17, 14] Operation: 91-77=14 Moving to Node #0,1 Current State: 72:[75, 17, 14], Operations: ['91-77=14'] Exploring Operation: 17-14=3, Resulting Numbers: [75, 3] Generated Node #0,1,0: 72:[75, 3] Operation: 17-14=3 Moving to Node #0,1,0 Current State: 72:[75, 3], Operations: ['91-77=14', '17-14=3'] Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 77, 55, 57, 98 ]
42
[ "98-77=21", "57-55=2", "21*2=42" ]
Current State: 42:[77, 55, 57, 98], Operations: [] Exploring Operation: 98-77=21, Resulting Numbers: [55, 57, 21] Generated Node #2: [55, 57, 21] from Operation: 98-77=21 Current State: 42:[55, 57, 21], Operations: ['98-77=21'] Exploring Operation: 57-55=2, Resulting Numbers: [21, 2] Generated Node #3: [21, 2] from Operation: 57-55=2 Current State: 42:[21, 2], Operations: ['98-77=21', '57-55=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[77, 55, 57, 98], Operations: [] Exploring Operation: 98-57=41, Resulting Numbers: [77, 55, 41] Generated Node #0,0: 42:[77, 55, 41] Operation: 98-57=41 Exploring Operation: 98-77=21, Resulting Numbers: [55, 57, 21] Generated Node #0,1: 42:[55, 57, 21] Operation: 98-77=21 Exploring Operation: 77-55=22, Resulting Numbers: [57, 98, 22] Generated Node #0,2: 42:[57, 98, 22] Operation: 77-55=22 Exploring Operation: 98-55=43, Resulting Numbers: [77, 57, 43] Generated Node #0,3: 42:[77, 57, 43] Operation: 98-55=43 Exploring Operation: 77-57=20, Resulting Numbers: [55, 98, 20] Generated Node #0,4: 42:[55, 98, 20] Operation: 77-57=20 Moving to Node #0,1 Current State: 42:[55, 57, 21], Operations: ['98-77=21'] Exploring Operation: 57+21=78, Resulting Numbers: [55, 78] Generated Node #0,1,0: 42:[55, 78] Operation: 57+21=78 Exploring Operation: 57-55=2, Resulting Numbers: [21, 2] Generated Node #0,1,1: 42:[21, 2] Operation: 57-55=2 Exploring Operation: 55-21=34, Resulting Numbers: [57, 34] Generated Node #0,1,2: 42:[57, 34] Operation: 55-21=34 Exploring Operation: 57-21=36, Resulting Numbers: [55, 36] Generated Node #0,1,3: 42:[55, 36] Operation: 57-21=36 Exploring Operation: 55+21=76, Resulting Numbers: [57, 76] Generated Node #0,1,4: 42:[57, 76] Operation: 55+21=76 Moving to Node #0,0 Current State: 42:[77, 55, 41], Operations: ['98-57=41'] Exploring Operation: 55+41=96, Resulting Numbers: [77, 96] Generated Node #0,0,0: 42:[77, 96] Operation: 55+41=96 Exploring Operation: 77-41=36, Resulting Numbers: [55, 36] Generated Node #0,0,1: 42:[55, 36] Operation: 77-41=36 Exploring Operation: 55-41=14, Resulting Numbers: [77, 14] Generated Node #0,0,2: 42:[77, 14] Operation: 55-41=14 Exploring Operation: 77-55=22, Resulting Numbers: [41, 22] Generated Node #0,0,3: 42:[41, 22] Operation: 77-55=22 Exploring Operation: 77+41=118, Resulting Numbers: [55, 118] Generated Node #0,0,4: 42:[55, 118] Operation: 77+41=118 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 42:[41, 22], Operations: ['98-57=41', '77-55=22'] Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,42 unequal: No Solution Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,42 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:[55, 36], Operations: ['98-57=41', '77-41=36'] Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,42 unequal: No Solution Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,42 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 #0,0,2 Current State: 42:[77, 14], Operations: ['98-57=41', '55-41=14'] Exploring Operation: 77*14=1078, Resulting Numbers: [1078] 1078,42 unequal: No Solution Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,42 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 #0,0,0 Current State: 42:[77, 96], Operations: ['98-57=41', '55+41=96'] Exploring Operation: 77*96=7392, Resulting Numbers: [7392] 7392,42 unequal: No Solution Exploring Operation: 96-77=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 77+96=173, Resulting Numbers: [173] 173,42 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 #0,0,4 Current State: 42:[55, 118], Operations: ['98-57=41', '77+41=118'] Exploring Operation: 118-55=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 55*118=6490, Resulting Numbers: [6490] 6490,42 unequal: No Solution Exploring Operation: 55+118=173, Resulting Numbers: [173] 173,42 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:[77, 57, 43], Operations: ['98-55=43'] Exploring Operation: 77+43=120, Resulting Numbers: [57, 120] Generated Node #0,3,0: 42:[57, 120] Operation: 77+43=120 Exploring Operation: 77-43=34, Resulting Numbers: [57, 34] Generated Node #0,3,1: 42:[57, 34] Operation: 77-43=34 Exploring Operation: 57-43=14, Resulting Numbers: [77, 14] Generated Node #0,3,2: 42:[77, 14] Operation: 57-43=14 Exploring Operation: 77-57=20, Resulting Numbers: [43, 20] Generated Node #0,3,3: 42:[43, 20] Operation: 77-57=20 Exploring Operation: 77+57=134, Resulting Numbers: [43, 134] Generated Node #0,3,4: 42:[43, 134] Operation: 77+57=134 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 42:[43, 20], Operations: ['98-55=43', '77-57=20'] Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,42 unequal: No Solution Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,42 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 #0,3,1 Current State: 42:[57, 34], Operations: ['98-55=43', '77-43=34'] Exploring Operation: 57+34=91, Resulting Numbers: [91] 91,42 unequal: No Solution Exploring Operation: 57*34=1938, Resulting Numbers: [1938] 1938,42 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,42 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:[77, 14], Operations: ['98-55=43', '57-43=14'] Exploring Operation: 77*14=1078, Resulting Numbers: [1078] 1078,42 unequal: No Solution Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,42 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:[57, 120], Operations: ['98-55=43', '77+43=120'] Exploring Operation: 57+120=177, Resulting Numbers: [177] 177,42 unequal: No Solution Exploring Operation: 120-57=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 57*120=6840, Resulting Numbers: [6840] 6840,42 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:[43, 134], Operations: ['98-55=43', '77+57=134'] Exploring Operation: 134-43=91, Resulting Numbers: [91] 91,42 unequal: No Solution Exploring Operation: 43+134=177, Resulting Numbers: [177] 177,42 unequal: No Solution Exploring Operation: 43*134=5762, Resulting Numbers: [5762] 5762,42 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: 42:[55, 98, 20], Operations: ['77-57=20'] Exploring Operation: 98-55=43, Resulting Numbers: [20, 43] Generated Node #0,4,0: 42:[20, 43] Operation: 98-55=43 Exploring Operation: 55+20=75, Resulting Numbers: [98, 75] Generated Node #0,4,1: 42:[98, 75] Operation: 55+20=75 Exploring Operation: 98-20=78, Resulting Numbers: [55, 78] Generated Node #0,4,2: 42:[55, 78] Operation: 98-20=78 Exploring Operation: 55-20=35, Resulting Numbers: [98, 35] Generated Node #0,4,3: 42:[98, 35] Operation: 55-20=35 Exploring Operation: 98+20=118, Resulting Numbers: [55, 118] Generated Node #0,4,4: 42:[55, 118] Operation: 98+20=118 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 42:[20, 43], Operations: ['77-57=20', '98-55=43'] Exploring Operation: 20*43=860, Resulting Numbers: [860] 860,42 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 20+43=63, Resulting Numbers: [63] 63,42 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:[55, 78], Operations: ['77-57=20', '98-20=78'] Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 55+78=133, Resulting Numbers: [133] 133,42 unequal: No Solution Exploring Operation: 55*78=4290, Resulting Numbers: [4290] 4290,42 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:[98, 35], Operations: ['77-57=20', '55-20=35'] Exploring Operation: 98+35=133, Resulting Numbers: [133] 133,42 unequal: No Solution Exploring Operation: 98*35=3430, Resulting Numbers: [3430] 3430,42 unequal: No Solution Exploring Operation: 98-35=63, Resulting Numbers: [63] 63,42 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:[98, 75], Operations: ['77-57=20', '55+20=75'] Exploring Operation: 98+75=173, Resulting Numbers: [173] 173,42 unequal: No Solution Exploring Operation: 98*75=7350, Resulting Numbers: [7350] 7350,42 unequal: No Solution Exploring Operation: 98-75=23, Resulting Numbers: [23] 23,42 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:[55, 118], Operations: ['77-57=20', '98+20=118'] Exploring Operation: 55+118=173, Resulting Numbers: [173] 173,42 unequal: No Solution Exploring Operation: 118-55=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 55*118=6490, Resulting Numbers: [6490] 6490,42 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: 42:[57, 98, 22], Operations: ['77-55=22'] Exploring Operation: 98-57=41, Resulting Numbers: [22, 41] Generated Node #0,2,0: 42:[22, 41] Operation: 98-57=41 Exploring Operation: 57-22=35, Resulting Numbers: [98, 35] Generated Node #0,2,1: 42:[98, 35] Operation: 57-22=35 Exploring Operation: 98+22=120, Resulting Numbers: [57, 120] Generated Node #0,2,2: 42:[57, 120] Operation: 98+22=120 Exploring Operation: 98-22=76, Resulting Numbers: [57, 76] Generated Node #0,2,3: 42:[57, 76] Operation: 98-22=76 Exploring Operation: 57+22=79, Resulting Numbers: [98, 79] Generated Node #0,2,4: 42:[98, 79] Operation: 57+22=79 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[22, 41], Operations: ['77-55=22', '98-57=41'] Exploring Operation: 22+41=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 22*41=902, Resulting Numbers: [902] 902,42 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,42 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:[57, 76], Operations: ['77-55=22', '98-22=76'] Exploring Operation: 57*76=4332, Resulting Numbers: [4332] 4332,42 unequal: No Solution Exploring Operation: 57+76=133, Resulting Numbers: [133] 133,42 unequal: No Solution Exploring Operation: 76-57=19, Resulting Numbers: [19] 19,42 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:[98, 35], Operations: ['77-55=22', '57-22=35'] Exploring Operation: 98-35=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 98+35=133, Resulting Numbers: [133] 133,42 unequal: No Solution Exploring Operation: 98*35=3430, Resulting Numbers: [3430] 3430,42 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:[57, 120], Operations: ['77-55=22', '98+22=120'] Exploring Operation: 120-57=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 57+120=177, Resulting Numbers: [177] 177,42 unequal: No Solution Exploring Operation: 57*120=6840, Resulting Numbers: [6840] 6840,42 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:[98, 79], Operations: ['77-55=22', '57+22=79'] Exploring Operation: 98+79=177, Resulting Numbers: [177] 177,42 unequal: No Solution Exploring Operation: 98*79=7742, Resulting Numbers: [7742] 7742,42 unequal: No Solution Exploring Operation: 98-79=19, Resulting Numbers: [19] 19,42 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: 42:[21, 2], Operations: ['98-77=21', '57-55=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[77, 55, 57, 98], Operations: [] Exploring Operation: 98-77=21, Resulting Numbers: [55, 57, 21] Generated Node #0,1: 42:[55, 57, 21] Operation: 98-77=21 Moving to Node #0,1 Current State: 42:[55, 57, 21], Operations: ['98-77=21'] Exploring Operation: 57-55=2, Resulting Numbers: [21, 2] Generated Node #0,1,1: 42:[21, 2] Operation: 57-55=2 Moving to Node #0,1,1 Current State: 42:[21, 2], Operations: ['98-77=21', '57-55=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.915799
hs_5
mult_heuristic
[ 56, 59, 10, 34 ]
50
[ "56+34=90", "90/10=9", "59-9=50" ]
Current State: 50:[56, 59, 10, 34], Operations: [] Exploring Operation: 56+34=90, Resulting Numbers: [59, 10, 90] Generated Node #2: [59, 10, 90] from Operation: 56+34=90 Current State: 50:[59, 10, 90], Operations: ['56+34=90'] Exploring Operation: 90/10=9, Resulting Numbers: [59, 9] Generated Node #3: [59, 9] from Operation: 90/10=9 Current State: 50:[59, 9], Operations: ['56+34=90', '90/10=9'] Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[56, 59, 10, 34], Operations: [] Exploring Operation: 59-34=25, Resulting Numbers: [56, 10, 25] Generated Node #0,0: 50:[56, 10, 25] Operation: 59-34=25 Moving to Node #0,0 Current State: 50:[56, 10, 25], Operations: ['59-34=25'] Exploring Operation: 56-10=46, Resulting Numbers: [25, 46] Generated Node #0,0,0: 50:[25, 46] Operation: 56-10=46 Moving to Node #0,0,0 Current State: 50:[25, 46], Operations: ['59-34=25', '56-10=46'] Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,50 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 41, 71, 40, 7 ]
23
[ "41*40=1640", "1640-7=1633", "1633/71=23" ]
Current State: 23:[41, 71, 40, 7], Operations: [] Exploring Operation: 41*40=1640, Resulting Numbers: [71, 7, 1640] Generated Node #2: [71, 7, 1640] from Operation: 41*40=1640 Current State: 23:[71, 7, 1640], Operations: ['41*40=1640'] Exploring Operation: 1640-7=1633, Resulting Numbers: [71, 1633] Generated Node #3: [71, 1633] from Operation: 1640-7=1633 Current State: 23:[71, 1633], Operations: ['41*40=1640', '1640-7=1633'] Exploring Operation: 1633/71=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[41, 71, 40, 7], Operations: [] Exploring Operation: 41-7=34, Resulting Numbers: [71, 40, 34] Generated Node #0,0: 23:[71, 40, 34] Operation: 41-7=34 Exploring Operation: 71-7=64, Resulting Numbers: [41, 40, 64] Generated Node #0,1: 23:[41, 40, 64] Operation: 71-7=64 Exploring Operation: 71-40=31, Resulting Numbers: [41, 7, 31] Generated Node #0,2: 23:[41, 7, 31] Operation: 71-40=31 Exploring Operation: 40-7=33, Resulting Numbers: [41, 71, 33] Generated Node #0,3: 23:[41, 71, 33] Operation: 40-7=33 Exploring Operation: 71-41=30, Resulting Numbers: [40, 7, 30] Generated Node #0,4: 23:[40, 7, 30] Operation: 71-41=30 Start Sub Search at level 1: Moving to Node #0,4 Current State: 23:[40, 7, 30], Operations: ['71-41=30'] Exploring Operation: 40-30=10, Resulting Numbers: [7, 10] Generated Node #0,4,0: 23:[7, 10] Operation: 40-30=10 Exploring Operation: 40+7=47, Resulting Numbers: [30, 47] Generated Node #0,4,1: 23:[30, 47] Operation: 40+7=47 Exploring Operation: 7+30=37, Resulting Numbers: [40, 37] Generated Node #0,4,2: 23:[40, 37] Operation: 7+30=37 Exploring Operation: 40-7=33, Resulting Numbers: [30, 33] Generated Node #0,4,3: 23:[30, 33] Operation: 40-7=33 Exploring Operation: 30-7=23, Resulting Numbers: [40, 23] Generated Node #0,4,4: 23:[40, 23] Operation: 30-7=23 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 23:[30, 33], Operations: ['71-41=30', '40-7=33'] Exploring Operation: 30*33=990, Resulting Numbers: [990] 990,23 unequal: No Solution Exploring Operation: 30+33=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,23 unequal: No Solution No 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: 23:[40, 23], Operations: ['71-41=30', '30-7=23'] Exploring Operation: 40*23=920, Resulting Numbers: [920] 920,23 unequal: No Solution Exploring Operation: 40+23=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,23 unequal: No Solution No 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: 23:[7, 10], Operations: ['71-41=30', '40-30=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 23:[30, 47], Operations: ['71-41=30', '40+7=47'] Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,23 unequal: No Solution No 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: 23:[40, 37], Operations: ['71-41=30', '7+30=37'] Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 40*37=1480, Resulting Numbers: [1480] 1480,23 unequal: No Solution Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,23 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: 23:[41, 7, 31], Operations: ['71-40=31'] Exploring Operation: 41-31=10, Resulting Numbers: [7, 10] Generated Node #0,2,0: 23:[7, 10] Operation: 41-31=10 Exploring Operation: 31-7=24, Resulting Numbers: [41, 24] Generated Node #0,2,1: 23:[41, 24] Operation: 31-7=24 Exploring Operation: 7+31=38, Resulting Numbers: [41, 38] Generated Node #0,2,2: 23:[41, 38] Operation: 7+31=38 Exploring Operation: 41-7=34, Resulting Numbers: [31, 34] Generated Node #0,2,3: 23:[31, 34] Operation: 41-7=34 Exploring Operation: 41+7=48, Resulting Numbers: [31, 48] Generated Node #0,2,4: 23:[31, 48] Operation: 41+7=48 Moving to Node #0,2,1 Current State: 23:[41, 24], Operations: ['71-40=31', '31-7=24'] Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[31, 34], Operations: ['71-40=31', '41-7=34'] Exploring Operation: 31*34=1054, Resulting Numbers: [1054] 1054,23 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 31+34=65, Resulting Numbers: [65] 65,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[7, 10], Operations: ['71-40=31', '41-31=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[41, 38], Operations: ['71-40=31', '7+31=38'] Exploring Operation: 41*38=1558, Resulting Numbers: [1558] 1558,23 unequal: No Solution Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,23 unequal: No Solution Moving to Node #0,2,4 Current State: 23:[31, 48], Operations: ['71-40=31', '41+7=48'] Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 31*48=1488, Resulting Numbers: [1488] 1488,23 unequal: No Solution Exploring Operation: 31+48=79, Resulting Numbers: [79] 79,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[71, 40, 34], Operations: ['41-7=34'] Exploring Operation: 71+40=111, Resulting Numbers: [34, 111] Generated Node #0,0,0: 23:[34, 111] Operation: 71+40=111 Exploring Operation: 40-34=6, Resulting Numbers: [71, 6] Generated Node #0,0,1: 23:[71, 6] Operation: 40-34=6 Exploring Operation: 71-34=37, Resulting Numbers: [40, 37] Generated Node #0,0,2: 23:[40, 37] Operation: 71-34=37 Exploring Operation: 71+34=105, Resulting Numbers: [40, 105] Generated Node #0,0,3: 23:[40, 105] Operation: 71+34=105 Exploring Operation: 71-40=31, Resulting Numbers: [34, 31] Generated Node #0,0,4: 23:[34, 31] Operation: 71-40=31 Moving to Node #0,0,4 Current State: 23:[34, 31], Operations: ['41-7=34', '71-40=31'] Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 34*31=1054, Resulting Numbers: [1054] 1054,23 unequal: No Solution Exploring Operation: 34+31=65, Resulting Numbers: [65] 65,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[40, 37], Operations: ['41-7=34', '71-34=37'] Exploring Operation: 40*37=1480, Resulting Numbers: [1480] 1480,23 unequal: No Solution Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[71, 6], Operations: ['41-7=34', '40-34=6'] Exploring Operation: 71*6=426, Resulting Numbers: [426] 426,23 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 71+6=77, Resulting Numbers: [77] 77,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[34, 111], Operations: ['41-7=34', '71+40=111'] Exploring Operation: 111-34=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 34*111=3774, Resulting Numbers: [3774] 3774,23 unequal: No Solution Exploring Operation: 34+111=145, Resulting Numbers: [145] 145,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[40, 105], Operations: ['41-7=34', '71+34=105'] Exploring Operation: 40+105=145, Resulting Numbers: [145] 145,23 unequal: No Solution Exploring Operation: 105-40=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 40*105=4200, Resulting Numbers: [4200] 4200,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[41, 40, 64], Operations: ['71-7=64'] Exploring Operation: 64-41=23, Resulting Numbers: [40, 23] Generated Node #0,1,0: 23:[40, 23] Operation: 64-41=23 Exploring Operation: 41-40=1, Resulting Numbers: [64, 1] Generated Node #0,1,1: 23:[64, 1] Operation: 41-40=1 Exploring Operation: 41+40=81, Resulting Numbers: [64, 81] Generated Node #0,1,2: 23:[64, 81] Operation: 41+40=81 Exploring Operation: 41+64=105, Resulting Numbers: [40, 105] Generated Node #0,1,3: 23:[40, 105] Operation: 41+64=105 Exploring Operation: 64-40=24, Resulting Numbers: [41, 24] Generated Node #0,1,4: 23:[41, 24] Operation: 64-40=24 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[40, 23], Operations: ['71-7=64', '64-41=23'] Exploring Operation: 40+23=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 40*23=920, Resulting Numbers: [920] 920,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 23:[41, 24], Operations: ['71-7=64', '64-40=24'] Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,23 unequal: No Solution Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,23 unequal: No Solution No 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: 23:[64, 1], Operations: ['71-7=64', '41-40=1'] Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 64+1=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 64/1=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,23 unequal: No Solution No 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: 23:[64, 81], Operations: ['71-7=64', '41+40=81'] Exploring Operation: 64+81=145, Resulting Numbers: [145] 145,23 unequal: No Solution Exploring Operation: 81-64=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 64*81=5184, Resulting Numbers: [5184] 5184,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 23:[40, 105], Operations: ['71-7=64', '41+64=105'] Exploring Operation: 40*105=4200, Resulting Numbers: [4200] 4200,23 unequal: No Solution Exploring Operation: 105-40=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 40+105=145, Resulting Numbers: [145] 145,23 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: 23:[41, 71, 33], Operations: ['40-7=33'] Exploring Operation: 71-33=38, Resulting Numbers: [41, 38] Generated Node #0,3,0: 23:[41, 38] Operation: 71-33=38 Exploring Operation: 41+71=112, Resulting Numbers: [33, 112] Generated Node #0,3,1: 23:[33, 112] Operation: 41+71=112 Exploring Operation: 41-33=8, Resulting Numbers: [71, 8] Generated Node #0,3,2: 23:[71, 8] Operation: 41-33=8 Exploring Operation: 71-41=30, Resulting Numbers: [33, 30] Generated Node #0,3,3: 23:[33, 30] Operation: 71-41=30 Exploring Operation: 41+33=74, Resulting Numbers: [71, 74] Generated Node #0,3,4: 23:[71, 74] Operation: 41+33=74 Moving to Node #0,3,3 Current State: 23:[33, 30], Operations: ['40-7=33', '71-41=30'] Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,23 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[41, 38], Operations: ['40-7=33', '71-33=38'] Exploring Operation: 41*38=1558, Resulting Numbers: [1558] 1558,23 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,23 unequal: No Solution Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[71, 8], Operations: ['40-7=33', '41-33=8'] Exploring Operation: 71+8=79, Resulting Numbers: [79] 79,23 unequal: No Solution Exploring Operation: 71-8=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 71*8=568, Resulting Numbers: [568] 568,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[33, 112], Operations: ['40-7=33', '41+71=112'] Exploring Operation: 33+112=145, Resulting Numbers: [145] 145,23 unequal: No Solution Exploring Operation: 112-33=79, Resulting Numbers: [79] 79,23 unequal: No Solution Exploring Operation: 33*112=3696, Resulting Numbers: [3696] 3696,23 unequal: No Solution Moving to Node #0,3,4 Current State: 23:[71, 74], Operations: ['40-7=33', '41+33=74'] Exploring Operation: 74-71=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 71*74=5254, Resulting Numbers: [5254] 5254,23 unequal: No Solution Exploring Operation: 71+74=145, Resulting Numbers: [145] 145,23 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
[ 29, 80, 42, 11 ]
44
[ "29+11=40", "80/40=2", "42+2=44" ]
Current State: 44:[29, 80, 42, 11], Operations: [] Exploring Operation: 29+11=40, Resulting Numbers: [80, 42, 40] Generated Node #2: [80, 42, 40] from Operation: 29+11=40 Current State: 44:[80, 42, 40], Operations: ['29+11=40'] Exploring Operation: 80/40=2, Resulting Numbers: [42, 2] Generated Node #3: [42, 2] from Operation: 80/40=2 Current State: 44:[42, 2], Operations: ['29+11=40', '80/40=2'] Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[29, 80, 42, 11], Operations: [] Exploring Operation: 80-29=51, Resulting Numbers: [42, 11, 51] Generated Node #0,0: 44:[42, 11, 51] Operation: 80-29=51 Moving to Node #0,0 Current State: 44:[42, 11, 51], Operations: ['80-29=51'] Exploring Operation: 51-42=9, Resulting Numbers: [11, 9] Generated Node #0,0,0: 44:[11, 9] Operation: 51-42=9 Moving to Node #0,0,0 Current State: 44:[11, 9], Operations: ['80-29=51', '51-42=9'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,44 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 57, 22, 32, 41 ]
35
[ "41-22=19", "57/19=3", "32+3=35" ]
Current State: 35:[57, 22, 32, 41], Operations: [] Exploring Operation: 41-22=19, Resulting Numbers: [57, 32, 19] Generated Node #2: [57, 32, 19] from Operation: 41-22=19 Current State: 35:[57, 32, 19], Operations: ['41-22=19'] Exploring Operation: 57/19=3, Resulting Numbers: [32, 3] Generated Node #3: [32, 3] from Operation: 57/19=3 Current State: 35:[32, 3], Operations: ['41-22=19', '57/19=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[57, 22, 32, 41], Operations: [] Exploring Operation: 57-32=25, Resulting Numbers: [22, 41, 25] Generated Node #0,0: 35:[22, 41, 25] Operation: 57-32=25 Exploring Operation: 32-22=10, Resulting Numbers: [57, 41, 10] Generated Node #0,1: 35:[57, 41, 10] Operation: 32-22=10 Exploring Operation: 41-22=19, Resulting Numbers: [57, 32, 19] Generated Node #0,2: 35:[57, 32, 19] Operation: 41-22=19 Exploring Operation: 57-22=35, Resulting Numbers: [32, 41, 35] Generated Node #0,3: 35:[32, 41, 35] Operation: 57-22=35 Exploring Operation: 57-41=16, Resulting Numbers: [22, 32, 16] Generated Node #0,4: 35:[22, 32, 16] Operation: 57-41=16 Moving to Node #0,3 Current State: 35:[32, 41, 35], Operations: ['57-22=35'] Exploring Operation: 32+41=73, Resulting Numbers: [35, 73] Generated Node #0,3,0: 35:[35, 73] Operation: 32+41=73 Exploring Operation: 35-32=3, Resulting Numbers: [41, 3] Generated Node #0,3,1: 35:[41, 3] Operation: 35-32=3 Exploring Operation: 41-35=6, Resulting Numbers: [32, 6] Generated Node #0,3,2: 35:[32, 6] Operation: 41-35=6 Exploring Operation: 41-32=9, Resulting Numbers: [35, 9] Generated Node #0,3,3: 35:[35, 9] Operation: 41-32=9 Exploring Operation: 32+35=67, Resulting Numbers: [41, 67] Generated Node #0,3,4: 35:[41, 67] Operation: 32+35=67 Moving to Node #0,4 Current State: 35:[22, 32, 16], Operations: ['57-41=16'] Exploring Operation: 22-16=6, Resulting Numbers: [32, 6] Generated Node #0,4,0: 35:[32, 6] Operation: 22-16=6 Exploring Operation: 32-22=10, Resulting Numbers: [16, 10] Generated Node #0,4,1: 35:[16, 10] Operation: 32-22=10 Exploring Operation: 32-16=16, Resulting Numbers: [22, 16] Generated Node #0,4,2: 35:[22, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [22, 2] Generated Node #0,4,3: 35:[22, 2] Operation: 32/16=2 Exploring Operation: 22+16=38, Resulting Numbers: [32, 38] Generated Node #0,4,4: 35:[32, 38] Operation: 22+16=38 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 35:[32, 6], Operations: ['57-41=16', '22-16=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,35 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 #0,4,4 Current State: 35:[32, 38], Operations: ['57-41=16', '22+16=38'] Exploring Operation: 32*38=1216, Resulting Numbers: [1216] 1216,35 unequal: No Solution Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,35 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 #0,4,1 Current State: 35:[16, 10], Operations: ['57-41=16', '32-22=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,35 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,35 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 #0,4,3 Current State: 35:[22, 2], Operations: ['57-41=16', '32/16=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,35 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,35 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 #0,4,2 Current State: 35:[22, 16], Operations: ['57-41=16', '32-16=16'] Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,35 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,35 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: 35:[22, 41, 25], Operations: ['57-32=25'] Exploring Operation: 25-22=3, Resulting Numbers: [41, 3] Generated Node #0,0,0: 35:[41, 3] Operation: 25-22=3 Exploring Operation: 41-22=19, Resulting Numbers: [25, 19] Generated Node #0,0,1: 35:[25, 19] Operation: 41-22=19 Exploring Operation: 22+25=47, Resulting Numbers: [41, 47] Generated Node #0,0,2: 35:[41, 47] Operation: 22+25=47 Exploring Operation: 22+41=63, Resulting Numbers: [25, 63] Generated Node #0,0,3: 35:[25, 63] Operation: 22+41=63 Exploring Operation: 41-25=16, Resulting Numbers: [22, 16] Generated Node #0,0,4: 35:[22, 16] Operation: 41-25=16 Moving to Node #0,1 Current State: 35:[57, 41, 10], Operations: ['32-22=10'] Exploring Operation: 41+10=51, Resulting Numbers: [57, 51] Generated Node #0,1,0: 35:[57, 51] Operation: 41+10=51 Exploring Operation: 57+10=67, Resulting Numbers: [41, 67] Generated Node #0,1,1: 35:[41, 67] Operation: 57+10=67 Exploring Operation: 57-41=16, Resulting Numbers: [10, 16] Generated Node #0,1,2: 35:[10, 16] Operation: 57-41=16 Exploring Operation: 57-10=47, Resulting Numbers: [41, 47] Generated Node #0,1,3: 35:[41, 47] Operation: 57-10=47 Exploring Operation: 41-10=31, Resulting Numbers: [57, 31] Generated Node #0,1,4: 35:[57, 31] Operation: 41-10=31 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 35:[10, 16], Operations: ['32-22=10', '57-41=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,35 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 #0,1,3 Current State: 35:[41, 47], Operations: ['32-22=10', '57-10=47'] Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,35 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,35 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 #0,1,4 Current State: 35:[57, 31], Operations: ['32-22=10', '41-10=31'] Exploring Operation: 57*31=1767, Resulting Numbers: [1767] 1767,35 unequal: No Solution Exploring Operation: 57+31=88, Resulting Numbers: [88] 88,35 unequal: No Solution Exploring Operation: 57-31=26, Resulting Numbers: [26] 26,35 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 #0,1,0 Current State: 35:[57, 51], Operations: ['32-22=10', '41+10=51'] Exploring Operation: 57-51=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 57+51=108, Resulting Numbers: [108] 108,35 unequal: No Solution Exploring Operation: 57*51=2907, Resulting Numbers: [2907] 2907,35 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 #0,1,1 Current State: 35:[41, 67], Operations: ['32-22=10', '57+10=67'] Exploring Operation: 41+67=108, Resulting Numbers: [108] 108,35 unequal: No Solution Exploring Operation: 41*67=2747, Resulting Numbers: [2747] 2747,35 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,35 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: 35:[57, 32, 19], Operations: ['41-22=19'] Exploring Operation: 57/19=3, Resulting Numbers: [32, 3] Generated Node #0,2,0: 35:[32, 3] Operation: 57/19=3 Exploring Operation: 57-19=38, Resulting Numbers: [32, 38] Generated Node #0,2,1: 35:[32, 38] Operation: 57-19=38 Exploring Operation: 32-19=13, Resulting Numbers: [57, 13] Generated Node #0,2,2: 35:[57, 13] Operation: 32-19=13 Exploring Operation: 57-32=25, Resulting Numbers: [19, 25] Generated Node #0,2,3: 35:[19, 25] Operation: 57-32=25 Exploring Operation: 32+19=51, Resulting Numbers: [57, 51] Generated Node #0,2,4: 35:[57, 51] Operation: 32+19=51 Moving to Node #0,3,3 Current State: 35:[35, 9], Operations: ['57-22=35', '41-32=9'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,35 unequal: No Solution Moving to Node #0,3,2 Current State: 35:[32, 6], Operations: ['57-22=35', '41-35=6'] Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,35 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[32, 3], Operations: ['41-22=19', '57/19=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,35 unequal: No Solution Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,35 unequal: No Solution Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[57, 22, 32, 41], Operations: [] Exploring Operation: 41-22=19, Resulting Numbers: [57, 32, 19] Generated Node #0,2: 35:[57, 32, 19] Operation: 41-22=19 Moving to Node #0,2 Current State: 35:[57, 32, 19], Operations: ['41-22=19'] Exploring Operation: 57/19=3, Resulting Numbers: [32, 3] Generated Node #0,2,0: 35:[32, 3] Operation: 57/19=3 Moving to Node #0,2,0 Current State: 35:[32, 3], Operations: ['41-22=19', '57/19=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.935764
hs_5
mult_heuristic
[ 80, 26, 93, 66 ]
79
[ "80+26=106", "93-66=27", "106-27=79" ]
Current State: 79:[80, 26, 93, 66], Operations: [] Exploring Operation: 80+26=106, Resulting Numbers: [93, 66, 106] Generated Node #2: [93, 66, 106] from Operation: 80+26=106 Current State: 79:[93, 66, 106], Operations: ['80+26=106'] Exploring Operation: 93-66=27, Resulting Numbers: [106, 27] Generated Node #3: [106, 27] from Operation: 93-66=27 Current State: 79:[106, 27], Operations: ['80+26=106', '93-66=27'] Exploring Operation: 106-27=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[80, 26, 93, 66], Operations: [] Exploring Operation: 80-26=54, Resulting Numbers: [93, 66, 54] Generated Node #0,0: 79:[93, 66, 54] Operation: 80-26=54 Exploring Operation: 26+66=92, Resulting Numbers: [80, 93, 92] Generated Node #0,1: 79:[80, 93, 92] Operation: 26+66=92 Exploring Operation: 93-26=67, Resulting Numbers: [80, 66, 67] Generated Node #0,2: 79:[80, 66, 67] Operation: 93-26=67 Exploring Operation: 80+26=106, Resulting Numbers: [93, 66, 106] Generated Node #0,3: 79:[93, 66, 106] Operation: 80+26=106 Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[80, 66, 67], Operations: ['93-26=67'] Exploring Operation: 80-66=14, Resulting Numbers: [67, 14] Generated Node #0,2,0: 79:[67, 14] Operation: 80-66=14 Exploring Operation: 66+67=133, Resulting Numbers: [80, 133] Generated Node #0,2,1: 79:[80, 133] Operation: 66+67=133 Exploring Operation: 80+66=146, Resulting Numbers: [67, 146] Generated Node #0,2,2: 79:[67, 146] Operation: 80+66=146 Exploring Operation: 80-67=13, Resulting Numbers: [66, 13] Generated Node #0,2,3: 79:[66, 13] Operation: 80-67=13 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 79:[80, 133], Operations: ['93-26=67', '66+67=133'] Exploring Operation: 133-80=53, Resulting Numbers: [53] 53,79 unequal: No Solution Exploring Operation: 80+133=213, Resulting Numbers: [213] 213,79 unequal: No Solution Exploring Operation: 80*133=10640, Resulting Numbers: [10640] 10640,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 79:[67, 14], Operations: ['93-26=67', '80-66=14'] Exploring Operation: 67*14=938, Resulting Numbers: [938] 938,79 unequal: No Solution Exploring Operation: 67+14=81, Resulting Numbers: [81] 81,79 unequal: No Solution Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 79:[67, 146], Operations: ['93-26=67', '80+66=146'] Exploring Operation: 146-67=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[80, 26, 93, 66], Operations: [] Exploring Operation: 93-26=67, Resulting Numbers: [80, 66, 67] Generated Node #0,2: 79:[80, 66, 67] Operation: 93-26=67 Moving to Node #0,2 Current State: 79:[80, 66, 67], Operations: ['93-26=67'] Exploring Operation: 80+66=146, Resulting Numbers: [67, 146] Generated Node #0,2,2: 79:[67, 146] Operation: 80+66=146 Moving to Node #0,2,2 Current State: 79:[67, 146], Operations: ['93-26=67', '80+66=146'] Exploring Operation: 146-67=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 10, 31, 65, 31 ]
30
[ "65-31=34", "34-31=3", "10*3=30" ]
Current State: 30:[10, 31, 65, 31], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [10, 34] Generated Node #2: [10, 34] from Operation: 65-31=34 Current State: 30:[10, 34], Operations: ['65-31=34'] Exploring Operation: 34-31=3, Resulting Numbers: [10, 3] Generated Node #3: [10, 3] from Operation: 34-31=3 Current State: 30:[10, 3], Operations: ['65-31=34', '34-31=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[10, 31, 65, 31], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [10, 31, 34] Generated Node #0,0: 30:[10, 31, 34] Operation: 65-31=34 Exploring Operation: 65-31=34, Resulting Numbers: [10, 31, 34] Generated Node #0,1: 30:[10, 31, 34] Operation: 65-31=34 Moving to Node #0,0 Current State: 30:[10, 31, 34], Operations: ['65-31=34'] Exploring Operation: 34-31=3, Resulting Numbers: [10, 3] Generated Node #0,0,0: 30:[10, 3] Operation: 34-31=3 Exploring Operation: 34-10=24, Resulting Numbers: [31, 24] Generated Node #0,0,1: 30:[31, 24] Operation: 34-10=24 Moving to Node #0,1 Current State: 30:[10, 31, 34], Operations: ['65-31=34'] Exploring Operation: 34-10=24, Resulting Numbers: [31, 24] Generated Node #0,1,0: 30:[31, 24] Operation: 34-10=24 Exploring Operation: 34-31=3, Resulting Numbers: [10, 3] Generated Node #0,1,1: 30:[10, 3] Operation: 34-31=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[10, 3], Operations: ['65-31=34', '34-31=3'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[10, 31, 65, 31], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [10, 31, 34] Generated Node #0,1: 30:[10, 31, 34] Operation: 65-31=34 Moving to Node #0,1 Current State: 30:[10, 31, 34], Operations: ['65-31=34'] Exploring Operation: 34-31=3, Resulting Numbers: [10, 3] Generated Node #0,1,1: 30:[10, 3] Operation: 34-31=3 Moving to Node #0,1,1 Current State: 30:[10, 3], Operations: ['65-31=34', '34-31=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 27, 83, 51, 29 ]
30
[ "27+83=110", "51+29=80", "110-80=30" ]
