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
[ 50, 18, 34, 35 ]
20
[ "18*35=630", "50+630=680", "680/34=20" ]
Current State: 20:[50, 18, 34, 35], Operations: [] Exploring Operation: 18*35=630, Resulting Numbers: [50, 34, 630] Generated Node #2: [50, 34, 630] from Operation: 18*35=630 Current State: 20:[50, 34, 630], Operations: ['18*35=630'] Exploring Operation: 50+630=680, Resulting Numbers: [34, 680] Generated Node #3: [34, 680] from Operation: 50+630=680 Current State: 20:[34, 680], Operations: ['18*35=630', '50+630=680'] Exploring Operation: 680/34=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[50, 18, 34, 35], Operations: [] Exploring Operation: 50-35=15, Resulting Numbers: [18, 34, 15] Generated Node #0,0: 20:[18, 34, 15] Operation: 50-35=15 Exploring Operation: 50-34=16, Resulting Numbers: [18, 35, 16] Generated Node #0,1: 20:[18, 35, 16] Operation: 50-34=16 Exploring Operation: 50-18=32, Resulting Numbers: [34, 35, 32] Generated Node #0,2: 20:[34, 35, 32] Operation: 50-18=32 Exploring Operation: 35-34=1, Resulting Numbers: [50, 18, 1] Generated Node #0,3: 20:[50, 18, 1] Operation: 35-34=1 Moving to Node #0,0 Current State: 20:[18, 34, 15], Operations: ['50-35=15'] Exploring Operation: 34-18=16, Resulting Numbers: [15, 16] Generated Node #0,0,0: 20:[15, 16] Operation: 34-18=16 Exploring Operation: 18-15=3, Resulting Numbers: [34, 3] Generated Node #0,0,1: 20:[34, 3] Operation: 18-15=3 Exploring Operation: 34-15=19, Resulting Numbers: [18, 19] Generated Node #0,0,2: 20:[18, 19] Operation: 34-15=19 Exploring Operation: 18+15=33, Resulting Numbers: [34, 33] Generated Node #0,0,3: 20:[34, 33] Operation: 18+15=33 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 20:[18, 19], Operations: ['50-35=15', '34-15=19'] Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,20 unequal: No Solution Exploring Operation: 18*19=342, Resulting Numbers: [342] 342,20 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 #0,0,0 Current State: 20:[15, 16], Operations: ['50-35=15', '34-18=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,20 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[34, 3], Operations: ['50-35=15', '18-15=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,20 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 #0,0,3 Current State: 20:[34, 33], Operations: ['50-35=15', '18+15=33'] Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,20 unequal: No Solution Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,20 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,20 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: 20:[18, 35, 16], Operations: ['50-34=16'] Exploring Operation: 35-18=17, Resulting Numbers: [16, 17] Generated Node #0,1,0: 20:[16, 17] Operation: 35-18=17 Exploring Operation: 35-16=19, Resulting Numbers: [18, 19] Generated Node #0,1,1: 20:[18, 19] Operation: 35-16=19 Exploring Operation: 18-16=2, Resulting Numbers: [35, 2] Generated Node #0,1,2: 20:[35, 2] Operation: 18-16=2 Exploring Operation: 18+16=34, Resulting Numbers: [35, 34] Generated Node #0,1,3: 20:[35, 34] Operation: 18+16=34 Moving to Node #0,3 Current State: 20:[50, 18, 1], Operations: ['35-34=1'] Exploring Operation: 18+1=19, Resulting Numbers: [50, 19] Generated Node #0,3,0: 20:[50, 19] Operation: 18+1=19 Exploring Operation: 50*1=50, Resulting Numbers: [18, 50] Generated Node #0,3,1: 20:[18, 50] Operation: 50*1=50 Exploring Operation: 50-18=32, Resulting Numbers: [1, 32] Generated Node #0,3,2: 20:[1, 32] Operation: 50-18=32 Exploring Operation: 50-1=49, Resulting