Current State: 30:[27, 83, 51, 29], Operations: [] Exploring Operation: 27+83=110, Resulting Numbers: [51, 29, 110] Generated Node #2: [51, 29, 110] from Operation: 27+83=110 Current State: 30:[51, 29, 110], Operations: ['27+83=110'] Exploring Operation: 51+29=80, Resulting Numbers: [110, 80] Generated Node #3: [110, 80] from Operation: 51+29=80 Current State: 30:[110, 80], Operations: ['27+83=110', '51+29=80'] Exploring Operation: 110-80=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[27, 83, 51, 29], Operations: [] Exploring Operation: 83-51=32, Resulting Numbers: [27, 29, 32] Generated Node #0,0: 30:[27, 29, 32] Operation: 83-51=32 Exploring Operation: 51-29=22, Resulting Numbers: [27, 83, 22] Generated Node #0,1: 30:[27, 83, 22] Operation: 51-29=22 Exploring Operation: 83-29=54, Resulting Numbers: [27, 51, 54] Generated Node #0,2: 30:[27, 51, 54] Operation: 83-29=54 Exploring Operation: 51-27=24, Resulting Numbers: [83, 29, 24] Generated Node #0,3: 30:[83, 29, 24] Operation: 51-27=24 Exploring Operation: 83-27=56, Resulting Numbers: [51, 29, 56] Generated Node #0,4: 30:[51, 29, 56] Operation: 83-27=56 Moving to Node #0,0 Current State: 30:[27, 29, 32], Operations: ['83-51=32'] Exploring Operation: 29-27=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 30:[32, 2] Operation: 29-27=2 Exploring Operation: 27+29=56, Resulting Numbers: [32, 56] Generated Node #0,0,1: 30:[32, 56] Operation: 27+29=56 Exploring Operation: 32-27=5, Resulting Numbers: [29, 5] Generated Node #0,0,2: 30:[29, 5] Operation: 32-27=5 Exploring Operation: 32-29=3, Resulting Numbers: [27, 3] Generated Node #0,0,3: 30:[27, 3] Operation: 32-29=3 Exploring Operation: 27+32=59, Resulting Numbers: [29, 59] Generated Node #0,0,4: 30:[29, 59] Operation: 27+32=59 Moving to Node #0,4 Current State: 30:[51, 29, 56], Operations: ['83-27=56'] Exploring Operation: 56-29=27, Resulting Numbers: [51, 27] Generated Node #0,4,0: 30:[51, 27] Operation: 56-29=27 Exploring Operation: 51-29=22, Resulting Numbers: [56, 22] Generated Node #0,4,1: 30:[56, 22] Operation: 51-29=22 Exploring Operation: 56-51=5, Resulting Numbers: [29, 5] Generated Node #0,4,2: 30:[29, 5] Operation: 56-51=5 Exploring Operation: 51+29=80, Resulting Numbers: [56, 80] Generated Node #0,4,3: 30:[56, 80] Operation: 51+29=80 Exploring Operation: 29+56=85, Resulting Numbers: [51, 85] Generated Node #0,4,4: 30:[51, 85] Operation: 29+56=85 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 30:[29, 5], Operations: ['83-27=56', '56-51=5'] Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,30 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 30:[51, 27], Operations: ['83-27=56', '56-29=27'] Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,30 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 51*27=1377, Resulting Numbers: [1377] 1377,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 30:[56, 22], Operations: ['83-27=56', '51-29=22'] Exploring Operation: 56+22=78, Resulting Numbers: [78] 78,30 unequal: No Solution Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 56*22=1232, Resulting Numbers: [1232] 1232,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 30:[56, 80], Operations: ['83-27=56', '51+29=80'] Exploring Operation: 56+80=136, Resulting Numbers: [136] 136,30 unequal: No Solution Exploring Operation: 80-56=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 56*80=4480, Resulting Numbers: [4480] 4480,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 30:[51, 85], Operations: ['83-27=56', '29+56=85'] Exploring Operation: 51+85=136, Resulting Numbers: [136] 136,30 unequal: No Solution Exploring Operation: 51*85=4335, Resulting Numbers: [4335] 4335,30 unequal: No Solution Exploring Operation: 85-51=34, Resulting Numbers: [34] 34,30 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: 30:[27, 51, 54], Operations: ['83-29=54'] Exploring Operation: 54-51=3, Resulting Numbers: [27, 3] Generated Node #0,2,0: 30:[27, 3] Operation: 54-51=3 Exploring Operation: 54-27=27, Resulting Numbers: [51, 27] Generated Node #0,2,1: 30:[51, 27] Operation: 54-27=27 Exploring Operation: 27+51=78, Resulting Numbers: [54, 78] Generated Node #0,2,2: 30:[54, 78] Operation: 27+51=78 Exploring Operation: 51-27=24, Resulting Numbers: [54, 24] Generated Node #0,2,3: 30:[54, 24] Operation: 51-27=24 Exploring Operation: 54/27=2, Resulting Numbers: [51, 2] Generated Node #0,2,4: 30:[51, 2] Operation: 54/27=2 Moving to Node #0,3 Current State: 30:[83, 29, 24], Operations: ['51-27=24'] Exploring Operation: 83+24=107, Resulting Numbers: [29, 107] Generated Node #0,3,0: 30:[29, 107] Operation: 83+24=107 Exploring Operation: 83-24=59, Resulting Numbers: [29, 59] Generated Node #0,3,1: 30:[29, 59] Operation: 83-24=59 Exploring Operation: 29+24=53, Resulting Numbers: [83, 53] Generated Node #0,3,2: 30:[83, 53] Operation: 29+24=53 Exploring Operation: 29-24=5, Resulting Numbers: [83, 5] Generated Node #0,3,3: 30:[83, 5] Operation: 29-24=5 Exploring Operation: 83-29=54, Resulting Numbers: [24, 54] Generated Node #0,3,4: 30:[24, 54] Operation: 83-29=54 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 30:[29, 59], Operations: ['51-27=24', '83-24=59'] Exploring Operation: 29+59=88, Resulting Numbers: [88] 88,30 unequal: No Solution Exploring Operation: 29*59=1711, Resulting Numbers: [1711] 1711,30 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[27, 83, 51, 29], Operations: [] Exploring Operation: 51-27=24, Resulting Numbers: [83, 29, 24] Generated Node #0,3: 30:[83, 29, 24] Operation: 51-27=24 Moving to Node #0,3 Current State: 30:[83, 29, 24], Operations: ['51-27=24'] Exploring Operation: 83-24=59, Resulting Numbers: [29, 59] Generated Node #0,3,1: 30:[29, 59] Operation: 83-24=59 Moving to Node #0,3,1 Current State: 30:[29, 59], Operations: ['51-27=24', '83-24=59'] Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
mult_heuristic
[ 32, 3, 96, 49 ]
43
[ "96/32=3", "49-3=46", "46-3=43" ]
Current State: 43:[32, 3, 96, 49], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [3, 49, 3] Generated Node #2: [3, 49, 3] from Operation: 96/32=3 Current State: 43:[3, 49, 3], Operations: ['96/32=3'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,43 equal: Goal Reached Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[32, 3, 96, 49], Operations: [] Exploring Operation: 96-49=47, Resulting Numbers: [32, 3, 47] Generated Node #0,0: 43:[32, 3, 47] Operation: 96-49=47 Exploring Operation: 32+3=35, Resulting Numbers: [96, 49, 35] Generated Node #0,1: 43:[96, 49, 35] Operation: 32+3=35 Exploring Operation: 96/3=32, Resulting Numbers: [32, 49, 32] Generated Node #0,2: 43:[32, 49, 32] Operation: 96/3=32 Exploring Operation: 96-32=64, Resulting Numbers: [3, 49, 64] Generated Node #0,3: 43:[3, 49, 64] Operation: 96-32=64 Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[32, 49, 32], Operations: ['96/3=32'] Exploring Operation: 49-32=17, Resulting Numbers: [32, 17] Generated Node #0,2,0: 43:[32, 17] Operation: 49-32=17 Exploring Operation: 49-32=17, Resulting Numbers: [32, 17] Generated Node #0,2,1: 43:[32, 17] Operation: 49-32=17 Exploring Operation: 32+32=64, Resulting Numbers: [49, 64] Generated Node #0,2,2: 43:[49, 64] Operation: 32+32=64 Exploring Operation: 32/32=1, Resulting Numbers: [49, 1] Generated Node #0,2,3: 43:[49, 1] Operation: 32/32=1 Moving to Node #0,2,2 Current State: 43:[49, 64], Operations: ['96/3=32', '32+32=64'] Exploring Operation: 49+64=113, Resulting Numbers: [113] 113,43 unequal: No Solution Exploring Operation: 49*64=3136, Resulting Numbers: [3136] 3136,43 unequal: No Solution Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[32, 17], Operations: ['96/3=32', '49-32=17'] Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,43 unequal: No Solution Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[32, 17], Operations: ['96/3=32', '49-32=17'] Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,43 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,43 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[49, 1], Operations: ['96/3=32', '32/32=1'] Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,43 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,43 unequal: No Solution Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,43 unequal: No Solution Exploring Operation: 49+1=50, Resulting Numbers: [50] 50,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[32, 3, 47], Operations: ['96-49=47'] Exploring Operation: 32-3=29, Resulting Numbers: [47, 29] Generated Node #0,0,0: 43:[47, 29] Operation: 32-3=29 Exploring Operation: 3+47=50, Resulting Numbers: [32, 50] Generated Node #0,0,1: 43:[32, 50] Operation: 3+47=50 Exploring Operation: 47-3=44, Resulting Numbers: [32, 44] Generated Node #0,0,2: 43:[32, 44] Operation: 47-3=44 Exploring Operation: 32+3=35, Resulting Numbers: [47, 35] Generated Node #0,0,3: 43:[47, 35] Operation: 32+3=35 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 43:[32, 44], Operations: ['96-49=47', '47-3=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,43 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,43 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 43:[47, 35], Operations: ['96-49=47', '32+3=35'] Exploring Operation: 47+35=82, Resulting Numbers: [82] 82,43 unequal: No Solution Exploring Operation: 47-35=12, Resulting Numbers: [12] 12,43 unequal: No Solution Exploring Operation: 47*35=1645, Resulting Numbers: [1645] 1645,43 unequal: No Solution No 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: 43:[47, 29], Operations: ['96-49=47', '32-3=29'] Exploring Operation: 47*29=1363, Resulting Numbers: [1363] 1363,43 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 47+29=76, Resulting Numbers: [76] 76,43 unequal: No Solution No 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: 43:[32, 50], Operations: ['96-49=47', '3+47=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,43 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,43 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: 43:[96, 49, 35], Operations: ['32+3=35'] Exploring Operation: 96-49=47, Resulting Numbers: [35, 47] Generated Node #0,1,0: 43:[35, 47] Operation: 96-49=47 Exploring Operation: 49-35=14, Resulting Numbers: [96, 14] Generated Node #0,1,1: 43:[96, 14] Operation: 49-35=14 Exploring Operation: 96+35=131, Resulting Numbers: [49, 131] Generated Node #0,1,2: 43:[49, 131] Operation: 96+35=131 Exploring Operation: 96-35=61, Resulting Numbers: [49, 61] Generated Node #0,1,3: 43:[49, 61] Operation: 96-35=61 Moving to Node #0,1,0 Current State: 43:[35, 47], Operations: ['32+3=35', '96-49=47'] Exploring Operation: 35*47=1645, Resulting Numbers: [1645] 1645,43 unequal: No Solution Exploring Operation: 47-35=12, Resulting Numbers: [12] 12,43 unequal: No Solution Exploring Operation: 35+47=82, Resulting Numbers: [82] 82,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[49, 61], Operations: ['32+3=35', '96-35=61'] Exploring Operation: 49+61=110, Resulting Numbers: [110] 110,43 unequal: No Solution Exploring Operation: 49*61=2989, Resulting Numbers: [2989] 2989,43 unequal: No Solution Exploring Operation: 61-49=12, Resulting Numbers: [12] 12,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[96, 14], Operations: ['32+3=35', '49-35=14'] Exploring Operation: 96+14=110, Resulting Numbers: [110] 110,43 unequal: No Solution Exploring Operation: 96*14=1344, Resulting Numbers: [1344] 1344,43 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[49, 131], Operations: ['32+3=35', '96+35=131'] Exploring Operation: 49*131=6419, Resulting Numbers: [6419] 6419,43 unequal: No Solution Exploring Operation: 131-49=82, Resulting Numbers: [82] 82,43 unequal: No Solution Exploring Operation: 49+131=180, Resulting Numbers: [180] 180,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 43:[3, 49, 64], Operations: ['96-32=64'] Exploring Operation: 3+64=67, Resulting Numbers: [49, 67] Generated Node #0,3,0: 43:[49, 67] Operation: 3+64=67 Exploring Operation: 64-3=61, Resulting Numbers: [49, 61] Generated Node #0,3,1: 43:[49, 61] Operation: 64-3=61 Exploring Operation: 3+49=52, Resulting Numbers: [64, 52] Generated Node #0,3,2: 43:[64, 52] Operation: 3+49=52 Exploring Operation: 49-3=46, Resulting Numbers: [64, 46] Generated Node #0,3,3: 43:[64, 46] Operation: 49-3=46 Moving to Node #0,3,1 Current State: 43:[49, 61], Operations: ['96-32=64', '64-3=61'] Exploring Operation: 49*61=2989, Resulting Numbers: [2989] 2989,43 unequal: No Solution Exploring Operation: 61-49=12, Resulting Numbers: [12] 12,43 unequal: No Solution Exploring Operation: 49+61=110, Resulting Numbers: [110] 110,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[64, 46], Operations: ['96-32=64', '49-3=46'] Exploring Operation: 64+46=110, Resulting Numbers: [110] 110,43 unequal: No Solution Exploring Operation: 64-46=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 64*46=2944, Resulting Numbers: [2944] 2944,43 unequal: No Solution Moving to Node #0,3,2 Current State: 43:[64, 52], Operations: ['96-32=64', '3+49=52'] Exploring Operation: 64*52=3328, Resulting Numbers: [3328] 3328,43 unequal: No Solution Exploring Operation: 64+52=116, Resulting Numbers: [116] 116,43 unequal: No Solution Exploring Operation: 64-52=12, Resulting Numbers: [12] 12,43 unequal: No Solution Moving to Node #0,3,0 Current State: 43:[49, 67], Operations: ['96-32=64', '3+64=67'] Exploring Operation: 49*67=3283, Resulting Numbers: [3283] 3283,43 unequal: No Solution Exploring Operation: 49+67=116, Resulting Numbers: [116] 116,43 unequal: No Solution Exploring Operation: 67-49=18, Resulting Numbers: [18] 18,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 37, 77, 44, 7 ]
92
[ "37+44=81", "77/7=11", "81+11=92" ]
Current State: 92:[37, 77, 44, 7], Operations: [] Exploring Operation: 37+44=81, Resulting Numbers: [77, 7, 81] Generated Node #2: [77, 7, 81] from Operation: 37+44=81 Current State: 92:[77, 7, 81], Operations: ['37+44=81'] Exploring Operation: 77/7=11, Resulting Numbers: [81, 11] Generated Node #3: [81, 11] from Operation: 77/7=11 Current State: 92:[81, 11], Operations: ['37+44=81', '77/7=11'] Exploring Operation: 81+11=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[37, 77, 44, 7], Operations: [] Exploring Operation: 37+7=44, Resulting Numbers: [77, 44, 44] Generated Node #0,0: 92:[77, 44, 44] Operation: 37+7=44 Exploring Operation: 77-37=40, Resulting Numbers: [44, 7, 40] Generated Node #0,1: 92:[44, 7, 40] Operation: 77-37=40 Exploring Operation: 77/7=11, Resulting Numbers: [37, 44, 11] Generated Node #0,2: 92:[37, 44, 11] Operation: 77/7=11 Exploring Operation: 77+7=84, Resulting Numbers: [37, 44, 84] Generated Node #0,3: 92:[37, 44, 84] Operation: 77+7=84 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[44, 7, 40], Operations: ['77-37=40'] Exploring Operation: 7+40=47, Resulting Numbers: [44, 47] Generated Node #0,1,0: 92:[44, 47] Operation: 7+40=47 Exploring Operation: 44-40=4, Resulting Numbers: [7, 4] Generated Node #0,1,1: 92:[7, 4] Operation: 44-40=4 Exploring Operation: 44+40=84, Resulting Numbers: [7, 84] Generated Node #0,1,2: 92:[7, 84] Operation: 44+40=84 Exploring Operation: 44+7=51, Resulting Numbers: [40, 51] Generated Node #0,1,3: 92:[40, 51] Operation: 44+7=51 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 92:[44, 47], Operations: ['77-37=40', '7+40=47'] Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,92 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,92 unequal: No Solution No 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: 92:[7, 4], Operations: ['77-37=40', '44-40=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,92 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,92 unequal: No Solution No 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: 92:[7, 84], Operations: ['77-37=40', '44+40=84'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 7+84=91, Resulting Numbers: [91] 91,92 unequal: No Solution Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,92 unequal: No Solution Exploring Operation: 7*84=588, Resulting Numbers: [588] 588,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 92:[40, 51], Operations: ['77-37=40', '44+7=51'] Exploring Operation: 40*51=2040, Resulting Numbers: [2040] 2040,92 unequal: No Solution Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,92 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: 92:[37, 44, 11], Operations: ['77/7=11'] Exploring Operation: 44/11=4, Resulting Numbers: [37, 4] Generated Node #0,2,0: 92:[37, 4] Operation: 44/11=4 Exploring Operation: 37-11=26, Resulting Numbers: [44, 26] Generated Node #0,2,1: 92:[44, 26] Operation: 37-11=26 Exploring Operation: 37+11=48, Resulting Numbers: [44, 48] Generated Node #0,2,2: 92:[44, 48] Operation: 37+11=48 Exploring Operation: 44-37=7, Resulting Numbers: [11, 7] Generated Node #0,2,3: 92:[11, 7] Operation: 44-37=7 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 92:[44, 48], Operations: ['77/7=11', '37+11=48'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 44*48=2112, Resulting Numbers: [2112] 2112,92 unequal: No Solution Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[37, 77, 44, 7], Operations: [] Exploring Operation: 77/7=11, Resulting Numbers: [37, 44, 11] Generated Node #0,2: 92:[37, 44, 11] Operation: 77/7=11 Moving to Node #0,2 Current State: 92:[37, 44, 11], Operations: ['77/7=11'] Exploring Operation: 37+11=48, Resulting Numbers: [44, 48] Generated Node #0,2,2: 92:[44, 48] Operation: 37+11=48 Moving to Node #0,2,2 Current State: 92:[44, 48], Operations: ['77/7=11', '37+11=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 61, 44, 35, 9 ]
20
[ "44-35=9", "9*9=81", "81-61=20" ]
Current State: 20:[61, 44, 35, 9], Operations: [] Exploring Operation: 44-35=9, Resulting Numbers: [61, 9, 9] Generated Node #2: [61, 9, 9] from Operation: 44-35=9 Current State: 20:[61, 9, 9], Operations: ['44-35=9'] Exploring Operation: 9*9=81, Resulting Numbers: [61, 81] Generated Node #3: [61, 81] from Operation: 9*9=81 Current State: 20:[61, 81], Operations: ['44-35=9', '9*9=81'] Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[61, 44, 35, 9], Operations: [] Exploring Operation: 61-35=26, Resulting Numbers: [44, 9, 26] Generated Node #0,0: 20:[44, 9, 26] Operation: 61-35=26 Exploring Operation: 44-35=9, Resulting Numbers: [61, 9, 9] Generated Node #0,1: 20:[61, 9, 9] Operation: 44-35=9 Exploring Operation: 61-9=52, Resulting Numbers: [44, 35, 52] Generated Node #0,2: 20:[44, 35, 52] Operation: 61-9=52 Exploring Operation: 61-44=17, Resulting Numbers: [35, 9, 17] Generated Node #0,3: 20:[35, 9, 17] Operation: 61-44=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 20:[35, 9, 17], Operations: ['61-44=17'] Exploring Operation: 35-17=18, Resulting Numbers: [9, 18] Generated Node #0,3,0: 20:[9, 18] Operation: 35-17=18 Exploring Operation: 35-9=26, Resulting Numbers: [17, 26] Generated Node #0,3,1: 20:[17, 26] Operation: 35-9=26 Exploring Operation: 9+17=26, Resulting Numbers: [35, 26] Generated Node #0,3,2: 20:[35, 26] Operation: 9+17=26 Exploring Operation: 17-9=8, Resulting Numbers: [35, 8] Generated Node #0,3,3: 20:[35, 8] Operation: 17-9=8 Moving to Node #0,3,0 Current State: 20:[9, 18], Operations: ['61-44=17', '35-17=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,20 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,20 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,20 unequal: No Solution Moving to Node #0,3,1 Current State: 20:[17, 26], Operations: ['61-44=17', '35-9=26'] Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,20 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,20 unequal: No Solution Moving to Node #0,3,3 Current State: 20:[35, 8], Operations: ['61-44=17', '17-9=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,20 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,20 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,20 unequal: No Solution Moving to Node #0,3,2 Current State: 20:[35, 26], Operations: ['61-44=17', '9+17=26'] Exploring Operation: 35*26=910, Resulting Numbers: [910] 910,20 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 35+26=61, Resulting Numbers: [61] 61,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[44, 9, 26], Operations: ['61-35=26'] Exploring Operation: 44-26=18, Resulting Numbers: [9, 18] Generated Node #0,0,0: 20:[9, 18] Operation: 44-26=18 Exploring Operation: 26-9=17, Resulting Numbers: [44, 17] Generated Node #0,0,1: 20:[44, 17] Operation: 26-9=17 Exploring Operation: 44-9=35, Resulting Numbers: [26, 35] Generated Node #0,0,2: 20:[26, 35] Operation: 44-9=35 Exploring Operation: 44+9=53, Resulting Numbers: [26, 53] Generated Node #0,0,3: 20:[26, 53] Operation: 44+9=53 Moving to Node #0,0,0 Current State: 20:[9, 18], Operations: ['61-35=26', '44-26=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,20 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,20 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,20 unequal: No Solution Moving to Node #0,0,2 Current State: 20:[26, 35], Operations: ['61-35=26', '44-9=35'] Exploring Operation: 26+35=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 26*35=910, Resulting Numbers: [910] 910,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[44, 17], Operations: ['61-35=26', '26-9=17'] Exploring Operation: 44+17=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 44*17=748, Resulting Numbers: [748] 748,20 unequal: No Solution Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,20 unequal: No Solution Moving to Node #0,0,3 Current State: 20:[26, 53], Operations: ['61-35=26', '44+9=53'] Exploring Operation: 26*53=1378, Resulting Numbers: [1378] 1378,20 unequal: No Solution Exploring Operation: 53-26=27, Resulting Numbers: [27] 27,20 unequal: No Solution Exploring Operation: 26+53=79, Resulting Numbers: [79] 79,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[61, 9, 9], Operations: ['44-35=9'] Exploring Operation: 61-9=52, Resulting Numbers: [9, 52] Generated Node #0,1,0: 20:[9, 52] Operation: 61-9=52 Exploring Operation: 61-9=52, Resulting Numbers: [9, 52] Generated Node #0,1,1: 20:[9, 52] Operation: 61-9=52 Exploring Operation: 9+9=18, Resulting Numbers: [61, 18] Generated Node #0,1,2: 20:[61, 18] Operation: 9+9=18 Exploring Operation: 9/9=1, Resulting Numbers: [61, 1] Generated Node #0,1,3: 20:[61, 1] Operation: 9/9=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[9, 52], Operations: ['44-35=9', '61-9=52'] Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,20 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,20 unequal: No Solution No 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: 20:[9, 52], Operations: ['44-35=9', '61-9=52'] Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,20 unequal: No Solution Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 20:[61, 1], Operations: ['44-35=9', '9/9=1'] Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,20 unequal: No Solution Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,20 unequal: No Solution No 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: 20:[61, 18], Operations: ['44-35=9', '9+9=18'] Exploring Operation: 61+18=79, Resulting Numbers: [79] 79,20 unequal: No Solution Exploring Operation: 61*18=1098, Resulting Numbers: [1098] 1098,20 unequal: No Solution Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,20 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: 20:[44, 35, 52], Operations: ['61-9=52'] Exploring Operation: 44+35=79, Resulting Numbers: [52, 79] Generated Node #0,2,0: 20:[52, 79] Operation: 44+35=79 Exploring Operation: 52-35=17, Resulting Numbers: [44, 17] Generated Node #0,2,1: 20:[44, 17] Operation: 52-35=17 Exploring Operation: 52-44=8, Resulting Numbers: [35, 8] Generated Node #0,2,2: 20:[35, 8] Operation: 52-44=8 Exploring Operation: 44-35=9, Resulting Numbers: [52, 9] Generated Node #0,2,3: 20:[52, 9] Operation: 44-35=9 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 20:[35, 8], Operations: ['61-9=52', '52-44=8'] Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,20 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,20 unequal: No Solution No 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: 20:[44, 17], Operations: ['61-9=52', '52-35=17'] Exploring Operation: 44+17=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,20 unequal: No Solution Exploring Operation: 44*17=748, Resulting Numbers: [748] 748,20 unequal: No Solution No 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: 20:[52, 9], Operations: ['61-9=52', '44-35=9'] Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 52+9=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 52*9=468, Resulting Numbers: [468] 468,20 unequal: No Solution No 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: 20:[52, 79], Operations: ['61-9=52', '44+35=79'] Exploring Operation: 52+79=131, Resulting Numbers: [131] 131,20 unequal: No Solution Exploring Operation: 52*79=4108, Resulting Numbers: [4108] 4108,20 unequal: No Solution Exploring Operation: 79-52=27, Resulting Numbers: [27] 27,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 77, 38, 76, 68 ]
86
[ "77*76=5852", "5852/38=154", "154-68=86" ]
Current State: 86:[77, 38, 76, 68], Operations: [] Exploring Operation: 77*76=5852, Resulting Numbers: [38, 68, 5852] Generated Node #2: [38, 68, 5852] from Operation: 77*76=5852 Current State: 86:[38, 68, 5852], Operations: ['77*76=5852'] Exploring Operation: 5852/38=154, Resulting Numbers: [68, 154] Generated Node #3: [68, 154] from Operation: 5852/38=154 Current State: 86:[68, 154], Operations: ['77*76=5852', '5852/38=154'] Exploring Operation: 154-68=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[77, 38, 76, 68], Operations: [] Exploring Operation: 76-68=8, Resulting Numbers: [77, 38, 8] Generated Node #0,0: 86:[77, 38, 8] Operation: 76-68=8 Exploring Operation: 77-68=9, Resulting Numbers: [38, 76, 9] Generated Node #0,1: 86:[38, 76, 9] Operation: 77-68=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[77, 38, 8], Operations: ['76-68=8'] Exploring Operation: 77-38=39, Resulting Numbers: [8, 39] Generated Node #0,0,0: 86:[8, 39] Operation: 77-38=39 Exploring Operation: 77+8=85, Resulting Numbers: [38, 85] Generated Node #0,0,1: 86:[38, 85] Operation: 77+8=85 Moving to Node #0,0,1 Current State: 86:[38, 85], Operations: ['76-68=8', '77+8=85'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 38+85=123, Resulting Numbers: [123] 123,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[8, 39], Operations: ['76-68=8', '77-38=39'] Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,86 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 #0,1 Current State: 86:[38, 76, 9], Operations: ['77-68=9'] Exploring Operation: 76/38=2, Resulting Numbers: [9, 2] Generated Node #0,1,0: 86:[9, 2] Operation: 76/38=2 Exploring Operation: 76+9=85, Resulting Numbers: [38, 85] Generated Node #0,1,1: 86:[38, 85] Operation: 76+9=85 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[38, 85], Operations: ['77-68=9', '76+9=85'] Exploring Operation: 38+85=123, Resulting Numbers: [123] 123,86 unequal: No Solution Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 86:[9, 2], Operations: ['77-68=9', '76/38=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 76, 80, 68, 27 ]
44
[ "80-76=4", "68/4=17", "27+17=44" ]
Current State: 44:[76, 80, 68, 27], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [68, 27, 4] Generated Node #2: [68, 27, 4] from Operation: 80-76=4 Current State: 44:[68, 27, 4], Operations: ['80-76=4'] Exploring Operation: 68/4=17, Resulting Numbers: [27, 17] Generated Node #3: [27, 17] from Operation: 68/4=17 Current State: 44:[27, 17], Operations: ['80-76=4', '68/4=17'] Exploring Operation: 27+17=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[76, 80, 68, 27], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [68, 27, 4] Generated Node #0,0: 44:[68, 27, 4] Operation: 80-76=4 Moving to Node #0,0 Current State: 44:[68, 27, 4], Operations: ['80-76=4'] Exploring Operation: 68-27=41, Resulting Numbers: [4, 41] Generated Node #0,0,0: 44:[4, 41] Operation: 68-27=41 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[4, 41], Operations: ['80-76=4', '68-27=41'] Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,44 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
[ 77, 46, 26, 35 ]
30
[ "77-46=31", "26+35=61", "61-31=30" ]
Current State: 30:[77, 46, 26, 35], Operations: [] Exploring Operation: 77-46=31, Resulting Numbers: [26, 35, 31] Generated Node #2: [26, 35, 31] from Operation: 77-46=31 Current State: 30:[26, 35, 31], Operations: ['77-46=31'] Exploring Operation: 26+35=61, Resulting Numbers: [31, 61] Generated Node #3: [31, 61] from Operation: 26+35=61 Current State: 30:[31, 61], Operations: ['77-46=31', '26+35=61'] Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[77, 46, 26, 35], Operations: [] Exploring Operation: 77-35=42, Resulting Numbers: [46, 26, 42] Generated Node #0,0: 30:[46, 26, 42] Operation: 77-35=42 Exploring Operation: 77-46=31, Resulting Numbers: [26, 35, 31] Generated Node #0,1: 30:[26, 35, 31] Operation: 77-46=31 Exploring Operation: 77-26=51, Resulting Numbers: [46, 35, 51] Generated Node #0,2: 30:[46, 35, 51] Operation: 77-26=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[26, 35, 31], Operations: ['77-46=31'] Exploring Operation: 35-26=9, Resulting Numbers: [31, 9] Generated Node #0,1,0: 30:[31, 9] Operation: 35-26=9 Exploring Operation: 31-26=5, Resulting Numbers: [35, 5] Generated Node #0,1,1: 30:[35, 5] Operation: 31-26=5 Exploring Operation: 35-31=4, Resulting Numbers: [26, 4] Generated Node #0,1,2: 30:[26, 4] Operation: 35-31=4 Moving to Node #0,1,0 Current State: 30:[31, 9], Operations: ['77-46=31', '35-26=9'] Exploring Operation: 31*9=279, Resulting Numbers: [279] 279,30 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 31+9=40, Resulting Numbers: [40] 40,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[35, 5], Operations: ['77-46=31', '31-26=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[77, 46, 26, 35], Operations: [] Exploring Operation: 77-46=31, Resulting Numbers: [26, 35, 31] Generated Node #0,1: 30:[26, 35, 31] Operation: 77-46=31 Moving to Node #0,1 Current State: 30:[26, 35, 31], Operations: ['77-46=31'] Exploring Operation: 31-26=5, Resulting Numbers: [35, 5] Generated Node #0,1,1: 30:[35, 5] Operation: 31-26=5 Moving to Node #0,1,1 Current State: 30:[35, 5], Operations: ['77-46=31', '31-26=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 3, 15, 1, 59 ]
37
[ "3-1=2", "15+59=74", "74/2=37" ]
Current State: 37:[3, 15, 1, 59], Operations: [] Exploring Operation: 3-1=2, Resulting Numbers: [15, 59, 2] Generated Node #2: [15, 59, 2] from Operation: 3-1=2 Current State: 37:[15, 59, 2], Operations: ['3-1=2'] Exploring Operation: 15+59=74, Resulting Numbers: [2, 74] Generated Node #3: [2, 74] from Operation: 15+59=74 Current State: 37:[2, 74], Operations: ['3-1=2', '15+59=74'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[3, 15, 1, 59], Operations: [] Exploring Operation: 3*15=45, Resulting Numbers: [1, 59, 45] Generated Node #0,0: 37:[1, 59, 45] Operation: 3*15=45 Exploring Operation: 3+15=18, Resulting Numbers: [1, 59, 18] Generated Node #0,1: 37:[1, 59, 18] Operation: 3+15=18 Exploring Operation: 3+1=4, Resulting Numbers: [15, 59, 4] Generated Node #0,2: 37:[15, 59, 4] Operation: 3+1=4 Exploring Operation: 59-3=56, Resulting Numbers: [15, 1, 56] Generated Node #0,3: 37:[15, 1, 56] Operation: 59-3=56 Moving to Node #0,0 Current State: 37:[1, 59, 45], Operations: ['3*15=45'] Exploring Operation: 1*59=59, Resulting Numbers: [45, 59] Generated Node #0,0,0: 37:[45, 59] Operation: 1*59=59 Exploring Operation: 45-1=44, Resulting Numbers: [59, 44] Generated Node #0,0,1: 37:[59, 44] Operation: 45-1=44 Exploring Operation: 59-1=58, Resulting Numbers: [45, 58] Generated Node #0,0,2: 37:[45, 58] Operation: 59-1=58 Exploring Operation: 59/1=59, Resulting Numbers: [45, 59] Generated Node #0,0,3: 37:[45, 59] Operation: 59/1=59 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[59, 44], Operations: ['3*15=45', '45-1=44'] Exploring Operation: 59*44=2596, Resulting Numbers: [2596] 2596,37 unequal: No Solution Exploring Operation: 59+44=103, Resulting Numbers: [103] 103,37 unequal: No Solution Exploring Operation: 59-44=15, Resulting Numbers: [15] 15,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[45, 58], Operations: ['3*15=45', '59-1=58'] Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 45+58=103, Resulting Numbers: [103] 103,37 unequal: No Solution Exploring Operation: 45*58=2610, Resulting Numbers: [2610] 2610,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[45, 59], Operations: ['3*15=45', '1*59=59'] Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,37 unequal: No Solution Exploring Operation: 45*59=2655, Resulting Numbers: [2655] 2655,37 unequal: No Solution Exploring Operation: 45+59=104, Resulting Numbers: [104] 104,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[45, 59], Operations: ['3*15=45', '59/1=59'] Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,37 unequal: No Solution Exploring Operation: 45*59=2655, Resulting Numbers: [2655] 2655,37 unequal: No Solution Exploring Operation: 45+59=104, Resulting Numbers: [104] 104,37 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: 37:[15, 59, 4], Operations: ['3+1=4'] Exploring Operation: 59-4=55, Resulting Numbers: [15, 55] Generated Node #0,2,0: 37:[15, 55] Operation: 59-4=55 Exploring Operation: 15*4=60, Resulting Numbers: [59, 60] Generated Node #0,2,1: 37:[59, 60] Operation: 15*4=60 Exploring Operation: 15+4=19, Resulting Numbers: [59, 19] Generated Node #0,2,2: 37:[59, 19] Operation: 15+4=19 Exploring Operation: 59-15=44, Resulting Numbers: [4, 44] Generated Node #0,2,3: 37:[4, 44] Operation: 59-15=44 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 37:[15, 55], Operations: ['3+1=4', '59-4=55'] Exploring Operation: 15+55=70, Resulting Numbers: [70] 70,37 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 15*55=825, Resulting Numbers: [825] 825,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 37:[59, 19], Operations: ['3+1=4', '15+4=19'] Exploring Operation: 59*19=1121, Resulting Numbers: [1121] 1121,37 unequal: No Solution Exploring Operation: 59-19=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 59+19=78, Resulting Numbers: [78] 78,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 37:[4, 44], Operations: ['3+1=4', '59-15=44'] Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 4*44=176, Resulting Numbers: [176] 176,37 unequal: No Solution Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 37:[59, 60], Operations: ['3+1=4', '15*4=60'] Exploring Operation: 59+60=119, Resulting Numbers: [119] 119,37 unequal: No Solution Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 59*60=3540, Resulting Numbers: [3540] 3540,37 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: 37:[1, 59, 18], Operations: ['3+15=18'] Exploring Operation: 59-1=58, Resulting Numbers: [18, 58] Generated Node #0,1,0: 37:[18, 58] Operation: 59-1=58 Exploring Operation: 1*59=59, Resulting Numbers: [18, 59] Generated Node #0,1,1: 37:[18, 59] Operation: 1*59=59 Exploring Operation: 1+18=19, Resulting Numbers: [59, 19] Generated Node #0,1,2: 37:[59, 19] Operation: 1+18=19 Exploring Operation: 59-18=41, Resulting Numbers: [1, 41] Generated Node #0,1,3: 37:[1, 41] Operation: 59-18=41 Moving to Node #0,3 Current State: 37:[15, 1, 56], Operations: ['59-3=56'] Exploring Operation: 15*1=15, Resulting Numbers: [56, 15] Generated Node #0,3,0: 37:[56, 15] Operation: 15*1=15 Exploring Operation: 56-1=55, Resulting Numbers: [15, 55] Generated Node #0,3,1: 37:[15, 55] Operation: 56-1=55 Exploring Operation: 15+1=16, Resulting Numbers: [56, 16] Generated Node #0,3,2: 37:[56, 16] Operation: 15+1=16 Exploring Operation: 56-15=41, Resulting Numbers: [1, 41] Generated Node #0,3,3: 37:[1, 41] Operation: 56-15=41 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 37:[15, 55], Operations: ['59-3=56', '56-1=55'] Exploring Operation: 15+55=70, Resulting Numbers: [70] 70,37 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 15*55=825, Resulting Numbers: [825] 825,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 37:[56, 16], Operations: ['59-3=56', '15+1=16'] Exploring Operation: 56-16=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 56+16=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 56*16=896, Resulting Numbers: [896] 896,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 37:[1, 41], Operations: ['59-3=56', '56-15=41'] Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,37 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,37 unequal: No Solution Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 37:[56, 15], Operations: ['59-3=56', '15*1=15'] Exploring Operation: 56*15=840, Resulting Numbers: [840] 840,37 unequal: No Solution Exploring Operation: 56+15=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,37 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: 37:[18, 58], Operations: ['3+15=18', '59-1=58'] Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 18*58=1044, Resulting Numbers: [1044] 1044,37 unequal: No Solution Exploring Operation: 18+58=76, Resulting Numbers: [76] 76,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[1, 41], Operations: ['3+15=18', '59-18=41'] Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,37 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,37 unequal: No Solution Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[59, 19], Operations: ['3+15=18', '1+18=19'] Exploring Operation: 59*19=1121, Resulting Numbers: [1121] 1121,37 unequal: No Solution Exploring Operation: 59-19=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 59+19=78, Resulting Numbers: [78] 78,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[18, 59], Operations: ['3+15=18', '1*59=59'] Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,37 unequal: No Solution Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,37 unequal: No Solution Exploring Operation: 18*59=1062, Resulting Numbers: [1062] 1062,37 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 3, 90, 7, 54 ]
63
[ "3+7=10", "90/10=9", "54+9=63" ]
Current State: 63:[3, 90, 7, 54], Operations: [] Exploring Operation: 3+7=10, Resulting Numbers: [90, 54, 10] Generated Node #2: [90, 54, 10] from Operation: 3+7=10 Current State: 63:[90, 54, 10], Operations: ['3+7=10'] Exploring Operation: 90/10=9, Resulting Numbers: [54, 9] Generated Node #3: [54, 9] from Operation: 90/10=9 Current State: 63:[54, 9], Operations: ['3+7=10', '90/10=9'] Exploring Operation: 54+9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[3, 90, 7, 54], Operations: [] Exploring Operation: 90-54=36, Resulting Numbers: [3, 7, 36] Generated Node #0,0: 63:[3, 7, 36] Operation: 90-54=36 Exploring Operation: 90/3=30, Resulting Numbers: [7, 54, 30] Generated Node #0,1: 63:[7, 54, 30] Operation: 90/3=30 Exploring Operation: 90-7=83, Resulting Numbers: [3, 54, 83] Generated Node #0,2: 63:[3, 54, 83] Operation: 90-7=83 Moving to Node #0,0 Current State: 63:[3, 7, 36], Operations: ['90-54=36'] Exploring Operation: 36-7=29, Resulting Numbers: [3, 29] Generated Node #0,0,0: 63:[3, 29] Operation: 36-7=29 Exploring Operation: 36/3=12, Resulting Numbers: [7, 12] Generated Node #0,0,1: 63:[7, 12] Operation: 36/3=12 Exploring Operation: 36-3=33, Resulting Numbers: [7, 33] Generated Node #0,0,2: 63:[7, 33] Operation: 36-3=33 Moving to Node #0,1 Current State: 63:[7, 54, 30], Operations: ['90/3=30'] Exploring Operation: 7+54=61, Resulting Numbers: [30, 61] Generated Node #0,1,0: 63:[30, 61] Operation: 7+54=61 Exploring Operation: 30-7=23, Resulting Numbers: [54, 23] Generated Node #0,1,1: 63:[54, 23] Operation: 30-7=23 Exploring Operation: 54-30=24, Resulting Numbers: [7, 24] Generated Node #0,1,2: 63:[7, 24] Operation: 54-30=24 Moving to Node #0,2 Current State: 63:[3, 54, 83], Operations: ['90-7=83'] Exploring Operation: 54/3=18, Resulting Numbers: [83, 18] Generated Node #0,2,0: 63:[83, 18] Operation: 54/3=18 Exploring Operation: 83-54=29, Resulting Numbers: [3, 29] Generated Node #0,2,1: 63:[3, 29] Operation: 83-54=29 Exploring Operation: 3+54=57, Resulting Numbers: [83, 57] Generated Node #0,2,2: 63:[83, 57] Operation: 3+54=57 Moving to Node #0,0,1 Current State: 63:[7, 12], Operations: ['90-54=36', '36/3=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,63 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,63 unequal: No Solution Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[7, 24], Operations: ['90/3=30', '54-30=24'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,63 unequal: No Solution Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[3, 29], Operations: ['90-7=83', '83-54=29'] Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,63 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[3, 29], Operations: ['90-54=36', '36-7=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,63 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[54, 23], Operations: ['90/3=30', '30-7=23'] Exploring Operation: 54*23=1242, Resulting Numbers: [1242] 1242,63 unequal: No Solution Exploring Operation: 54+23=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[30, 61], Operations: ['90/3=30', '7+54=61'] Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,63 unequal: No Solution Exploring Operation: 30*61=1830, Resulting Numbers: [1830] 1830,63 unequal: No Solution Exploring Operation: 30+61=91, Resulting Numbers: [91] 91,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[7, 33], Operations: ['90-54=36', '36-3=33'] Exploring Operation: 7*33=231, Resulting Numbers: [231] 231,63 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 7+33=40, Resulting Numbers: [40] 40,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[83, 18], Operations: ['90-7=83', '54/3=18'] Exploring Operation: 83+18=101, Resulting Numbers: [101] 101,63 unequal: No Solution Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,63 unequal: No Solution Exploring Operation: 83*18=1494, Resulting Numbers: [1494] 1494,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[83, 57], Operations: ['90-7=83', '3+54=57'] Exploring Operation: 83-57=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 83+57=140, Resulting Numbers: [140] 140,63 unequal: No Solution Exploring Operation: 83*57=4731, Resulting Numbers: [4731] 4731,63 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 50, 47, 59, 10 ]
28
[ "50+47=97", "59+10=69", "97-69=28" ]
Current State: 28:[50, 47, 59, 10], Operations: [] Exploring Operation: 50+47=97, Resulting Numbers: [59, 10, 97] Generated Node #2: [59, 10, 97] from Operation: 50+47=97 Current State: 28:[59, 10, 97], Operations: ['50+47=97'] Exploring Operation: 59+10=69, Resulting Numbers: [97, 69] Generated Node #3: [97, 69] from Operation: 59+10=69 Current State: 28:[97, 69], Operations: ['50+47=97', '59+10=69'] Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[50, 47, 59, 10], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [47, 10, 9] Generated Node #0,0: 28:[47, 10, 9] Operation: 59-50=9 Exploring Operation: 50/10=5, Resulting Numbers: [47, 59, 5] Generated Node #0,1: 28:[47, 59, 5] Operation: 50/10=5 Exploring Operation: 59-47=12, Resulting Numbers: [50, 10, 12] Generated Node #0,2: 28:[50, 10, 12] Operation: 59-47=12 Exploring Operation: 50-10=40, Resulting Numbers: [47, 59, 40] Generated Node #0,3: 28:[47, 59, 40] Operation: 50-10=40 Exploring Operation: 50-47=3, Resulting Numbers: [59, 10, 3] Generated Node #0,4: 28:[59, 10, 3] Operation: 50-47=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[47, 10, 9], Operations: ['59-50=9'] Exploring Operation: 10+9=19, Resulting Numbers: [47, 19] Generated Node #0,0,0: 28:[47, 19] Operation: 10+9=19 Exploring Operation: 47-10=37, Resulting Numbers: [9, 37] Generated Node #0,0,1: 28:[9, 37] Operation: 47-10=37 Exploring Operation: 47-9=38, Resulting Numbers: [10, 38] Generated Node #0,0,2: 28:[10, 38] Operation: 47-9=38 Exploring Operation: 47+10=57, Resulting Numbers: [9, 57] Generated Node #0,0,3: 28:[9, 57] Operation: 47+10=57 Exploring Operation: 10-9=1, Resulting Numbers: [47, 1] Generated Node #0,0,4: 28:[47, 1] Operation: 10-9=1 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[9, 37], Operations: ['59-50=9', '47-10=37'] Exploring Operation: 9+37=46, Resulting Numbers: [46] 46,28 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[50, 47, 59, 10], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [47, 10, 9] Generated Node #0,0: 28:[47, 10, 9] Operation: 59-50=9 Moving to Node #0,0 Current State: 28:[47, 10, 9], Operations: ['59-50=9'] Exploring Operation: 47-10=37, Resulting Numbers: [9, 37] Generated Node #0,0,1: 28:[9, 37] Operation: 47-10=37 Moving to Node #0,0,1 Current State: 28:[9, 37], Operations: ['59-50=9', '47-10=37'] Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 73, 74, 5, 90 ]
52
[ "73+74=147", "5+90=95", "147-95=52" ]
Current State: 52:[73, 74, 5, 90], Operations: [] Exploring Operation: 73+74=147, Resulting Numbers: [5, 90, 147] Generated Node #2: [5, 90, 147] from Operation: 73+74=147 Current State: 52:[5, 90, 147], Operations: ['73+74=147'] Exploring Operation: 5+90=95, Resulting Numbers: [147, 95] Generated Node #3: [147, 95] from Operation: 5+90=95 Current State: 52:[147, 95], Operations: ['73+74=147', '5+90=95'] Exploring Operation: 147-95=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[73, 74, 5, 90], Operations: [] Exploring Operation: 73-5=68, Resulting Numbers: [74, 90, 68] Generated Node #0,0: 52:[74, 90, 68] Operation: 73-5=68 Exploring Operation: 90/5=18, Resulting Numbers: [73, 74, 18] Generated Node #0,1: 52:[73, 74, 18] Operation: 90/5=18 Exploring Operation: 90-74=16, Resulting Numbers: [73, 5, 16] Generated Node #0,2: 52:[73, 5, 16] Operation: 90-74=16 Exploring Operation: 90-73=17, Resulting Numbers: [74, 5, 17] Generated Node #0,3: 52:[74, 5, 17] Operation: 90-73=17 Exploring Operation: 74-73=1, Resulting Numbers: [5, 90, 1] Generated Node #0,4: 52:[5, 90, 1] Operation: 74-73=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[73, 5, 16], Operations: ['90-74=16'] Exploring Operation: 73+5=78, Resulting Numbers: [16, 78] Generated Node #0,2,0: 52:[16, 78] Operation: 73+5=78 Exploring Operation: 16-5=11, Resulting Numbers: [73, 11] Generated Node #0,2,1: 52:[73, 11] Operation: 16-5=11 Exploring Operation: 73-5=68, Resulting Numbers: [16, 68] Generated Node #0,2,2: 52:[16, 68] Operation: 73-5=68 Exploring Operation: 5+16=21, Resulting Numbers: [73, 21] Generated Node #0,2,3: 52:[73, 21] Operation: 5+16=21 Exploring Operation: 73-16=57, Resulting Numbers: [5, 57] Generated Node #0,2,4: 52:[5, 57] Operation: 73-16=57 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 52:[5, 57], Operations: ['90-74=16', '73-16=57'] Exploring Operation: 5+57=62, Resulting Numbers: [62] 62,52 unequal: No Solution Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[73, 74, 5, 90], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [73, 5, 16] Generated Node #0,2: 52:[73, 5, 16] Operation: 90-74=16 Moving to Node #0,2 Current State: 52:[73, 5, 16], Operations: ['90-74=16'] Exploring Operation: 73-16=57, Resulting Numbers: [5, 57] Generated Node #0,2,4: 52:[5, 57] Operation: 73-16=57 Moving to Node #0,2,4 Current State: 52:[5, 57], Operations: ['90-74=16', '73-16=57'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 19, 47, 3, 25 ]
79
[ "19*3=57", "47-25=22", "57+22=79" ]
Current State: 79:[19, 47, 3, 25], Operations: [] Exploring Operation: 19*3=57, Resulting Numbers: [47, 25, 57] Generated Node #2: [47, 25, 57] from Operation: 19*3=57 Current State: 79:[47, 25, 57], Operations: ['19*3=57'] Exploring Operation: 47-25=22, Resulting Numbers: [57, 22] Generated Node #3: [57, 22] from Operation: 47-25=22 Current State: 79:[57, 22], Operations: ['19*3=57', '47-25=22'] Exploring Operation: 57+22=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[19, 47, 3, 25], Operations: [] Exploring Operation: 3*25=75, Resulting Numbers: [19, 47, 75] Generated Node #0,0: 79:[19, 47, 75] Operation: 3*25=75 Exploring Operation: 19*3=57, Resulting Numbers: [47, 25, 57] Generated Node #0,1: 79:[47, 25, 57] Operation: 19*3=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[19, 47, 75], Operations: ['3*25=75'] Exploring Operation: 19+47=66, Resulting Numbers: [75, 66] Generated Node #0,0,0: 79:[75, 66] Operation: 19+47=66 Exploring Operation: 19+75=94, Resulting Numbers: [47, 94] Generated Node #0,0,1: 79:[47, 94] Operation: 19+75=94 Moving to Node #0,0,0 Current State: 79:[75, 66], Operations: ['3*25=75', '19+47=66'] Exploring Operation: 75+66=141, Resulting Numbers: [141] 141,79 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[47, 94], Operations: ['3*25=75', '19+75=94'] Exploring Operation: 47+94=141, Resulting Numbers: [141] 141,79 unequal: No Solution Exploring Operation: 94-47=47, Resulting Numbers: [47] 47,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[47, 25, 57], Operations: ['19*3=57'] Exploring Operation: 47+25=72, Resulting Numbers: [57, 72] Generated Node #0,1,0: 79:[57, 72] Operation: 47+25=72 Exploring Operation: 25+57=82, Resulting Numbers: [47, 82] Generated Node #0,1,1: 79:[47, 82] Operation: 25+57=82 Moving to Node #0,1,0 Current State: 79:[57, 72], Operations: ['19*3=57', '47+25=72'] Exploring Operation: 57+72=129, Resulting Numbers: [129] 129,79 unequal: No Solution Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[47, 82], Operations: ['19*3=57', '25+57=82'] Exploring Operation: 82-47=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 47+82=129, Resulting Numbers: [129] 129,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 70, 13, 96, 42 ]
29
[ "70+13=83", "96-42=54", "83-54=29" ]
Current State: 29:[70, 13, 96, 42], Operations: [] Exploring Operation: 70+13=83, Resulting Numbers: [96, 42, 83] Generated Node #2: [96, 42, 83] from Operation: 70+13=83 Current State: 29:[96, 42, 83], Operations: ['70+13=83'] Exploring Operation: 96-42=54, Resulting Numbers: [83, 54] Generated Node #3: [83, 54] from Operation: 96-42=54 Current State: 29:[83, 54], Operations: ['70+13=83', '96-42=54'] Exploring Operation: 83-54=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[70, 13, 96, 42], Operations: [] Exploring Operation: 96-42=54, Resulting Numbers: [70, 13, 54] Generated Node #0,0: 29:[70, 13, 54] Operation: 96-42=54 Exploring Operation: 70-42=28, Resulting Numbers: [13, 96, 28] Generated Node #0,1: 29:[13, 96, 28] Operation: 70-42=28 Exploring Operation: 96-70=26, Resulting Numbers: [13, 42, 26] Generated Node #0,2: 29:[13, 42, 26] Operation: 96-70=26 Exploring Operation: 70-13=57, Resulting Numbers: [96, 42, 57] Generated Node #0,3: 29:[96, 42, 57] Operation: 70-13=57 Exploring Operation: 96-13=83, Resulting Numbers: [70, 42, 83] Generated Node #0,4: 29:[70, 42, 83] Operation: 96-13=83 Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[13, 42, 26], Operations: ['96-70=26'] Exploring Operation: 42-13=29, Resulting Numbers: [26, 29] Generated Node #0,2,0: 29:[26, 29] Operation: 42-13=29 Exploring Operation: 26-13=13, Resulting Numbers: [42, 13] Generated Node #0,2,1: 29:[42, 13] Operation: 26-13=13 Exploring Operation: 13+26=39, Resulting Numbers: [42, 39] Generated Node #0,2,2: 29:[42, 39] Operation: 13+26=39 Exploring Operation: 13+42=55, Resulting Numbers: [26, 55] Generated Node #0,2,3: 29:[26, 55] Operation: 13+42=55 Exploring Operation: 42-26=16, Resulting Numbers: [13, 16] Generated Node #0,2,4: 29:[13, 16] Operation: 42-26=16 Moving to Node #0,2,0 Current State: 29:[26, 29], Operations: ['96-70=26', '42-13=29'] Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,29 unequal: No Solution Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,29 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[42, 39], Operations: ['96-70=26', '13+26=39'] Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,29 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,29 unequal: No Solution Exploring Operation: 42*39=1638, Resulting Numbers: [1638] 1638,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[42, 13], Operations: ['96-70=26', '26-13=13'] Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[70, 13, 96, 42], Operations: [] Exploring Operation: 96-70=26, Resulting Numbers: [13, 42, 26] Generated Node #0,2: 29:[13, 42, 26] Operation: 96-70=26 Moving to Node #0,2 Current State: 29:[13, 42, 26], Operations: ['96-70=26'] Exploring Operation: 26-13=13, Resulting Numbers: [42, 13] Generated Node #0,2,1: 29:[42, 13] Operation: 26-13=13 Moving to Node #0,2,1 Current State: 29:[42, 13], Operations: ['96-70=26', '26-13=13'] Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 27, 42, 46, 34 ]
51
[ "27+42=69", "34*69=2346", "2346/46=51" ]
Current State: 51:[27, 42, 46, 34], Operations: [] Exploring Operation: 27+42=69, Resulting Numbers: [46, 34, 69] Generated Node #2: [46, 34, 69] from Operation: 27+42=69 Current State: 51:[46, 34, 69], Operations: ['27+42=69'] Exploring Operation: 34*69=2346, Resulting Numbers: [46, 2346] Generated Node #3: [46, 2346] from Operation: 34*69=2346 Current State: 51:[46, 2346], Operations: ['27+42=69', '34*69=2346'] Exploring Operation: 2346/46=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[27, 42, 46, 34], Operations: [] Exploring Operation: 42-34=8, Resulting Numbers: [27, 46, 8] Generated Node #0,0: 51:[27, 46, 8] Operation: 42-34=8 Exploring Operation: 27+34=61, Resulting Numbers: [42, 46, 61] Generated Node #0,1: 51:[42, 46, 61] Operation: 27+34=61 Exploring Operation: 34-27=7, Resulting Numbers: [42, 46, 7] Generated Node #0,2: 51:[42, 46, 7] Operation: 34-27=7 Exploring Operation: 42-27=15, Resulting Numbers: [46, 34, 15] Generated Node #0,3: 51:[46, 34, 15] Operation: 42-27=15 Moving to Node #0,2 Current State: 51:[42, 46, 7], Operations: ['34-27=7'] Exploring Operation: 46-42=4, Resulting Numbers: [7, 4] Generated Node #0,2,0: 51:[7, 4] Operation: 46-42=4 Exploring Operation: 46+7=53, Resulting Numbers: [42, 53] Generated Node #0,2,1: 51:[42, 53] Operation: 46+7=53 Exploring Operation: 42/7=6, Resulting Numbers: [46, 6] Generated Node #0,2,2: 51:[46, 6] Operation: 42/7=6 Exploring Operation: 42+7=49, Resulting Numbers: [46, 49] Generated Node #0,2,3: 51:[46, 49] Operation: 42+7=49 Moving to Node #0,0 Current State: 51:[27, 46, 8], Operations: ['42-34=8'] Exploring Operation: 46+8=54, Resulting Numbers: [27, 54] Generated Node #0,0,0: 51:[27, 54] Operation: 46+8=54 Exploring Operation: 27-8=19, Resulting Numbers: [46, 19] Generated Node #0,0,1: 51:[46, 19] Operation: 27-8=19 Exploring Operation: 46-27=19, Resulting Numbers: [8, 19] Generated Node #0,0,2: 51:[8, 19] Operation: 46-27=19 Exploring Operation: 27+8=35, Resulting Numbers: [46, 35] Generated Node #0,0,3: 51:[46, 35] Operation: 27+8=35 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[46, 19], Operations: ['42-34=8', '27-8=19'] Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 51:[8, 19], Operations: ['42-34=8', '46-27=19'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[27, 54], Operations: ['42-34=8', '46+8=54'] Exploring Operation: 54-27=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 27*54=1458, Resulting Numbers: [1458] 1458,51 unequal: No Solution Exploring Operation: 27+54=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 54/27=2, Resulting Numbers: [2] 2,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 51:[46, 35], Operations: ['42-34=8', '27+8=35'] Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,51 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,51 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: 51:[46, 34, 15], Operations: ['42-27=15'] Exploring Operation: 34+15=49, Resulting Numbers: [46, 49] Generated Node #0,3,0: 51:[46, 49] Operation: 34+15=49 Exploring Operation: 46+15=61, Resulting Numbers: [34, 61] Generated Node #0,3,1: 51:[34, 61] Operation: 46+15=61 Exploring Operation: 34-15=19, Resulting Numbers: [46, 19] Generated Node #0,3,2: 51:[46, 19] Operation: 34-15=19 Exploring Operation: 46-34=12, Resulting Numbers: [15, 12] Generated Node #0,3,3: 51:[15, 12] Operation: 46-34=12 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 51:[46, 49], Operations: ['42-27=15', '34+15=49'] Exploring Operation: 46+49=95, Resulting Numbers: [95] 95,51 unequal: No Solution Exploring Operation: 46*49=2254, Resulting Numbers: [2254] 2254,51 unequal: No Solution Exploring Operation: 49-46=3, Resulting Numbers: [3] 3,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 51:[46, 19], Operations: ['42-27=15', '34-15=19'] Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,51 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 51:[15, 12], Operations: ['42-27=15', '46-34=12'] Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 15*12=180, Resulting Numbers: [180] 180,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 51:[34, 61], Operations: ['42-27=15', '46+15=61'] Exploring Operation: 34+61=95, Resulting Numbers: [95] 95,51 unequal: No Solution Exploring Operation: 34*61=2074, Resulting Numbers: [2074] 2074,51 unequal: No Solution Exploring Operation: 61-34=27, Resulting Numbers: [27] 27,51 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: 51:[42, 46, 61], Operations: ['27+34=61'] Exploring Operation: 42+46=88, Resulting Numbers: [61, 88] Generated Node #0,1,0: 51:[61, 88] Operation: 42+46=88 Exploring Operation: 61-42=19, Resulting Numbers: [46, 19] Generated Node #0,1,1: 51:[46, 19] Operation: 61-42=19 Exploring Operation: 46-42=4, Resulting Numbers: [61, 4] Generated Node #0,1,2: 51:[61, 4] Operation: 46-42=4 Exploring Operation: 61-46=15, Resulting Numbers: [42, 15] Generated Node #0,1,3: 51:[42, 15] Operation: 61-46=15 Moving to Node #0,2,0 Current State: 51:[7, 4], Operations: ['34-27=7', '46-42=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[46, 49], Operations: ['34-27=7', '42+7=49'] Exploring Operation: 46+49=95, Resulting Numbers: [95] 95,51 unequal: No Solution Exploring Operation: 46*49=2254, Resulting Numbers: [2254] 2254,51 unequal: No Solution Exploring Operation: 49-46=3, Resulting Numbers: [3] 3,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[46, 19], Operations: ['27+34=61', '61-42=19'] Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[46, 6], Operations: ['34-27=7', '42/7=6'] Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,51 unequal: No Solution Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[61, 4], Operations: ['27+34=61', '46-42=4'] Exploring Operation: 61*4=244, Resulting Numbers: [244] 244,51 unequal: No Solution Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[42, 53], Operations: ['34-27=7', '46+7=53'] Exploring Operation: 42*53=2226, Resulting Numbers: [2226] 2226,51 unequal: No Solution Exploring Operation: 42+53=95, Resulting Numbers: [95] 95,51 unequal: No Solution Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[42, 15], Operations: ['27+34=61', '61-46=15'] Exploring Operation: 42*15=630, Resulting Numbers: [630] 630,51 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 42+15=57, Resulting Numbers: [57] 57,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[61, 88], Operations: ['27+34=61', '42+46=88'] Exploring Operation: 61+88=149, Resulting Numbers: [149] 149,51 unequal: No Solution Exploring Operation: 88-61=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 61*88=5368, Resulting Numbers: [5368] 5368,51 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 66, 86, 42, 29 ]
51
[ "86-66=20", "42+29=71", "71-20=51" ]
Current State: 51:[66, 86, 42, 29], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [42, 29, 20] Generated Node #2: [42, 29, 20] from Operation: 86-66=20 Current State: 51:[42, 29, 20], Operations: ['86-66=20'] Exploring Operation: 42+29=71, Resulting Numbers: [20, 71] Generated Node #3: [20, 71] from Operation: 42+29=71 Current State: 51:[20, 71], Operations: ['86-66=20', '42+29=71'] Exploring Operation: 71-20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[66, 86, 42, 29], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [42, 29, 20] Generated Node #0,0: 51:[42, 29, 20] Operation: 86-66=20 Moving to Node #0,0 Current State: 51:[42, 29, 20], Operations: ['86-66=20'] Exploring Operation: 42-29=13, Resulting Numbers: [20, 13] Generated Node #0,0,0: 51:[20, 13] Operation: 42-29=13 Moving to Node #0,0,0 Current State: 51:[20, 13], Operations: ['86-66=20', '42-29=13'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,51 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 64, 68, 62, 6 ]
89
[ "64+62=126", "126/6=21", "68+21=89" ]
Current State: 89:[64, 68, 62, 6], Operations: [] Exploring Operation: 64+62=126, Resulting Numbers: [68, 6, 126] Generated Node #2: [68, 6, 126] from Operation: 64+62=126 Current State: 89:[68, 6, 126], Operations: ['64+62=126'] Exploring Operation: 126/6=21, Resulting Numbers: [68, 21] Generated Node #3: [68, 21] from Operation: 126/6=21 Current State: 89:[68, 21], Operations: ['64+62=126', '126/6=21'] Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[64, 68, 62, 6], Operations: [] Exploring Operation: 68+6=74, Resulting Numbers: [64, 62, 74] Generated Node #0,0: 89:[64, 62, 74] Operation: 68+6=74 Exploring Operation: 62+6=68, Resulting Numbers: [64, 68, 68] Generated Node #0,1: 89:[64, 68, 68] Operation: 62+6=68 Exploring Operation: 64+6=70, Resulting Numbers: [68, 62, 70] Generated Node #0,2: 89:[68, 62, 70] Operation: 64+6=70 Exploring Operation: 64-6=58, Resulting Numbers: [68, 62, 58] Generated Node #0,3: 89:[68, 62, 58] Operation: 64-6=58 Moving to Node #0,0 Current State: 89:[64, 62, 74], Operations: ['68+6=74'] Exploring Operation: 64-62=2, Resulting Numbers: [74, 2] Generated Node #0,0,0: 89:[74, 2] Operation: 64-62=2 Exploring Operation: 62+74=136, Resulting Numbers: [64, 136] Generated Node #0,0,1: 89:[64, 136] Operation: 62+74=136 Exploring Operation: 64+62=126, Resulting Numbers: [74, 126] Generated Node #0,0,2: 89:[74, 126] Operation: 64+62=126 Exploring Operation: 64+74=138, Resulting Numbers: [62, 138] Generated Node #0,0,3: 89:[62, 138] Operation: 64+74=138 Moving to Node #0,2 Current State: 89:[68, 62, 70], Operations: ['64+6=70'] Exploring Operation: 68+70=138, Resulting Numbers: [62, 138] Generated Node #0,2,0: 89:[62, 138] Operation: 68+70=138 Exploring Operation: 68+62=130, Resulting Numbers: [70, 130] Generated Node #0,2,1: 89:[70, 130] Operation: 68+62=130 Exploring Operation: 62+70=132, Resulting Numbers: [68, 132] Generated Node #0,2,2: 89:[68, 132] Operation: 62+70=132 Exploring Operation: 68-62=6, Resulting Numbers: [70, 6] Generated Node #0,2,3: 89:[70, 6] Operation: 68-62=6 Moving to Node #0,1 Current State: 89:[64, 68, 68], Operations: ['62+6=68'] Exploring Operation: 68-64=4, Resulting Numbers: [68, 4] Generated Node #0,1,0: 89:[68, 4] Operation: 68-64=4 Exploring Operation: 68+68=136, Resulting Numbers: [64, 136] Generated Node #0,1,1: 89:[64, 136] Operation: 68+68=136 Exploring Operation: 64+68=132, Resulting Numbers: [68, 132] Generated Node #0,1,2: 89:[68, 132] Operation: 64+68=132 Exploring Operation: 64+68=132, Resulting Numbers: [68, 132] Generated Node #0,1,3: 89:[68, 132] Operation: 64+68=132 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[68, 132], Operations: ['62+6=68', '64+68=132'] Exploring Operation: 68+132=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 68*132=8976, Resulting Numbers: [8976] 8976,89 unequal: No Solution Exploring Operation: 132-68=64, Resulting Numbers: [64] 64,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 89:[68, 132], Operations: ['62+6=68', '64+68=132'] Exploring Operation: 68+132=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 132-68=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 68*132=8976, Resulting Numbers: [8976] 8976,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[64, 136], Operations: ['62+6=68', '68+68=136'] Exploring Operation: 64+136=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 64*136=8704, Resulting Numbers: [8704] 8704,89 unequal: No Solution Exploring Operation: 136-64=72, Resulting Numbers: [72] 72,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[68, 4], Operations: ['62+6=68', '68-64=4'] Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 68*4=272, Resulting Numbers: [272] 272,89 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,89 unequal: No Solution Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 89:[68, 62, 58], Operations: ['64-6=58'] Exploring Operation: 68-58=10, Resulting Numbers: [62, 10] Generated Node #0,3,0: 89:[62, 10] Operation: 68-58=10 Exploring Operation: 62+58=120, Resulting Numbers: [68, 120] Generated Node #0,3,1: 89:[68, 120] Operation: 62+58=120 Exploring Operation: 68+58=126, Resulting Numbers: [62, 126] Generated Node #0,3,2: 89:[62, 126] Operation: 68+58=126 Exploring Operation: 68+62=130, Resulting Numbers: [58, 130] Generated Node #0,3,3: 89:[58, 130] Operation: 68+62=130 Moving to Node #0,0,2 Current State: 89:[74, 126], Operations: ['68+6=74', '64+62=126'] Exploring Operation: 74*126=9324, Resulting Numbers: [9324] 9324,89 unequal: No Solution Exploring Operation: 126-74=52, Resulting Numbers: [52] 52,89 unequal: No Solution Exploring Operation: 74+126=200, Resulting Numbers: [200] 200,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[68, 120], Operations: ['64-6=58', '62+58=120'] Exploring Operation: 68*120=8160, Resulting Numbers: [8160] 8160,89 unequal: No Solution Exploring Operation: 120-68=52, Resulting Numbers: [52] 52,89 unequal: No Solution Exploring Operation: 68+120=188, Resulting Numbers: [188] 188,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[70, 130], Operations: ['64+6=70', '68+62=130'] Exploring Operation: 70+130=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 70*130=9100, Resulting Numbers: [9100] 9100,89 unequal: No Solution Exploring Operation: 130-70=60, Resulting Numbers: [60] 60,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[68, 132], Operations: ['64+6=70', '62+70=132'] Exploring Operation: 132-68=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 68*132=8976, Resulting Numbers: [8976] 8976,89 unequal: No Solution Exploring Operation: 68+132=200, Resulting Numbers: [200] 200,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[62, 126], Operations: ['64-6=58', '68+58=126'] Exploring Operation: 62*126=7812, Resulting Numbers: [7812] 7812,89 unequal: No Solution Exploring Operation: 126-62=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 62+126=188, Resulting Numbers: [188] 188,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[58, 130], Operations: ['64-6=58', '68+62=130'] Exploring Operation: 130-58=72, Resulting Numbers: [72] 72,89 unequal: No Solution Exploring Operation: 58+130=188, Resulting Numbers: [188] 188,89 unequal: No Solution Exploring Operation: 58*130=7540, Resulting Numbers: [7540] 7540,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[64, 136], Operations: ['68+6=74', '62+74=136'] Exploring Operation: 64*136=8704, Resulting Numbers: [8704] 8704,89 unequal: No Solution Exploring Operation: 64+136=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 136-64=72, Resulting Numbers: [72] 72,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[62, 138], Operations: ['64+6=70', '68+70=138'] Exploring Operation: 62+138=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 138-62=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 62*138=8556, Resulting Numbers: [8556] 8556,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[62, 138], Operations: ['68+6=74', '64+74=138'] Exploring Operation: 62*138=8556, Resulting Numbers: [8556] 8556,89 unequal: No Solution Exploring Operation: 62+138=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 138-62=76, Resulting Numbers: [76] 76,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[74, 2], Operations: ['68+6=74', '64-62=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,89 unequal: No Solution Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 74*2=148, Resulting Numbers: [148] 148,89 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[70, 6], Operations: ['64+6=70', '68-62=6'] Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 70*6=420, Resulting Numbers: [420] 420,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[62, 10], Operations: ['64-6=58', '68-58=10'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,89 unequal: No Solution Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,89 unequal: No Solution Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,89 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 77, 72, 13, 19 ]
65
[ "19-13=6", "72/6=12", "77-12=65" ]
Current State: 65:[77, 72, 13, 19], Operations: [] Exploring Operation: 19-13=6, Resulting Numbers: [77, 72, 6] Generated Node #2: [77, 72, 6] from Operation: 19-13=6 Current State: 65:[77, 72, 6], Operations: ['19-13=6'] Exploring Operation: 72/6=12, Resulting Numbers: [77, 12] Generated Node #3: [77, 12] from Operation: 72/6=12 Current State: 65:[77, 12], Operations: ['19-13=6', '72/6=12'] Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[77, 72, 13, 19], Operations: [] Exploring Operation: 77-13=64, Resulting Numbers: [72, 19, 64] Generated Node #0,0: 65:[72, 19, 64] Operation: 77-13=64 Exploring Operation: 77-72=5, Resulting Numbers: [13, 19, 5] Generated Node #0,1: 65:[13, 19, 5] Operation: 77-72=5 Exploring Operation: 77-19=58, Resulting Numbers: [72, 13, 58] Generated Node #0,2: 65:[72, 13, 58] Operation: 77-19=58 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[13, 19, 5], Operations: ['77-72=5'] Exploring Operation: 13*5=65, Resulting Numbers: [19, 65] Generated Node #0,1,0: 65:[19, 65] Operation: 13*5=65 Exploring Operation: 19-13=6, Resulting Numbers: [5, 6] Generated Node #0,1,1: 65:[5, 6] Operation: 19-13=6 Exploring Operation: 19-5=14, Resulting Numbers: [13, 14] Generated Node #0,1,2: 65:[13, 14] Operation: 19-5=14 Moving to Node #0,1,1 Current State: 65:[5, 6], Operations: ['77-72=5', '19-13=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[13, 14], Operations: ['77-72=5', '19-5=14'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[19, 65], Operations: ['77-72=5', '13*5=65'] Exploring Operation: 19*65=1235, Resulting Numbers: [1235] 1235,65 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 19+65=84, Resulting Numbers: [84] 84,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[72, 19, 64], Operations: ['77-13=64'] Exploring Operation: 72-64=8, Resulting Numbers: [19, 8] Generated Node #0,0,0: 65:[19, 8] Operation: 72-64=8 Exploring Operation: 72-19=53, Resulting Numbers: [64, 53] Generated Node #0,0,1: 65:[64, 53] Operation: 72-19=53 Exploring Operation: 19+64=83, Resulting Numbers: [72, 83] Generated Node #0,0,2: 65:[72, 83] Operation: 19+64=83 Moving to Node #0,0,0 Current State: 65:[19, 8], Operations: ['77-13=64', '72-64=8'] Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[64, 53], Operations: ['77-13=64', '72-19=53'] Exploring Operation: 64*53=3392, Resulting Numbers: [3392] 3392,65 unequal: No Solution Exploring Operation: 64+53=117, Resulting Numbers: [117] 117,65 unequal: No Solution Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[72, 83], Operations: ['77-13=64', '19+64=83'] Exploring Operation: 72+83=155, Resulting Numbers: [155] 155,65 unequal: No Solution Exploring Operation: 83-72=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 72*83=5976, Resulting Numbers: [5976] 5976,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[72, 13, 58], Operations: ['77-19=58'] Exploring Operation: 72-58=14, Resulting Numbers: [13, 14] Generated Node #0,2,0: 65:[13, 14] Operation: 72-58=14 Exploring Operation: 13+58=71, Resulting Numbers: [72, 71] Generated Node #0,2,1: 65:[72, 71] Operation: 13+58=71 Exploring Operation: 72-13=59, Resulting Numbers: [58, 59] Generated Node #0,2,2: 65:[58, 59] Operation: 72-13=59 Moving to Node #0,2,0 Current State: 65:[13, 14], Operations: ['77-19=58', '72-58=14'] Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,65 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[72, 71], Operations: ['77-19=58', '13+58=71'] Exploring Operation: 72+71=143, Resulting Numbers: [143] 143,65 unequal: No Solution Exploring Operation: 72*71=5112, Resulting Numbers: [5112] 5112,65 unequal: No Solution Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[58, 59], Operations: ['77-19=58', '72-13=59'] Exploring Operation: 58+59=117, Resulting Numbers: [117] 117,65 unequal: No Solution Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 58*59=3422, Resulting Numbers: [3422] 3422,65 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
[ 39, 75, 48, 75 ]
88
[ "39+48=87", "75/75=1", "87+1=88" ]
Current State: 88:[39, 75, 48, 75], Operations: [] Exploring Operation: 39+48=87, Resulting Numbers: [75, 75, 87] Generated Node #2: [75, 75, 87] from Operation: 39+48=87 Current State: 88:[75, 75, 87], Operations: ['39+48=87'] Exploring Operation: 75/75=1, Resulting Numbers: [87, 1] Generated Node #3: [87, 1] from Operation: 75/75=1 Current State: 88:[87, 1], Operations: ['39+48=87', '75/75=1'] Exploring Operation: 87+1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[39, 75, 48, 75], Operations: [] Exploring Operation: 75-48=27, Resulting Numbers: [39, 75, 27] Generated Node #0,0: 88:[39, 75, 27] Operation: 75-48=27 Exploring Operation: 75-75=0, Resulting Numbers: [39, 48, 0] Generated Node #0,1: 88:[39, 48, 0] Operation: 75-75=0 Exploring Operation: 75/75=1, Resulting Numbers: [39, 48, 1] Generated Node #0,2: 88:[39, 48, 1] Operation: 75/75=1 Exploring Operation: 75-48=27, Resulting Numbers: [39, 75, 27] Generated Node #0,3: 88:[39, 75, 27] Operation: 75-48=27 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[39, 48, 1], Operations: ['75/75=1'] Exploring Operation: 48-39=9, Resulting Numbers: [1, 9] Generated Node #0,2,0: 88:[1, 9] Operation: 48-39=9 Exploring Operation: 39+1=40, Resulting Numbers: [48, 40] Generated Node #0,2,1: 88:[48, 40] Operation: 39+1=40 Exploring Operation: 39+48=87, Resulting Numbers: [1, 87] Generated Node #0,2,2: 88:[1, 87] Operation: 39+48=87 Exploring Operation: 48-1=47, Resulting Numbers: [39, 47] Generated Node #0,2,3: 88:[39, 47] Operation: 48-1=47 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 88:[1, 9], Operations: ['75/75=1', '48-39=9'] Exploring Operation: 1*9=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 1+9=10, Resulting Numbers: [10] 10,88 unequal: No Solution No 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: 88:[1, 87], Operations: ['75/75=1', '39+48=87'] Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,88 unequal: No Solution Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[39, 75, 48, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [39, 48, 1] Generated Node #0,2: 88:[39, 48, 1] Operation: 75/75=1 Moving to Node #0,2 Current State: 88:[39, 48, 1], Operations: ['75/75=1'] Exploring Operation: 39+48=87, Resulting Numbers: [1, 87] Generated Node #0,2,2: 88:[1, 87] Operation: 39+48=87 Moving to Node #0,2,2 Current State: 88:[1, 87], Operations: ['75/75=1', '39+48=87'] Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 8, 31, 41, 69 ]
87
[ "31-8=23", "41+69=110", "110-23=87" ]
Current State: 87:[8, 31, 41, 69], Operations: [] Exploring Operation: 31-8=23, Resulting Numbers: [41, 69, 23] Generated Node #2: [41, 69, 23] from Operation: 31-8=23 Current State: 87:[41, 69, 23], Operations: ['31-8=23'] Exploring Operation: 41+69=110, Resulting Numbers: [23, 110] Generated Node #3: [23, 110] from Operation: 41+69=110 Current State: 87:[23, 110], Operations: ['31-8=23', '41+69=110'] Exploring Operation: 110-23=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[8, 31, 41, 69], Operations: [] Exploring Operation: 69-41=28, Resulting Numbers: [8, 31, 28] Generated Node #0,0: 87:[8, 31, 28] Operation: 69-41=28 Exploring Operation: 41-8=33, Resulting Numbers: [31, 69, 33] Generated Node #0,1: 87:[31, 69, 33] Operation: 41-8=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[8, 31, 28], Operations: ['69-41=28'] Exploring Operation: 31-8=23, Resulting Numbers: [28, 23] Generated Node #0,0,0: 87:[28, 23] Operation: 31-8=23 Exploring Operation: 31-28=3, Resulting Numbers: [8, 3] Generated Node #0,0,1: 87:[8, 3] Operation: 31-28=3 Moving to Node #0,0,1 Current State: 87:[8, 3], Operations: ['69-41=28', '31-28=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[28, 23], Operations: ['69-41=28', '31-8=23'] Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,87 unequal: No Solution Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[31, 69, 33], Operations: ['41-8=33'] Exploring Operation: 69-33=36, Resulting Numbers: [31, 36] Generated Node #0,1,0: 87:[31, 36] Operation: 69-33=36 Exploring Operation: 69-31=38, Resulting Numbers: [33, 38] Generated Node #0,1,1: 87:[33, 38] Operation: 69-31=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[31, 36], Operations: ['41-8=33', '69-33=36'] Exploring Operation: 31+36=67, Resulting Numbers: [67] 67,87 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[33, 38], Operations: ['41-8=33', '69-31=38'] Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,87 unequal: No Solution Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 91, 36, 31, 93 ]
49
[ "93-91=2", "36/2=18", "31+18=49" ]
Current State: 49:[91, 36, 31, 93], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [36, 31, 2] Generated Node #2: [36, 31, 2] from Operation: 93-91=2 Current State: 49:[36, 31, 2], Operations: ['93-91=2'] Exploring Operation: 36/2=18, Resulting Numbers: [31, 18] Generated Node #3: [31, 18] from Operation: 36/2=18 Current State: 49:[31, 18], Operations: ['93-91=2', '36/2=18'] Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[91, 36, 31, 93], Operations: [] Exploring Operation: 93/31=3, Resulting Numbers: [91, 36, 3] Generated Node #0,0: 49:[91, 36, 3] Operation: 93/31=3 Exploring Operation: 93-91=2, Resulting Numbers: [36, 31, 2] Generated Node #0,1: 49:[36, 31, 2] Operation: 93-91=2 Exploring Operation: 91-36=55, Resulting Numbers: [31, 93, 55] Generated Node #0,2: 49:[31, 93, 55] Operation: 91-36=55 Exploring Operation: 91-31=60, Resulting Numbers: [36, 93, 60] Generated Node #0,3: 49:[36, 93, 60] Operation: 91-31=60 Exploring Operation: 93-36=57, Resulting Numbers: [91, 31, 57] Generated Node #0,4: 49:[91, 31, 57] Operation: 93-36=57 Moving to Node #0,1 Current State: 49:[36, 31, 2], Operations: ['93-91=2'] Exploring Operation: 36+2=38, Resulting Numbers: [31, 38] Generated Node #0,1,0: 49:[31, 38] Operation: 36+2=38 Exploring Operation: 31*2=62, Resulting Numbers: [36, 62] Generated Node #0,1,1: 49:[36, 62] Operation: 31*2=62 Exploring Operation: 36-31=5, Resulting Numbers: [2, 5] Generated Node #0,1,2: 49:[2, 5] Operation: 36-31=5 Exploring Operation: 36/2=18, Resulting Numbers: [31, 18] Generated Node #0,1,3: 49:[31, 18] Operation: 36/2=18 Exploring Operation: 36+31=67, Resulting Numbers: [2, 67] Generated Node #0,1,4: 49:[2, 67] Operation: 36+31=67 Moving to Node #0,0 Current State: 49:[91, 36, 3], Operations: ['93/31=3'] Exploring Operation: 91+3=94, Resulting Numbers: [36, 94] Generated Node #0,0,0: 49:[36, 94] Operation: 91+3=94 Exploring Operation: 36+3=39, Resulting Numbers: [91, 39] Generated Node #0,0,1: 49:[91, 39] Operation: 36+3=39 Exploring Operation: 91-3=88, Resulting Numbers: [36, 88] Generated Node #0,0,2: 49:[36, 88] Operation: 91-3=88 Exploring Operation: 91-36=55, Resulting Numbers: [3, 55] Generated Node #0,0,3: 49:[3, 55] Operation: 91-36=55 Exploring Operation: 36/3=12, Resulting Numbers: [91, 12] Generated Node #0,0,4: 49:[91, 12] Operation: 36/3=12 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 49:[3, 55], Operations: ['93/31=3', '91-36=55'] Exploring Operation: 3*55=165, Resulting Numbers: [165] 165,49 unequal: No Solution Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 49:[91, 12], Operations: ['93/31=3', '36/3=12'] Exploring Operation: 91+12=103, Resulting Numbers: [103] 103,49 unequal: No Solution Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,49 unequal: No Solution Exploring Operation: 91*12=1092, Resulting Numbers: [1092] 1092,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 49:[91, 39], Operations: ['93/31=3', '36+3=39'] Exploring Operation: 91+39=130, Resulting Numbers: [130] 130,49 unequal: No Solution Exploring Operation: 91*39=3549, Resulting Numbers: [3549] 3549,49 unequal: No Solution Exploring Operation: 91-39=52, Resulting Numbers: [52] 52,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 49:[36, 88], Operations: ['93/31=3', '91-3=88'] Exploring Operation: 88-36=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 36+88=124, Resulting Numbers: [124] 124,49 unequal: No Solution Exploring Operation: 36*88=3168, Resulting Numbers: [3168] 3168,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[36, 94], Operations: ['93/31=3', '91+3=94'] Exploring Operation: 36+94=130, Resulting Numbers: [130] 130,49 unequal: No Solution Exploring Operation: 36*94=3384, Resulting Numbers: [3384] 3384,49 unequal: No Solution Exploring Operation: 94-36=58, Resulting Numbers: [58] 58,49 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: 49:[31, 93, 55], Operations: ['91-36=55'] Exploring Operation: 93-31=62, Resulting Numbers: [55, 62] Generated Node #0,2,0: 49:[55, 62] Operation: 93-31=62 Exploring Operation: 55-31=24, Resulting Numbers: [93, 24] Generated Node #0,2,1: 49:[93, 24] Operation: 55-31=24 Exploring Operation: 93/31=3, Resulting Numbers: [55, 3] Generated Node #0,2,2: 49:[55, 3] Operation: 93/31=3 Exploring Operation: 93-55=38, Resulting Numbers: [31, 38] Generated Node #0,2,3: 49:[31, 38] Operation: 93-55=38 Exploring Operation: 31+93=124, Resulting Numbers: [55, 124] Generated Node #0,2,4: 49:[55, 124] Operation: 31+93=124 Moving to Node #0,3 Current State: 49:[36, 93, 60], Operations: ['91-31=60'] Exploring Operation: 93-60=33, Resulting Numbers: [36, 33] Generated Node #0,3,0: 49:[36, 33] Operation: 93-60=33 Exploring Operation: 93-36=57, Resulting Numbers: [60, 57] Generated Node #0,3,1: 49:[60, 57] Operation: 93-36=57 Exploring Operation: 36+93=129, Resulting Numbers: [60, 129] Generated Node #0,3,2: 49:[60, 129] Operation: 36+93=129 Exploring Operation: 36+60=96, Resulting Numbers: [93, 96] Generated Node #0,3,3: 49:[93, 96] Operation: 36+60=96 Exploring Operation: 60-36=24, Resulting Numbers: [93, 24] Generated Node #0,3,4: 49:[93, 24] Operation: 60-36=24 Moving to Node #0,4 Current State: 49:[91, 31, 57], Operations: ['93-36=57'] Exploring Operation: 91-31=60, Resulting Numbers: [57, 60] Generated Node #0,4,0: 49:[57, 60] Operation: 91-31=60 Exploring Operation: 57-31=26, Resulting Numbers: [91, 26] Generated Node #0,4,1: 49:[91, 26] Operation: 57-31=26 Exploring Operation: 91+31=122, Resulting Numbers: [57, 122] Generated Node #0,4,2: 49:[57, 122] Operation: 91+31=122 Exploring Operation: 31+57=88, Resulting Numbers: [91, 88] Generated Node #0,4,3: 49:[91, 88] Operation: 31+57=88 Exploring Operation: 91-57=34, Resulting Numbers: [31, 34] Generated Node #0,4,4: 49:[31, 34] Operation: 91-57=34 Moving to Node #0,1,2 Current State: 49:[2, 5], Operations: ['93-91=2', '36-31=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[55, 3], Operations: ['91-36=55', '93/31=3'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 55*3=165, Resulting Numbers: [165] 165,49 unequal: No Solution Exploring Operation: 55+3=58, Resulting Numbers: [58] 58,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[55, 62], Operations: ['91-36=55', '93-31=62'] Exploring Operation: 55+62=117, Resulting Numbers: [117] 117,49 unequal: No Solution Exploring Operation: 55*62=3410, Resulting Numbers: [3410] 3410,49 unequal: No Solution Exploring Operation: 62-55=7, Resulting Numbers: [7] 7,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[60, 57], Operations: ['91-31=60', '93-36=57'] Exploring Operation: 60+57=117, Resulting Numbers: [117] 117,49 unequal: No Solution Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 60*57=3420, Resulting Numbers: [3420] 3420,49 unequal: No Solution Moving to Node #0,4,0 Current State: 49:[57, 60], Operations: ['93-36=57', '91-31=60'] Exploring Operation: 57+60=117, Resulting Numbers: [117] 117,49 unequal: No Solution Exploring Operation: 57*60=3420, Resulting Numbers: [3420] 3420,49 unequal: No Solution Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,49 unequal: No Solution Moving to Node #0,1,4 Current State: 49:[2, 67], Operations: ['93-91=2', '36+31=67'] Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,49 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,49 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[36, 62], Operations: ['93-91=2', '31*2=62'] Exploring Operation: 36+62=98, Resulting Numbers: [98] 98,49 unequal: No Solution Exploring Operation: 36*62=2232, Resulting Numbers: [2232] 2232,49 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,49 unequal: No Solution Moving to Node #0,3,0 Current State: 49:[36, 33], Operations: ['91-31=60', '93-60=33'] Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,49 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 36*33=1188, Resulting Numbers: [1188] 1188,49 unequal: No Solution Moving to Node #0,1,3 Current State: 49:[31, 18], Operations: ['93-91=2', '36/2=18'] Exploring Operation: 31*18=558, Resulting Numbers: [558] 558,49 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,49 unequal: No Solution Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[91, 36, 31, 93], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [36, 31, 2] Generated Node #0,1: 49:[36, 31, 2] Operation: 93-91=2 Moving to Node #0,1 Current State: 49:[36, 31, 2], Operations: ['93-91=2'] Exploring Operation: 36/2=18, Resulting Numbers: [31, 18] Generated Node #0,1,3: 49:[31, 18] Operation: 36/2=18 Moving to Node #0,1,3 Current State: 49:[31, 18], Operations: ['93-91=2', '36/2=18'] Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