Numbers: [18, 49] Generated Node #0,3,3: 20:[18, 49] Operation: 50-1=49 Moving to Node #0,2 Current State: 20:[34, 35, 32], Operations: ['50-18=32'] Exploring Operation: 35-34=1, Resulting Numbers: [32, 1] Generated Node #0,2,0: 20:[32, 1] Operation: 35-34=1 Exploring Operation: 35-32=3, Resulting Numbers: [34, 3] Generated Node #0,2,1: 20:[34, 3] Operation: 35-32=3 Exploring Operation: 34+35=69, Resulting Numbers: [32, 69] Generated Node #0,2,2: 20:[32, 69] Operation: 34+35=69 Exploring Operation: 34-32=2, Resulting Numbers: [35, 2] Generated Node #0,2,3: 20:[35, 2] Operation: 34-32=2 Moving to Node #0,1,1 Current State: 20:[18, 19], Operations: ['50-34=16', '35-16=19'] Exploring Operation: 18*19=342, Resulting Numbers: [342] 342,20 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[16, 17], Operations: ['50-34=16', '35-18=17'] Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,20 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,20 unequal: No Solution Moving to Node #0,3,2 Current State: 20:[1, 32], Operations: ['35-34=1', '50-18=32'] Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 1*32=32, Resulting Numbers: [32] 32,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[32, 1], Operations: ['50-18=32', '35-34=1'] Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[35, 2], Operations: ['50-34=16', '18-16=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,20 unequal: No Solution Moving to Node #0,2,3 Current State: 20:[35, 2], Operations: ['50-18=32', '34-32=2'] Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,20 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[34, 3], Operations: ['50-18=32', '35-32=3'] Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,20 unequal: No Solution Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,20 unequal: No Solution Moving to Node #0,1,3 Current State: 20:[35, 34], Operations: ['50-34=16', '18+16=34'] Exploring Operation: 35+34=69, Resulting Numbers: [69] 69,20 unequal: No Solution Exploring Operation: 35*34=1190, Resulting Numbers: [1190] 1190,20 unequal: No Solution Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,20 unequal: No Solution Moving to Node #0,3,3 Current State: 20:[18, 49], Operations: ['35-34=1', '50-1=49'] Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 18+49=67, Resulting Numbers: [67] 67,20 unequal: No Solution Exploring Operation: 18*49=882, Resulting Numbers: [882] 882,20 unequal: No Solution Moving to Node #0,3,0 Current State: 20:[50, 19], Operations: ['35-34=1', '18+1=19'] Exploring Operation: 50*19=950, Resulting Numbers: [950] 950,20 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 50+19=69, Resulting Numbers: [69] 69,20 unequal: No Solution Moving to Node #0,3,1 Current State: 20:[18, 50], Operations: ['35-34=1', '50*1=50'] Exploring Operation: 50-18=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 18+50=68, Resulting Numbers: [68] 68,20 unequal: No Solution Exploring Operation: 18*50=900, Resulting Numbers: [900] 900,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[32, 69], Operations: ['50-18=32', '34+35=69'] Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,20 unequal: No Solution Exploring Operation: 32*69=2208, Resulting Numbers: [2208] 2208,20 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,20 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 55, 28, 98, 21 ]
61
[ "28+98=126", "126/21=6", "55+6=61" ]