0.934028
hs_5
mult_heuristic
[ 10, 78, 17, 23 ]
27
[ "78-10=68", "68/17=4", "23+4=27" ]
Current State: 27:[10, 78, 17, 23], Operations: [] Exploring Operation: 78-10=68, Resulting Numbers: [17, 23, 68] Generated Node #2: [17, 23, 68] from Operation: 78-10=68 Current State: 27:[17, 23, 68], Operations: ['78-10=68'] Exploring Operation: 68/17=4, Resulting Numbers: [23, 4] Generated Node #3: [23, 4] from Operation: 68/17=4 Current State: 27:[23, 4], Operations: ['78-10=68', '68/17=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[10, 78, 17, 23], Operations: [] Exploring Operation: 78-17=61, Resulting Numbers: [10, 23, 61] Generated Node #0,0: 27:[10, 23, 61] Operation: 78-17=61 Exploring Operation: 10+17=27, Resulting Numbers: [78, 23, 27] Generated Node #0,1: 27:[78, 23, 27] Operation: 10+17=27 Exploring Operation: 78-10=68, Resulting Numbers: [17, 23, 68] Generated Node #0,2: 27:[17, 23, 68] Operation: 78-10=68 Exploring Operation: 78-23=55, Resulting Numbers: [10, 17, 55] Generated Node #0,3: 27:[10, 17, 55] Operation: 78-23=55 Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[10, 17, 55], Operations: ['78-23=55'] Exploring Operation: 55-17=38, Resulting Numbers: [10, 38] Generated Node #0,3,0: 27:[10, 38] Operation: 55-17=38 Exploring Operation: 10+17=27, Resulting Numbers: [55, 27] Generated Node #0,3,1: 27:[55, 27] Operation: 10+17=27 Exploring Operation: 55-10=45, Resulting Numbers: [17, 45] Generated Node #0,3,2: 27:[17, 45] Operation: 55-10=45 Exploring Operation: 17-10=7, Resulting Numbers: [55, 7] Generated Node #0,3,3: 27:[55, 7] Operation: 17-10=7 Moving to Node #0,3,0 Current State: 27:[10, 38], Operations: ['78-23=55', '55-17=38'] Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,27 unequal: No Solution Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[17, 45], Operations: ['78-23=55', '55-10=45'] Exploring Operation: 17*45=765, Resulting Numbers: [765] 765,27 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,27 unequal: No Solution Moving to Node #0,3,1 Current State: 27:[55, 27], Operations: ['78-23=55', '10+17=27'] Exploring Operation: 55-27=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 55*27=1485, Resulting Numbers: [1485] 1485,27 unequal: No Solution Exploring Operation: 55+27=82, Resulting Numbers: [82] 82,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[55, 7], Operations: ['78-23=55', '17-10=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,27 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,27 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,27 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 Current State: 27:[10, 23, 61], Operations: ['78-17=61'] Exploring Operation: 23-10=13, Resulting Numbers: [61, 13] Generated Node #0,0,0: 27:[61, 13] Operation: 23-10=13 Exploring Operation: 61-10=51, Resulting Numbers: [23, 51] Generated Node #0,0,1: 27:[23, 51] Operation: 61-10=51 Exploring Operation: 61-23=38, Resulting Numbers: [10, 38] Generated Node #0,0,2: 27:[10, 38] Operation: 61-23=38 Exploring Operation: 10+23=33, Resulting Numbers: [61, 33] Generated Node #0,0,3: 27:[61, 33] Operation: 10+23=33 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 27:[10, 38], Operations: ['78-17=61', '61-23=38'] Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,27 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,27 unequal: No Solution No 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: 27:[23, 51], Operations: ['78-17=61', '61-10=51'] Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,27 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,27 unequal: No Solution No 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: 27:[61, 13], Operations: ['78-17=61', '23-10=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,27 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,27 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 27:[61, 33], Operations: ['78-17=61', '10+23=33'] Exploring Operation: 61*33=2013, Resulting Numbers: [2013] 2013,27 unequal: No Solution Exploring Operation: 61+33=94, Resulting Numbers: [94] 94,27 unequal: No Solution Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,27 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: 27:[17, 23, 68], Operations: ['78-10=68'] Exploring Operation: 68-23=45, Resulting Numbers: [17, 45] Generated Node #0,2,0: 27:[17, 45] Operation: 68-23=45 Exploring Operation: 68-17=51, Resulting Numbers: [23, 51] Generated Node #0,2,1: 27:[23, 51] Operation: 68-17=51 Exploring Operation: 68/17=4, Resulting Numbers: [23, 4] Generated Node #0,2,2: 27:[23, 4] Operation: 68/17=4 Exploring Operation: 23-17=6, Resulting Numbers: [68, 6] Generated Node #0,2,3: 27:[68, 6] Operation: 23-17=6 Moving to Node #0,2,2 Current State: 27:[23, 4], Operations: ['78-10=68', '68/17=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[10, 78, 17, 23], Operations: [] Exploring Operation: 78-10=68, Resulting Numbers: [17, 23, 68] Generated Node #0,2: 27:[17, 23, 68] Operation: 78-10=68 Moving to Node #0,2 Current State: 27:[17, 23, 68], Operations: ['78-10=68'] Exploring Operation: 68/17=4, Resulting Numbers: [23, 4] Generated Node #0,2,2: 27:[23, 4] Operation: 68/17=4 Moving to Node #0,2,2 Current State: 27:[23, 4], Operations: ['78-10=68', '68/17=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_4
sum_heuristic
[ 24, 49, 78, 69 ]
16
[ "49-24=25", "78-69=9", "25-9=16" ]
Current State: 16:[24, 49, 78, 69], Operations: [] Exploring Operation: 49-24=25, Resulting Numbers: [78, 69, 25] Generated Node #2: [78, 69, 25] from Operation: 49-24=25 Current State: 16:[78, 69, 25], Operations: ['49-24=25'] Exploring Operation: 78-69=9, Resulting Numbers: [25, 9] Generated Node #3: [25, 9] from Operation: 78-69=9 Current State: 16:[25, 9], Operations: ['49-24=25', '78-69=9'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[24, 49, 78, 69], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [24, 49, 9] Generated Node #0,0: 16:[24, 49, 9] Operation: 78-69=9 Exploring Operation: 69-49=20, Resulting Numbers: [24, 78, 20] Generated Node #0,1: 16:[24, 78, 20] Operation: 69-49=20 Exploring Operation: 78-49=29, Resulting Numbers: [24, 69, 29] Generated Node #0,2: 16:[24, 69, 29] Operation: 78-49=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[24, 49, 9], Operations: ['78-69=9'] Exploring Operation: 49-9=40, Resulting Numbers: [24, 40] Generated Node #0,0,0: 16:[24, 40] Operation: 49-9=40 Exploring Operation: 24-9=15, Resulting Numbers: [49, 15] Generated Node #0,0,1: 16:[49, 15] Operation: 24-9=15 Exploring Operation: 49-24=25, Resulting Numbers: [9, 25] Generated Node #0,0,2: 16:[9, 25] Operation: 49-24=25 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 16:[9, 25], Operations: ['78-69=9', '49-24=25'] Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 9*25=225, Resulting Numbers: [225] 225,16 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[24, 49, 78, 69], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [24, 49, 9] Generated Node #0,0: 16:[24, 49, 9] Operation: 78-69=9 Moving to Node #0,0 Current State: 16:[24, 49, 9], Operations: ['78-69=9'] Exploring Operation: 49-24=25, Resulting Numbers: [9, 25] Generated Node #0,0,2: 16:[9, 25] Operation: 49-24=25 Moving to Node #0,0,2 Current State: 16:[9, 25], Operations: ['78-69=9', '49-24=25'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 13, 9, 3, 7 ]
70
[ "9/3=3", "13-3=10", "7*10=70" ]
Current State: 70:[13, 9, 3, 7], Operations: [] Exploring Operation: 9/3=3, Resulting Numbers: [13, 7, 3] Generated Node #2: [13, 7, 3] from Operation: 9/3=3 Current State: 70:[13, 7, 3], Operations: ['9/3=3'] Exploring Operation: 13-3=10, Resulting Numbers: [7, 10] Generated Node #3: [7, 10] from Operation: 13-3=10 Current State: 70:[7, 10], Operations: ['9/3=3', '13-3=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[13, 9, 3, 7], Operations: [] Exploring Operation: 9/3=3, Resulting Numbers: [13, 7, 3] Generated Node #0,0: 70:[13, 7, 3] Operation: 9/3=3 Exploring Operation: 13-9=4, Resulting Numbers: [3, 7, 4] Generated Node #0,1: 70:[3, 7, 4] Operation: 13-9=4 Exploring Operation: 9-3=6, Resulting Numbers: [13, 7, 6] Generated Node #0,2: 70:[13, 7, 6] Operation: 9-3=6 Exploring Operation: 13-3=10, Resulting Numbers: [9, 7, 10] Generated Node #0,3: 70:[9, 7, 10] Operation: 13-3=10 Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[9, 7, 10], Operations: ['13-3=10'] Exploring Operation: 9+7=16, Resulting Numbers: [10, 16] Generated Node #0,3,0: 70:[10, 16] Operation: 9+7=16 Exploring Operation: 7*10=70, Resulting Numbers: [9, 70] Generated Node #0,3,1: 70:[9, 70] Operation: 7*10=70 Exploring Operation: 10-9=1, Resulting Numbers: [7, 1] Generated Node #0,3,2: 70:[7, 1] Operation: 10-9=1 Exploring Operation: 9-7=2, Resulting Numbers: [10, 2] Generated Node #0,3,3: 70:[10, 2] Operation: 9-7=2 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 70:[10, 2], Operations: ['13-3=10', '9-7=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,70 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 70:[9, 70], Operations: ['13-3=10', '7*10=70'] Exploring Operation: 9*70=630, Resulting Numbers: [630] 630,70 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,70 unequal: No Solution Exploring Operation: 9+70=79, Resulting Numbers: [79] 79,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 70:[7, 1], Operations: ['13-3=10', '10-9=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 70:[10, 16], Operations: ['13-3=10', '9+7=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,70 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[13, 7, 3], Operations: ['9/3=3'] Exploring Operation: 13+3=16, Resulting Numbers: [7, 16] Generated Node #0,0,0: 70:[7, 16] Operation: 13+3=16 Exploring Operation: 13-7=6, Resulting Numbers: [3, 6] Generated Node #0,0,1: 70:[3, 6] Operation: 13-7=6 Exploring Operation: 7+3=10, Resulting Numbers: [13, 10] Generated Node #0,0,2: 70:[13, 10] Operation: 7+3=10 Exploring Operation: 13-3=10, Resulting Numbers: [7, 10] Generated Node #0,0,3: 70:[7, 10] Operation: 13-3=10 Moving to Node #0,0,3 Current State: 70:[7, 10], Operations: ['9/3=3', '13-3=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[13, 9, 3, 7], Operations: [] Exploring Operation: 9/3=3, Resulting Numbers: [13, 7, 3] Generated Node #0,0: 70:[13, 7, 3] Operation: 9/3=3 Moving to Node #0,0 Current State: 70:[13, 7, 3], Operations: ['9/3=3'] Exploring Operation: 13-3=10, Resulting Numbers: [7, 10] Generated Node #0,0,3: 70:[7, 10] Operation: 13-3=10 Moving to Node #0,0,3 Current State: 70:[7, 10], Operations: ['9/3=3', '13-3=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 1, 42, 32, 74 ]
64
[ "1*42=42", "32+74=106", "106-42=64" ]
Current State: 64:[1, 42, 32, 74], Operations: [] Exploring Operation: 1*42=42, Resulting Numbers: [32, 74, 42] Generated Node #2: [32, 74, 42] from Operation: 1*42=42 Current State: 64:[32, 74, 42], Operations: ['1*42=42'] Exploring Operation: 32+74=106, Resulting Numbers: [42, 106] Generated Node #3: [42, 106] from Operation: 32+74=106 Current State: 64:[42, 106], Operations: ['1*42=42', '32+74=106'] Exploring Operation: 106-42=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[1, 42, 32, 74], Operations: [] Exploring Operation: 42-32=10, Resulting Numbers: [1, 74, 10] Generated Node #0,0: 64:[1, 74, 10] Operation: 42-32=10 Exploring Operation: 74-42=32, Resulting Numbers: [1, 32, 32] Generated Node #0,1: 64:[1, 32, 32] Operation: 74-42=32 Moving to Node #0,1 Current State: 64:[1, 32, 32], Operations: ['74-42=32'] Exploring Operation: 1*32=32, Resulting Numbers: [32, 32] Generated Node #0,1,0: 64:[32, 32] Operation: 1*32=32 Exploring Operation: 32/1=32, Resulting Numbers: [32, 32] Generated Node #0,1,1: 64:[32, 32] Operation: 32/1=32 Moving to Node #0,0 Current State: 64:[1, 74, 10], Operations: ['42-32=10'] Exploring Operation: 74-10=64, Resulting Numbers: [1, 64] Generated Node #0,0,0: 64:[1, 64] Operation: 74-10=64 Exploring Operation: 74-1=73, Resulting Numbers: [10, 73] Generated Node #0,0,1: 64:[10, 73] Operation: 74-1=73 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[1, 64], Operations: ['42-32=10', '74-10=64'] Exploring Operation: 1*64=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[1, 42, 32, 74], Operations: [] Exploring Operation: 42-32=10, Resulting Numbers: [1, 74, 10] Generated Node #0,0: 64:[1, 74, 10] Operation: 42-32=10 Moving to Node #0,0 Current State: 64:[1, 74, 10], Operations: ['42-32=10'] Exploring Operation: 74-10=64, Resulting Numbers: [1, 64] Generated Node #0,0,0: 64:[1, 64] Operation: 74-10=64 Moving to Node #0,0,0 Current State: 64:[1, 64], Operations: ['42-32=10', '74-10=64'] Exploring Operation: 1*64=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 63, 2, 53, 1 ]
59
[ "63+53=116", "116/2=58", "1+58=59" ]
Current State: 59:[63, 2, 53, 1], Operations: [] Exploring Operation: 63+53=116, Resulting Numbers: [2, 1, 116] Generated Node #2: [2, 1, 116] from Operation: 63+53=116 Current State: 59:[2, 1, 116], Operations: ['63+53=116'] Exploring Operation: 116/2=58, Resulting Numbers: [1, 58] Generated Node #3: [1, 58] from Operation: 116/2=58 Current State: 59:[1, 58], Operations: ['63+53=116', '116/2=58'] Exploring Operation: 1+58=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[63, 2, 53, 1], Operations: [] Exploring Operation: 63-1=62, Resulting Numbers: [2, 53, 62] Generated Node #0,0: 59:[2, 53, 62] Operation: 63-1=62 Exploring Operation: 2+1=3, Resulting Numbers: [63, 53, 3] Generated Node #0,1: 59:[63, 53, 3] Operation: 2+1=3 Exploring Operation: 63-2=61, Resulting Numbers: [53, 1, 61] Generated Node #0,2: 59:[53, 1, 61] Operation: 63-2=61 Exploring Operation: 53+1=54, Resulting Numbers: [63, 2, 54] Generated Node #0,3: 59:[63, 2, 54] Operation: 53+1=54 Exploring Operation: 2+53=55, Resulting Numbers: [63, 1, 55] Generated Node #0,4: 59:[63, 1, 55] Operation: 2+53=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[2, 53, 62], Operations: ['63-1=62'] Exploring Operation: 62-2=60, Resulting Numbers: [53, 60] Generated Node #0,0,0: 59:[53, 60] Operation: 62-2=60 Exploring Operation: 2+53=55, Resulting Numbers: [62, 55] Generated Node #0,0,1: 59:[62, 55] Operation: 2+53=55 Exploring Operation: 62/2=31, Resulting Numbers: [53, 31] Generated Node #0,0,2: 59:[53, 31] Operation: 62/2=31 Exploring Operation: 53-2=51, Resulting Numbers: [62, 51] Generated Node #0,0,3: 59:[62, 51] Operation: 53-2=51 Exploring Operation: 2+62=64, Resulting Numbers: [53, 64] Generated Node #0,0,4: 59:[53, 64] Operation: 2+62=64 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[53, 60], Operations: ['63-1=62', '62-2=60'] Exploring Operation: 53+60=113, Resulting Numbers: [113] 113,59 unequal: No Solution Exploring Operation: 53*60=3180, Resulting Numbers: [3180] 3180,59 unequal: No Solution Exploring Operation: 60-53=7, Resulting Numbers: [7] 7,59 unequal: No Solution No 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: 59:[62, 55], Operations: ['63-1=62', '2+53=55'] Exploring Operation: 62*55=3410, Resulting Numbers: [3410] 3410,59 unequal: No Solution Exploring Operation: 62-55=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 62+55=117, Resulting Numbers: [117] 117,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 59:[62, 51], Operations: ['63-1=62', '53-2=51'] Exploring Operation: 62+51=113, Resulting Numbers: [113] 113,59 unequal: No Solution Exploring Operation: 62-51=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 62*51=3162, Resulting Numbers: [3162] 3162,59 unequal: No Solution No 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: 59:[53, 64], Operations: ['63-1=62', '2+62=64'] Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 53*64=3392, Resulting Numbers: [3392] 3392,59 unequal: No Solution Exploring Operation: 53+64=117, Resulting Numbers: [117] 117,59 unequal: No Solution No 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: 59:[53, 31], Operations: ['63-1=62', '62/2=31'] Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,59 unequal: No Solution Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,59 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: 59:[63, 53, 3], Operations: ['2+1=3'] Exploring Operation: 53+3=56, Resulting Numbers: [63, 56] Generated Node #0,1,0: 59:[63, 56] Operation: 53+3=56 Exploring Operation: 63-3=60, Resulting Numbers: [53, 60] Generated Node #0,1,1: 59:[53, 60] Operation: 63-3=60 Exploring Operation: 63/3=21, Resulting Numbers: [53, 21] Generated Node #0,1,2: 59:[53, 21] Operation: 63/3=21 Exploring Operation: 53-3=50, Resulting Numbers: [63, 50] Generated Node #0,1,3: 59:[63, 50] Operation: 53-3=50 Exploring Operation: 63+3=66, Resulting Numbers: [53, 66] Generated Node #0,1,4: 59:[53, 66] Operation: 63+3=66 Moving to Node #0,1,0 Current State: 59:[63, 56], Operations: ['2+1=3', '53+3=56'] Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,59 unequal: No Solution Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[53, 60], Operations: ['2+1=3', '63-3=60'] Exploring Operation: 60-53=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 53+60=113, Resulting Numbers: [113] 113,59 unequal: No Solution Exploring Operation: 53*60=3180, Resulting Numbers: [3180] 3180,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[63, 50], Operations: ['2+1=3', '53-3=50'] Exploring Operation: 63*50=3150, Resulting Numbers: [3150] 3150,59 unequal: No Solution Exploring Operation: 63+50=113, Resulting Numbers: [113] 113,59 unequal: No Solution Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[53, 66], Operations: ['2+1=3', '63+3=66'] Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[53, 21], Operations: ['2+1=3', '63/3=21'] Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,59 unequal: No Solution Exploring Operation: 53+21=74, Resulting Numbers: [74] 74,59 unequal: No Solution Exploring Operation: 53*21=1113, Resulting Numbers: [1113] 1113,59 unequal: No Solution No 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: 59:[53, 1, 61], Operations: ['63-2=61'] Exploring Operation: 53+1=54, Resulting Numbers: [61, 54] Generated Node #0,2,0: 59:[61, 54] Operation: 53+1=54 Exploring Operation: 53/1=53, Resulting Numbers: [61, 53] Generated Node #0,2,1: 59:[61, 53] Operation: 53/1=53 Exploring Operation: 61-1=60, Resulting Numbers: [53, 60] Generated Node #0,2,2: 59:[53, 60] Operation: 61-1=60 Exploring Operation: 1*61=61, Resulting Numbers: [53, 61] Generated Node #0,2,3: 59:[53, 61] Operation: 1*61=61 Exploring Operation: 53*1=53, Resulting Numbers: [61, 53] Generated Node #0,2,4: 59:[61, 53] Operation: 53*1=53 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 59:[61, 54], Operations: ['63-2=61', '53+1=54'] Exploring Operation: 61-54=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 61+54=115, Resulting Numbers: [115] 115,59 unequal: No Solution Exploring Operation: 61*54=3294, Resulting Numbers: [3294] 3294,59 unequal: No Solution No 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: 59:[53, 60], Operations: ['63-2=61', '61-1=60'] Exploring Operation: 53+60=113, Resulting Numbers: [113] 113,59 unequal: No Solution Exploring Operation: 60-53=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 53*60=3180, Resulting Numbers: [3180] 3180,59 unequal: No Solution No 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: 59:[61, 53], Operations: ['63-2=61', '53/1=53'] Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 61+53=114, Resulting Numbers: [114] 114,59 unequal: No Solution Exploring Operation: 61*53=3233, Resulting Numbers: [3233] 3233,59 unequal: No Solution No 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: 59:[53, 61], Operations: ['63-2=61', '1*61=61'] Exploring Operation: 53*61=3233, Resulting Numbers: [3233] 3233,59 unequal: No Solution Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 53+61=114, Resulting Numbers: [114] 114,59 unequal: No Solution No 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: 59:[61, 53], Operations: ['63-2=61', '53*1=53'] Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 61+53=114, Resulting Numbers: [114] 114,59 unequal: No Solution Exploring Operation: 61*53=3233, Resulting Numbers: [3233] 3233,59 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: 59:[63, 2, 54], Operations: ['53+1=54'] Exploring Operation: 54/2=27, Resulting Numbers: [63, 27] Generated Node #0,3,0: 59:[63, 27] Operation: 54/2=27 Exploring Operation: 63+2=65, Resulting Numbers: [54, 65] Generated Node #0,3,1: 59:[54, 65] Operation: 63+2=65 Exploring Operation: 2+54=56, Resulting Numbers: [63, 56] Generated Node #0,3,2: 59:[63, 56] Operation: 2+54=56 Exploring Operation: 54-2=52, Resulting Numbers: [63, 52] Generated Node #0,3,3: 59:[63, 52] Operation: 54-2=52 Exploring Operation: 63-2=61, Resulting Numbers: [54, 61] Generated Node #0,3,4: 59:[54, 61] Operation: 63-2=61 Moving to Node #0,3,2 Current State: 59:[63, 56], Operations: ['53+1=54', '2+54=56'] Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,59 unequal: No Solution Moving to Node #0,3,4 Current State: 59:[54, 61], Operations: ['53+1=54', '63-2=61'] Exploring Operation: 61-54=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 54+61=115, Resulting Numbers: [115] 115,59 unequal: No Solution Exploring Operation: 54*61=3294, Resulting Numbers: [3294] 3294,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[54, 65], Operations: ['53+1=54', '63+2=65'] Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,59 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[63, 52], Operations: ['53+1=54', '54-2=52'] Exploring Operation: 63+52=115, Resulting Numbers: [115] 115,59 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 63*52=3276, Resulting Numbers: [3276] 3276,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[63, 27], Operations: ['53+1=54', '54/2=27'] Exploring Operation: 63-27=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 63+27=90, Resulting Numbers: [90] 90,59 unequal: No Solution Exploring Operation: 63*27=1701, Resulting Numbers: [1701] 1701,59 unequal: No Solution No 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: 59:[63, 1, 55], Operations: ['2+53=55'] Exploring Operation: 1+55=56, Resulting Numbers: [63, 56] Generated Node #0,4,0: 59:[63, 56] Operation: 1+55=56 Exploring Operation: 63-1=62, Resulting Numbers: [55, 62] Generated Node #0,4,1: 59:[55, 62] Operation: 63-1=62 Exploring Operation: 63*1=63, Resulting Numbers: [55, 63] Generated Node #0,4,2: 59:[55, 63] Operation: 63*1=63 Exploring Operation: 1*55=55, Resulting Numbers: [63, 55] Generated Node #0,4,3: 59:[63, 55] Operation: 1*55=55 Exploring Operation: 63/1=63, Resulting Numbers: [55, 63] Generated Node #0,4,4: 59:[55, 63] Operation: 63/1=63 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 59:[63, 56], Operations: ['2+53=55', '1+55=56'] Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,59 unequal: No Solution Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 59:[55, 62], Operations: ['2+53=55', '63-1=62'] Exploring Operation: 55*62=3410, Resulting Numbers: [3410] 3410,59 unequal: No Solution Exploring Operation: 55+62=117, Resulting Numbers: [117] 117,59 unequal: No Solution Exploring Operation: 62-55=7, Resulting Numbers: [7] 7,59 unequal: No Solution No 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: 59:[55, 63], Operations: ['2+53=55', '63*1=63'] Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,59 unequal: No Solution No 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: 59:[63, 55], Operations: ['2+53=55', '1*55=55'] Exploring Operation: 63*55=3465, Resulting Numbers: [3465] 3465,59 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 63+55=118, Resulting Numbers: [118] 118,59 unequal: No Solution No 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: 59:[55, 63], Operations: ['2+53=55', '63/1=63'] Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,59 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 55, 8, 2, 56 ]
96
[ "56/8=7", "55-7=48", "2*48=96" ]
Current State: 96:[55, 8, 2, 56], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [55, 2, 7] Generated Node #2: [55, 2, 7] from Operation: 56/8=7 Current State: 96:[55, 2, 7], Operations: ['56/8=7'] Exploring Operation: 55-7=48, Resulting Numbers: [2, 48] Generated Node #3: [2, 48] from Operation: 55-7=48 Current State: 96:[2, 48], Operations: ['56/8=7', '55-7=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[55, 8, 2, 56], Operations: [] Exploring Operation: 56-55=1, Resulting Numbers: [8, 2, 1] Generated Node #0,0: 96:[8, 2, 1] Operation: 56-55=1 Exploring Operation: 56-8=48, Resulting Numbers: [55, 2, 48] Generated Node #0,1: 96:[55, 2, 48] Operation: 56-8=48 Exploring Operation: 56/8=7, Resulting Numbers: [55, 2, 7] Generated Node #0,2: 96:[55, 2, 7] Operation: 56/8=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[8, 2, 1], Operations: ['56-55=1'] Exploring Operation: 8/1=8, Resulting Numbers: [2, 8] Generated Node #0,0,0: 96:[2, 8] Operation: 8/1=8 Exploring Operation: 8*1=8, Resulting Numbers: [2, 8] Generated Node #0,0,1: 96:[2, 8] Operation: 8*1=8 Exploring Operation: 2+1=3, Resulting Numbers: [8, 3] Generated Node #0,0,2: 96:[8, 3] Operation: 2+1=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[2, 8], Operations: ['56-55=1', '8/1=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[2, 8], Operations: ['56-55=1', '8*1=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[8, 3], Operations: ['56-55=1', '2+1=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[55, 2, 48], Operations: ['56-8=48'] Exploring Operation: 55-2=53, Resulting Numbers: [48, 53] Generated Node #0,1,0: 96:[48, 53] Operation: 55-2=53 Exploring Operation: 55+48=103, Resulting Numbers: [2, 103] Generated Node #0,1,1: 96:[2, 103] Operation: 55+48=103 Exploring Operation: 55-48=7, Resulting Numbers: [2, 7] Generated Node #0,1,2: 96:[2, 7] Operation: 55-48=7 Moving to Node #0,1,2 Current State: 96:[2, 7], Operations: ['56-8=48', '55-48=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[48, 53], Operations: ['56-8=48', '55-2=53'] Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 48*53=2544, Resulting Numbers: [2544] 2544,96 unequal: No Solution Exploring Operation: 48+53=101, Resulting Numbers: [101] 101,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[2, 103], Operations: ['56-8=48', '55+48=103'] Exploring Operation: 103-2=101, Resulting Numbers: [101] 101,96 unequal: No Solution Exploring Operation: 2+103=105, Resulting Numbers: [105] 105,96 unequal: No Solution Exploring Operation: 2*103=206, Resulting Numbers: [206] 206,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[55, 2, 7], Operations: ['56/8=7'] Exploring Operation: 55-2=53, Resulting Numbers: [7, 53] Generated Node #0,2,0: 96:[7, 53] Operation: 55-2=53 Exploring Operation: 55-7=48, Resulting Numbers: [2, 48] Generated Node #0,2,1: 96:[2, 48] Operation: 55-7=48 Exploring Operation: 2+7=9, Resulting Numbers: [55, 9] Generated Node #0,2,2: 96:[55, 9] Operation: 2+7=9 Moving to Node #0,2,1 Current State: 96:[2, 48], Operations: ['56/8=7', '55-7=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[55, 8, 2, 56], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [55, 2, 7] Generated Node #0,2: 96:[55, 2, 7] Operation: 56/8=7 Moving to Node #0,2 Current State: 96:[55, 2, 7], Operations: ['56/8=7'] Exploring Operation: 55-7=48, Resulting Numbers: [2, 48] Generated Node #0,2,1: 96:[2, 48] Operation: 55-7=48 Moving to Node #0,2,1 Current State: 96:[2, 48], Operations: ['56/8=7', '55-7=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 19, 49, 65, 79 ]
67
[ "19+79=98", "98/49=2", "65+2=67" ]
Current State: 67:[19, 49, 65, 79], Operations: [] Exploring Operation: 19+79=98, Resulting Numbers: [49, 65, 98] Generated Node #2: [49, 65, 98] from Operation: 19+79=98 Current State: 67:[49, 65, 98], Operations: ['19+79=98'] Exploring Operation: 98/49=2, Resulting Numbers: [65, 2] Generated Node #3: [65, 2] from Operation: 98/49=2 Current State: 67:[65, 2], Operations: ['19+79=98', '98/49=2'] Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[19, 49, 65, 79], Operations: [] Exploring Operation: 79-19=60, Resulting Numbers: [49, 65, 60] Generated Node #0,0: 67:[49, 65, 60] Operation: 79-19=60 Exploring Operation: 19+49=68, Resulting Numbers: [65, 79, 68] Generated Node #0,1: 67:[65, 79, 68] Operation: 19+49=68 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[65, 79, 68], Operations: ['19+49=68'] Exploring Operation: 79-68=11, Resulting Numbers: [65, 11] Generated Node #0,1,0: 67:[65, 11] Operation: 79-68=11 Exploring Operation: 79-65=14, Resulting Numbers: [68, 14] Generated Node #0,1,1: 67:[68, 14] Operation: 79-65=14 Moving to Node #0,1,1 Current State: 67:[68, 14], Operations: ['19+49=68', '79-65=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[65, 11], Operations: ['19+49=68', '79-68=11'] Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 65+11=76, Resulting Numbers: [76] 76,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[49, 65, 60], Operations: ['79-19=60'] Exploring Operation: 49+65=114, Resulting Numbers: [60, 114] Generated Node #0,0,0: 67:[60, 114] Operation: 49+65=114 Exploring Operation: 49+60=109, Resulting Numbers: [65, 109] Generated Node #0,0,1: 67:[65, 109] Operation: 49+60=109 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 67:[65, 109], Operations: ['79-19=60', '49+60=109'] Exploring Operation: 65+109=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 109-65=44, Resulting Numbers: [44] 44,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[60, 114], Operations: ['79-19=60', '49+65=114'] Exploring Operation: 114-60=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 60+114=174, Resulting Numbers: [174] 174,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 54, 11, 85, 74 ]
53
[ "85-11=74", "74/74=1", "54-1=53" ]
Current State: 53:[54, 11, 85, 74], Operations: [] Exploring Operation: 85-11=74, Resulting Numbers: [54, 74, 74] Generated Node #2: [54, 74, 74] from Operation: 85-11=74 Current State: 53:[54, 74, 74], Operations: ['85-11=74'] Exploring Operation: 74/74=1, Resulting Numbers: [54, 1] Generated Node #3: [54, 1] from Operation: 74/74=1 Current State: 53:[54, 1], Operations: ['85-11=74', '74/74=1'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[54, 11, 85, 74], Operations: [] Exploring Operation: 54-11=43, Resulting Numbers: [85, 74, 43] Generated Node #0,0: 53:[85, 74, 43] Operation: 54-11=43 Exploring Operation: 54+11=65, Resulting Numbers: [85, 74, 65] Generated Node #0,1: 53:[85, 74, 65] Operation: 54+11=65 Exploring Operation: 85-11=74, Resulting Numbers: [54, 74, 74] Generated Node #0,2: 53:[54, 74, 74] Operation: 85-11=74 Exploring Operation: 74-11=63, Resulting Numbers: [54, 85, 63] Generated Node #0,3: 53:[54, 85, 63] Operation: 74-11=63 Moving to Node #0,2 Current State: 53:[54, 74, 74], Operations: ['85-11=74'] Exploring Operation: 74-54=20, Resulting Numbers: [74, 20] Generated Node #0,2,0: 53:[74, 20] Operation: 74-54=20 Exploring Operation: 74-54=20, Resulting Numbers: [74, 20] Generated Node #0,2,1: 53:[74, 20] Operation: 74-54=20 Exploring Operation: 74/74=1, Resulting Numbers: [54, 1] Generated Node #0,2,2: 53:[54, 1] Operation: 74/74=1 Exploring Operation: 74-74=0, Resulting Numbers: [54, 0] Generated Node #0,2,3: 53:[54, 0] Operation: 74-74=0 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 53:[54, 1], Operations: ['85-11=74', '74/74=1'] Exploring Operation: 54+1=55, Resulting Numbers: [55] 55,53 unequal: No Solution Exploring Operation: 54*1=54, Resulting Numbers: [54] 54,53 unequal: No Solution Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,53 unequal: No Solution Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[54, 11, 85, 74], Operations: [] Exploring Operation: 85-11=74, Resulting Numbers: [54, 74, 74] Generated Node #0,2: 53:[54, 74, 74] Operation: 85-11=74 Moving to Node #0,2 Current State: 53:[54, 74, 74], Operations: ['85-11=74'] Exploring Operation: 74/74=1, Resulting Numbers: [54, 1] Generated Node #0,2,2: 53:[54, 1] Operation: 74/74=1 Moving to Node #0,2,2 Current State: 53:[54, 1], Operations: ['85-11=74', '74/74=1'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 87, 64, 12, 64 ]
53
[ "87-64=23", "12+64=76", "76-23=53" ]
Current State: 53:[87, 64, 12, 64], Operations: [] Exploring Operation: 87-64=23, Resulting Numbers: [12, 23] Generated Node #2: [12, 23] from Operation: 87-64=23 Current State: 53:[12, 23], Operations: ['87-64=23'] Exploring Operation: 12+64=76, Resulting Numbers: [23, 76] Generated Node #3: [23, 76] from Operation: 12+64=76 Current State: 53:[23, 76], Operations: ['87-64=23', '12+64=76'] Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[87, 64, 12, 64], Operations: [] Exploring Operation: 64-12=52, Resulting Numbers: [87, 64, 52] Generated Node #0,0: 53:[87, 64, 52] Operation: 64-12=52 Exploring Operation: 87-12=75, Resulting Numbers: [64, 64, 75] Generated Node #0,1: 53:[64, 64, 75] Operation: 87-12=75 Exploring Operation: 64-12=52, Resulting Numbers: [87, 64, 52] Generated Node #0,2: 53:[87, 64, 52] Operation: 64-12=52 Moving to Node #0,1 Current State: 53:[64, 64, 75], Operations: ['87-12=75'] Exploring Operation: 75-64=11, Resulting Numbers: [64, 11] Generated Node #0,1,0: 53:[64, 11] Operation: 75-64=11 Exploring Operation: 75-64=11, Resulting Numbers: [64, 11] Generated Node #0,1,1: 53:[64, 11] Operation: 75-64=11 Exploring Operation: 64/64=1, Resulting Numbers: [75, 1] Generated Node #0,1,2: 53:[75, 1] Operation: 64/64=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[64, 11], Operations: ['87-12=75', '75-64=11'] Exploring Operation: 64*11=704, Resulting Numbers: [704] 704,53 unequal: No Solution Exploring Operation: 64+11=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 64-11=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[87, 64, 12, 64], Operations: [] Exploring Operation: 87-12=75, Resulting Numbers: [64, 64, 75] Generated Node #0,1: 53:[64, 64, 75] Operation: 87-12=75 Moving to Node #0,1 Current State: 53:[64, 64, 75], Operations: ['87-12=75'] Exploring Operation: 75-64=11, Resulting Numbers: [64, 11] Generated Node #0,1,0: 53:[64, 11] Operation: 75-64=11 Moving to Node #0,1,0 Current State: 53:[64, 11], Operations: ['87-12=75', '75-64=11'] Exploring Operation: 64-11=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 36, 56, 69, 69 ]
91
[ "36+56=92", "69/69=1", "92-1=91" ]
Current State: 91:[36, 56, 69, 69], Operations: [] Exploring Operation: 36+56=92, Resulting Numbers: [69, 69, 92] Generated Node #2: [69, 69, 92] from Operation: 36+56=92 Current State: 91:[69, 69, 92], Operations: ['36+56=92'] Exploring Operation: 69/69=1, Resulting Numbers: [92, 1] Generated Node #3: [92, 1] from Operation: 69/69=1 Current State: 91:[92, 1], Operations: ['36+56=92', '69/69=1'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[36, 56, 69, 69], Operations: [] Exploring Operation: 69-56=13, Resulting Numbers: [36, 69, 13] Generated Node #0,0: 91:[36, 69, 13] Operation: 69-56=13 Exploring Operation: 36+56=92, Resulting Numbers: [69, 69, 92] Generated Node #0,1: 91:[69, 69, 92] Operation: 36+56=92 Exploring Operation: 69-56=13, Resulting Numbers: [36, 69, 13] Generated Node #0,2: 91:[36, 69, 13] Operation: 69-56=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[36, 69, 13], Operations: ['69-56=13'] Exploring Operation: 36-13=23, Resulting Numbers: [69, 23] Generated Node #0,0,0: 91:[69, 23] Operation: 36-13=23 Exploring Operation: 36+69=105, Resulting Numbers: [13, 105] Generated Node #0,0,1: 91:[13, 105] Operation: 36+69=105 Exploring Operation: 69-36=33, Resulting Numbers: [13, 33] Generated Node #0,0,2: 91:[13, 33] Operation: 69-36=33 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[13, 105], Operations: ['69-56=13', '36+69=105'] Exploring Operation: 13+105=118, Resulting Numbers: [118] 118,91 unequal: No Solution Exploring Operation: 13*105=1365, Resulting Numbers: [1365] 1365,91 unequal: No Solution Exploring Operation: 105-13=92, Resulting Numbers: [92] 92,91 unequal: No Solution No 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: 91:[13, 33], Operations: ['69-56=13', '69-36=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,91 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,91 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,91 unequal: No Solution No 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: 91:[69, 23], Operations: ['69-56=13', '36-13=23'] Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,91 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 69+23=92, Resulting Numbers: [92] 92,91 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: 91:[69, 69, 92], Operations: ['36+56=92'] Exploring Operation: 69-69=0, Resulting Numbers: [92, 0] Generated Node #0,1,0: 91:[92, 0] Operation: 69-69=0 Exploring Operation: 69/69=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 91:[92, 1] Operation: 69/69=1 Exploring Operation: 92-69=23, Resulting Numbers: [69, 23] Generated Node #0,1,2: 91:[69, 23] Operation: 92-69=23 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[92, 1], Operations: ['36+56=92', '69/69=1'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[36, 56, 69, 69], Operations: [] Exploring Operation: 36+56=92, Resulting Numbers: [69, 69, 92] Generated Node #0,1: 91:[69, 69, 92] Operation: 36+56=92 Moving to Node #0,1 Current State: 91:[69, 69, 92], Operations: ['36+56=92'] Exploring Operation: 69/69=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 91:[92, 1] Operation: 69/69=1 Moving to Node #0,1,1 Current State: 91:[92, 1], Operations: ['36+56=92', '69/69=1'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 25, 44, 44, 74 ]
39
[ "25+44=69", "74-44=30", "69-30=39" ]
Current State: 39:[25, 44, 44, 74], Operations: [] Exploring Operation: 25+44=69, Resulting Numbers: [74, 69] Generated Node #2: [74, 69] from Operation: 25+44=69 Current State: 39:[74, 69], Operations: ['25+44=69'] Exploring Operation: 74-44=30, Resulting Numbers: [69, 30] Generated Node #3: [69, 30] from Operation: 74-44=30 Current State: 39:[69, 30], Operations: ['25+44=69', '74-44=30'] Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[25, 44, 44, 74], Operations: [] Exploring Operation: 74-25=49, Resulting Numbers: [44, 44, 49] Generated Node #0,0: 39:[44, 44, 49] Operation: 74-25=49 Exploring Operation: 74-44=30, Resulting Numbers: [25, 44, 30] Generated Node #0,1: 39:[25, 44, 30] Operation: 74-44=30 Moving to Node #0,0 Current State: 39:[44, 44, 49], Operations: ['74-25=49'] Exploring Operation: 49-44=5, Resulting Numbers: [44, 5] Generated Node #0,0,0: 39:[44, 5] Operation: 49-44=5 Exploring Operation: 49-44=5, Resulting Numbers: [44, 5] Generated Node #0,0,1: 39:[44, 5] Operation: 49-44=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[44, 5], Operations: ['74-25=49', '49-44=5'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[25, 44, 44, 74], Operations: [] Exploring Operation: 74-25=49, Resulting Numbers: [44, 44, 49] Generated Node #0,0: 39:[44, 44, 49] Operation: 74-25=49 Moving to Node #0,0 Current State: 39:[44, 44, 49], Operations: ['74-25=49'] Exploring Operation: 49-44=5, Resulting Numbers: [44, 5] Generated Node #0,0,0: 39:[44, 5] Operation: 49-44=5 Moving to Node #0,0,0 Current State: 39:[44, 5], Operations: ['74-25=49', '49-44=5'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 58, 31, 65, 13 ]
32
[ "58-31=27", "65/13=5", "27+5=32" ]
Current State: 32:[58, 31, 65, 13], Operations: [] Exploring Operation: 58-31=27, Resulting Numbers: [65, 13, 27] Generated Node #2: [65, 13, 27] from Operation: 58-31=27 Current State: 32:[65, 13, 27], Operations: ['58-31=27'] Exploring Operation: 65/13=5, Resulting Numbers: [27, 5] Generated Node #3: [27, 5] from Operation: 65/13=5 Current State: 32:[27, 5], Operations: ['58-31=27', '65/13=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[58, 31, 65, 13], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [58, 13, 34] Generated Node #0,0: 32:[58, 13, 34] Operation: 65-31=34 Exploring Operation: 65-58=7, Resulting Numbers: [31, 13, 7] Generated Node #0,1: 32:[31, 13, 7] Operation: 65-58=7 Exploring Operation: 65/13=5, Resulting Numbers: [58, 31, 5] Generated Node #0,2: 32:[58, 31, 5] Operation: 65/13=5 Exploring Operation: 58-13=45, Resulting Numbers: [31, 65, 45] Generated Node #0,3: 32:[31, 65, 45] Operation: 58-13=45 Exploring Operation: 58-31=27, Resulting Numbers: [65, 13, 27] Generated Node #0,4: 32:[65, 13, 27] Operation: 58-31=27 Moving to Node #0,1 Current State: 32:[31, 13, 7], Operations: ['65-58=7'] Exploring Operation: 31+7=38, Resulting Numbers: [13, 38] Generated Node #0,1,0: 32:[13, 38] Operation: 31+7=38 Exploring Operation: 13+7=20, Resulting Numbers: [31, 20] Generated Node #0,1,1: 32:[31, 20] Operation: 13+7=20 Exploring Operation: 13-7=6, Resulting Numbers: [31, 6] Generated Node #0,1,2: 32:[31, 6] Operation: 13-7=6 Exploring Operation: 31-7=24, Resulting Numbers: [13, 24] Generated Node #0,1,3: 32:[13, 24] Operation: 31-7=24 Exploring Operation: 31-13=18, Resulting Numbers: [7, 18] Generated Node #0,1,4: 32:[7, 18] Operation: 31-13=18 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[31, 6], Operations: ['65-58=7', '13-7=6'] Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 31*6=186, Resulting Numbers: [186] 186,32 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 32:[7, 18], Operations: ['65-58=7', '31-13=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[31, 20], Operations: ['65-58=7', '13+7=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[13, 38], Operations: ['65-58=7', '31+7=38'] Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 13*38=494, Resulting Numbers: [494] 494,32 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[13, 24], Operations: ['65-58=7', '31-7=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 32:[58, 31, 5], Operations: ['65/13=5'] Exploring Operation: 58+5=63, Resulting Numbers: [31, 63] Generated Node #0,2,0: 32:[31, 63] Operation: 58+5=63 Exploring Operation: 31+5=36, Resulting Numbers: [58, 36] Generated Node #0,2,1: 32:[58, 36] Operation: 31+5=36 Exploring Operation: 58-31=27, Resulting Numbers: [5, 27] Generated Node #0,2,2: 32:[5, 27] Operation: 58-31=27 Exploring Operation: 58-5=53, Resulting Numbers: [31, 53] Generated Node #0,2,3: 32:[31, 53] Operation: 58-5=53 Exploring Operation: 31-5=26, Resulting Numbers: [58, 26] Generated Node #0,2,4: 32:[58, 26] Operation: 31-5=26 Moving to Node #0,0 Current State: 32:[58, 13, 34], Operations: ['65-31=34'] Exploring Operation: 13+34=47, Resulting Numbers: [58, 47] Generated Node #0,0,0: 32:[58, 47] Operation: 13+34=47 Exploring Operation: 58-13=45, Resulting Numbers: [34, 45] Generated Node #0,0,1: 32:[34, 45] Operation: 58-13=45 Exploring Operation: 34-13=21, Resulting Numbers: [58, 21] Generated Node #0,0,2: 32:[58, 21] Operation: 34-13=21 Exploring Operation: 58-34=24, Resulting Numbers: [13, 24] Generated Node #0,0,3: 32:[13, 24] Operation: 58-34=24 Exploring Operation: 58+13=71, Resulting Numbers: [34, 71] Generated Node #0,0,4: 32:[34, 71] Operation: 58+13=71 Moving to Node #0,4 Current State: 32:[65, 13, 27], Operations: ['58-31=27'] Exploring Operation: 65-13=52, Resulting Numbers: [27, 52] Generated Node #0,4,0: 32:[27, 52] Operation: 65-13=52 Exploring Operation: 27-13=14, Resulting Numbers: [65, 14] Generated Node #0,4,1: 32:[65, 14] Operation: 27-13=14 Exploring Operation: 65/13=5, Resulting Numbers: [27, 5] Generated Node #0,4,2: 32:[27, 5] Operation: 65/13=5 Exploring Operation: 65-27=38, Resulting Numbers: [13, 38] Generated Node #0,4,3: 32:[13, 38] Operation: 65-27=38 Exploring Operation: 13+27=40, Resulting Numbers: [65, 40] Generated Node #0,4,4: 32:[65, 40] Operation: 13+27=40 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 32:[27, 5], Operations: ['58-31=27', '65/13=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[58, 31, 65, 13], Operations: [] Exploring Operation: 58-31=27, Resulting Numbers: [65, 13, 27] Generated Node #0,4: 32:[65, 13, 27] Operation: 58-31=27 Moving to Node #0,4 Current State: 32:[65, 13, 27], Operations: ['58-31=27'] Exploring Operation: 65/13=5, Resulting Numbers: [27, 5] Generated Node #0,4,2: 32:[27, 5] Operation: 65/13=5 Moving to Node #0,4,2 Current State: 32:[27, 5], Operations: ['58-31=27', '65/13=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_5
mult_heuristic
[ 44, 72, 84, 4 ]
92
[ "84-72=12", "4*12=48", "44+48=92" ]
Current State: 92:[44, 72, 84, 4], Operations: [] Exploring Operation: 84-72=12, Resulting Numbers: [44, 4, 12] Generated Node #2: [44, 4, 12] from Operation: 84-72=12 Current State: 92:[44, 4, 12], Operations: ['84-72=12'] Exploring Operation: 4*12=48, Resulting Numbers: [44, 48] Generated Node #3: [44, 48] from Operation: 4*12=48 Current State: 92:[44, 48], Operations: ['84-72=12', '4*12=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[44, 72, 84, 4], Operations: [] Exploring Operation: 72-44=28, Resulting Numbers: [84, 4, 28] Generated Node #0,0: 92:[84, 4, 28] Operation: 72-44=28 Exploring Operation: 84-72=12, Resulting Numbers: [44, 4, 12] Generated Node #0,1: 92:[44, 4, 12] Operation: 84-72=12 Moving to Node #0,1 Current State: 92:[44, 4, 12], Operations: ['84-72=12'] Exploring Operation: 12/4=3, Resulting Numbers: [44, 3] Generated Node #0,1,0: 92:[44, 3] Operation: 12/4=3 Exploring Operation: 4*12=48, Resulting Numbers: [44, 48] Generated Node #0,1,1: 92:[44, 48] Operation: 4*12=48 Moving to Node #0,0 Current State: 92:[84, 4, 28], Operations: ['72-44=28'] Exploring Operation: 84/28=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 92:[4, 3] Operation: 84/28=3 Exploring Operation: 84/4=21, Resulting Numbers: [28, 21] Generated Node #0,0,1: 92:[28, 21] Operation: 84/4=21 Moving to Node #0,0,0 Current State: 92:[4, 3], Operations: ['72-44=28', '84/28=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[44, 3], Operations: ['84-72=12', '12/4=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,92 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[44, 48], Operations: ['84-72=12', '4*12=48'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[44, 72, 84, 4], Operations: [] Exploring Operation: 84-72=12, Resulting Numbers: [44, 4, 12] Generated Node #0,1: 92:[44, 4, 12] Operation: 84-72=12 Moving to Node #0,1 Current State: 92:[44, 4, 12], Operations: ['84-72=12'] Exploring Operation: 4*12=48, Resulting Numbers: [44, 48] Generated Node #0,1,1: 92:[44, 48] Operation: 4*12=48 Moving to Node #0,1,1 Current State: 92:[44, 48], Operations: ['84-72=12', '4*12=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 56, 51, 40, 7 ]
38
[ "56-51=5", "40-7=33", "5+33=38" ]
Current State: 38:[56, 51, 40, 7], Operations: [] Exploring Operation: 56-51=5, Resulting Numbers: [40, 7, 5] Generated Node #2: [40, 7, 5] from Operation: 56-51=5 Current State: 38:[40, 7, 5], Operations: ['56-51=5'] Exploring Operation: 40-7=33, Resulting Numbers: [5, 33] Generated Node #3: [5, 33] from Operation: 40-7=33 Current State: 38:[5, 33], Operations: ['56-51=5', '40-7=33'] Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[56, 51, 40, 7], Operations: [] Exploring Operation: 56-51=5, Resulting Numbers: [40, 7, 5] Generated Node #0,0: 38:[40, 7, 5] Operation: 56-51=5 Exploring Operation: 56-40=16, Resulting Numbers: [51, 7, 16] Generated Node #0,1: 38:[51, 7, 16] Operation: 56-40=16 Exploring Operation: 56/7=8, Resulting Numbers: [51, 40, 8] Generated Node #0,2: 38:[51, 40, 8] Operation: 56/7=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[40, 7, 5], Operations: ['56-51=5'] Exploring Operation: 40-7=33, Resulting Numbers: [5, 33] Generated Node #0,0,0: 38:[5, 33] Operation: 40-7=33 Exploring Operation: 7*5=35, Resulting Numbers: [40, 35] Generated Node #0,0,1: 38:[40, 35] Operation: 7*5=35 Exploring Operation: 7-5=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 38:[40, 2] Operation: 7-5=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 38:[40, 2], Operations: ['56-51=5', '7-5=2'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,38 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[56, 51, 40, 7], Operations: [] Exploring Operation: 56-51=5, Resulting Numbers: [40, 7, 5] Generated Node #0,0: 38:[40, 7, 5] Operation: 56-51=5 Moving to Node #0,0 Current State: 38:[40, 7, 5], Operations: ['56-51=5'] Exploring Operation: 7-5=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 38:[40, 2] Operation: 7-5=2 Moving to Node #0,0,2 Current State: 38:[40, 2], Operations: ['56-51=5', '7-5=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 29, 45, 57, 22 ]
51
[ "29*45=1305", "57*22=1254", "1305-1254=51" ]
Current State: 51:[29, 45, 57, 22], Operations: [] Exploring Operation: 29*45=1305, Resulting Numbers: [57, 22, 1305] Generated Node #2: [57, 22, 1305] from Operation: 29*45=1305 Current State: 51:[57, 22, 1305], Operations: ['29*45=1305'] Exploring Operation: 57*22=1254, Resulting Numbers: [1305, 1254] Generated Node #3: [1305, 1254] from Operation: 57*22=1254 Current State: 51:[1305, 1254], Operations: ['29*45=1305', '57*22=1254'] Exploring Operation: 1305-1254=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[29, 45, 57, 22], Operations: [] Exploring Operation: 29-22=7, Resulting Numbers: [45, 57, 7] Generated Node #0,0: 51:[45, 57, 7] Operation: 29-22=7 Exploring Operation: 29+22=51, Resulting Numbers: [45, 57, 51] Generated Node #0,1: 51:[45, 57, 51] Operation: 29+22=51 Exploring Operation: 57-29=28, Resulting Numbers: [45, 22, 28] Generated Node #0,2: 51:[45, 22, 28] Operation: 57-29=28 Exploring Operation: 45-29=16, Resulting Numbers: [57, 22, 16] Generated Node #0,3: 51:[57, 22, 16] Operation: 45-29=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[45, 57, 51], Operations: ['29+22=51'] Exploring Operation: 57-51=6, Resulting Numbers: [45, 6] Generated Node #0,1,0: 51:[45, 6] Operation: 57-51=6 Exploring Operation: 57-45=12, Resulting Numbers: [51, 12] Generated Node #0,1,1: 51:[51, 12] Operation: 57-45=12 Exploring Operation: 45+57=102, Resulting Numbers: [51, 102] Generated Node #0,1,2: 51:[51, 102] Operation: 45+57=102 Exploring Operation: 51-45=6, Resulting Numbers: [57, 6] Generated Node #0,1,3: 51:[57, 6] Operation: 51-45=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[51, 12], Operations: ['29+22=51', '57-45=12'] Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,51 unequal: No Solution Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,51 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[45, 6], Operations: ['29+22=51', '57-51=6'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,51 unequal: No Solution Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,51 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[29, 45, 57, 22], Operations: [] Exploring Operation: 29+22=51, Resulting Numbers: [45, 57, 51] Generated Node #0,1: 51:[45, 57, 51] Operation: 29+22=51 Moving to Node #0,1 Current State: 51:[45, 57, 51], Operations: ['29+22=51'] Exploring Operation: 57-51=6, Resulting Numbers: [45, 6] Generated Node #0,1,0: 51:[45, 6] Operation: 57-51=6 Moving to Node #0,1,0 Current State: 51:[45, 6], Operations: ['29+22=51', '57-51=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 73, 4, 11, 28 ]
86
[ "73-4=69", "28-11=17", "69+17=86" ]
Current State: 86:[73, 4, 11, 28], Operations: [] Exploring Operation: 73-4=69, Resulting Numbers: [11, 28, 69] Generated Node #2: [11, 28, 69] from Operation: 73-4=69 Current State: 86:[11, 28, 69], Operations: ['73-4=69'] Exploring Operation: 28-11=17, Resulting Numbers: [69, 17] Generated Node #3: [69, 17] from Operation: 28-11=17 Current State: 86:[69, 17], Operations: ['73-4=69', '28-11=17'] Exploring Operation: 69+17=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[73, 4, 11, 28], Operations: [] Exploring Operation: 28/4=7, Resulting Numbers: [73, 11, 7] Generated Node #0,0: 86:[73, 11, 7] Operation: 28/4=7 Exploring Operation: 73+28=101, Resulting Numbers: [4, 11, 101] Generated Node #0,1: 86:[4, 11, 101] Operation: 73+28=101 Exploring Operation: 73+11=84, Resulting Numbers: [4, 28, 84] Generated Node #0,2: 86:[4, 28, 84] Operation: 73+11=84 Exploring Operation: 73-28=45, Resulting Numbers: [4, 11, 45] Generated Node #0,3: 86:[4, 11, 45] Operation: 73-28=45 Exploring Operation: 11+28=39, Resulting Numbers: [73, 4, 39] Generated Node #0,4: 86:[73, 4, 39] Operation: 11+28=39 Moving to Node #0,3 Current State: 86:[4, 11, 45], Operations: ['73-28=45'] Exploring Operation: 45-4=41, Resulting Numbers: [11, 41] Generated Node #0,3,0: 86:[11, 41] Operation: 45-4=41 Exploring Operation: 45-11=34, Resulting Numbers: [4, 34] Generated Node #0,3,1: 86:[4, 34] Operation: 45-11=34 Exploring Operation: 4*11=44, Resulting Numbers: [45, 44] Generated Node #0,3,2: 86:[45, 44] Operation: 4*11=44 Exploring Operation: 11-4=7, Resulting Numbers: [45, 7] Generated Node #0,3,3: 86:[45, 7] Operation: 11-4=7 Exploring Operation: 4+11=15, Resulting Numbers: [45, 15] Generated Node #0,3,4: 86:[45, 15] Operation: 4+11=15 Moving to Node #0,4 Current State: 86:[73, 4, 39], Operations: ['11+28=39'] Exploring Operation: 73+4=77, Resulting Numbers: [39, 77] Generated Node #0,4,0: 86:[39, 77] Operation: 73+4=77 Exploring Operation: 4+39=43, Resulting Numbers: [73, 43] Generated Node #0,4,1: 86:[73, 43] Operation: 4+39=43 Exploring Operation: 73-39=34, Resulting Numbers: [4, 34] Generated Node #0,4,2: 86:[4, 34] Operation: 73-39=34 Exploring Operation: 39-4=35, Resulting Numbers: [73, 35] Generated Node #0,4,3: 86:[73, 35] Operation: 39-4=35 Exploring Operation: 73-4=69, Resulting Numbers: [39, 69] Generated Node #0,4,4: 86:[39, 69] Operation: 73-4=69 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 86:[4, 34], Operations: ['11+28=39', '73-39=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,86 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 #0,4,0 Current State: 86:[39, 77], Operations: ['11+28=39', '73+4=77'] Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 39+77=116, Resulting Numbers: [116] 116,86 unequal: No Solution Exploring Operation: 39*77=3003, Resulting Numbers: [3003] 3003,86 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 #0,4,1 Current State: 86:[73, 43], Operations: ['11+28=39', '4+39=43'] Exploring Operation: 73+43=116, Resulting Numbers: [116] 116,86 unequal: No Solution Exploring Operation: 73-43=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 73*43=3139, Resulting Numbers: [3139] 3139,86 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 #0,4,3 Current State: 86:[73, 35], Operations: ['11+28=39', '39-4=35'] Exploring Operation: 73+35=108, Resulting Numbers: [108] 108,86 unequal: No Solution Exploring Operation: 73*35=2555, Resulting Numbers: [2555] 2555,86 unequal: No Solution Exploring Operation: 73-35=38, Resulting Numbers: [38] 38,86 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 #0,4,4 Current State: 86:[39, 69], Operations: ['11+28=39', '73-4=69'] Exploring Operation: 39*69=2691, Resulting Numbers: [2691] 2691,86 unequal: No Solution Exploring Operation: 39+69=108, Resulting Numbers: [108] 108,86 unequal: No Solution Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,86 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: 86:[4, 28, 84], Operations: ['73+11=84'] Exploring Operation: 4+28=32, Resulting Numbers: [84, 32] Generated Node #0,2,0: 86:[84, 32] Operation: 4+28=32 Exploring Operation: 4+84=88, Resulting Numbers: [28, 88] Generated Node #0,2,1: 86:[28, 88] Operation: 4+84=88 Exploring Operation: 28/4=7, Resulting Numbers: [84, 7] Generated Node #0,2,2: 86:[84, 7] Operation: 28/4=7 Exploring Operation: 84/28=3, Resulting Numbers: [4, 3] Generated Node #0,2,3: 86:[4, 3] Operation: 84/28=3 Exploring Operation: 84-28=56, Resulting Numbers: [4, 56] Generated Node #0,2,4: 86:[4, 56] Operation: 84-28=56 Moving to Node #0,1 Current State: 86:[4, 11, 101], Operations: ['73+28=101'] Exploring Operation: 101-11=90, Resulting Numbers: [4, 90] Generated Node #0,1,0: 86:[4, 90] Operation: 101-11=90 Exploring Operation: 101-4=97, Resulting Numbers: [11, 97] Generated Node #0,1,1: 86:[11, 97] Operation: 101-4=97 Exploring Operation: 4*11=44, Resulting Numbers: [101, 44] Generated Node #0,1,2: 86:[101, 44] Operation: 4*11=44 Exploring Operation: 11-4=7, Resulting Numbers: [101, 7] Generated Node #0,1,3: 86:[101, 7] Operation: 11-4=7 Exploring Operation: 4+11=15, Resulting Numbers: [101, 15] Generated Node #0,1,4: 86:[101, 15] Operation: 4+11=15 Moving to Node #0,0 Current State: 86:[73, 11, 7], Operations: ['28/4=7'] Exploring Operation: 11*7=77, Resulting Numbers: [73, 77] Generated Node #0,0,0: 86:[73, 77] Operation: 11*7=77 Exploring Operation: 73-11=62, Resulting Numbers: [7, 62] Generated Node #0,0,1: 86:[7, 62] Operation: 73-11=62 Exploring Operation: 73+7=80, Resulting Numbers: [11, 80] Generated Node #0,0,2: 86:[11, 80] Operation: 73+7=80 Exploring Operation: 73+11=84, Resulting Numbers: [7, 84] Generated Node #0,0,3: 86:[7, 84] Operation: 73+11=84 Exploring Operation: 11-7=4, Resulting Numbers: [73, 4] Generated Node #0,0,4: 86:[73, 4] Operation: 11-7=4 Moving to Node #0,3,2 Current State: 86:[45, 44], Operations: ['73-28=45', '4*11=44'] Exploring Operation: 45*44=1980, Resulting Numbers: [1980] 1980,86 unequal: No Solution Exploring Operation: 45+44=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,2,3 Current State: 86:[4, 3], Operations: ['73+11=84', '84/28=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[4, 90], Operations: ['73+28=101', '101-11=90'] Exploring Operation: 4+90=94, Resulting Numbers: [94] 94,86 unequal: No Solution Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[73, 4, 11, 28], Operations: [] Exploring Operation: 73+28=101, Resulting Numbers: [4, 11, 101] Generated Node #0,1: 86:[4, 11, 101] Operation: 73+28=101 Moving to Node #0,1 Current State: 86:[4, 11, 101], Operations: ['73+28=101'] Exploring Operation: 101-11=90, Resulting Numbers: [4, 90] Generated Node #0,1,0: 86:[4, 90] Operation: 101-11=90 Moving to Node #0,1,0 Current State: 86:[4, 90], Operations: ['73+28=101', '101-11=90'] Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.950521
hs_5
sum_heuristic
[ 96, 8, 17, 10 ]
77
[ "96+8=104", "17+10=27", "104-27=77" ]
Current State: 77:[96, 8, 17, 10], Operations: [] Exploring Operation: 96+8=104, Resulting Numbers: [17, 10, 104] Generated Node #2: [17, 10, 104] from Operation: 96+8=104 Current State: 77:[17, 10, 104], Operations: ['96+8=104'] Exploring Operation: 17+10=27, Resulting Numbers: [104, 27] Generated Node #3: [104, 27] from Operation: 17+10=27 Current State: 77:[104, 27], Operations: ['96+8=104', '17+10=27'] Exploring Operation: 104-27=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[96, 8, 17, 10], Operations: [] Exploring Operation: 96/8=12, Resulting Numbers: [17, 10, 12] Generated Node #0,0: 77:[17, 10, 12] Operation: 96/8=12 Exploring Operation: 96-17=79, Resulting Numbers: [8, 10, 79] Generated Node #0,1: 77:[8, 10, 79] Operation: 96-17=79 Exploring Operation: 96-8=88, Resulting Numbers: [17, 10, 88] Generated Node #0,2: 77:[17, 10, 88] Operation: 96-8=88 Exploring Operation: 96-10=86, Resulting Numbers: [8, 17, 86] Generated Node #0,3: 77:[8, 17, 86] Operation: 96-10=86 Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[8, 10, 79], Operations: ['96-17=79'] Exploring Operation: 79-8=71, Resulting Numbers: [10, 71] Generated Node #0,1,0: 77:[10, 71] Operation: 79-8=71 Exploring Operation: 8+10=18, Resulting Numbers: [79, 18] Generated Node #0,1,1: 77:[79, 18] Operation: 8+10=18 Exploring Operation: 10-8=2, Resulting Numbers: [79, 2] Generated Node #0,1,2: 77:[79, 2] Operation: 10-8=2 Exploring Operation: 8*10=80, Resulting Numbers: [79, 80] Generated Node #0,1,3: 77:[79, 80] Operation: 8*10=80 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 77:[79, 80], Operations: ['96-17=79', '8*10=80'] Exploring Operation: 80-79=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 79+80=159, Resulting Numbers: [159] 159,77 unequal: No Solution Exploring Operation: 79*80=6320, Resulting Numbers: [6320] 6320,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[10, 71], Operations: ['96-17=79', '79-8=71'] Exploring Operation: 10+71=81, Resulting Numbers: [81] 81,77 unequal: No Solution Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,77 unequal: No Solution Exploring Operation: 10*71=710, Resulting Numbers: [710] 710,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 77:[79, 2], Operations: ['96-17=79', '10-8=2'] Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,77 unequal: No Solution Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,77 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[96, 8, 17, 10], Operations: [] Exploring Operation: 96-17=79, Resulting Numbers: [8, 10, 79] Generated Node #0,1: 77:[8, 10, 79] Operation: 96-17=79 Moving to Node #0,1 Current State: 77:[8, 10, 79], Operations: ['96-17=79'] Exploring Operation: 10-8=2, Resulting Numbers: [79, 2] Generated Node #0,1,2: 77:[79, 2] Operation: 10-8=2 Moving to Node #0,1,2 Current State: 77:[79, 2], Operations: ['96-17=79', '10-8=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 62, 33, 91, 63 ]
93
[ "91*63=5733", "33+5733=5766", "5766/62=93" ]
Current State: 93:[62, 33, 91, 63], Operations: [] Exploring Operation: 91*63=5733, Resulting Numbers: [62, 33, 5733] Generated Node #2: [62, 33, 5733] from Operation: 91*63=5733 Current State: 93:[62, 33, 5733], Operations: ['91*63=5733'] Exploring Operation: 33+5733=5766, Resulting Numbers: [62, 5766] Generated Node #3: [62, 5766] from Operation: 33+5733=5766 Current State: 93:[62, 5766], Operations: ['91*63=5733', '33+5733=5766'] Exploring Operation: 5766/62=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[62, 33, 91, 63], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [91, 63, 29] Generated Node #0,0: 93:[91, 63, 29] Operation: 62-33=29 Exploring Operation: 62+33=95, Resulting Numbers: [91, 63, 95] Generated Node #0,1: 93:[91, 63, 95] Operation: 62+33=95 Exploring Operation: 63-62=1, Resulting Numbers: [33, 91, 1] Generated Node #0,2: 93:[33, 91, 1] Operation: 63-62=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[33, 91, 1], Operations: ['63-62=1'] Exploring Operation: 33-1=32, Resulting Numbers: [91, 32] Generated Node #0,2,0: 93:[91, 32] Operation: 33-1=32 Exploring Operation: 33*1=33, Resulting Numbers: [91, 33] Generated Node #0,2,1: 93:[91, 33] Operation: 33*1=33 Exploring Operation: 91+1=92, Resulting Numbers: [33, 92] Generated Node #0,2,2: 93:[33, 92] Operation: 91+1=92 Moving to Node #0,2,0 Current State: 93:[91, 32], Operations: ['63-62=1', '33-1=32'] Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,93 unequal: No Solution Exploring Operation: 91*32=2912, Resulting Numbers: [2912] 2912,93 unequal: No Solution Exploring Operation: 91+32=123, Resulting Numbers: [123] 123,93 unequal: No Solution Moving to Node #0,2,2 Current State: 93:[33, 92], Operations: ['63-62=1', '91+1=92'] Exploring Operation: 33*92=3036, Resulting Numbers: [3036] 3036,93 unequal: No Solution Exploring Operation: 92-33=59, Resulting Numbers: [59] 59,93 unequal: No Solution Exploring Operation: 33+92=125, Resulting Numbers: [125] 125,93 unequal: No Solution Moving to Node #0,2,1 Current State: 93:[91, 33], Operations: ['63-62=1', '33*1=33'] Exploring Operation: 91*33=3003, Resulting Numbers: [3003] 3003,93 unequal: No Solution Exploring Operation: 91+33=124, Resulting Numbers: [124] 124,93 unequal: No Solution Exploring Operation: 91-33=58, Resulting Numbers: [58] 58,93 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 Current State: 93:[91, 63, 29], Operations: ['62-33=29'] Exploring Operation: 63+29=92, Resulting Numbers: [91, 92] Generated Node #0,0,0: 93:[91, 92] Operation: 63+29=92 Exploring Operation: 91-63=28, Resulting Numbers: [29, 28] Generated Node #0,0,1: 93:[29, 28] Operation: 91-63=28 Exploring Operation: 63-29=34, Resulting Numbers: [91, 34] Generated Node #0,0,2: 93:[91, 34] Operation: 63-29=34 Moving to Node #0,0,0 Current State: 93:[91, 92], Operations: ['62-33=29', '63+29=92'] Exploring Operation: 91+92=183, Resulting Numbers: [183] 183,93 unequal: No Solution Exploring Operation: 91*92=8372, Resulting Numbers: [8372] 8372,93 unequal: No Solution Exploring Operation: 92-91=1, Resulting Numbers: [1] 1,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[29, 28], Operations: ['62-33=29', '91-63=28'] Exploring Operation: 29*28=812, Resulting Numbers: [812] 812,93 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 29+28=57, Resulting Numbers: [57] 57,93 unequal: No Solution Moving to Node #0,0,2 Current State: 93:[91, 34], Operations: ['62-33=29', '63-29=34'] Exploring Operation: 91*34=3094, Resulting Numbers: [3094] 3094,93 unequal: No Solution Exploring Operation: 91-34=57, Resulting Numbers: [57] 57,93 unequal: No Solution Exploring Operation: 91+34=125, Resulting Numbers: [125] 125,93 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 #0,1 Current State: 93:[91, 63, 95], Operations: ['62+33=95'] Exploring Operation: 91-63=28, Resulting Numbers: [95, 28] Generated Node #0,1,0: 93:[95, 28] Operation: 91-63=28 Exploring Operation: 95-91=4, Resulting Numbers: [63, 4] Generated Node #0,1,1: 93:[63, 4] Operation: 95-91=4 Exploring Operation: 95-63=32, Resulting Numbers: [91, 32] Generated Node #0,1,2: 93:[91, 32] Operation: 95-63=32 Moving to Node #0,1,2 Current State: 93:[91, 32], Operations: ['62+33=95', '95-63=32'] Exploring Operation: 91*32=2912, Resulting Numbers: [2912] 2912,93 unequal: No Solution Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,93 unequal: No Solution Exploring Operation: 91+32=123, Resulting Numbers: [123] 123,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[95, 28], Operations: ['62+33=95', '91-63=28'] Exploring Operation: 95-28=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 95*28=2660, Resulting Numbers: [2660] 2660,93 unequal: No Solution Exploring Operation: 95+28=123, Resulting Numbers: [123] 123,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[63, 4], Operations: ['62+33=95', '95-91=4'] Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,93 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,93 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
[ 81, 48, 6, 75 ]
49
[ "81-6=75", "75/75=1", "48+1=49" ]
Current State: 49:[81, 48, 6, 75], Operations: [] Exploring Operation: 81-6=75, Resulting Numbers: [48, 75, 75] Generated Node #2: [48, 75, 75] from Operation: 81-6=75 Current State: 49:[48, 75, 75], Operations: ['81-6=75'] Exploring Operation: 75/75=1, Resulting Numbers: [48, 1] Generated Node #3: [48, 1] from Operation: 75/75=1 Current State: 49:[48, 1], Operations: ['81-6=75', '75/75=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[81, 48, 6, 75], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [48, 6, 6] Generated Node #0,0: 49:[48, 6, 6] Operation: 81-75=6 Exploring Operation: 81-48=33, Resulting Numbers: [6, 75, 33] Generated Node #0,1: 49:[6, 75, 33] Operation: 81-48=33 Exploring Operation: 81-6=75, Resulting Numbers: [48, 75, 75] Generated Node #0,2: 49:[48, 75, 75] Operation: 81-6=75 Exploring Operation: 75-6=69, Resulting Numbers: [81, 48, 69] Generated Node #0,3: 49:[81, 48, 69] Operation: 75-6=69 Exploring Operation: 75-48=27, Resulting Numbers: [81, 6, 27] Generated Node #0,4: 49:[81, 6, 27] Operation: 75-48=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[48, 6, 6], Operations: ['81-75=6'] Exploring Operation: 6+6=12, Resulting Numbers: [48, 12] Generated Node #0,0,0: 49:[48, 12] Operation: 6+6=12 Exploring Operation: 48+6=54, Resulting Numbers: [6, 54] Generated Node #0,0,1: 49:[6, 54] Operation: 48+6=54 Exploring Operation: 48/6=8, Resulting Numbers: [6, 8] Generated Node #0,0,2: 49:[6, 8] Operation: 48/6=8 Exploring Operation: 48/6=8, Resulting Numbers: [6, 8] Generated Node #0,0,3: 49:[6, 8] Operation: 48/6=8 Exploring Operation: 48+6=54, Resulting Numbers: [6, 54] Generated Node #0,0,4: 49:[6, 54] Operation: 48+6=54 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[6, 8], Operations: ['81-75=6', '48/6=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,49 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 49:[6, 8], Operations: ['81-75=6', '48/6=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[48, 12], Operations: ['81-75=6', '6+6=12'] Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,49 unequal: No Solution Exploring Operation: 48*12=576, Resulting Numbers: [576] 576,49 unequal: No Solution Exploring Operation: 48+12=60, Resulting Numbers: [60] 60,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[6, 54], Operations: ['81-75=6', '48+6=54'] Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,49 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,49 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 49:[6, 54], Operations: ['81-75=6', '48+6=54'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,49 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,49 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[6, 75, 33], Operations: ['81-48=33'] Exploring Operation: 6+75=81, Resulting Numbers: [33, 81] Generated Node #0,1,0: 49:[33, 81] Operation: 6+75=81 Exploring Operation: 6+33=39, Resulting Numbers: [75, 39] Generated Node #0,1,1: 49:[75, 39] Operation: 6+33=39 Exploring Operation: 75-6=69, Resulting Numbers: [33, 69] Generated Node #0,1,2: 49:[33, 69] Operation: 75-6=69 Exploring Operation: 75-33=42, Resulting Numbers: [6, 42] Generated Node #0,1,3: 49:[6, 42] Operation: 75-33=42 Exploring Operation: 33-6=27, Resulting Numbers: [75, 27] Generated Node #0,1,4: 49:[75, 27] Operation: 33-6=27 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 49:[6, 42], Operations: ['81-48=33', '75-33=42'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,49 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[75, 39], Operations: ['81-48=33', '6+33=39'] Exploring Operation: 75+39=114, Resulting Numbers: [114] 114,49 unequal: No Solution Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 75*39=2925, Resulting Numbers: [2925] 2925,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 49:[33, 69], Operations: ['81-48=33', '75-6=69'] Exploring Operation: 33+69=102, Resulting Numbers: [102] 102,49 unequal: No Solution Exploring Operation: 33*69=2277, Resulting Numbers: [2277] 2277,49 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 49:[75, 27], Operations: ['81-48=33', '33-6=27'] Exploring Operation: 75*27=2025, Resulting Numbers: [2025] 2025,49 unequal: No Solution Exploring Operation: 75+27=102, Resulting Numbers: [102] 102,49 unequal: No Solution Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[33, 81], Operations: ['81-48=33', '6+75=81'] Exploring Operation: 33*81=2673, Resulting Numbers: [2673] 2673,49 unequal: No Solution Exploring Operation: 81-33=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 33+81=114, Resulting Numbers: [114] 114,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[48, 75, 75], Operations: ['81-6=75'] Exploring Operation: 75-75=0, Resulting Numbers: [48, 0] Generated Node #0,2,0: 49:[48, 0] Operation: 75-75=0 Exploring Operation: 48+75=123, Resulting Numbers: [75, 123] Generated Node #0,2,1: 49:[75, 123] Operation: 48+75=123 Exploring Operation: 75-48=27, Resulting Numbers: [75, 27] Generated Node #0,2,2: 49:[75, 27] Operation: 75-48=27 Exploring Operation: 75-48=27, Resulting Numbers: [75, 27] Generated Node #0,2,3: 49:[75, 27] Operation: 75-48=27 Exploring Operation: 75/75=1, Resulting Numbers: [48, 1] Generated Node #0,2,4: 49:[48, 1] Operation: 75/75=1 Moving to Node #0,2,4 Current State: 49:[48, 1], Operations: ['81-6=75', '75/75=1'] Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[81, 48, 6, 75], Operations: [] Exploring Operation: 81-6=75, Resulting Numbers: [48, 75, 75] Generated Node #0,2: 49:[48, 75, 75] Operation: 81-6=75 Moving to Node #0,2 Current State: 49:[48, 75, 75], Operations: ['81-6=75'] Exploring Operation: 75/75=1, Resulting Numbers: [48, 1] Generated Node #0,2,4: 49:[48, 1] Operation: 75/75=1 Moving to Node #0,2,4 Current State: 49:[48, 1], Operations: ['81-6=75', '75/75=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
sum_heuristic
[ 62, 83, 62, 97 ]
14
[ "62+83=145", "62+97=159", "159-145=14" ]
Current State: 14:[62, 83, 62, 97], Operations: [] Exploring Operation: 62+83=145, Resulting Numbers: [97, 145] Generated Node #2: [97, 145] from Operation: 62+83=145 Current State: 14:[97, 145], Operations: ['62+83=145'] Exploring Operation: 62+97=159, Resulting Numbers: [145, 159] Generated Node #3: [145, 159] from Operation: 62+97=159 Current State: 14:[145, 159], Operations: ['62+83=145', '62+97=159'] Exploring Operation: 159-145=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[62, 83, 62, 97], Operations: [] Exploring Operation: 97-62=35, Resulting Numbers: [83, 62, 35] Generated Node #0,0: 14:[83, 62, 35] Operation: 97-62=35 Exploring Operation: 97-83=14, Resulting Numbers: [62, 62, 14] Generated Node #0,1: 14:[62, 62, 14] Operation: 97-83=14 Exploring Operation: 83-62=21, Resulting Numbers: [62, 97, 21] Generated Node #0,2: 14:[62, 97, 21] Operation: 83-62=21 Moving to Node #0,1 Current State: 14:[62, 62, 14], Operations: ['97-83=14'] Exploring Operation: 62-14=48, Resulting Numbers: [62, 48] Generated Node #0,1,0: 14:[62, 48] Operation: 62-14=48 Exploring Operation: 62-62=0, Resulting Numbers: [14, 0] Generated Node #0,1,1: 14:[14, 0] Operation: 62-62=0 Exploring Operation: 62/62=1, Resulting Numbers: [14, 1] Generated Node #0,1,2: 14:[14, 1] Operation: 62/62=1 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 14:[14, 1], Operations: ['97-83=14', '62/62=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[62, 83, 62, 97], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [62, 62, 14] Generated Node #0,1: 14:[62, 62, 14] Operation: 97-83=14 Moving to Node #0,1 Current State: 14:[62, 62, 14], Operations: ['97-83=14'] Exploring Operation: 62/62=1, Resulting Numbers: [14, 1] Generated Node #0,1,2: 14:[14, 1] Operation: 62/62=1 Moving to Node #0,1,2 Current State: 14:[14, 1], Operations: ['97-83=14', '62/62=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 64, 44, 64, 91 ]
48
[ "64/64=1", "91-44=47", "1+47=48" ]
Current State: 48:[64, 44, 64, 91], Operations: [] Exploring Operation: 64/64=1, Resulting Numbers: [44, 91, 1] Generated Node #2: [44, 91, 1] from Operation: 64/64=1 Current State: 48:[44, 91, 1], Operations: ['64/64=1'] Exploring Operation: 91-44=47, Resulting Numbers: [1, 47] Generated Node #3: [1, 47] from Operation: 91-44=47 Current State: 48:[1, 47], Operations: ['64/64=1', '91-44=47'] Exploring Operation: 1+47=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[64, 44, 64, 91], Operations: [] Exploring Operation: 91-64=27, Resulting Numbers: [44, 64, 27] Generated Node #0,0: 48:[44, 64, 27] Operation: 91-64=27 Exploring Operation: 91-64=27, Resulting Numbers: [64, 44, 27] Generated Node #0,1: 48:[64, 44, 27] Operation: 91-64=27 Exploring Operation: 91-44=47, Resulting Numbers: [64, 64, 47] Generated Node #0,2: 48:[64, 64, 47] Operation: 91-44=47 Moving to Node #0,0 Current State: 48:[44, 64, 27], Operations: ['91-64=27'] Exploring Operation: 64-44=20, Resulting Numbers: [27, 20] Generated Node #0,0,0: 48:[27, 20] Operation: 64-44=20 Exploring Operation: 44-27=17, Resulting Numbers: [64, 17] Generated Node #0,0,1: 48:[64, 17] Operation: 44-27=17 Exploring Operation: 64-27=37, Resulting Numbers: [44, 37] Generated Node #0,0,2: 48:[44, 37] Operation: 64-27=37 Moving to Node #0,1 Current State: 48:[64, 44, 27], Operations: ['91-64=27'] Exploring Operation: 44-27=17, Resulting Numbers: [64, 17] Generated Node #0,1,0: 48:[64, 17] Operation: 44-27=17 Exploring Operation: 64-27=37, Resulting Numbers: [44, 37] Generated Node #0,1,1: 48:[44, 37] Operation: 64-27=37 Exploring Operation: 64-44=20, Resulting Numbers: [27, 20] Generated Node #0,1,2: 48:[27, 20] Operation: 64-44=20 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 48:[27, 20], Operations: ['91-64=27', '64-44=20'] Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,48 unequal: No Solution Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 27-20=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 #0,1,1 Current State: 48:[44, 37], Operations: ['91-64=27', '64-27=37'] Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,48 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,48 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:[64, 17], Operations: ['91-64=27', '44-27=17'] Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 64+17=81, Resulting Numbers: [81] 81,48 unequal: No Solution Exploring Operation: 64*17=1088, Resulting Numbers: [1088] 1088,48 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: 48:[64, 64, 47], Operations: ['91-44=47'] Exploring Operation: 64/64=1, Resulting Numbers: [47, 1] Generated Node #0,2,0: 48:[47, 1] Operation: 64/64=1 Exploring Operation: 64-64=0, Resulting Numbers: [47, 0] Generated Node #0,2,1: 48:[47, 0] Operation: 64-64=0 Exploring Operation: 64-47=17, Resulting Numbers: [64, 17] Generated Node #0,2,2: 48:[64, 17] Operation: 64-47=17 Moving to Node #0,2,0 Current State: 48:[47, 1], Operations: ['91-44=47', '64/64=1'] Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[64, 44, 64, 91], Operations: [] Exploring Operation: 91-44=47, Resulting Numbers: [64, 64, 47] Generated Node #0,2: 48:[64, 64, 47] Operation: 91-44=47 Moving to Node #0,2 Current State: 48:[64, 64, 47], Operations: ['91-44=47'] Exploring Operation: 64/64=1, Resulting Numbers: [47, 1] Generated Node #0,2,0: 48:[47, 1] Operation: 64/64=1 Moving to Node #0,2,0 Current State: 48:[47, 1], Operations: ['91-44=47', '64/64=1'] Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 36, 62, 86, 80 ]
56
[ "86-80=6", "36/6=6", "62-6=56" ]