Current State: 61:[55, 28, 98, 21], Operations: [] Exploring Operation: 28+98=126, Resulting Numbers: [55, 21, 126] Generated Node #2: [55, 21, 126] from Operation: 28+98=126 Current State: 61:[55, 21, 126], Operations: ['28+98=126'] Exploring Operation: 126/21=6, Resulting Numbers: [55, 6] Generated Node #3: [55, 6] from Operation: 126/21=6 Current State: 61:[55, 6], Operations: ['28+98=126', '126/21=6'] Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[55, 28, 98, 21], Operations: [] Exploring Operation: 28+21=49, Resulting Numbers: [55, 98, 49] Generated Node #0,0: 61:[55, 98, 49] Operation: 28+21=49 Exploring Operation: 98-28=70, Resulting Numbers: [55, 21, 70] Generated Node #0,1: 61:[55, 21, 70] Operation: 98-28=70 Exploring Operation: 98-21=77, Resulting Numbers: [55, 28, 77] Generated Node #0,2: 61:[55, 28, 77] Operation: 98-21=77 Moving to Node #0,0 Current State: 61:[55, 98, 49], Operations: ['28+21=49'] Exploring Operation: 98-55=43, Resulting Numbers: [49, 43] Generated Node #0,0,0: 61:[49, 43] Operation: 98-55=43 Exploring Operation: 98-49=49, Resulting Numbers: [55, 49] Generated Node #0,0,1: 61:[55, 49] Operation: 98-49=49 Exploring Operation: 98/49=2, Resulting Numbers: [55, 2] Generated Node #0,0,2: 61:[55, 2] Operation: 98/49=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[55, 49], Operations: ['28+21=49', '98-49=49'] Exploring Operation: 55*49=2695, Resulting Numbers: [2695] 2695,61 unequal: No Solution Exploring Operation: 55+49=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[49, 43], Operations: ['28+21=49', '98-55=43'] Exploring Operation: 49+43=92, Resulting Numbers: [92] 92,61 unequal: No Solution Exploring Operation: 49-43=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 49*43=2107, Resulting Numbers: [2107] 2107,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[55, 2], Operations: ['28+21=49', '98/49=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,61 unequal: No Solution Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,61 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 61:[55, 21, 70], Operations: ['98-28=70'] Exploring Operation: 70-21=49, Resulting Numbers: [55, 49] Generated Node #0,1,0: 61:[55, 49] Operation: 70-21=49 Exploring Operation: 55+21=76, Resulting Numbers: [70, 76] Generated Node #0,1,1: 61:[70, 76] Operation: 55+21=76 Exploring Operation: 55-21=34, Resulting Numbers: [70, 34] Generated Node #0,1,2: 61:[70, 34] Operation: 55-21=34 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[55, 49], Operations: ['98-28=70', '70-21=49'] Exploring Operation: 55*49=2695, Resulting Numbers: [2695] 2695,61 unequal: No Solution Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 55+49=104, Resulting Numbers: [104] 104,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[70, 76], Operations: ['98-28=70', '55+21=76'] Exploring Operation: 70*76=5320, Resulting Numbers: [5320] 5320,61 unequal: No Solution Exploring Operation: 70+76=146, Resulting Numbers: [146] 146,61 unequal: No Solution Exploring Operation: 76-70=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[70, 34], Operations: ['98-28=70', '55-21=34'] Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,61 unequal: No Solution Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,61 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,61 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: 61:[55, 28, 77], Operations: ['98-21=77'] Exploring Operation: 77-28=49, Resulting Numbers: [55, 49] Generated Node #0,2,0: 61:[55, 49] Operation: 77-28=49 Exploring Operation: 55+28=83, Resulting Numbers: [77, 83] Generated Node #0,2,1: 61:[77, 83] Operation: 55+28=83 Exploring Operation: 55-28=27, Resulting Numbers: [77, 27] Generated Node #0,2,2: 61:[77, 27] Operation: 55-28=27 Moving to Node #0,2,0 Current State: 61:[55, 49], Operations: ['98-21=77', '77-28=49'] Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 55*49=2695, Resulting Numbers: [2695] 2695,61 unequal: No Solution Exploring Operation: 55+49=104, Resulting Numbers: [104] 104,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[77, 83], Operations: ['98-21=77', '55+28=83'] Exploring Operation: 77*83=6391, Resulting Numbers: [6391] 6391,61 unequal: No Solution Exploring Operation: 77+83=160, Resulting Numbers: [160] 160,61 unequal: No Solution Exploring Operation: 83-77=6, Resulting Numbers: [6] 6,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[77, 27], Operations: ['98-21=77', '55-28=27'] Exploring Operation: 77+27=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 77*27=2079, Resulting Numbers: [2079] 2079,61 unequal: No Solution Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,61 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 85, 24, 99, 25 ]
82
[ "99-24=75", "75/25=3", "85-3=82" ]
Current State: 82:[85, 24, 99, 25], Operations: [] Exploring Operation: 99-24=75, Resulting Numbers: [85, 25, 75] Generated Node #2: [85, 25, 75] from Operation: 99-24=75 Current State: 82:[85, 25, 75], Operations: ['99-24=75'] Exploring Operation: 75/25=3, Resulting Numbers: [85, 3] Generated Node #3: [85, 3] from Operation: 75/25=3 Current State: 82:[85, 3], Operations: ['99-24=75', '75/25=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[85, 24, 99, 25], Operations: [] Exploring Operation: 24+25=49, Resulting Numbers: [85, 99, 49] Generated Node #0,0: 82:[85, 99, 49] Operation: 24+25=49 Exploring Operation: 25-24=1, Resulting Numbers: [85, 99, 1] Generated Node #0,1: 82:[85, 99, 1] Operation: 25-24=1 Exploring Operation: 99-24=75, Resulting Numbers: [85, 25, 75] Generated Node #0,2: 82:[85, 25, 75] Operation: 99-24=75 Moving to Node #0,1 Current State: 82:[85, 99, 1], Operations: ['25-24=1'] Exploring Operation: 99-85=14, Resulting Numbers: [1, 14] Generated Node #0,1,0: 82:[1, 14] Operation: 99-85=14 Exploring Operation: 85-1=84, Resulting Numbers: [99, 84] Generated Node #0,1,1: 82:[99, 84] Operation: 85-1=84 Exploring Operation: 99-1=98, Resulting Numbers: [85, 98] Generated Node #0,1,2: 82:[85, 98] Operation: 99-1=98 Moving to Node #0,2 Current State: 82:[85, 25, 75], Operations: ['99-24=75'] Exploring Operation: 75-25=50, Resulting Numbers: [85, 50] Generated Node #0,2,0: 82:[85, 50] Operation: 75-25=50 Exploring Operation: 75/25=3, Resulting Numbers: [85, 3] Generated Node #0,2,1: 82:[85, 3] Operation: 75/25=3 Exploring Operation: 25+75=100, Resulting Numbers: [85, 100] Generated Node #0,2,2: 82:[85, 100] Operation: 25+75=100 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 82:[85, 3], Operations: ['99-24=75', '75/25=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[85, 24, 99, 25], Operations: [] Exploring Operation: 99-24=75, Resulting Numbers: [85, 25, 75] Generated Node #0,2: 82:[85, 25, 75] Operation: 99-24=75 Moving to Node #0,2 Current State: 82:[85, 25, 75], Operations: ['99-24=75'] Exploring Operation: 75/25=3, Resulting Numbers: [85, 3] Generated Node #0,2,1: 82:[85, 3] Operation: 75/25=3 Moving to Node #0,2,1 Current State: 82:[85, 3], Operations: ['99-24=75', '75/25=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 25, 90, 35, 36 ]
41
[ "90+35=125", "125/25=5", "36+5=41" ]