Current State: 56:[36, 62, 86, 80], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [36, 62, 6] Generated Node #2: [36, 62, 6] from Operation: 86-80=6 Current State: 56:[36, 62, 6], Operations: ['86-80=6'] Exploring Operation: 36/6=6, Resulting Numbers: [62, 6] Generated Node #3: [62, 6] from Operation: 36/6=6 Current State: 56:[62, 6], Operations: ['86-80=6', '36/6=6'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[36, 62, 86, 80], Operations: [] Exploring Operation: 86-62=24, Resulting Numbers: [36, 80, 24] Generated Node #0,0: 56:[36, 80, 24] Operation: 86-62=24 Exploring Operation: 80-36=44, Resulting Numbers: [62, 86, 44] Generated Node #0,1: 56:[62, 86, 44] Operation: 80-36=44 Exploring Operation: 80-62=18, Resulting Numbers: [36, 86, 18] Generated Node #0,2: 56:[36, 86, 18] Operation: 80-62=18 Exploring Operation: 86-80=6, Resulting Numbers: [36, 62, 6] Generated Node #0,3: 56:[36, 62, 6] Operation: 86-80=6 Exploring Operation: 86-36=50, Resulting Numbers: [62, 80, 50] Generated Node #0,4: 56:[62, 80, 50] Operation: 86-36=50 Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[36, 62, 6], Operations: ['86-80=6'] Exploring Operation: 36/6=6, Resulting Numbers: [62, 6] Generated Node #0,3,0: 56:[62, 6] Operation: 36/6=6 Exploring Operation: 62-36=26, Resulting Numbers: [6, 26] Generated Node #0,3,1: 56:[6, 26] Operation: 62-36=26 Exploring Operation: 36-6=30, Resulting Numbers: [62, 30] Generated Node #0,3,2: 56:[62, 30] Operation: 36-6=30 Exploring Operation: 36+6=42, Resulting Numbers: [62, 42] Generated Node #0,3,3: 56:[62, 42] Operation: 36+6=42 Exploring Operation: 62-6=56, Resulting Numbers: [36, 56] Generated Node #0,3,4: 56:[36, 56] Operation: 62-6=56 Moving to Node #0,3,1 Current State: 56:[6, 26], Operations: ['86-80=6', '62-36=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,56 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,56 unequal: No Solution Moving to Node #0,3,0 Current State: 56:[62, 6], Operations: ['86-80=6', '36/6=6'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[36, 62, 86, 80], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [36, 62, 6] Generated Node #0,3: 56:[36, 62, 6] Operation: 86-80=6 Moving to Node #0,3 Current State: 56:[36, 62, 6], Operations: ['86-80=6'] Exploring Operation: 36/6=6, Resulting Numbers: [62, 6] Generated Node #0,3,0: 56:[62, 6] Operation: 36/6=6 Moving to Node #0,3,0 Current State: 56:[62, 6], Operations: ['86-80=6', '36/6=6'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 50, 36, 16, 2 ]
53
[ "50-16=34", "34/2=17", "36+17=53" ]
Current State: 53:[50, 36, 16, 2], Operations: [] Exploring Operation: 50-16=34, Resulting Numbers: [36, 2, 34] Generated Node #2: [36, 2, 34] from Operation: 50-16=34 Current State: 53:[36, 2, 34], Operations: ['50-16=34'] Exploring Operation: 34/2=17, Resulting Numbers: [36, 17] Generated Node #3: [36, 17] from Operation: 34/2=17 Current State: 53:[36, 17], Operations: ['50-16=34', '34/2=17'] Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[50, 36, 16, 2], Operations: [] Exploring Operation: 16*2=32, Resulting Numbers: [50, 36, 32] Generated Node #0,0: 53:[50, 36, 32] Operation: 16*2=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[50, 36, 32], Operations: ['16*2=32'] Exploring Operation: 36+32=68, Resulting Numbers: [50, 68] Generated Node #0,0,0: 53:[50, 68] Operation: 36+32=68 Moving to Node #0,0,0 Current State: 53:[50, 68], Operations: ['16*2=32', '36+32=68'] Exploring Operation: 68-50=18, Resulting Numbers: [18] 18,53 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, 25, 20, 33 ]
64
[ "25-14=11", "20+33=53", "11+53=64" ]
Current State: 64:[14, 25, 20, 33], Operations: [] Exploring Operation: 25-14=11, Resulting Numbers: [20, 33, 11] Generated Node #2: [20, 33, 11] from Operation: 25-14=11 Current State: 64:[20, 33, 11], Operations: ['25-14=11'] Exploring Operation: 20+33=53, Resulting Numbers: [11, 53] Generated Node #3: [11, 53] from Operation: 20+33=53 Current State: 64:[11, 53], Operations: ['25-14=11', '20+33=53'] Exploring Operation: 11+53=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[14, 25, 20, 33], Operations: [] Exploring Operation: 25-14=11, Resulting Numbers: [20, 33, 11] Generated Node #0,0: 64:[20, 33, 11] Operation: 25-14=11 Exploring Operation: 25-20=5, Resulting Numbers: [14, 33, 5] Generated Node #0,1: 64:[14, 33, 5] Operation: 25-20=5 Exploring Operation: 33-25=8, Resulting Numbers: [14, 20, 8] Generated Node #0,2: 64:[14, 20, 8] Operation: 33-25=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[14, 33, 5], Operations: ['25-20=5'] Exploring Operation: 33-14=19, Resulting Numbers: [5, 19] Generated Node #0,1,0: 64:[5, 19] Operation: 33-14=19 Exploring Operation: 14+5=19, Resulting Numbers: [33, 19] Generated Node #0,1,1: 64:[33, 19] Operation: 14+5=19 Exploring Operation: 14-5=9, Resulting Numbers: [33, 9] Generated Node #0,1,2: 64:[33, 9] Operation: 14-5=9 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 64:[33, 9], Operations: ['25-20=5', '14-5=9'] Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 33*9=297, Resulting Numbers: [297] 297,64 unequal: No Solution Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,64 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 #0,1,0 Current State: 64:[5, 19], Operations: ['25-20=5', '33-14=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,64 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,64 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,64 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 #0,1,1 Current State: 64:[33, 19], Operations: ['25-20=5', '14+5=19'] Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,64 unequal: No Solution Exploring Operation: 33*19=627, Resulting Numbers: [627] 627,64 unequal: No Solution Exploring Operation: 33+19=52, Resulting Numbers: [52] 52,64 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: 64:[14, 20, 8], Operations: ['33-25=8'] Exploring Operation: 14-8=6, Resulting Numbers: [20, 6] Generated Node #0,2,0: 64:[20, 6] Operation: 14-8=6 Exploring Operation: 20-14=6, Resulting Numbers: [8, 6] Generated Node #0,2,1: 64:[8, 6] Operation: 20-14=6 Exploring Operation: 14+20=34, Resulting Numbers: [8, 34] Generated Node #0,2,2: 64:[8, 34] Operation: 14+20=34 Moving to Node #0,2,1 Current State: 64:[8, 6], Operations: ['33-25=8', '20-14=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,64 unequal: No Solution Moving to Node #0,2,2 Current State: 64:[8, 34], Operations: ['33-25=8', '14+20=34'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,64 unequal: No Solution Moving to Node #0,2,0 Current State: 64:[20, 6], Operations: ['33-25=8', '14-8=6'] Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,64 unequal: No Solution Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[20, 33, 11], Operations: ['25-14=11'] Exploring Operation: 20-11=9, Resulting Numbers: [33, 9] Generated Node #0,0,0: 64:[33, 9] Operation: 20-11=9 Exploring Operation: 20+11=31, Resulting Numbers: [33, 31] Generated Node #0,0,1: 64:[33, 31] Operation: 20+11=31 Exploring Operation: 33/11=3, Resulting Numbers: [20, 3] Generated Node #0,0,2: 64:[20, 3] Operation: 33/11=3 Moving to Node #0,0,0 Current State: 64:[33, 9], Operations: ['25-14=11', '20-11=9'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,64 unequal: No Solution Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 33*9=297, Resulting Numbers: [297] 297,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[33, 31], Operations: ['25-14=11', '20+11=31'] Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,64 unequal: No Solution Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[14, 25, 20, 33], Operations: [] Exploring Operation: 25-14=11, Resulting Numbers: [20, 33, 11] Generated Node #0,0: 64:[20, 33, 11] Operation: 25-14=11 Moving to Node #0,0 Current State: 64:[20, 33, 11], Operations: ['25-14=11'] Exploring Operation: 20+11=31, Resulting Numbers: [33, 31] Generated Node #0,0,1: 64:[33, 31] Operation: 20+11=31 Moving to Node #0,0,1 Current State: 64:[33, 31], Operations: ['25-14=11', '20+11=31'] Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_3
mult_heuristic
[ 4, 5, 75, 14 ]
51
[ "4+5=9", "14*9=126", "126-75=51" ]
Current State: 51:[4, 5, 75, 14], Operations: [] Exploring Operation: 4+5=9, Resulting Numbers: [75, 14, 9] Generated Node #2: [75, 14, 9] from Operation: 4+5=9 Current State: 51:[75, 14, 9], Operations: ['4+5=9'] Exploring Operation: 14*9=126, Resulting Numbers: [75, 126] Generated Node #3: [75, 126] from Operation: 14*9=126 Current State: 51:[75, 126], Operations: ['4+5=9', '14*9=126'] Exploring Operation: 126-75=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[4, 5, 75, 14], Operations: [] Exploring Operation: 75-4=71, Resulting Numbers: [5, 14, 71] Generated Node #0,0: 51:[5, 14, 71] Operation: 75-4=71 Exploring Operation: 75-5=70, Resulting Numbers: [4, 14, 70] Generated Node #0,1: 51:[4, 14, 70] Operation: 75-5=70 Exploring Operation: 75/5=15, Resulting Numbers: [4, 14, 15] Generated Node #0,2: 51:[4, 14, 15] Operation: 75/5=15 Exploring Operation: 75-14=61, Resulting Numbers: [4, 5, 61] Generated Node #0,3: 51:[4, 5, 61] Operation: 75-14=61 Moving to Node #0,2 Current State: 51:[4, 14, 15], Operations: ['75/5=15'] Exploring Operation: 4*14=56, Resulting Numbers: [15, 56] Generated Node #0,2,0: 51:[15, 56] Operation: 4*14=56 Exploring Operation: 15-14=1, Resulting Numbers: [4, 1] Generated Node #0,2,1: 51:[4, 1] Operation: 15-14=1 Exploring Operation: 4+15=19, Resulting Numbers: [14, 19] Generated Node #0,2,2: 51:[14, 19] Operation: 4+15=19 Exploring Operation: 4+14=18, Resulting Numbers: [15, 18] Generated Node #0,2,3: 51:[15, 18] Operation: 4+14=18 Moving to Node #0,3 Current State: 51:[4, 5, 61], Operations: ['75-14=61'] Exploring Operation: 61-5=56, Resulting Numbers: [4, 56] Generated Node #0,3,0: 51:[4, 56] Operation: 61-5=56 Exploring Operation: 4*5=20, Resulting Numbers: [61, 20] Generated Node #0,3,1: 51:[61, 20] Operation: 4*5=20 Exploring Operation: 5-4=1, Resulting Numbers: [61, 1] Generated Node #0,3,2: 51:[61, 1] Operation: 5-4=1 Exploring Operation: 61-4=57, Resulting Numbers: [5, 57] Generated Node #0,3,3: 51:[5, 57] Operation: 61-4=57 Moving to Node #0,1 Current State: 51:[4, 14, 70], Operations: ['75-5=70'] Exploring Operation: 4+14=18, Resulting Numbers: [70, 18] Generated Node #0,1,0: 51:[70, 18] Operation: 4+14=18 Exploring Operation: 70-14=56, Resulting Numbers: [4, 56] Generated Node #0,1,1: 51:[4, 56] Operation: 70-14=56 Exploring Operation: 70/14=5, Resulting Numbers: [4, 5] Generated Node #0,1,2: 51:[4, 5] Operation: 70/14=5 Exploring Operation: 70-4=66, Resulting Numbers: [14, 66] Generated Node #0,1,3: 51:[14, 66] Operation: 70-4=66 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 51:[4, 5], Operations: ['75-5=70', '70/14=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,51 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 51:[4, 56], Operations: ['75-5=70', '70-14=56'] Exploring Operation: 4+56=60, Resulting Numbers: [60] 60,51 unequal: No Solution Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 4*56=224, Resulting Numbers: [224] 224,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 51:[14, 66], Operations: ['75-5=70', '70-4=66'] Exploring Operation: 14+66=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 14*66=924, Resulting Numbers: [924] 924,51 unequal: No Solution Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 51:[70, 18], Operations: ['75-5=70', '4+14=18'] Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,51 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 51:[5, 14, 71], Operations: ['75-4=71'] Exploring Operation: 71-5=66, Resulting Numbers: [14, 66] Generated Node #0,0,0: 51:[14, 66] Operation: 71-5=66 Exploring Operation: 71-14=57, Resulting Numbers: [5, 57] Generated Node #0,0,1: 51:[5, 57] Operation: 71-14=57 Exploring Operation: 14-5=9, Resulting Numbers: [71, 9] Generated Node #0,0,2: 51:[71, 9] Operation: 14-5=9 Exploring Operation: 5+14=19, Resulting Numbers: [71, 19] Generated Node #0,0,3: 51:[71, 19] Operation: 5+14=19 Moving to Node #0,2,1 Current State: 51:[4, 1], Operations: ['75/5=15', '15-14=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[15, 18], Operations: ['75/5=15', '4+14=18'] Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,51 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[14, 19], Operations: ['75/5=15', '4+15=19'] Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 14+19=33, Resulting Numbers: [33] 33,51 unequal: No Solution Exploring Operation: 14*19=266, Resulting Numbers: [266] 266,51 unequal: No Solution Moving to Node #0,3,0 Current State: 51:[4, 56], Operations: ['75-14=61', '61-5=56'] Exploring Operation: 4*56=224, Resulting Numbers: [224] 224,51 unequal: No Solution Exploring Operation: 4+56=60, Resulting Numbers: [60] 60,51 unequal: No Solution Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[15, 56], Operations: ['75/5=15', '4*14=56'] Exploring Operation: 15*56=840, Resulting Numbers: [840] 840,51 unequal: No Solution Exploring Operation: 15+56=71, Resulting Numbers: [71] 71,51 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,51 unequal: No Solution Moving to Node #0,3,3 Current State: 51:[5, 57], Operations: ['75-14=61', '61-4=57'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 5*57=285, Resulting Numbers: [285] 285,51 unequal: No Solution Exploring Operation: 5+57=62, Resulting Numbers: [62] 62,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[5, 57], Operations: ['75-4=71', '71-14=57'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 5*57=285, Resulting Numbers: [285] 285,51 unequal: No Solution Exploring Operation: 5+57=62, Resulting Numbers: [62] 62,51 unequal: No Solution Moving to Node #0,3,2 Current State: 51:[61, 1], Operations: ['75-14=61', '5-4=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,51 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,51 unequal: No Solution Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,51 unequal: No Solution Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,51 unequal: No Solution Moving to Node #0,3,1 Current State: 51:[61, 20], Operations: ['75-14=61', '4*5=20'] Exploring Operation: 61*20=1220, Resulting Numbers: [1220] 1220,51 unequal: No Solution Exploring Operation: 61+20=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 61-20=41, Resulting Numbers: [41] 41,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[14, 66], Operations: ['75-4=71', '71-5=66'] Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 14+66=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 14*66=924, Resulting Numbers: [924] 924,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[71, 19], Operations: ['75-4=71', '5+14=19'] Exploring Operation: 71-19=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 71*19=1349, Resulting Numbers: [1349] 1349,51 unequal: No Solution Exploring Operation: 71+19=90, Resulting Numbers: [90] 90,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[71, 9], Operations: ['75-4=71', '14-5=9'] Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,51 unequal: No Solution Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,51 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 15, 4, 89, 11 ]
88
[ "15-4=11", "11/11=1", "89-1=88" ]
Current State: 88:[15, 4, 89, 11], Operations: [] Exploring Operation: 15-4=11, Resulting Numbers: [89, 11, 11] Generated Node #2: [89, 11, 11] from Operation: 15-4=11 Current State: 88:[89, 11, 11], Operations: ['15-4=11'] Exploring Operation: 11/11=1, Resulting Numbers: [89, 1] Generated Node #3: [89, 1] from Operation: 11/11=1 Current State: 88:[89, 1], Operations: ['15-4=11', '11/11=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[15, 4, 89, 11], Operations: [] Exploring Operation: 15+11=26, Resulting Numbers: [4, 89, 26] Generated Node #0,0: 88:[4, 89, 26] Operation: 15+11=26 Exploring Operation: 15-11=4, Resulting Numbers: [4, 89, 4] Generated Node #0,1: 88:[4, 89, 4] Operation: 15-11=4 Exploring Operation: 15-4=11, Resulting Numbers: [89, 11, 11] Generated Node #0,2: 88:[89, 11, 11] Operation: 15-4=11 Exploring Operation: 4*11=44, Resulting Numbers: [15, 89, 44] Generated Node #0,3: 88:[15, 89, 44] Operation: 4*11=44 Exploring Operation: 15+4=19, Resulting Numbers: [89, 11, 19] Generated Node #0,4: 88:[89, 11, 19] Operation: 15+4=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[4, 89, 4], Operations: ['15-11=4'] Exploring Operation: 4/4=1, Resulting Numbers: [89, 1] Generated Node #0,1,0: 88:[89, 1] Operation: 4/4=1 Exploring Operation: 89-4=85, Resulting Numbers: [4, 85] Generated Node #0,1,1: 88:[4, 85] Operation: 89-4=85 Exploring Operation: 4+4=8, Resulting Numbers: [89, 8] Generated Node #0,1,2: 88:[89, 8] Operation: 4+4=8 Exploring Operation: 4-4=0, Resulting Numbers: [89, 0] Generated Node #0,1,3: 88:[89, 0] Operation: 4-4=0 Exploring Operation: 89-4=85, Resulting Numbers: [4, 85] Generated Node #0,1,4: 88:[4, 85] Operation: 89-4=85 Moving to Node #0,1,2 Current State: 88:[89, 8], Operations: ['15-11=4', '4+4=8'] Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,88 unequal: No Solution Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,88 unequal: No Solution Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[89, 1], Operations: ['15-11=4', '4/4=1'] Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[15, 4, 89, 11], Operations: [] Exploring Operation: 15-11=4, Resulting Numbers: [4, 89, 4] Generated Node #0,1: 88:[4, 89, 4] Operation: 15-11=4 Moving to Node #0,1 Current State: 88:[4, 89, 4], Operations: ['15-11=4'] Exploring Operation: 4/4=1, Resulting Numbers: [89, 1] Generated Node #0,1,0: 88:[89, 1] Operation: 4/4=1 Moving to Node #0,1,0 Current State: 88:[89, 1], Operations: ['15-11=4', '4/4=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 23, 9, 77, 58 ]
38
[ "77+58=135", "135/9=15", "23+15=38" ]
Current State: 38:[23, 9, 77, 58], Operations: [] Exploring Operation: 77+58=135, Resulting Numbers: [23, 9, 135] Generated Node #2: [23, 9, 135] from Operation: 77+58=135 Current State: 38:[23, 9, 135], Operations: ['77+58=135'] Exploring Operation: 135/9=15, Resulting Numbers: [23, 15] Generated Node #3: [23, 15] from Operation: 135/9=15 Current State: 38:[23, 15], Operations: ['77+58=135', '135/9=15'] Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[23, 9, 77, 58], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [23, 9, 19] Generated Node #0,0: 38:[23, 9, 19] Operation: 77-58=19 Moving to Node #0,0 Current State: 38:[23, 9, 19], Operations: ['77-58=19'] Exploring Operation: 23-9=14, Resulting Numbers: [19, 14] Generated Node #0,0,0: 38:[19, 14] Operation: 23-9=14 Moving to Node #0,0,0 Current State: 38:[19, 14], Operations: ['77-58=19', '23-9=14'] Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,38 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 79, 42, 18, 46 ]
65
[ "79-42=37", "46-18=28", "37+28=65" ]
Current State: 65:[79, 42, 18, 46], Operations: [] Exploring Operation: 79-42=37, Resulting Numbers: [18, 46, 37] Generated Node #2: [18, 46, 37] from Operation: 79-42=37 Current State: 65:[18, 46, 37], Operations: ['79-42=37'] Exploring Operation: 46-18=28, Resulting Numbers: [37, 28] Generated Node #3: [37, 28] from Operation: 46-18=28 Current State: 65:[37, 28], Operations: ['79-42=37', '46-18=28'] Exploring Operation: 37+28=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[79, 42, 18, 46], Operations: [] Exploring Operation: 18+46=64, Resulting Numbers: [79, 42, 64] Generated Node #0,0: 65:[79, 42, 64] Operation: 18+46=64 Exploring Operation: 46-42=4, Resulting Numbers: [79, 18, 4] Generated Node #0,1: 65:[79, 18, 4] Operation: 46-42=4 Exploring Operation: 42+46=88, Resulting Numbers: [79, 18, 88] Generated Node #0,2: 65:[79, 18, 88] Operation: 42+46=88 Exploring Operation: 42+18=60, Resulting Numbers: [79, 46, 60] Generated Node #0,3: 65:[79, 46, 60] Operation: 42+18=60 Moving to Node #0,1 Current State: 65:[79, 18, 4], Operations: ['46-42=4'] Exploring Operation: 18-4=14, Resulting Numbers: [79, 14] Generated Node #0,1,0: 65:[79, 14] Operation: 18-4=14 Exploring Operation: 79-4=75, Resulting Numbers: [18, 75] Generated Node #0,1,1: 65:[18, 75] Operation: 79-4=75 Exploring Operation: 18*4=72, Resulting Numbers: [79, 72] Generated Node #0,1,2: 65:[79, 72] Operation: 18*4=72 Exploring Operation: 79-18=61, Resulting Numbers: [4, 61] Generated Node #0,1,3: 65:[4, 61] Operation: 79-18=61 Moving to Node #0,3 Current State: 65:[79, 46, 60], Operations: ['42+18=60'] Exploring Operation: 60-46=14, Resulting Numbers: [79, 14] Generated Node #0,3,0: 65:[79, 14] Operation: 60-46=14 Exploring Operation: 79-46=33, Resulting Numbers: [60, 33] Generated Node #0,3,1: 65:[60, 33] Operation: 79-46=33 Exploring Operation: 46+60=106, Resulting Numbers: [79, 106] Generated Node #0,3,2: 65:[79, 106] Operation: 46+60=106 Exploring Operation: 79-60=19, Resulting Numbers: [46, 19] Generated Node #0,3,3: 65:[46, 19] Operation: 79-60=19 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 65:[79, 14], Operations: ['42+18=60', '60-46=14'] Exploring Operation: 79+14=93, Resulting Numbers: [93] 93,65 unequal: No Solution Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[79, 42, 18, 46], Operations: [] Exploring Operation: 42+18=60, Resulting Numbers: [79, 46, 60] Generated Node #0,3: 65:[79, 46, 60] Operation: 42+18=60 Moving to Node #0,3 Current State: 65:[79, 46, 60], Operations: ['42+18=60'] Exploring Operation: 60-46=14, Resulting Numbers: [79, 14] Generated Node #0,3,0: 65:[79, 14] Operation: 60-46=14 Moving to Node #0,3,0 Current State: 65:[79, 14], Operations: ['42+18=60', '60-46=14'] Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 11, 79, 69, 59 ]
59
[ "79-11=68", "69-68=1", "59*1=59" ]
Current State: 59:[11, 79, 69, 59], Operations: [] Exploring Operation: 79-11=68, Resulting Numbers: [69, 59, 68] Generated Node #2: [69, 59, 68] from Operation: 79-11=68 Current State: 59:[69, 59, 68], Operations: ['79-11=68'] Exploring Operation: 69-68=1, Resulting Numbers: [59, 1] Generated Node #3: [59, 1] from Operation: 69-68=1 Current State: 59:[59, 1], Operations: ['79-11=68', '69-68=1'] Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[11, 79, 69, 59], Operations: [] Exploring Operation: 79-11=68, Resulting Numbers: [69, 59, 68] Generated Node #0,0: 59:[69, 59, 68] Operation: 79-11=68 Exploring Operation: 11+79=90, Resulting Numbers: [69, 59, 90] Generated Node #0,1: 59:[69, 59, 90] Operation: 11+79=90 Exploring Operation: 69-11=58, Resulting Numbers: [79, 59, 58] Generated Node #0,2: 59:[79, 59, 58] Operation: 69-11=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[69, 59, 68], Operations: ['79-11=68'] Exploring Operation: 69-59=10, Resulting Numbers: [68, 10] Generated Node #0,0,0: 59:[68, 10] Operation: 69-59=10 Exploring Operation: 68-59=9, Resulting Numbers: [69, 9] Generated Node #0,0,1: 59:[69, 9] Operation: 68-59=9 Exploring Operation: 69-68=1, Resulting Numbers: [59, 1] Generated Node #0,0,2: 59:[59, 1] Operation: 69-68=1 Moving to Node #0,0,0 Current State: 59:[68, 10], Operations: ['79-11=68', '69-59=10'] Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,59 unequal: No Solution Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,59 unequal: No Solution Exploring Operation: 68*10=680, Resulting Numbers: [680] 680,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[59, 1], Operations: ['79-11=68', '69-68=1'] Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[11, 79, 69, 59], Operations: [] Exploring Operation: 79-11=68, Resulting Numbers: [69, 59, 68] Generated Node #0,0: 59:[69, 59, 68] Operation: 79-11=68 Moving to Node #0,0 Current State: 59:[69, 59, 68], Operations: ['79-11=68'] Exploring Operation: 69-68=1, Resulting Numbers: [59, 1] Generated Node #0,0,2: 59:[59, 1] Operation: 69-68=1 Moving to Node #0,0,2 Current State: 59:[59, 1], Operations: ['79-11=68', '69-68=1'] Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 48, 64, 24, 94 ]
15
[ "48/24=2", "94-64=30", "30/2=15" ]
Current State: 15:[48, 64, 24, 94], Operations: [] Exploring Operation: 48/24=2, Resulting Numbers: [64, 94, 2] Generated Node #2: [64, 94, 2] from Operation: 48/24=2 Current State: 15:[64, 94, 2], Operations: ['48/24=2'] Exploring Operation: 94-64=30, Resulting Numbers: [2, 30] Generated Node #3: [2, 30] from Operation: 94-64=30 Current State: 15:[2, 30], Operations: ['48/24=2', '94-64=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[48, 64, 24, 94], Operations: [] Exploring Operation: 94-64=30, Resulting Numbers: [48, 24, 30] Generated Node #0,0: 15:[48, 24, 30] Operation: 94-64=30 Exploring Operation: 94-48=46, Resulting Numbers: [64, 24, 46] Generated Node #0,1: 15:[64, 24, 46] Operation: 94-48=46 Exploring Operation: 64-48=16, Resulting Numbers: [24, 94, 16] Generated Node #0,2: 15:[24, 94, 16] Operation: 64-48=16 Exploring Operation: 48/24=2, Resulting Numbers: [64, 94, 2] Generated Node #0,3: 15:[64, 94, 2] Operation: 48/24=2 Moving to Node #0,0 Current State: 15:[48, 24, 30], Operations: ['94-64=30'] Exploring Operation: 30-24=6, Resulting Numbers: [48, 6] Generated Node #0,0,0: 15:[48, 6] Operation: 30-24=6 Exploring Operation: 48-30=18, Resulting Numbers: [24, 18] Generated Node #0,0,1: 15:[24, 18] Operation: 48-30=18 Exploring Operation: 48/24=2, Resulting Numbers: [30, 2] Generated Node #0,0,2: 15:[30, 2] Operation: 48/24=2 Exploring Operation: 48-24=24, Resulting Numbers: [30, 24] Generated Node #0,0,3: 15:[30, 24] Operation: 48-24=24 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[24, 18], Operations: ['94-64=30', '48-30=18'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,15 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,15 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 #0,0,2 Current State: 15:[30, 2], Operations: ['94-64=30', '48/24=2'] Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,15 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,15 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[48, 64, 24, 94], Operations: [] Exploring Operation: 94-64=30, Resulting Numbers: [48, 24, 30] Generated Node #0,0: 15:[48, 24, 30] Operation: 94-64=30 Moving to Node #0,0 Current State: 15:[48, 24, 30], Operations: ['94-64=30'] Exploring Operation: 48/24=2, Resulting Numbers: [30, 2] Generated Node #0,0,2: 15:[30, 2] Operation: 48/24=2 Moving to Node #0,0,2 Current State: 15:[30, 2], Operations: ['94-64=30', '48/24=2'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 73, 43, 55, 1 ]
85
[ "73-43=30", "55*1=55", "30+55=85" ]
Current State: 85:[73, 43, 55, 1], Operations: [] Exploring Operation: 73-43=30, Resulting Numbers: [55, 1, 30] Generated Node #2: [55, 1, 30] from Operation: 73-43=30 Current State: 85:[55, 1, 30], Operations: ['73-43=30'] Exploring Operation: 55*1=55, Resulting Numbers: [30, 55] Generated Node #3: [30, 55] from Operation: 55*1=55 Current State: 85:[30, 55], Operations: ['73-43=30', '55*1=55'] Exploring Operation: 30+55=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[73, 43, 55, 1], Operations: [] Exploring Operation: 73-43=30, Resulting Numbers: [55, 1, 30] Generated Node #0,0: 85:[55, 1, 30] Operation: 73-43=30 Exploring Operation: 73-55=18, Resulting Numbers: [43, 1, 18] Generated Node #0,1: 85:[43, 1, 18] Operation: 73-55=18 Exploring Operation: 43+55=98, Resulting Numbers: [73, 1, 98] Generated Node #0,2: 85:[73, 1, 98] Operation: 43+55=98 Exploring Operation: 55-43=12, Resulting Numbers: [73, 1, 12] Generated Node #0,3: 85:[73, 1, 12] Operation: 55-43=12 Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[73, 1, 12], Operations: ['55-43=12'] Exploring Operation: 73*1=73, Resulting Numbers: [12, 73] Generated Node #0,3,0: 85:[12, 73] Operation: 73*1=73 Exploring Operation: 1+12=13, Resulting Numbers: [73, 13] Generated Node #0,3,1: 85:[73, 13] Operation: 1+12=13 Exploring Operation: 73+1=74, Resulting Numbers: [12, 74] Generated Node #0,3,2: 85:[12, 74] Operation: 73+1=74 Exploring Operation: 73+12=85, Resulting Numbers: [1, 85] Generated Node #0,3,3: 85:[1, 85] Operation: 73+12=85 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 85:[1, 85], Operations: ['55-43=12', '73+12=85'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[73, 43, 55, 1], Operations: [] Exploring Operation: 55-43=12, Resulting Numbers: [73, 1, 12] Generated Node #0,3: 85:[73, 1, 12] Operation: 55-43=12 Moving to Node #0,3 Current State: 85:[73, 1, 12], Operations: ['55-43=12'] Exploring Operation: 73+12=85, Resulting Numbers: [1, 85] Generated Node #0,3,3: 85:[1, 85] Operation: 73+12=85 Moving to Node #0,3,3 Current State: 85:[1, 85], Operations: ['55-43=12', '73+12=85'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 4, 1, 30, 13 ]
95
[ "4+1=5", "13*5=65", "30+65=95" ]
Current State: 95:[4, 1, 30, 13], Operations: [] Exploring Operation: 4+1=5, Resulting Numbers: [30, 13, 5] Generated Node #2: [30, 13, 5] from Operation: 4+1=5 Current State: 95:[30, 13, 5], Operations: ['4+1=5'] Exploring Operation: 13*5=65, Resulting Numbers: [30, 65] Generated Node #3: [30, 65] from Operation: 13*5=65 Current State: 95:[30, 65], Operations: ['4+1=5', '13*5=65'] Exploring Operation: 30+65=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[4, 1, 30, 13], Operations: [] Exploring Operation: 30-13=17, Resulting Numbers: [4, 1, 17] Generated Node #0,0: 95:[4, 1, 17] Operation: 30-13=17 Exploring Operation: 4+1=5, Resulting Numbers: [30, 13, 5] Generated Node #0,1: 95:[30, 13, 5] Operation: 4+1=5 Moving to Node #0,0 Current State: 95:[4, 1, 17], Operations: ['30-13=17'] Exploring Operation: 1+17=18, Resulting Numbers: [4, 18] Generated Node #0,0,0: 95:[4, 18] Operation: 1+17=18 Exploring Operation: 4+1=5, Resulting Numbers: [17, 5] Generated Node #0,0,1: 95:[17, 5] Operation: 4+1=5 Moving to Node #0,1 Current State: 95:[30, 13, 5], Operations: ['4+1=5'] Exploring Operation: 30-13=17, Resulting Numbers: [5, 17] Generated Node #0,1,0: 95:[5, 17] Operation: 30-13=17 Exploring Operation: 30/5=6, Resulting Numbers: [13, 6] Generated Node #0,1,1: 95:[13, 6] Operation: 30/5=6 Moving to Node #0,0,0 Current State: 95:[4, 18], Operations: ['30-13=17', '1+17=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,95 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[5, 17], Operations: ['4+1=5', '30-13=17'] Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[17, 5], Operations: ['30-13=17', '4+1=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[13, 6], Operations: ['4+1=5', '30/5=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,95 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 34, 26, 52, 23 ]
45
[ "34*52=1768", "1768/26=68", "68-23=45" ]
Current State: 45:[34, 26, 52, 23], Operations: [] Exploring Operation: 34*52=1768, Resulting Numbers: [26, 23, 1768] Generated Node #2: [26, 23, 1768] from Operation: 34*52=1768 Current State: 45:[26, 23, 1768], Operations: ['34*52=1768'] Exploring Operation: 1768/26=68, Resulting Numbers: [23, 68] Generated Node #3: [23, 68] from Operation: 1768/26=68 Current State: 45:[23, 68], Operations: ['34*52=1768', '1768/26=68'] Exploring Operation: 68-23=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[34, 26, 52, 23], Operations: [] Exploring Operation: 34-23=11, Resulting Numbers: [26, 52, 11] Generated Node #0,0: 45:[26, 52, 11] Operation: 34-23=11 Exploring Operation: 26-23=3, Resulting Numbers: [34, 52, 3] Generated Node #0,1: 45:[34, 52, 3] Operation: 26-23=3 Exploring Operation: 52/26=2, Resulting Numbers: [34, 23, 2] Generated Node #0,2: 45:[34, 23, 2] Operation: 52/26=2 Exploring Operation: 34-26=8, Resulting Numbers: [52, 23, 8] Generated Node #0,3: 45:[52, 23, 8] Operation: 34-26=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 45:[52, 23, 8], Operations: ['34-26=8'] Exploring Operation: 52-8=44, Resulting Numbers: [23, 44] Generated Node #0,3,0: 45:[23, 44] Operation: 52-8=44 Exploring Operation: 23-8=15, Resulting Numbers: [52, 15] Generated Node #0,3,1: 45:[52, 15] Operation: 23-8=15 Exploring Operation: 23+8=31, Resulting Numbers: [52, 31] Generated Node #0,3,2: 45:[52, 31] Operation: 23+8=31 Exploring Operation: 52-23=29, Resulting Numbers: [8, 29] Generated Node #0,3,3: 45:[8, 29] Operation: 52-23=29 Moving to Node #0,3,1 Current State: 45:[52, 15], Operations: ['34-26=8', '23-8=15'] Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,45 unequal: No Solution Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,45 unequal: No Solution Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[23, 44], Operations: ['34-26=8', '52-8=44'] Exploring Operation: 23*44=1012, Resulting Numbers: [1012] 1012,45 unequal: No Solution Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,45 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[8, 29], Operations: ['34-26=8', '52-23=29'] Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,45 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[52, 31], Operations: ['34-26=8', '23+8=31'] Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,45 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[34, 52, 3], Operations: ['26-23=3'] Exploring Operation: 52-34=18, Resulting Numbers: [3, 18] Generated Node #0,1,0: 45:[3, 18] Operation: 52-34=18 Exploring Operation: 52-3=49, Resulting Numbers: [34, 49] Generated Node #0,1,1: 45:[34, 49] Operation: 52-3=49 Exploring Operation: 34+3=37, Resulting Numbers: [52, 37] Generated Node #0,1,2: 45:[52, 37] Operation: 34+3=37 Exploring Operation: 34-3=31, Resulting Numbers: [52, 31] Generated Node #0,1,3: 45:[52, 31] Operation: 34-3=31 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[3, 18], Operations: ['26-23=3', '52-34=18'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[34, 49], Operations: ['26-23=3', '52-3=49'] Exploring Operation: 34*49=1666, Resulting Numbers: [1666] 1666,45 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 45:[52, 37], Operations: ['26-23=3', '34+3=37'] Exploring Operation: 52+37=89, Resulting Numbers: [89] 89,45 unequal: No Solution Exploring Operation: 52*37=1924, Resulting Numbers: [1924] 1924,45 unequal: No Solution Exploring Operation: 52-37=15, Resulting Numbers: [15] 15,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 45:[52, 31], Operations: ['26-23=3', '34-3=31'] Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,45 unequal: No Solution Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[26, 52, 11], Operations: ['34-23=11'] Exploring Operation: 26-11=15, Resulting Numbers: [52, 15] Generated Node #0,0,0: 45:[52, 15] Operation: 26-11=15 Exploring Operation: 52/26=2, Resulting Numbers: [11, 2] Generated Node #0,0,1: 45:[11, 2] Operation: 52/26=2 Exploring Operation: 26+11=37, Resulting Numbers: [52, 37] Generated Node #0,0,2: 45:[52, 37] Operation: 26+11=37 Exploring Operation: 52-26=26, Resulting Numbers: [11, 26] Generated Node #0,0,3: 45:[11, 26] Operation: 52-26=26 Moving to Node #0,0,1 Current State: 45:[11, 2], Operations: ['34-23=11', '52/26=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[52, 15], Operations: ['34-23=11', '26-11=15'] Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,45 unequal: No Solution Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,45 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[11, 26], Operations: ['34-23=11', '52-26=26'] Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,45 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[52, 37], Operations: ['34-23=11', '26+11=37'] Exploring Operation: 52*37=1924, Resulting Numbers: [1924] 1924,45 unequal: No Solution Exploring Operation: 52-37=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 52+37=89, Resulting Numbers: [89] 89,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[34, 23, 2], Operations: ['52/26=2'] Exploring Operation: 34-23=11, Resulting Numbers: [2, 11] Generated Node #0,2,0: 45:[2, 11] Operation: 34-23=11 Exploring Operation: 34+23=57, Resulting Numbers: [2, 57] Generated Node #0,2,1: 45:[2, 57] Operation: 34+23=57 Exploring Operation: 23*2=46, Resulting Numbers: [34, 46] Generated Node #0,2,2: 45:[34, 46] Operation: 23*2=46 Exploring Operation: 34/2=17, Resulting Numbers: [23, 17] Generated Node #0,2,3: 45:[23, 17] Operation: 34/2=17 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 45:[2, 11], Operations: ['52/26=2', '34-23=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 45:[23, 17], Operations: ['52/26=2', '34/2=17'] Exploring Operation: 23*17=391, Resulting Numbers: [391] 391,45 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 23+17=40, Resulting Numbers: [40] 40,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 45:[34, 46], Operations: ['52/26=2', '23*2=46'] Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,45 unequal: No Solution Exploring Operation: 34*46=1564, Resulting Numbers: [1564] 1564,45 unequal: No Solution Exploring Operation: 34+46=80, Resulting Numbers: [80] 80,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 45:[2, 57], Operations: ['52/26=2', '34+23=57'] Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,45 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,45 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 43, 14, 2, 5 ]
20
[ "43*2=86", "14+86=100", "100/5=20" ]
Current State: 20:[43, 14, 2, 5], Operations: [] Exploring Operation: 43*2=86, Resulting Numbers: [14, 5, 86] Generated Node #2: [14, 5, 86] from Operation: 43*2=86 Current State: 20:[14, 5, 86], Operations: ['43*2=86'] Exploring Operation: 14+86=100, Resulting Numbers: [5, 100] Generated Node #3: [5, 100] from Operation: 14+86=100 Current State: 20:[5, 100], Operations: ['43*2=86', '14+86=100'] Exploring Operation: 100/5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[43, 14, 2, 5], Operations: [] Exploring Operation: 43-14=29, Resulting Numbers: [2, 5, 29] Generated Node #0,0: 20:[2, 5, 29] Operation: 43-14=29 Moving to Node #0,0 Current State: 20:[2, 5, 29], Operations: ['43-14=29'] Exploring Operation: 29-5=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 20:[2, 24] Operation: 29-5=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[2, 24], Operations: ['43-14=29', '29-5=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,20 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
[ 68, 40, 8, 61 ]
25
[ "68-40=28", "61-8=53", "53-28=25" ]
Current State: 25:[68, 40, 8, 61], Operations: [] Exploring Operation: 68-40=28, Resulting Numbers: [8, 61, 28] Generated Node #2: [8, 61, 28] from Operation: 68-40=28 Current State: 25:[8, 61, 28], Operations: ['68-40=28'] Exploring Operation: 61-8=53, Resulting Numbers: [28, 53] Generated Node #3: [28, 53] from Operation: 61-8=53 Current State: 25:[28, 53], Operations: ['68-40=28', '61-8=53'] Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[68, 40, 8, 61], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [68, 61, 5] Generated Node #0,0: 25:[68, 61, 5] Operation: 40/8=5 Exploring Operation: 68-40=28, Resulting Numbers: [8, 61, 28] Generated Node #0,1: 25:[8, 61, 28] Operation: 68-40=28 Exploring Operation: 61-40=21, Resulting Numbers: [68, 8, 21] Generated Node #0,2: 25:[68, 8, 21] Operation: 61-40=21 Exploring Operation: 68-61=7, Resulting Numbers: [40, 8, 7] Generated Node #0,3: 25:[40, 8, 7] Operation: 68-61=7 Moving to Node #0,3 Current State: 25:[40, 8, 7], Operations: ['68-61=7'] Exploring Operation: 40-8=32, Resulting Numbers: [7, 32] Generated Node #0,3,0: 25:[7, 32] Operation: 40-8=32 Exploring Operation: 40-7=33, Resulting Numbers: [8, 33] Generated Node #0,3,1: 25:[8, 33] Operation: 40-7=33 Exploring Operation: 8-7=1, Resulting Numbers: [40, 1] Generated Node #0,3,2: 25:[40, 1] Operation: 8-7=1 Exploring Operation: 40/8=5, Resulting Numbers: [7, 5] Generated Node #0,3,3: 25:[7, 5] Operation: 40/8=5 Moving to Node #0,1 Current State: 25:[8, 61, 28], Operations: ['68-40=28'] Exploring Operation: 28-8=20, Resulting Numbers: [61, 20] Generated Node #0,1,0: 25:[61, 20] Operation: 28-8=20 Exploring Operation: 61-28=33, Resulting Numbers: [8, 33] Generated Node #0,1,1: 25:[8, 33] Operation: 61-28=33 Exploring Operation: 8+61=69, Resulting Numbers: [28, 69] Generated Node #0,1,2: 25:[28, 69] Operation: 8+61=69 Exploring Operation: 61-8=53, Resulting Numbers: [28, 53] Generated Node #0,1,3: 25:[28, 53] Operation: 61-8=53 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[8, 33], Operations: ['68-40=28', '61-28=33'] Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[68, 40, 8, 61], Operations: [] Exploring Operation: 68-40=28, Resulting Numbers: [8, 61, 28] Generated Node #0,1: 25:[8, 61, 28] Operation: 68-40=28 Moving to Node #0,1 Current State: 25:[8, 61, 28], Operations: ['68-40=28'] Exploring Operation: 61-28=33, Resulting Numbers: [8, 33] Generated Node #0,1,1: 25:[8, 33] Operation: 61-28=33 Moving to Node #0,1,1 Current State: 25:[8, 33], Operations: ['68-40=28', '61-28=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 85, 10, 83, 77 ]
72
[ "85-83=2", "10/2=5", "77-5=72" ]
Current State: 72:[85, 10, 83, 77], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [10, 77, 2] Generated Node #2: [10, 77, 2] from Operation: 85-83=2 Current State: 72:[10, 77, 2], Operations: ['85-83=2'] Exploring Operation: 10/2=5, Resulting Numbers: [77, 5] Generated Node #3: [77, 5] from Operation: 10/2=5 Current State: 72:[77, 5], Operations: ['85-83=2', '10/2=5'] Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[85, 10, 83, 77], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [10, 77, 2] Generated Node #0,0: 72:[10, 77, 2] Operation: 85-83=2 Exploring Operation: 85-77=8, Resulting Numbers: [10, 83, 8] Generated Node #0,1: 72:[10, 83, 8] Operation: 85-77=8 Moving to Node #0,0 Current State: 72:[10, 77, 2], Operations: ['85-83=2'] Exploring Operation: 77-2=75, Resulting Numbers: [10, 75] Generated Node #0,0,0: 72:[10, 75] Operation: 77-2=75 Exploring Operation: 77-10=67, Resulting Numbers: [2, 67] Generated Node #0,0,1: 72:[2, 67] Operation: 77-10=67 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[10, 75], Operations: ['85-83=2', '77-2=75'] Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,72 unequal: No Solution Exploring Operation: 10+75=85, Resulting Numbers: [85] 85,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[2, 67], Operations: ['85-83=2', '77-10=67'] Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,72 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,72 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: 72:[10, 83, 8], Operations: ['85-77=8'] Exploring Operation: 83-8=75, Resulting Numbers: [10, 75] Generated Node #0,1,0: 72:[10, 75] Operation: 83-8=75 Exploring Operation: 83-10=73, Resulting Numbers: [8, 73] Generated Node #0,1,1: 72:[8, 73] Operation: 83-10=73 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[8, 73], Operations: ['85-77=8', '83-10=73'] Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,72 unequal: No Solution Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[10, 75], Operations: ['85-77=8', '83-8=75'] Exploring Operation: 10+75=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 13, 80, 85, 96 ]
40
[ "13+85=98", "98-96=2", "80/2=40" ]
Current State: 40:[13, 80, 85, 96], Operations: [] Exploring Operation: 13+85=98, Resulting Numbers: [80, 96, 98] Generated Node #2: [80, 96, 98] from Operation: 13+85=98 Current State: 40:[80, 96, 98], Operations: ['13+85=98'] Exploring Operation: 98-96=2, Resulting Numbers: [80, 2] Generated Node #3: [80, 2] from Operation: 98-96=2 Current State: 40:[80, 2], Operations: ['13+85=98', '98-96=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[13, 80, 85, 96], Operations: [] Exploring Operation: 85-80=5, Resulting Numbers: [13, 96, 5] Generated Node #0,0: 40:[13, 96, 5] Operation: 85-80=5 Exploring Operation: 85-13=72, Resulting Numbers: [80, 96, 72] Generated Node #0,1: 40:[80, 96, 72] Operation: 85-13=72 Exploring Operation: 96-85=11, Resulting Numbers: [13, 80, 11] Generated Node #0,2: 40:[13, 80, 11] Operation: 96-85=11 Exploring Operation: 80-13=67, Resulting Numbers: [85, 96, 67] Generated Node #0,3: 40:[85, 96, 67] Operation: 80-13=67 Exploring Operation: 96-80=16, Resulting Numbers: [13, 85, 16] Generated Node #0,4: 40:[13, 85, 16] Operation: 96-80=16 Moving to Node #0,2 Current State: 40:[13, 80, 11], Operations: ['96-85=11'] Exploring Operation: 13-11=2, Resulting Numbers: [80, 2] Generated Node #0,2,0: 40:[80, 2] Operation: 13-11=2 Exploring Operation: 13+11=24, Resulting Numbers: [80, 24] Generated Node #0,2,1: 40:[80, 24] Operation: 13+11=24 Exploring Operation: 13+80=93, Resulting Numbers: [11, 93] Generated Node #0,2,2: 40:[11, 93] Operation: 13+80=93 Exploring Operation: 80-11=69, Resulting Numbers: [13, 69] Generated Node #0,2,3: 40:[13, 69] Operation: 80-11=69 Exploring Operation: 80-13=67, Resulting Numbers: [11, 67] Generated Node #0,2,4: 40:[11, 67] Operation: 80-13=67 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 40:[11, 67], Operations: ['96-85=11', '80-13=67'] Exploring Operation: 11+67=78, Resulting Numbers: [78] 78,40 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 11*67=737, Resulting Numbers: [737] 737,40 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 #0,2,3 Current State: 40:[13, 69], Operations: ['96-85=11', '80-11=69'] Exploring Operation: 13+69=82, Resulting Numbers: [82] 82,40 unequal: No Solution Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 13*69=897, Resulting Numbers: [897] 897,40 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 #0,2,0 Current State: 40:[80, 2], Operations: ['96-85=11', '13-11=2'] Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,40 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[13, 80, 85, 96], Operations: [] Exploring Operation: 96-85=11, Resulting Numbers: [13, 80, 11] Generated Node #0,2: 40:[13, 80, 11] Operation: 96-85=11 Moving to Node #0,2 Current State: 40:[13, 80, 11], Operations: ['96-85=11'] Exploring Operation: 13-11=2, Resulting Numbers: [80, 2] Generated Node #0,2,0: 40:[80, 2] Operation: 13-11=2 Moving to Node #0,2,0 Current State: 40:[80, 2], Operations: ['96-85=11', '13-11=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 2, 51, 71, 68 ]
90
[ "51-2=49", "71+68=139", "139-49=90" ]
Current State: 90:[2, 51, 71, 68], Operations: [] Exploring Operation: 51-2=49, Resulting Numbers: [71, 68, 49] Generated Node #2: [71, 68, 49] from Operation: 51-2=49 Current State: 90:[71, 68, 49], Operations: ['51-2=49'] Exploring Operation: 71+68=139, Resulting Numbers: [49, 139] Generated Node #3: [49, 139] from Operation: 71+68=139 Current State: 90:[49, 139], Operations: ['51-2=49', '71+68=139'] Exploring Operation: 139-49=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[2, 51, 71, 68], Operations: [] Exploring Operation: 71-68=3, Resulting Numbers: [2, 51, 3] Generated Node #0,0: 90:[2, 51, 3] Operation: 71-68=3 Exploring Operation: 68-51=17, Resulting Numbers: [2, 71, 17] Generated Node #0,1: 90:[2, 71, 17] Operation: 68-51=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[2, 51, 3], Operations: ['71-68=3'] Exploring Operation: 51-3=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 90:[2, 48] Operation: 51-3=48 Exploring Operation: 51/3=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 90:[2, 17] Operation: 51/3=17 Moving to Node #0,0,1 Current State: 90:[2, 17], Operations: ['71-68=3', '51/3=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[2, 48], Operations: ['71-68=3', '51-3=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[2, 71, 17], Operations: ['68-51=17'] Exploring Operation: 71+17=88, Resulting Numbers: [2, 88] Generated Node #0,1,0: 90:[2, 88] Operation: 71+17=88 Exploring Operation: 71-17=54, Resulting Numbers: [2, 54] Generated Node #0,1,1: 90:[2, 54] Operation: 71-17=54 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[2, 88], Operations: ['68-51=17', '71+17=88'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,90 unequal: No Solution Exploring Operation: 2+88=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[2, 51, 71, 68], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [2, 71, 17] Generated Node #0,1: 90:[2, 71, 17] Operation: 68-51=17 Moving to Node #0,1 Current State: 90:[2, 71, 17], Operations: ['68-51=17'] Exploring Operation: 71+17=88, Resulting Numbers: [2, 88] Generated Node #0,1,0: 90:[2, 88] Operation: 71+17=88 Moving to Node #0,1,0 Current State: 90:[2, 88], Operations: ['68-51=17', '71+17=88'] Exploring Operation: 2+88=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 19, 4, 41, 82 ]
35
[ "19*4=76", "82-41=41", "76-41=35" ]
Current State: 35:[19, 4, 41, 82], Operations: [] Exploring Operation: 19*4=76, Resulting Numbers: [41, 82, 76] Generated Node #2: [41, 82, 76] from Operation: 19*4=76 Current State: 35:[41, 82, 76], Operations: ['19*4=76'] Exploring Operation: 82-41=41, Resulting Numbers: [76, 41] Generated Node #3: [76, 41] from Operation: 82-41=41 Current State: 35:[76, 41], Operations: ['19*4=76', '82-41=41'] Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[19, 4, 41, 82], Operations: [] Exploring Operation: 19-4=15, Resulting Numbers: [41, 82, 15] Generated Node #0,0: 35:[41, 82, 15] Operation: 19-4=15 Exploring Operation: 82-19=63, Resulting Numbers: [4, 41, 63] Generated Node #0,1: 35:[4, 41, 63] Operation: 82-19=63 Exploring Operation: 82/41=2, Resulting Numbers: [19, 4, 2] Generated Node #0,2: 35:[19, 4, 2] Operation: 82/41=2 Exploring Operation: 82-41=41, Resulting Numbers: [19, 4, 41] Generated Node #0,3: 35:[19, 4, 41] Operation: 82-41=41 Moving to Node #0,2 Current State: 35:[19, 4, 2], Operations: ['82/41=2'] Exploring Operation: 19-4=15, Resulting Numbers: [2, 15] Generated Node #0,2,0: 35:[2, 15] Operation: 19-4=15 Exploring Operation: 19*2=38, Resulting Numbers: [4, 38] Generated Node #0,2,1: 35:[4, 38] Operation: 19*2=38 Exploring Operation: 4+2=6, Resulting Numbers: [19, 6] Generated Node #0,2,2: 35:[19, 6] Operation: 4+2=6 Exploring Operation: 19-2=17, Resulting Numbers: [4, 17] Generated Node #0,2,3: 35:[4, 17] Operation: 19-2=17 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 35:[4, 38], Operations: ['82/41=2', '19*2=38'] Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,35 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:[2, 15], Operations: ['82/41=2', '19-4=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,35 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,35 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 #0,2,3 Current State: 35:[4, 17], Operations: ['82/41=2', '19-2=17'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,35 unequal: No Solution Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,35 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:[19, 6], Operations: ['82/41=2', '4+2=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,35 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,35 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: 35:[19, 4, 41], Operations: ['82-41=41'] Exploring Operation: 19-4=15, Resulting Numbers: [41, 15] Generated Node #0,3,0: 35:[41, 15] Operation: 19-4=15 Exploring Operation: 41-4=37, Resulting Numbers: [19, 37] Generated Node #0,3,1: 35:[19, 37] Operation: 41-4=37 Exploring Operation: 41-19=22, Resulting Numbers: [4, 22] Generated Node #0,3,2: 35:[4, 22] Operation: 41-19=22 Exploring Operation: 19+4=23, Resulting Numbers: [41, 23] Generated Node #0,3,3: 35:[41, 23] Operation: 19+4=23 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 35:[41, 15], Operations: ['82-41=41', '19-4=15'] Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 41+15=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 41*15=615, Resulting Numbers: [615] 615,35 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 #0,3,1 Current State: 35:[19, 37], Operations: ['82-41=41', '41-4=37'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,35 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,35 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 #0,3,2 Current State: 35:[4, 22], Operations: ['82-41=41', '41-19=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,35 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,35 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 #0,3,3 Current State: 35:[41, 23], Operations: ['82-41=41', '19+4=23'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,35 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,35 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:[4, 41, 63], Operations: ['82-19=63'] Exploring Operation: 41-4=37, Resulting Numbers: [63, 37] Generated Node #0,1,0: 35:[63, 37] Operation: 41-4=37 Exploring Operation: 4+41=45, Resulting Numbers: [63, 45] Generated Node #0,1,1: 35:[63, 45] Operation: 4+41=45 Exploring Operation: 63-4=59, Resulting Numbers: [41, 59] Generated Node #0,1,2: 35:[41, 59] Operation: 63-4=59 Exploring Operation: 63-41=22, Resulting Numbers: [4, 22] Generated Node #0,1,3: 35:[4, 22] Operation: 63-41=22 Moving to Node #0,0 Current State: 35:[41, 82, 15], Operations: ['19-4=15'] Exploring Operation: 82-15=67, Resulting Numbers: [41, 67] Generated Node #0,0,0: 35:[41, 67] Operation: 82-15=67 Exploring Operation: 82-41=41, Resulting Numbers: [15, 41] Generated Node #0,0,1: 35:[15, 41] Operation: 82-41=41 Exploring Operation: 82/41=2, Resulting Numbers: [15, 2] Generated Node #0,0,2: 35:[15, 2] Operation: 82/41=2 Exploring Operation: 41-15=26, Resulting Numbers: [82, 26] Generated Node #0,0,3: 35:[82, 26] Operation: 41-15=26 Moving to Node #0,0,2 Current State: 35:[15, 2], Operations: ['19-4=15', '82/41=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,35 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[15, 41], Operations: ['19-4=15', '82-41=41'] Exploring Operation: 15+41=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 15*41=615, Resulting Numbers: [615] 615,35 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,35 unequal: No Solution Moving to Node #0,1,3 Current State: 35:[4, 22], Operations: ['82-19=63', '63-41=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,35 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[41, 59], Operations: ['82-19=63', '63-4=59'] Exploring Operation: 41+59=100, Resulting Numbers: [100] 100,35 unequal: No Solution Exploring Operation: 59-41=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 41*59=2419, Resulting Numbers: [2419] 2419,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[63, 37], Operations: ['82-19=63', '41-4=37'] Exploring Operation: 63-37=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 63*37=2331, Resulting Numbers: [2331] 2331,35 unequal: No Solution Exploring Operation: 63+37=100, Resulting Numbers: [100] 100,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[63, 45], Operations: ['82-19=63', '4+41=45'] Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 63*45=2835, Resulting Numbers: [2835] 2835,35 unequal: No Solution Exploring Operation: 63+45=108, Resulting Numbers: [108] 108,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[41, 67], Operations: ['19-4=15', '82-15=67'] Exploring Operation: 41*67=2747, Resulting Numbers: [2747] 2747,35 unequal: No Solution Exploring Operation: 41+67=108, Resulting Numbers: [108] 108,35 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[82, 26], Operations: ['19-4=15', '41-15=26'] Exploring Operation: 82-26=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 82+26=108, Resulting Numbers: [108] 108,35 unequal: No Solution Exploring Operation: 82*26=2132, Resulting Numbers: [2132] 2132,35 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 17, 99, 50, 82 ]
16
[ "17+99=116", "50+82=132", "132-116=16" ]
Current State: 16:[17, 99, 50, 82], Operations: [] Exploring Operation: 17+99=116, Resulting Numbers: [50, 82, 116] Generated Node #2: [50, 82, 116] from Operation: 17+99=116 Current State: 16:[50, 82, 116], Operations: ['17+99=116'] Exploring Operation: 50+82=132, Resulting Numbers: [116, 132] Generated Node #3: [116, 132] from Operation: 50+82=132 Current State: 16:[116, 132], Operations: ['17+99=116', '50+82=132'] Exploring Operation: 132-116=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[17, 99, 50, 82], Operations: [] Exploring Operation: 99-82=17, Resulting Numbers: [17, 50, 17] Generated Node #0,0: 16:[17, 50, 17] Operation: 99-82=17 Moving to Node #0,0 Current State: 16:[17, 50, 17], Operations: ['99-82=17'] Exploring Operation: 50-17=33, Resulting Numbers: [17, 33] Generated Node #0,0,0: 16:[17, 33] Operation: 50-17=33 Moving to Node #0,0,0 Current State: 16:[17, 33], Operations: ['99-82=17', '50-17=33'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[17, 99, 50, 82], Operations: [] Exploring Operation: 99-82=17, Resulting Numbers: [17, 50, 17] Generated Node #0,0: 16:[17, 50, 17] Operation: 99-82=17 Moving to Node #0,0 Current State: 16:[17, 50, 17], Operations: ['99-82=17'] Exploring Operation: 50-17=33, Resulting Numbers: [17, 33] Generated Node #0,0,0: 16:[17, 33] Operation: 50-17=33 Moving to Node #0,0,0 Current State: 16:[17, 33], Operations: ['99-82=17', '50-17=33'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 92, 16, 90, 69 ]
97
[ "92-16=76", "90-69=21", "76+21=97" ]
Current State: 97:[92, 16, 90, 69], Operations: [] Exploring Operation: 92-16=76, Resulting Numbers: [90, 69, 76] Generated Node #2: [90, 69, 76] from Operation: 92-16=76 Current State: 97:[90, 69, 76], Operations: ['92-16=76'] Exploring Operation: 90-69=21, Resulting Numbers: [76, 21] Generated Node #3: [76, 21] from Operation: 90-69=21 Current State: 97:[76, 21], Operations: ['92-16=76', '90-69=21'] Exploring Operation: 76+21=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[92, 16, 90, 69], Operations: [] Exploring Operation: 16+69=85, Resulting Numbers: [92, 90, 85] Generated Node #0,0: 97:[92, 90, 85] Operation: 16+69=85 Exploring Operation: 92+16=108, Resulting Numbers: [90, 69, 108] Generated Node #0,1: 97:[90, 69, 108] Operation: 92+16=108 Exploring Operation: 16+90=106, Resulting Numbers: [92, 69, 106] Generated Node #0,2: 97:[92, 69, 106] Operation: 16+90=106 Moving to Node #0,0 Current State: 97:[92, 90, 85], Operations: ['16+69=85'] Exploring Operation: 90+85=175, Resulting Numbers: [92, 175] Generated Node #0,0,0: 97:[92, 175] Operation: 90+85=175 Exploring Operation: 92+85=177, Resulting Numbers: [90, 177] Generated Node #0,0,1: 97:[90, 177] Operation: 92+85=177 Exploring Operation: 92+90=182, Resulting Numbers: [85, 182] Generated Node #0,0,2: 97:[85, 182] Operation: 92+90=182 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[92, 175], Operations: ['16+69=85', '90+85=175'] Exploring Operation: 175-92=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 92+175=267, Resulting Numbers: [267] 267,97 unequal: No Solution Exploring Operation: 92*175=16100, Resulting Numbers: [16100] 16100,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[90, 177], Operations: ['16+69=85', '92+85=177'] Exploring Operation: 177-90=87, Resulting Numbers: [87] 87,97 unequal: No Solution Exploring Operation: 90+177=267, Resulting Numbers: [267] 267,97 unequal: No Solution Exploring Operation: 90*177=15930, Resulting Numbers: [15930] 15930,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[85, 182], Operations: ['16+69=85', '92+90=182'] Exploring Operation: 182-85=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[92, 16, 90, 69], Operations: [] Exploring Operation: 16+69=85, Resulting Numbers: [92, 90, 85] Generated Node #0,0: 97:[92, 90, 85] Operation: 16+69=85 Moving to Node #0,0 Current State: 97:[92, 90, 85], Operations: ['16+69=85'] Exploring Operation: 92+90=182, Resulting Numbers: [85, 182] Generated Node #0,0,2: 97:[85, 182] Operation: 92+90=182 Moving to Node #0,0,2 Current State: 97:[85, 182], Operations: ['16+69=85', '92+90=182'] Exploring Operation: 182-85=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 80, 59, 3, 56 ]
71
[ "59-56=3", "3*3=9", "80-9=71" ]
Current State: 71:[80, 59, 3, 56], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [80, 3, 3] Generated Node #2: [80, 3, 3] from Operation: 59-56=3 Current State: 71:[80, 3, 3], Operations: ['59-56=3'] Exploring Operation: 3*3=9, Resulting Numbers: [80, 9] Generated Node #3: [80, 9] from Operation: 3*3=9 Current State: 71:[80, 9], Operations: ['59-56=3', '3*3=9'] Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[80, 59, 3, 56], Operations: [] Exploring Operation: 59+3=62, Resulting Numbers: [80, 56, 62] Generated Node #0,0: 71:[80, 56, 62] Operation: 59+3=62 Exploring Operation: 80-3=77, Resulting Numbers: [59, 56, 77] Generated Node #0,1: 71:[59, 56, 77] Operation: 80-3=77 Exploring Operation: 3+56=59, Resulting Numbers: [80, 59, 59] Generated Node #0,2: 71:[80, 59, 59] Operation: 3+56=59 Exploring Operation: 80+3=83, Resulting Numbers: [59, 56, 83] Generated Node #0,3: 71:[59, 56, 83] Operation: 80+3=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[80, 56, 62], Operations: ['59+3=62'] Exploring Operation: 80-56=24, Resulting Numbers: [62, 24] Generated Node #0,0,0: 71:[62, 24] Operation: 80-56=24 Exploring Operation: 80+56=136, Resulting Numbers: [62, 136] Generated Node #0,0,1: 71:[62, 136] Operation: 80+56=136 Exploring Operation: 56+62=118, Resulting Numbers: [80, 118] Generated Node #0,0,2: 71:[80, 118] Operation: 56+62=118 Exploring Operation: 80-62=18, Resulting Numbers: [56, 18] Generated Node #0,0,3: 71:[56, 18] Operation: 80-62=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[62, 24], Operations: ['59+3=62', '80-56=24'] Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,71 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,71 unequal: No Solution No 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: 71:[80, 118], Operations: ['59+3=62', '56+62=118'] Exploring Operation: 118-80=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 80+118=198, Resulting Numbers: [198] 198,71 unequal: No Solution Exploring Operation: 80*118=9440, Resulting Numbers: [9440] 9440,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 71:[56, 18], Operations: ['59+3=62', '80-62=18'] Exploring Operation: 56+18=74, Resulting Numbers: [74] 74,71 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 56*18=1008, Resulting Numbers: [1008] 1008,71 unequal: No Solution No 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: 71:[62, 136], Operations: ['59+3=62', '80+56=136'] Exploring Operation: 136-62=74, Resulting Numbers: [74] 74,71 unequal: No Solution Exploring Operation: 62*136=8432, Resulting Numbers: [8432] 8432,71 unequal: No Solution Exploring Operation: 62+136=198, Resulting Numbers: [198] 198,71 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: 71:[59, 56, 77], Operations: ['80-3=77'] Exploring Operation: 59-56=3, Resulting Numbers: [77, 3] Generated Node #0,1,0: 71:[77, 3] Operation: 59-56=3 Exploring Operation: 59+56=115, Resulting Numbers: [77, 115] Generated Node #0,1,1: 71:[77, 115] Operation: 59+56=115 Exploring Operation: 77-59=18, Resulting Numbers: [56, 18] Generated Node #0,1,2: 71:[56, 18] Operation: 77-59=18 Exploring Operation: 77-56=21, Resulting Numbers: [59, 21] Generated Node #0,1,3: 71:[59, 21] Operation: 77-56=21 Moving to Node #0,1,1 Current State: 71:[77, 115], Operations: ['80-3=77', '59+56=115'] Exploring Operation: 77*115=8855, Resulting Numbers: [8855] 8855,71 unequal: No Solution Exploring Operation: 115-77=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 77+115=192, Resulting Numbers: [192] 192,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[59, 21], Operations: ['80-3=77', '77-56=21'] Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 59*21=1239, Resulting Numbers: [1239] 1239,71 unequal: No Solution Exploring Operation: 59+21=80, Resulting Numbers: [80] 80,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[56, 18], Operations: ['80-3=77', '77-59=18'] Exploring Operation: 56*18=1008, Resulting Numbers: [1008] 1008,71 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 56+18=74, Resulting Numbers: [74] 74,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[77, 3], Operations: ['80-3=77', '59-56=3'] Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,71 unequal: No Solution Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,71 unequal: No Solution Exploring Operation: 77*3=231, Resulting Numbers: [231] 231,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[80, 59, 59], Operations: ['3+56=59'] Exploring Operation: 59+59=118, Resulting Numbers: [80, 118] Generated Node #0,2,0: 71:[80, 118] Operation: 59+59=118 Exploring Operation: 80-59=21, Resulting Numbers: [59, 21] Generated Node #0,2,1: 71:[59, 21] Operation: 80-59=21 Exploring Operation: 80-59=21, Resulting Numbers: [59, 21] Generated Node #0,2,2: 71:[59, 21] Operation: 80-59=21 Exploring Operation: 59/59=1, Resulting Numbers: [80, 1] Generated Node #0,2,3: 71:[80, 1] Operation: 59/59=1 Moving to Node #0,2,0 Current State: 71:[80, 118], Operations: ['3+56=59', '59+59=118'] Exploring Operation: 80+118=198, Resulting Numbers: [198] 198,71 unequal: No Solution Exploring Operation: 118-80=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 80*118=9440, Resulting Numbers: [9440] 9440,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[59, 21], Operations: ['3+56=59', '80-59=21'] Exploring Operation: 59+21=80, Resulting Numbers: [80] 80,71 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 59*21=1239, Resulting Numbers: [1239] 1239,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[59, 21], Operations: ['3+56=59', '80-59=21'] Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,71 unequal: No Solution Exploring Operation: 59*21=1239, Resulting Numbers: [1239] 1239,71 unequal: No Solution Exploring Operation: 59+21=80, Resulting Numbers: [80] 80,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[80, 1], Operations: ['3+56=59', '59/59=1'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,71 unequal: No Solution Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,71 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,71 unequal: No Solution Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,71 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 #0,3 Current State: 71:[59, 56, 83], Operations: ['80+3=83'] Exploring Operation: 83-59=24, Resulting Numbers: [56, 24] Generated Node #0,3,0: 71:[56, 24] Operation: 83-59=24 Exploring Operation: 83-56=27, Resulting Numbers: [59, 27] Generated Node #0,3,1: 71:[59, 27] Operation: 83-56=27 Exploring Operation: 59-56=3, Resulting Numbers: [83, 3] Generated Node #0,3,2: 71:[83, 3] Operation: 59-56=3 Exploring Operation: 59+56=115, Resulting Numbers: [83, 115] Generated Node #0,3,3: 71:[83, 115] Operation: 59+56=115 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 71:[59, 27], Operations: ['80+3=83', '83-56=27'] Exploring Operation: 59*27=1593, Resulting Numbers: [1593] 1593,71 unequal: No Solution Exploring Operation: 59+27=86, Resulting Numbers: [86] 86,71 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,71 unequal: No Solution No 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: 71:[83, 115], Operations: ['80+3=83', '59+56=115'] Exploring Operation: 115-83=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 83*115=9545, Resulting Numbers: [9545] 9545,71 unequal: No Solution Exploring Operation: 83+115=198, Resulting Numbers: [198] 198,71 unequal: No Solution No 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: 71:[56, 24], Operations: ['80+3=83', '83-59=24'] Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 56*24=1344, Resulting Numbers: [1344] 1344,71 unequal: No Solution Exploring Operation: 56+24=80, Resulting Numbers: [80] 80,71 unequal: No Solution No 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: 71:[83, 3], Operations: ['80+3=83', '59-56=3'] Exploring Operation: 83*3=249, Resulting Numbers: [249] 249,71 unequal: No Solution Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,71 unequal: No Solution Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 21, 22, 49, 7 ]
85
[ "21+22=43", "49-7=42", "43+42=85" ]
Current State: 85:[21, 22, 49, 7], Operations: [] Exploring Operation: 21+22=43, Resulting Numbers: [49, 7, 43] Generated Node #2: [49, 7, 43] from Operation: 21+22=43 Current State: 85:[49, 7, 43], Operations: ['21+22=43'] Exploring Operation: 49-7=42, Resulting Numbers: [43, 42] Generated Node #3: [43, 42] from Operation: 49-7=42 Current State: 85:[43, 42], Operations: ['21+22=43', '49-7=42'] Exploring Operation: 43+42=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[21, 22, 49, 7], Operations: [] Exploring Operation: 22+49=71, Resulting Numbers: [21, 7, 71] Generated Node #0,0: 85:[21, 7, 71] Operation: 22+49=71 Exploring Operation: 49-22=27, Resulting Numbers: [21, 7, 27] Generated Node #0,1: 85:[21, 7, 27] Operation: 49-22=27 Exploring Operation: 21+49=70, Resulting Numbers: [22, 7, 70] Generated Node #0,2: 85:[22, 7, 70] Operation: 21+49=70 Exploring Operation: 49-21=28, Resulting Numbers: [22, 7, 28] Generated Node #0,3: 85:[22, 7, 28] Operation: 49-21=28 Exploring Operation: 49/7=7, Resulting Numbers: [21, 22, 7] Generated Node #0,4: 85:[21, 22, 7] Operation: 49/7=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 85:[21, 22, 7], Operations: ['49/7=7'] Exploring Operation: 22-21=1, Resulting Numbers: [7, 1] Generated Node #0,4,0: 85:[7, 1] Operation: 22-21=1 Exploring Operation: 21+7=28, Resulting Numbers: [22, 28] Generated Node #0,4,1: 85:[22, 28] Operation: 21+7=28 Exploring Operation: 22-7=15, Resulting Numbers: [21, 15] Generated Node #0,4,2: 85:[21, 15] Operation: 22-7=15 Exploring Operation: 21-7=14, Resulting Numbers: [22, 14] Generated Node #0,4,3: 85:[22, 14] Operation: 21-7=14 Exploring Operation: 21/7=3, Resulting Numbers: [22, 3] Generated Node #0,4,4: 85:[22, 3] Operation: 21/7=3 Moving to Node #0,4,0 Current State: 85:[7, 1], Operations: ['49/7=7', '22-21=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[21, 15], Operations: ['49/7=7', '22-7=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,85 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,85 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[22, 3], Operations: ['49/7=7', '21/7=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,85 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[22, 14], Operations: ['49/7=7', '21-7=14'] Exploring Operation: 22*14=308, Resulting Numbers: [308] 308,85 unequal: No Solution Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,85 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[22, 28], Operations: ['49/7=7', '21+7=28'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,85 unequal: No Solution Exploring Operation: 22*28=616, Resulting Numbers: [616] 616,85 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 #0,1 Current State: 85:[21, 7, 27], Operations: ['49-22=27'] Exploring Operation: 21/7=3, Resulting Numbers: [27, 3] Generated Node #0,1,0: 85:[27, 3] Operation: 21/7=3 Exploring Operation: 21-7=14, Resulting Numbers: [27, 14] Generated Node #0,1,1: 85:[27, 14] Operation: 21-7=14 Exploring Operation: 21+7=28, Resulting Numbers: [27, 28] Generated Node #0,1,2: 85:[27, 28] Operation: 21+7=28 Exploring Operation: 27-21=6, Resulting Numbers: [7, 6] Generated Node #0,1,3: 85:[7, 6] Operation: 27-21=6 Exploring Operation: 27-7=20, Resulting Numbers: [21, 20] Generated Node #0,1,4: 85:[21, 20] Operation: 27-7=20 Moving to Node #0,1,3 Current State: 85:[7, 6], Operations: ['49-22=27', '27-21=6'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,85 unequal: No Solution Moving to Node #0,1,4 Current State: 85:[21, 20], Operations: ['49-22=27', '27-7=20'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,85 unequal: No Solution Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[27, 3], Operations: ['49-22=27', '21/7=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,85 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[27, 14], Operations: ['49-22=27', '21-7=14'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 27+14=41, Resulting Numbers: [41] 41,85 unequal: No Solution Exploring Operation: 27*14=378, Resulting Numbers: [378] 378,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[27, 28], Operations: ['49-22=27', '21+7=28'] Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,85 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[22, 7, 28], Operations: ['49-21=28'] Exploring Operation: 22-7=15, Resulting Numbers: [28, 15] Generated Node #0,3,0: 85:[28, 15] Operation: 22-7=15 Exploring Operation: 28/7=4, Resulting Numbers: [22, 4] Generated Node #0,3,1: 85:[22, 4] Operation: 28/7=4 Exploring Operation: 28-22=6, Resulting Numbers: [7, 6] Generated Node #0,3,2: 85:[7, 6] Operation: 28-22=6 Exploring Operation: 28-7=21, Resulting Numbers: [22, 21] Generated Node #0,3,3: 85:[22, 21] Operation: 28-7=21 Exploring Operation: 22+7=29, Resulting Numbers: [28, 29] Generated Node #0,3,4: 85:[28, 29] Operation: 22+7=29 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 85:[7, 6], Operations: ['49-21=28', '28-22=6'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,85 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 #0,3,1 Current State: 85:[22, 4], Operations: ['49-21=28', '28/7=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,85 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,85 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 #0,3,3 Current State: 85:[22, 21], Operations: ['49-21=28', '28-7=21'] Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 22*21=462, Resulting Numbers: [462] 462,85 unequal: No Solution Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,85 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 #0,3,0 Current State: 85:[28, 15], Operations: ['49-21=28', '22-7=15'] Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,85 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,85 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 #0,3,4 Current State: 85:[28, 29], Operations: ['49-21=28', '22+7=29'] Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,85 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[21, 7, 71], Operations: ['22+49=71'] Exploring Operation: 21+7=28, Resulting Numbers: [71, 28] Generated Node #0,0,0: 85:[71, 28] Operation: 21+7=28 Exploring Operation: 21-7=14, Resulting Numbers: [71, 14] Generated Node #0,0,1: 85:[71, 14] Operation: 21-7=14 Exploring Operation: 7+71=78, Resulting Numbers: [21, 78] Generated Node #0,0,2: 85:[21, 78] Operation: 7+71=78 Exploring Operation: 21+71=92, Resulting Numbers: [7, 92] Generated Node #0,0,3: 85:[7, 92] Operation: 21+71=92 Exploring Operation: 21/7=3, Resulting Numbers: [71, 3] Generated Node #0,0,4: 85:[71, 3] Operation: 21/7=3 Moving to Node #0,0,3 Current State: 85:[7, 92], Operations: ['22+49=71', '21+71=92'] Exploring Operation: 7*92=644, Resulting Numbers: [644] 644,85 unequal: No Solution Exploring Operation: 7+92=99, Resulting Numbers: [99] 99,85 unequal: No Solution Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[21, 22, 49, 7], Operations: [] Exploring Operation: 22+49=71, Resulting Numbers: [21, 7, 71] Generated Node #0,0: 85:[21, 7, 71] Operation: 22+49=71 Moving to Node #0,0 Current State: 85:[21, 7, 71], Operations: ['22+49=71'] Exploring Operation: 21+71=92, Resulting Numbers: [7, 92] Generated Node #0,0,3: 85:[7, 92] Operation: 21+71=92 Moving to Node #0,0,3 Current State: 85:[7, 92], Operations: ['22+49=71', '21+71=92'] Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.931424
hs_5
mult_heuristic
[ 46, 59, 24, 37 ]
44
[ "46+59=105", "24+37=61", "105-61=44" ]
Current State: 44:[46, 59, 24, 37], Operations: [] Exploring Operation: 46+59=105, Resulting Numbers: [24, 37, 105] Generated Node #2: [24, 37, 105] from Operation: 46+59=105 Current State: 44:[24, 37, 105], Operations: ['46+59=105'] Exploring Operation: 24+37=61, Resulting Numbers: [105, 61] Generated Node #3: [105, 61] from Operation: 24+37=61 Current State: 44:[105, 61], Operations: ['46+59=105', '24+37=61'] Exploring Operation: 105-61=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[46, 59, 24, 37], Operations: [] Exploring Operation: 59-37=22, Resulting Numbers: [46, 24, 22] Generated Node #0,0: 44:[46, 24, 22] Operation: 59-37=22 Moving to Node #0,0 Current State: 44:[46, 24, 22], Operations: ['59-37=22'] Exploring Operation: 46-24=22, Resulting Numbers: [22, 22] Generated Node #0,0,0: 44:[22, 22] Operation: 46-24=22 Moving to Node #0,0,0 Current State: 44:[22, 22], Operations: ['59-37=22', '46-24=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[46, 59, 24, 37], Operations: [] Exploring Operation: 59-37=22, Resulting Numbers: [46, 24, 22] Generated Node #0,0: 44:[46, 24, 22] Operation: 59-37=22 Moving to Node #0,0 Current State: 44:[46, 24, 22], Operations: ['59-37=22'] Exploring Operation: 46-24=22, Resulting Numbers: [22, 22] Generated Node #0,0,0: 44:[22, 22] Operation: 46-24=22 Moving to Node #0,0,0 Current State: 44:[22, 22], Operations: ['59-37=22', '46-24=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 2, 18, 11, 16 ]
79
[ "18+16=34", "2*34=68", "11+68=79" ]