Current State: 41:[25, 90, 35, 36], Operations: [] Exploring Operation: 90+35=125, Resulting Numbers: [25, 36, 125] Generated Node #2: [25, 36, 125] from Operation: 90+35=125 Current State: 41:[25, 36, 125], Operations: ['90+35=125'] Exploring Operation: 125/25=5, Resulting Numbers: [36, 5] Generated Node #3: [36, 5] from Operation: 125/25=5 Current State: 41:[36, 5], Operations: ['90+35=125', '125/25=5'] Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[25, 90, 35, 36], Operations: [] Exploring Operation: 90-35=55, Resulting Numbers: [25, 36, 55] Generated Node #0,0: 41:[25, 36, 55] Operation: 90-35=55 Exploring Operation: 90-25=65, Resulting Numbers: [35, 36, 65] Generated Node #0,1: 41:[35, 36, 65] Operation: 90-25=65 Exploring Operation: 90-36=54, Resulting Numbers: [25, 35, 54] Generated Node #0,2: 41:[25, 35, 54] Operation: 90-36=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[25, 36, 55], Operations: ['90-35=55'] Exploring Operation: 25+36=61, Resulting Numbers: [55, 61] Generated Node #0,0,0: 41:[55, 61] Operation: 25+36=61 Exploring Operation: 55-36=19, Resulting Numbers: [25, 19] Generated Node #0,0,1: 41:[25, 19] Operation: 55-36=19 Exploring Operation: 55-25=30, Resulting Numbers: [36, 30] Generated Node #0,0,2: 41:[36, 30] Operation: 55-25=30 Moving to Node #0,0,2 Current State: 41:[36, 30], Operations: ['90-35=55', '55-25=30'] Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 36*30=1080, Resulting Numbers: [1080] 1080,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[55, 61], Operations: ['90-35=55', '25+36=61'] Exploring Operation: 55+61=116, Resulting Numbers: [116] 116,41 unequal: No Solution Exploring Operation: 55*61=3355, Resulting Numbers: [3355] 3355,41 unequal: No Solution Exploring Operation: 61-55=6, Resulting Numbers: [6] 6,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[25, 19], Operations: ['90-35=55', '55-36=19'] Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[35, 36, 65], Operations: ['90-25=65'] Exploring Operation: 35+36=71, Resulting Numbers: [65, 71] Generated Node #0,1,0: 41:[65, 71] Operation: 35+36=71 Exploring Operation: 65-36=29, Resulting Numbers: [35, 29] Generated Node #0,1,1: 41:[35, 29] Operation: 65-36=29 Exploring Operation: 65-35=30, Resulting Numbers: [36, 30] Generated Node #0,1,2: 41:[36, 30] Operation: 65-35=30 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 41:[36, 30], Operations: ['90-25=65', '65-35=30'] Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 36*30=1080, Resulting Numbers: [1080] 1080,41 unequal: No Solution Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[35, 29], Operations: ['90-25=65', '65-36=29'] Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,41 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[65, 71], Operations: ['90-25=65', '35+36=71'] Exploring Operation: 71-65=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 65*71=4615, Resulting Numbers: [4615] 4615,41 unequal: No Solution Exploring Operation: 65+71=136, Resulting Numbers: [136] 136,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[25, 35, 54], Operations: ['90-36=54'] Exploring Operation: 25+35=60, Resulting Numbers: [54, 60] Generated Node #0,2,0: 41:[54, 60] Operation: 25+35=60 Exploring Operation: 54-35=19, Resulting Numbers: [25, 19] Generated Node #0,2,1: 41:[25, 19] Operation: 54-35=19 Exploring Operation: 54-25=29, Resulting Numbers: [35, 29] Generated Node #0,2,2: 41:[35, 29] Operation: 54-25=29 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 41:[35, 29], Operations: ['90-36=54', '54-25=29'] Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,41 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 41:[54, 60], Operations: ['90-36=54', '25+35=60'] Exploring Operation: 54*60=3240, Resulting Numbers: [3240] 3240,41 unequal: No Solution Exploring Operation: 54+60=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 60-54=6, Resulting Numbers: [6] 6,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 41:[25, 19], Operations: ['90-36=54', '54-35=19'] Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 11, 42, 7, 51 ]
36
[ "11-7=4", "51-42=9", "4*9=36" ]
Current State: 36:[11, 42, 7, 51], Operations: [] Exploring Operation: 11-7=4, Resulting Numbers: [42, 51, 4] Generated Node #2: [42, 51, 4] from Operation: 11-7=4 Current State: 36:[42, 51, 4], Operations: ['11-7=4'] Exploring Operation: 51-42=9, Resulting Numbers: [4, 9] Generated Node #3: [4, 9] from Operation: 51-42=9 Current State: 36:[4, 9], Operations: ['11-7=4', '51-42=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[11, 42, 7, 51], Operations: [] Exploring Operation: 51-11=40, Resulting Numbers: [42, 7, 40] Generated Node #0,0: 36:[42, 7, 40] Operation: 51-11=40 Exploring Operation: 51-7=44, Resulting Numbers: [11, 42, 44] Generated Node #0,1: 36:[11, 42, 44] Operation: 51-7=44 Exploring Operation: 42/7=6, Resulting Numbers: [11, 51, 6] Generated Node #0,2: 36:[11, 51, 6] Operation: 42/7=6 Exploring Operation: 51-42=9, Resulting Numbers: [11, 7, 9] Generated Node #0,3: 36:[11, 7, 9] Operation: 51-42=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 36:[11, 7, 9], Operations: ['51-42=9'] Exploring Operation: 11-7=4, Resulting Numbers: [9, 4] Generated Node #0,3,0: 36:[9, 4] Operation: 11-7=4 Exploring Operation: 11-9=2, Resulting Numbers: [7, 2] Generated Node #0,3,1: 36:[7, 2] Operation: 11-9=2 Exploring Operation: 9-7=2, Resulting Numbers: [11, 2] Generated Node #0,3,2: 36:[11, 2] Operation: 9-7=2 Exploring Operation: 11+7=18, Resulting Numbers: [9, 18] Generated Node #0,3,3: 36:[9, 18] Operation: 11+7=18 Moving to Node #0,3,0 Current State: 36:[9, 4], Operations: ['51-42=9', '11-7=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[11, 42, 7, 51], Operations: [] Exploring Operation: 51-42=9, Resulting Numbers: [11, 7, 9] Generated Node #0,3: 36:[11, 7, 9] Operation: 51-42=9 Moving to Node #0,3 Current State: 36:[11, 7, 9], Operations: ['51-42=9'] Exploring Operation: 11-7=4, Resulting Numbers: [9, 4] Generated Node #0,3,0: 36:[9, 4] Operation: 11-7=4 Moving to Node #0,3,0 Current State: 36:[9, 4], Operations: ['51-42=9', '11-7=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 3, 29, 88, 2 ]
27
[ "88-3=85", "29*2=58", "85-58=27" ]
Current State: 27:[3, 29, 88, 2], Operations: [] Exploring Operation: 88-3=85, Resulting Numbers: [29, 2, 85] Generated Node #2: [29, 2, 85] from Operation: 88-3=85 Current State: 27:[29, 2, 85], Operations: ['88-3=85'] Exploring Operation: 29*2=58, Resulting Numbers: [85, 58] Generated Node #3: [85, 58] from Operation: 29*2=58 Current State: 27:[85, 58], Operations: ['88-3=85', '29*2=58'] Exploring Operation: 85-58=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[3, 29, 88, 2], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [3, 29, 44] Generated Node #0,0: 27:[3, 29, 44] Operation: 88/2=44 Exploring Operation: 29-2=27, Resulting Numbers: [3, 88, 27] Generated Node #0,1: 27:[3, 88, 27] Operation: 29-2=27 Exploring Operation: 88-3=85, Resulting Numbers: [29, 2, 85] Generated Node #0,2: 27:[29, 2, 85] Operation: 88-3=85 Exploring Operation: 88-2=86, Resulting Numbers: [3, 29, 86] Generated Node #0,3: 27:[3, 29, 86] Operation: 88-2=86 Exploring Operation: 88-29=59, Resulting