Current State: 79:[2, 18, 11, 16], Operations: [] Exploring Operation: 18+16=34, Resulting Numbers: [2, 11, 34] Generated Node #2: [2, 11, 34] from Operation: 18+16=34 Current State: 79:[2, 11, 34], Operations: ['18+16=34'] Exploring Operation: 2*34=68, Resulting Numbers: [11, 68] Generated Node #3: [11, 68] from Operation: 2*34=68 Current State: 79:[11, 68], Operations: ['18+16=34', '2*34=68'] Exploring Operation: 11+68=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[2, 18, 11, 16], Operations: [] Exploring Operation: 2*18=36, Resulting Numbers: [11, 16, 36] Generated Node #0,0: 79:[11, 16, 36] Operation: 2*18=36 Exploring Operation: 2*16=32, Resulting Numbers: [18, 11, 32] Generated Node #0,1: 79:[18, 11, 32] Operation: 2*16=32 Exploring Operation: 2+11=13, Resulting Numbers: [18, 16, 13] Generated Node #0,2: 79:[18, 16, 13] Operation: 2+11=13 Exploring Operation: 2*11=22, Resulting Numbers: [18, 16, 22] Generated Node #0,3: 79:[18, 16, 22] Operation: 2*11=22 Exploring Operation: 2+18=20, Resulting Numbers: [11, 16, 20] Generated Node #0,4: 79:[11, 16, 20] Operation: 2+18=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[11, 16, 36], Operations: ['2*18=36'] Exploring Operation: 16-11=5, Resulting Numbers: [36, 5] Generated Node #0,0,0: 79:[36, 5] Operation: 16-11=5 Exploring Operation: 11+36=47, Resulting Numbers: [16, 47] Generated Node #0,0,1: 79:[16, 47] Operation: 11+36=47 Exploring Operation: 36-11=25, Resulting Numbers: [16, 25] Generated Node #0,0,2: 79:[16, 25] Operation: 36-11=25 Exploring Operation: 11+16=27, Resulting Numbers: [36, 27] Generated Node #0,0,3: 79:[36, 27] Operation: 11+16=27 Exploring Operation: 16+36=52, Resulting Numbers: [11, 52] Generated Node #0,0,4: 79:[11, 52] Operation: 16+36=52 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[16, 47], Operations: ['2*18=36', '11+36=47'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 16*47=752, Resulting Numbers: [752] 752,79 unequal: No Solution Exploring Operation: 16+47=63, Resulting Numbers: [63] 63,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 79:[36, 27], Operations: ['2*18=36', '11+16=27'] Exploring Operation: 36+27=63, Resulting Numbers: [63] 63,79 unequal: No Solution Exploring Operation: 36*27=972, Resulting Numbers: [972] 972,79 unequal: No Solution Exploring Operation: 36-27=9, Resulting Numbers: [9] 9,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 79:[11, 52], Operations: ['2*18=36', '16+36=52'] Exploring Operation: 11*52=572, Resulting Numbers: [572] 572,79 unequal: No Solution Exploring Operation: 11+52=63, Resulting Numbers: [63] 63,79 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[36, 5], Operations: ['2*18=36', '16-11=5'] Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 36*5=180, Resulting Numbers: [180] 180,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[16, 25], Operations: ['2*18=36', '36-11=25'] Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,79 unequal: No Solution Exploring Operation: 16*25=400, Resulting Numbers: [400] 400,79 unequal: No Solution Exploring Operation: 16+25=41, Resulting Numbers: [41] 41,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[18, 11, 32], Operations: ['2*16=32'] Exploring Operation: 32-11=21, Resulting Numbers: [18, 21] Generated Node #0,1,0: 79:[18, 21] Operation: 32-11=21 Exploring Operation: 18+32=50, Resulting Numbers: [11, 50] Generated Node #0,1,1: 79:[11, 50] Operation: 18+32=50 Exploring Operation: 18+11=29, Resulting Numbers: [32, 29] Generated Node #0,1,2: 79:[32, 29] Operation: 18+11=29 Exploring Operation: 11+32=43, Resulting Numbers: [18, 43] Generated Node #0,1,3: 79:[18, 43] Operation: 11+32=43 Exploring Operation: 18-11=7, Resulting Numbers: [32, 7] Generated Node #0,1,4: 79:[32, 7] Operation: 18-11=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 79:[11, 50], Operations: ['2*16=32', '18+32=50'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,79 unequal: No Solution Exploring Operation: 11+50=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 11*50=550, Resulting Numbers: [550] 550,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[32, 29], Operations: ['2*16=32', '18+11=29'] Exploring Operation: 32*29=928, Resulting Numbers: [928] 928,79 unequal: No Solution Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 32+29=61, Resulting Numbers: [61] 61,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 79:[18, 43], Operations: ['2*16=32', '11+32=43'] Exploring Operation: 18+43=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 18*43=774, Resulting Numbers: [774] 774,79 unequal: No Solution Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[18, 21], Operations: ['2*16=32', '32-11=21'] Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,79 unequal: No Solution Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,79 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 79:[32, 7], Operations: ['2*16=32', '18-11=7'] Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,79 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[18, 16, 22], Operations: ['2*11=22'] Exploring Operation: 18-16=2, Resulting Numbers: [22, 2] Generated Node #0,3,0: 79:[22, 2] Operation: 18-16=2 Exploring Operation: 18+22=40, Resulting Numbers: [16, 40] Generated Node #0,3,1: 79:[16, 40] Operation: 18+22=40 Exploring Operation: 16+22=38, Resulting Numbers: [18, 38] Generated Node #0,3,2: 79:[18, 38] Operation: 16+22=38 Exploring Operation: 22-16=6, Resulting Numbers: [18, 6] Generated Node #0,3,3: 79:[18, 6] Operation: 22-16=6 Exploring Operation: 18+16=34, Resulting Numbers: [22, 34] Generated Node #0,3,4: 79:[22, 34] Operation: 18+16=34 Moving to Node #0,3,1 Current State: 79:[16, 40], Operations: ['2*11=22', '18+22=40'] Exploring Operation: 16*40=640, Resulting Numbers: [640] 640,79 unequal: No Solution Exploring Operation: 16+40=56, Resulting Numbers: [56] 56,79 unequal: No Solution Exploring Operation: 40-16=24, Resulting Numbers: [24] 24,79 unequal: No Solution Moving to Node #0,3,4 Current State: 79:[22, 34], Operations: ['2*11=22', '18+16=34'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 22+34=56, Resulting Numbers: [56] 56,79 unequal: No Solution Exploring Operation: 22*34=748, Resulting Numbers: [748] 748,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[18, 38], Operations: ['2*11=22', '16+22=38'] Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,79 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,79 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[22, 2], Operations: ['2*11=22', '18-16=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,79 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,79 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[18, 6], Operations: ['2*11=22', '22-16=6'] Exploring Operation: 18*6=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,79 unequal: No Solution No 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: 79:[18, 16, 13], Operations: ['2+11=13'] Exploring Operation: 16+13=29, Resulting Numbers: [18, 29] Generated Node #0,2,0: 79:[18, 29] Operation: 16+13=29 Exploring Operation: 18-13=5, Resulting Numbers: [16, 5] Generated Node #0,2,1: 79:[16, 5] Operation: 18-13=5 Exploring Operation: 18+16=34, Resulting Numbers: [13, 34] Generated Node #0,2,2: 79:[13, 34] Operation: 18+16=34 Exploring Operation: 16-13=3, Resulting Numbers: [18, 3] Generated Node #0,2,3: 79:[18, 3] Operation: 16-13=3 Exploring Operation: 18+13=31, Resulting Numbers: [16, 31] Generated Node #0,2,4: 79:[16, 31] Operation: 18+13=31 Moving to Node #0,2,0 Current State: 79:[18, 29], Operations: ['2+11=13', '16+13=29'] Exploring Operation: 18*29=522, Resulting Numbers: [522] 522,79 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,79 unequal: No Solution Moving to Node #0,2,4 Current State: 79:[16, 31], Operations: ['2+11=13', '18+13=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,79 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 16*31=496, Resulting Numbers: [496] 496,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[13, 34], Operations: ['2+11=13', '18+16=34'] Exploring Operation: 13+34=47, Resulting Numbers: [47] 47,79 unequal: No Solution Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 13*34=442, Resulting Numbers: [442] 442,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[16, 5], Operations: ['2+11=13', '18-13=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[18, 3], Operations: ['2+11=13', '16-13=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,79 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,79 unequal: No Solution No 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: 79:[11, 16, 20], Operations: ['2+18=20'] Exploring Operation: 11+16=27, Resulting Numbers: [20, 27] Generated Node #0,4,0: 79:[20, 27] Operation: 11+16=27 Exploring Operation: 16+20=36, Resulting Numbers: [11, 36] Generated Node #0,4,1: 79:[11, 36] Operation: 16+20=36 Exploring Operation: 11+20=31, Resulting Numbers: [16, 31] Generated Node #0,4,2: 79:[16, 31] Operation: 11+20=31 Exploring Operation: 20-11=9, Resulting Numbers: [16, 9] Generated Node #0,4,3: 79:[16, 9] Operation: 20-11=9 Exploring Operation: 16-11=5, Resulting Numbers: [20, 5] Generated Node #0,4,4: 79:[20, 5] Operation: 16-11=5 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 79:[20, 27], Operations: ['2+18=20', '11+16=27'] Exploring Operation: 20*27=540, Resulting Numbers: [540] 540,79 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 79:[11, 36], Operations: ['2+18=20', '16+20=36'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,79 unequal: No Solution Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 79:[16, 31], Operations: ['2+18=20', '11+20=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,79 unequal: No Solution Exploring Operation: 16*31=496, Resulting Numbers: [496] 496,79 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 79:[16, 9], Operations: ['2+18=20', '20-11=9'] Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 79:[20, 5], Operations: ['2+18=20', '16-11=5'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,79 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 61, 80, 8, 78 ]
71
[ "61+80=141", "78-8=70", "141-70=71" ]
Current State: 71:[61, 80, 8, 78], Operations: [] Exploring Operation: 61+80=141, Resulting Numbers: [8, 78, 141] Generated Node #2: [8, 78, 141] from Operation: 61+80=141 Current State: 71:[8, 78, 141], Operations: ['61+80=141'] Exploring Operation: 78-8=70, Resulting Numbers: [141, 70] Generated Node #3: [141, 70] from Operation: 78-8=70 Current State: 71:[141, 70], Operations: ['61+80=141', '78-8=70'] Exploring Operation: 141-70=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[61, 80, 8, 78], Operations: [] Exploring Operation: 61+8=69, Resulting Numbers: [80, 78, 69] Generated Node #0,0: 71:[80, 78, 69] Operation: 61+8=69 Moving to Node #0,0 Current State: 71:[80, 78, 69], Operations: ['61+8=69'] Exploring Operation: 80-69=11, Resulting Numbers: [78, 11] Generated Node #0,0,0: 71:[78, 11] Operation: 80-69=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[78, 11], Operations: ['61+8=69', '80-69=11'] Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,71 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
[ 79, 48, 85, 8 ]
46
[ "79-48=31", "85-8=77", "77-31=46" ]
Current State: 46:[79, 48, 85, 8], Operations: [] Exploring Operation: 79-48=31, Resulting Numbers: [85, 8, 31] Generated Node #2: [85, 8, 31] from Operation: 79-48=31 Current State: 46:[85, 8, 31], Operations: ['79-48=31'] Exploring Operation: 85-8=77, Resulting Numbers: [31, 77] Generated Node #3: [31, 77] from Operation: 85-8=77 Current State: 46:[31, 77], Operations: ['79-48=31', '85-8=77'] Exploring Operation: 77-31=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[79, 48, 85, 8], Operations: [] Exploring Operation: 79-48=31, Resulting Numbers: [85, 8, 31] Generated Node #0,0: 46:[85, 8, 31] Operation: 79-48=31 Exploring Operation: 79-8=71, Resulting Numbers: [48, 85, 71] Generated Node #0,1: 46:[48, 85, 71] Operation: 79-8=71 Exploring Operation: 85-79=6, Resulting Numbers: [48, 8, 6] Generated Node #0,2: 46:[48, 8, 6] Operation: 85-79=6 Exploring Operation: 85-48=37, Resulting Numbers: [79, 8, 37] Generated Node #0,3: 46:[79, 8, 37] Operation: 85-48=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[48, 8, 6], Operations: ['85-79=6'] Exploring Operation: 8-6=2, Resulting Numbers: [48, 2] Generated Node #0,2,0: 46:[48, 2] Operation: 8-6=2 Exploring Operation: 48/8=6, Resulting Numbers: [6, 6] Generated Node #0,2,1: 46:[6, 6] Operation: 48/8=6 Exploring Operation: 48-8=40, Resulting Numbers: [6, 40] Generated Node #0,2,2: 46:[6, 40] Operation: 48-8=40 Exploring Operation: 8*6=48, Resulting Numbers: [48, 48] Generated Node #0,2,3: 46:[48, 48] Operation: 8*6=48 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 46:[48, 2], Operations: ['85-79=6', '8-6=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[79, 48, 85, 8], Operations: [] Exploring Operation: 85-79=6, Resulting Numbers: [48, 8, 6] Generated Node #0,2: 46:[48, 8, 6] Operation: 85-79=6 Moving to Node #0,2 Current State: 46:[48, 8, 6], Operations: ['85-79=6'] Exploring Operation: 8-6=2, Resulting Numbers: [48, 2] Generated Node #0,2,0: 46:[48, 2] Operation: 8-6=2 Moving to Node #0,2,0 Current State: 46:[48, 2], Operations: ['85-79=6', '8-6=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 20, 26, 53, 72 ]
55
[ "72-20=52", "52/26=2", "53+2=55" ]
Current State: 55:[20, 26, 53, 72], Operations: [] Exploring Operation: 72-20=52, Resulting Numbers: [26, 53, 52] Generated Node #2: [26, 53, 52] from Operation: 72-20=52 Current State: 55:[26, 53, 52], Operations: ['72-20=52'] Exploring Operation: 52/26=2, Resulting Numbers: [53, 2] Generated Node #3: [53, 2] from Operation: 52/26=2 Current State: 55:[53, 2], Operations: ['72-20=52', '52/26=2'] Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[20, 26, 53, 72], Operations: [] Exploring Operation: 26-20=6, Resulting Numbers: [53, 72, 6] Generated Node #0,0: 55:[53, 72, 6] Operation: 26-20=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[53, 72, 6], Operations: ['26-20=6'] Exploring Operation: 72/6=12, Resulting Numbers: [53, 12] Generated Node #0,0,0: 55:[53, 12] Operation: 72/6=12 Moving to Node #0,0,0 Current State: 55:[53, 12], Operations: ['26-20=6', '72/6=12'] Exploring Operation: 53+12=65, Resulting Numbers: [65] 65,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 45, 53, 25, 15 ]
26
[ "45*15=675", "675/25=27", "53-27=26" ]
Current State: 26:[45, 53, 25, 15], Operations: [] Exploring Operation: 45*15=675, Resulting Numbers: [53, 25, 675] Generated Node #2: [53, 25, 675] from Operation: 45*15=675 Current State: 26:[53, 25, 675], Operations: ['45*15=675'] Exploring Operation: 675/25=27, Resulting Numbers: [53, 27] Generated Node #3: [53, 27] from Operation: 675/25=27 Current State: 26:[53, 27], Operations: ['45*15=675', '675/25=27'] Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[45, 53, 25, 15], Operations: [] Exploring Operation: 53-45=8, Resulting Numbers: [25, 15, 8] Generated Node #0,0: 26:[25, 15, 8] Operation: 53-45=8 Exploring Operation: 45-15=30, Resulting Numbers: [53, 25, 30] Generated Node #0,1: 26:[53, 25, 30] Operation: 45-15=30 Exploring Operation: 53-25=28, Resulting Numbers: [45, 15, 28] Generated Node #0,2: 26:[45, 15, 28] Operation: 53-25=28 Exploring Operation: 45/15=3, Resulting Numbers: [53, 25, 3] Generated Node #0,3: 26:[53, 25, 3] Operation: 45/15=3 Moving to Node #0,0 Current State: 26:[25, 15, 8], Operations: ['53-45=8'] Exploring Operation: 25-15=10, Resulting Numbers: [8, 10] Generated Node #0,0,0: 26:[8, 10] Operation: 25-15=10 Exploring Operation: 25-8=17, Resulting Numbers: [15, 17] Generated Node #0,0,1: 26:[15, 17] Operation: 25-8=17 Exploring Operation: 15-8=7, Resulting Numbers: [25, 7] Generated Node #0,0,2: 26:[25, 7] Operation: 15-8=7 Exploring Operation: 15+8=23, Resulting Numbers: [25, 23] Generated Node #0,0,3: 26:[25, 23] Operation: 15+8=23 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 26:[25, 23], Operations: ['53-45=8', '15+8=23'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,26 unequal: No Solution Exploring Operation: 25*23=575, Resulting Numbers: [575] 575,26 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:[15, 17], Operations: ['53-45=8', '25-8=17'] Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,26 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,26 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:[25, 7], Operations: ['53-45=8', '15-8=7'] Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,26 unequal: No Solution Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,26 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,26 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 #0,0,0 Current State: 26:[8, 10], Operations: ['53-45=8', '25-15=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,26 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,26 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:[45, 15, 28], Operations: ['53-25=28'] Exploring Operation: 45/15=3, Resulting Numbers: [28, 3] Generated Node #0,2,0: 26:[28, 3] Operation: 45/15=3 Exploring Operation: 45-15=30, Resulting Numbers: [28, 30] Generated Node #0,2,1: 26:[28, 30] Operation: 45-15=30 Exploring Operation: 45-28=17, Resulting Numbers: [15, 17] Generated Node #0,2,2: 26:[15, 17] Operation: 45-28=17 Exploring Operation: 28-15=13, Resulting Numbers: [45, 13] Generated Node #0,2,3: 26:[45, 13] Operation: 28-15=13 Moving to Node #0,3 Current State: 26:[53, 25, 3], Operations: ['45/15=3'] Exploring Operation: 53-3=50, Resulting Numbers: [25, 50] Generated Node #0,3,0: 26:[25, 50] Operation: 53-3=50 Exploring Operation: 53-25=28, Resulting Numbers: [3, 28] Generated Node #0,3,1: 26:[3, 28] Operation: 53-25=28 Exploring Operation: 53+3=56, Resulting Numbers: [25, 56] Generated Node #0,3,2: 26:[25, 56] Operation: 53+3=56 Exploring Operation: 25+3=28, Resulting Numbers: [53, 28] Generated Node #0,3,3: 26:[53, 28] Operation: 25+3=28 Moving to Node #0,1 Current State: 26:[53, 25, 30], Operations: ['45-15=30'] Exploring Operation: 30-25=5, Resulting Numbers: [53, 5] Generated Node #0,1,0: 26:[53, 5] Operation: 30-25=5 Exploring Operation: 53+25=78, Resulting Numbers: [30, 78] Generated Node #0,1,1: 26:[30, 78] Operation: 53+25=78 Exploring Operation: 53-30=23, Resulting Numbers: [25, 23] Generated Node #0,1,2: 26:[25, 23] Operation: 53-30=23 Exploring Operation: 53-25=28, Resulting Numbers: [30, 28] Generated Node #0,1,3: 26:[30, 28] Operation: 53-25=28 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[25, 23], Operations: ['45-15=30', '53-30=23'] Exploring Operation: 25*23=575, Resulting Numbers: [575] 575,26 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,26 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 #0,1,3 Current State: 26:[30, 28], Operations: ['45-15=30', '53-25=28'] Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,26 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,26 unequal: No Solution Exploring Operation: 30-28=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 #0,1,0 Current State: 26:[53, 5], Operations: ['45-15=30', '30-25=5'] Exploring Operation: 53*5=265, Resulting Numbers: [265] 265,26 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,26 unequal: No Solution Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,26 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 #0,1,1 Current State: 26:[30, 78], Operations: ['45-15=30', '53+25=78'] Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,26 unequal: No Solution Exploring Operation: 30*78=2340, Resulting Numbers: [2340] 2340,26 unequal: No Solution Exploring Operation: 30+78=108, Resulting Numbers: [108] 108,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 26:[28, 3], Operations: ['53-25=28', '45/15=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,26 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,26 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,26 unequal: No Solution Moving to Node #0,3,1 Current State: 26:[3, 28], Operations: ['45/15=3', '53-25=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,26 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,26 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[15, 17], Operations: ['53-25=28', '45-28=17'] Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,26 unequal: No Solution Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,26 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[28, 30], Operations: ['53-25=28', '45-15=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,26 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[45, 13], Operations: ['53-25=28', '28-15=13'] Exploring Operation: 45-13=32, Resulting Numbers: [32] 32,26 unequal: No Solution Exploring Operation: 45*13=585, Resulting Numbers: [585] 585,26 unequal: No Solution Exploring Operation: 45+13=58, Resulting Numbers: [58] 58,26 unequal: No Solution Moving to Node #0,3,0 Current State: 26:[25, 50], Operations: ['45/15=3', '53-3=50'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 25*50=1250, Resulting Numbers: [1250] 1250,26 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 25+50=75, Resulting Numbers: [75] 75,26 unequal: No Solution Moving to Node #0,3,3 Current State: 26:[53, 28], Operations: ['45/15=3', '25+3=28'] Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,26 unequal: No Solution Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,26 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,26 unequal: No Solution Moving to Node #0,3,2 Current State: 26:[25, 56], Operations: ['45/15=3', '53+3=56'] Exploring Operation: 25+56=81, Resulting Numbers: [81] 81,26 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,26 unequal: No Solution Exploring Operation: 25*56=1400, Resulting Numbers: [1400] 1400,26 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 5, 64, 46, 26 ]
40
[ "64-46=18", "26-18=8", "5*8=40" ]
Current State: 40:[5, 64, 46, 26], Operations: [] Exploring Operation: 64-46=18, Resulting Numbers: [5, 26, 18] Generated Node #2: [5, 26, 18] from Operation: 64-46=18 Current State: 40:[5, 26, 18], Operations: ['64-46=18'] Exploring Operation: 26-18=8, Resulting Numbers: [5, 8] Generated Node #3: [5, 8] from Operation: 26-18=8 Current State: 40:[5, 8], Operations: ['64-46=18', '26-18=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[5, 64, 46, 26], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [5, 46, 38] Generated Node #0,0: 40:[5, 46, 38] Operation: 64-26=38 Exploring Operation: 64-46=18, Resulting Numbers: [5, 26, 18] Generated Node #0,1: 40:[5, 26, 18] Operation: 64-46=18 Moving to Node #0,0 Current State: 40:[5, 46, 38], Operations: ['64-26=38'] Exploring Operation: 46-38=8, Resulting Numbers: [5, 8] Generated Node #0,0,0: 40:[5, 8] Operation: 46-38=8 Exploring Operation: 46-5=41, Resulting Numbers: [38, 41] Generated Node #0,0,1: 40:[38, 41] Operation: 46-5=41 Moving to Node #0,1 Current State: 40:[5, 26, 18], Operations: ['64-46=18'] Exploring Operation: 26-18=8, Resulting Numbers: [5, 8] Generated Node #0,1,0: 40:[5, 8] Operation: 26-18=8 Exploring Operation: 26-5=21, Resulting Numbers: [18, 21] Generated Node #0,1,1: 40:[18, 21] Operation: 26-5=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[5, 8], Operations: ['64-46=18', '26-18=8'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[5, 64, 46, 26], Operations: [] Exploring Operation: 64-46=18, Resulting Numbers: [5, 26, 18] Generated Node #0,1: 40:[5, 26, 18] Operation: 64-46=18 Moving to Node #0,1 Current State: 40:[5, 26, 18], Operations: ['64-46=18'] Exploring Operation: 26-18=8, Resulting Numbers: [5, 8] Generated Node #0,1,0: 40:[5, 8] Operation: 26-18=8 Moving to Node #0,1,0 Current State: 40:[5, 8], Operations: ['64-46=18', '26-18=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 70, 96, 82, 20 ]
12
[ "82-70=12", "96/12=8", "20-8=12" ]
Current State: 12:[70, 96, 82, 20], Operations: [] Exploring Operation: 82-70=12, Resulting Numbers: [96, 20, 12] Generated Node #2: [96, 20, 12] from Operation: 82-70=12 Current State: 12:[96, 20, 12], Operations: ['82-70=12'] Exploring Operation: 96/12=8, Resulting Numbers: [20, 8] Generated Node #3: [20, 8] from Operation: 96/12=8 Current State: 12:[20, 8], Operations: ['82-70=12', '96/12=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[70, 96, 82, 20], Operations: [] Exploring Operation: 96-20=76, Resulting Numbers: [70, 82, 76] Generated Node #0,0: 12:[70, 82, 76] Operation: 96-20=76 Exploring Operation: 82-70=12, Resulting Numbers: [96, 20, 12] Generated Node #0,1: 12:[96, 20, 12] Operation: 82-70=12 Exploring Operation: 96-70=26, Resulting Numbers: [82, 20, 26] Generated Node #0,2: 12:[82, 20, 26] Operation: 96-70=26 Exploring Operation: 96-82=14, Resulting Numbers: [70, 20, 14] Generated Node #0,3: 12:[70, 20, 14] Operation: 96-82=14 Exploring Operation: 70-20=50, Resulting Numbers: [96, 82, 50] Generated Node #0,4: 12:[96, 82, 50] Operation: 70-20=50 Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[70, 20, 14], Operations: ['96-82=14'] Exploring Operation: 70-14=56, Resulting Numbers: [20, 56] Generated Node #0,3,0: 12:[20, 56] Operation: 70-14=56 Exploring Operation: 70-20=50, Resulting Numbers: [14, 50] Generated Node #0,3,1: 12:[14, 50] Operation: 70-20=50 Exploring Operation: 70+20=90, Resulting Numbers: [14, 90] Generated Node #0,3,2: 12:[14, 90] Operation: 70+20=90 Exploring Operation: 70/14=5, Resulting Numbers: [20, 5] Generated Node #0,3,3: 12:[20, 5] Operation: 70/14=5 Exploring Operation: 20-14=6, Resulting Numbers: [70, 6] Generated Node #0,3,4: 12:[70, 6] Operation: 20-14=6 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 12:[20, 5], Operations: ['96-82=14', '70/14=5'] 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 Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 12:[14, 50], Operations: ['96-82=14', '70-20=50'] Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,12 unequal: No Solution Exploring Operation: 14*50=700, Resulting Numbers: [700] 700,12 unequal: No Solution Exploring Operation: 14+50=64, Resulting Numbers: [64] 64,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 12:[20, 56], Operations: ['96-82=14', '70-14=56'] Exploring Operation: 20*56=1120, Resulting Numbers: [1120] 1120,12 unequal: No Solution Exploring Operation: 20+56=76, Resulting Numbers: [76] 76,12 unequal: No Solution Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 12:[70, 6], Operations: ['96-82=14', '20-14=6'] Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,12 unequal: No Solution Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,12 unequal: No Solution Exploring Operation: 70*6=420, Resulting Numbers: [420] 420,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 12:[14, 90], Operations: ['96-82=14', '70+20=90'] Exploring Operation: 90-14=76, Resulting Numbers: [76] 76,12 unequal: No Solution Exploring Operation: 14+90=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 14*90=1260, Resulting Numbers: [1260] 1260,12 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: 12:[96, 20, 12], Operations: ['82-70=12'] Exploring Operation: 96-12=84, Resulting Numbers: [20, 84] Generated Node #0,1,0: 12:[20, 84] Operation: 96-12=84 Exploring Operation: 20-12=8, Resulting Numbers: [96, 8] Generated Node #0,1,1: 12:[96, 8] Operation: 20-12=8 Exploring Operation: 96-20=76, Resulting Numbers: [12, 76] Generated Node #0,1,2: 12:[12, 76] Operation: 96-20=76 Exploring Operation: 96/12=8, Resulting Numbers: [20, 8] Generated Node #0,1,3: 12:[20, 8] Operation: 96/12=8 Exploring Operation: 96+20=116, Resulting Numbers: [12, 116] Generated Node #0,1,4: 12:[12, 116] Operation: 96+20=116 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 12:[20, 8], Operations: ['82-70=12', '96/12=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[70, 96, 82, 20], Operations: [] Exploring Operation: 82-70=12, Resulting Numbers: [96, 20, 12] Generated Node #0,1: 12:[96, 20, 12] Operation: 82-70=12 Moving to Node #0,1 Current State: 12:[96, 20, 12], Operations: ['82-70=12'] Exploring Operation: 96/12=8, Resulting Numbers: [20, 8] Generated Node #0,1,3: 12:[20, 8] Operation: 96/12=8 Moving to Node #0,1,3 Current State: 12:[20, 8], Operations: ['82-70=12', '96/12=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 28, 68, 35, 63 ]
35
[ "35-28=7", "68-63=5", "7*5=35" ]
Current State: 35:[28, 68, 35, 63], Operations: [] Exploring Operation: 35-28=7, Resulting Numbers: [68, 63, 7] Generated Node #2: [68, 63, 7] from Operation: 35-28=7 Current State: 35:[68, 63, 7], Operations: ['35-28=7'] Exploring Operation: 68-63=5, Resulting Numbers: [7, 5] Generated Node #3: [7, 5] from Operation: 68-63=5 Current State: 35:[7, 5], Operations: ['35-28=7', '68-63=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[28, 68, 35, 63], Operations: [] Exploring Operation: 63-28=35, Resulting Numbers: [68, 35, 35] Generated Node #0,0: 35:[68, 35, 35] Operation: 63-28=35 Exploring Operation: 68-63=5, Resulting Numbers: [28, 35, 5] Generated Node #0,1: 35:[28, 35, 5] Operation: 68-63=5 Exploring Operation: 68-28=40, Resulting Numbers: [35, 63, 40] Generated Node #0,2: 35:[35, 63, 40] Operation: 68-28=40 Moving to Node #0,1 Current State: 35:[28, 35, 5], Operations: ['68-63=5'] Exploring Operation: 35-28=7, Resulting Numbers: [5, 7] Generated Node #0,1,0: 35:[5, 7] Operation: 35-28=7 Exploring Operation: 35/5=7, Resulting Numbers: [28, 7] Generated Node #0,1,1: 35:[28, 7] Operation: 35/5=7 Exploring Operation: 28+5=33, Resulting Numbers: [35, 33] Generated Node #0,1,2: 35:[35, 33] Operation: 28+5=33 Moving to Node #0,0 Current State: 35:[68, 35, 35], Operations: ['63-28=35'] Exploring Operation: 68-35=33, Resulting Numbers: [35, 33] Generated Node #0,0,0: 35:[35, 33] Operation: 68-35=33 Exploring Operation: 68-35=33, Resulting Numbers: [35, 33] Generated Node #0,0,1: 35:[35, 33] Operation: 68-35=33 Exploring Operation: 35/35=1, Resulting Numbers: [68, 1] Generated Node #0,0,2: 35:[68, 1] Operation: 35/35=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[35, 33], Operations: ['63-28=35', '68-35=33'] Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,35 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,35 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:[35, 33], Operations: ['63-28=35', '68-35=33'] Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,35 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:[68, 1], Operations: ['63-28=35', '35/35=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,35 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,35 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: 35:[35, 63, 40], Operations: ['68-28=40'] Exploring Operation: 63-40=23, Resulting Numbers: [35, 23] Generated Node #0,2,0: 35:[35, 23] Operation: 63-40=23 Exploring Operation: 63-35=28, Resulting Numbers: [40, 28] Generated Node #0,2,1: 35:[40, 28] Operation: 63-35=28 Exploring Operation: 40-35=5, Resulting Numbers: [63, 5] Generated Node #0,2,2: 35:[63, 5] Operation: 40-35=5 Moving to Node #0,1,0 Current State: 35:[5, 7], Operations: ['68-63=5', '35-28=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[28, 68, 35, 63], Operations: [] Exploring Operation: 68-63=5, Resulting Numbers: [28, 35, 5] Generated Node #0,1: 35:[28, 35, 5] Operation: 68-63=5 Moving to Node #0,1 Current State: 35:[28, 35, 5], Operations: ['68-63=5'] Exploring Operation: 35-28=7, Resulting Numbers: [5, 7] Generated Node #0,1,0: 35:[5, 7] Operation: 35-28=7 Moving to Node #0,1,0 Current State: 35:[5, 7], Operations: ['68-63=5', '35-28=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 86, 84, 23, 59 ]
18
[ "86-84=2", "59-23=36", "36/2=18" ]
Current State: 18:[86, 84, 23, 59], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [23, 59, 2] Generated Node #2: [23, 59, 2] from Operation: 86-84=2 Current State: 18:[23, 59, 2], Operations: ['86-84=2'] Exploring Operation: 59-23=36, Resulting Numbers: [2, 36] Generated Node #3: [2, 36] from Operation: 59-23=36 Current State: 18:[2, 36], Operations: ['86-84=2', '59-23=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[86, 84, 23, 59], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [23, 59, 2] Generated Node #0,0: 18:[23, 59, 2] Operation: 86-84=2 Exploring Operation: 84-59=25, Resulting Numbers: [86, 23, 25] Generated Node #0,1: 18:[86, 23, 25] Operation: 84-59=25 Exploring Operation: 86-59=27, Resulting Numbers: [84, 23, 27] Generated Node #0,2: 18:[84, 23, 27] Operation: 86-59=27 Moving to Node #0,0 Current State: 18:[23, 59, 2], Operations: ['86-84=2'] Exploring Operation: 23-2=21, Resulting Numbers: [59, 21] Generated Node #0,0,0: 18:[59, 21] Operation: 23-2=21 Exploring Operation: 59-23=36, Resulting Numbers: [2, 36] Generated Node #0,0,1: 18:[2, 36] Operation: 59-23=36 Exploring Operation: 59-2=57, Resulting Numbers: [23, 57] Generated Node #0,0,2: 18:[23, 57] Operation: 59-2=57 Moving to Node #0,1 Current State: 18:[86, 23, 25], Operations: ['84-59=25'] Exploring Operation: 86-25=61, Resulting Numbers: [23, 61] Generated Node #0,1,0: 18:[23, 61] Operation: 86-25=61 Exploring Operation: 86-23=63, Resulting Numbers: [25, 63] Generated Node #0,1,1: 18:[25, 63] Operation: 86-23=63 Exploring Operation: 25-23=2, Resulting Numbers: [86, 2] Generated Node #0,1,2: 18:[86, 2] Operation: 25-23=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[23, 61], Operations: ['84-59=25', '86-25=61'] Exploring Operation: 23+61=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 23*61=1403, Resulting Numbers: [1403] 1403,18 unequal: No Solution Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,18 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:[25, 63], Operations: ['84-59=25', '86-23=63'] Exploring Operation: 25+63=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 25*63=1575, Resulting Numbers: [1575] 1575,18 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:[86, 2], Operations: ['84-59=25', '25-23=2'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 86+2=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,18 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:[84, 23, 27], Operations: ['86-59=27'] Exploring Operation: 84-23=61, Resulting Numbers: [27, 61] Generated Node #0,2,0: 18:[27, 61] Operation: 84-23=61 Exploring Operation: 84-27=57, Resulting Numbers: [23, 57] Generated Node #0,2,1: 18:[23, 57] Operation: 84-27=57 Exploring Operation: 27-23=4, Resulting Numbers: [84, 4] Generated Node #0,2,2: 18:[84, 4] Operation: 27-23=4 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[23, 57], Operations: ['86-59=27', '84-27=57'] Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 23+57=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 23*57=1311, Resulting Numbers: [1311] 1311,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[27, 61], Operations: ['86-59=27', '84-23=61'] Exploring Operation: 27*61=1647, Resulting Numbers: [1647] 1647,18 unequal: No Solution Exploring Operation: 61-27=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 27+61=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 #0,2,2 Current State: 18:[84, 4], Operations: ['86-59=27', '27-23=4'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 84+4=88, Resulting Numbers: [88] 88,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 18:[2, 36], Operations: ['86-84=2', '59-23=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[86, 84, 23, 59], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [23, 59, 2] Generated Node #0,0: 18:[23, 59, 2] Operation: 86-84=2 Moving to Node #0,0 Current State: 18:[23, 59, 2], Operations: ['86-84=2'] Exploring Operation: 59-23=36, Resulting Numbers: [2, 36] Generated Node #0,0,1: 18:[2, 36] Operation: 59-23=36 Moving to Node #0,0,1 Current State: 18:[2, 36], Operations: ['86-84=2', '59-23=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.96875
hs_3
sum_heuristic
[ 72, 49, 66, 9 ]
34
[ "72-49=23", "66-9=57", "57-23=34" ]
Current State: 34:[72, 49, 66, 9], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [66, 9, 23] Generated Node #2: [66, 9, 23] from Operation: 72-49=23 Current State: 34:[66, 9, 23], Operations: ['72-49=23'] Exploring Operation: 66-9=57, Resulting Numbers: [23, 57] Generated Node #3: [23, 57] from Operation: 66-9=57 Current State: 34:[23, 57], Operations: ['72-49=23', '66-9=57'] Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[72, 49, 66, 9], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [49, 9, 6] Generated Node #0,0: 34:[49, 9, 6] Operation: 72-66=6 Exploring Operation: 72/9=8, Resulting Numbers: [49, 66, 8] Generated Node #0,1: 34:[49, 66, 8] Operation: 72/9=8 Exploring Operation: 66-49=17, Resulting Numbers: [72, 9, 17] Generated Node #0,2: 34:[72, 9, 17] Operation: 66-49=17 Exploring Operation: 72-49=23, Resulting Numbers: [66, 9, 23] Generated Node #0,3: 34:[66, 9, 23] Operation: 72-49=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[49, 9, 6], Operations: ['72-66=6'] Exploring Operation: 9+6=15, Resulting Numbers: [49, 15] Generated Node #0,0,0: 34:[49, 15] Operation: 9+6=15 Exploring Operation: 9-6=3, Resulting Numbers: [49, 3] Generated Node #0,0,1: 34:[49, 3] Operation: 9-6=3 Exploring Operation: 49-9=40, Resulting Numbers: [6, 40] Generated Node #0,0,2: 34:[6, 40] Operation: 49-9=40 Exploring Operation: 49-6=43, Resulting Numbers: [9, 43] Generated Node #0,0,3: 34:[9, 43] Operation: 49-6=43 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 34:[6, 40], Operations: ['72-66=6', '49-9=40'] Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,34 unequal: No Solution Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,34 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[72, 49, 66, 9], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [49, 9, 6] Generated Node #0,0: 34:[49, 9, 6] Operation: 72-66=6 Moving to Node #0,0 Current State: 34:[49, 9, 6], Operations: ['72-66=6'] Exploring Operation: 49-9=40, Resulting Numbers: [6, 40] Generated Node #0,0,2: 34:[6, 40] Operation: 49-9=40 Moving to Node #0,0,2 Current State: 34:[6, 40], Operations: ['72-66=6', '49-9=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 24, 60, 11, 40 ]
12
[ "24+11=35", "40-35=5", "60/5=12" ]
Current State: 12:[24, 60, 11, 40], Operations: [] Exploring Operation: 24+11=35, Resulting Numbers: [60, 40, 35] Generated Node #2: [60, 40, 35] from Operation: 24+11=35 Current State: 12:[60, 40, 35], Operations: ['24+11=35'] Exploring Operation: 40-35=5, Resulting Numbers: [60, 5] Generated Node #3: [60, 5] from Operation: 40-35=5 Current State: 12:[60, 5], Operations: ['24+11=35', '40-35=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[24, 60, 11, 40], Operations: [] Exploring Operation: 60-11=49, Resulting Numbers: [24, 40, 49] Generated Node #0,0: 12:[24, 40, 49] Operation: 60-11=49 Exploring Operation: 40-24=16, Resulting Numbers: [60, 11, 16] Generated Node #0,1: 12:[60, 11, 16] Operation: 40-24=16 Exploring Operation: 60-40=20, Resulting Numbers: [24, 11, 20] Generated Node #0,2: 12:[24, 11, 20] Operation: 60-40=20 Exploring Operation: 60-24=36, Resulting Numbers: [11, 40, 36] Generated Node #0,3: 12:[11, 40, 36] Operation: 60-24=36 Exploring Operation: 24-11=13, Resulting Numbers: [60, 40, 13] Generated Node #0,4: 12:[60, 40, 13] Operation: 24-11=13 Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[24, 11, 20], Operations: ['60-40=20'] Exploring Operation: 24-20=4, Resulting Numbers: [11, 4] Generated Node #0,2,0: 12:[11, 4] Operation: 24-20=4 Exploring Operation: 11+20=31, Resulting Numbers: [24, 31] Generated Node #0,2,1: 12:[24, 31] Operation: 11+20=31 Exploring Operation: 24+11=35, Resulting Numbers: [20, 35] Generated Node #0,2,2: 12:[20, 35] Operation: 24+11=35 Exploring Operation: 24-11=13, Resulting Numbers: [20, 13] Generated Node #0,2,3: 12:[20, 13] Operation: 24-11=13 Exploring Operation: 20-11=9, Resulting Numbers: [24, 9] Generated Node #0,2,4: 12:[24, 9] Operation: 20-11=9 Moving to Node #0,2,0 Current State: 12:[11, 4], Operations: ['60-40=20', '24-20=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,12 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,12 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[20, 13], Operations: ['60-40=20', '24-11=13'] Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,12 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,12 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,12 unequal: No Solution Moving to Node #0,2,4 Current State: 12:[24, 9], Operations: ['60-40=20', '20-11=9'] Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,12 unequal: No Solution Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[24, 31], Operations: ['60-40=20', '11+20=31'] Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,12 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[20, 35], Operations: ['60-40=20', '24+11=35'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,12 unequal: No Solution Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[60, 11, 16], Operations: ['40-24=16'] Exploring Operation: 60-11=49, Resulting Numbers: [16, 49] Generated Node #0,1,0: 12:[16, 49] Operation: 60-11=49 Exploring Operation: 16-11=5, Resulting Numbers: [60, 5] Generated Node #0,1,1: 12:[60, 5] Operation: 16-11=5 Exploring Operation: 60+11=71, Resulting Numbers: [16, 71] Generated Node #0,1,2: 12:[16, 71] Operation: 60+11=71 Exploring Operation: 60-16=44, Resulting Numbers: [11, 44] Generated Node #0,1,3: 12:[11, 44] Operation: 60-16=44 Exploring Operation: 11+16=27, Resulting Numbers: [60, 27] Generated Node #0,1,4: 12:[60, 27] Operation: 11+16=27 Moving to Node #0,1,3 Current State: 12:[11, 44], Operations: ['40-24=16', '60-16=44'] Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 11+44=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 11*44=484, Resulting Numbers: [484] 484,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[16, 49], Operations: ['40-24=16', '60-11=49'] Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 16*49=784, Resulting Numbers: [784] 784,12 unequal: No Solution Exploring Operation: 16+49=65, Resulting Numbers: [65] 65,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[60, 5], Operations: ['40-24=16', '16-11=5'] Exploring Operation: 60*5=300, Resulting Numbers: [300] 300,12 unequal: No Solution Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[24, 60, 11, 40], Operations: [] Exploring Operation: 40-24=16, Resulting Numbers: [60, 11, 16] Generated Node #0,1: 12:[60, 11, 16] Operation: 40-24=16 Moving to Node #0,1 Current State: 12:[60, 11, 16], Operations: ['40-24=16'] Exploring Operation: 16-11=5, Resulting Numbers: [60, 5] Generated Node #0,1,1: 12:[60, 5] Operation: 16-11=5 Moving to Node #0,1,1 Current State: 12:[60, 5], Operations: ['40-24=16', '16-11=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic
[ 41, 47, 32, 93 ]
99
[ "47-41=6", "32*6=192", "192-93=99" ]
Current State: 99:[41, 47, 32, 93], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [32, 93, 6] Generated Node #2: [32, 93, 6] from Operation: 47-41=6 Current State: 99:[32, 93, 6], Operations: ['47-41=6'] Exploring Operation: 32*6=192, Resulting Numbers: [93, 192] Generated Node #3: [93, 192] from Operation: 32*6=192 Current State: 99:[93, 192], Operations: ['47-41=6', '32*6=192'] Exploring Operation: 192-93=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[41, 47, 32, 93], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [32, 93, 6] Generated Node #0,0: 99:[32, 93, 6] Operation: 47-41=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[32, 93, 6], Operations: ['47-41=6'] Exploring Operation: 93+6=99, Resulting Numbers: [32, 99] Generated Node #0,0,0: 99:[32, 99] Operation: 93+6=99 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[32, 99], Operations: ['47-41=6', '93+6=99'] Exploring Operation: 32+99=131, Resulting Numbers: [131] 131,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic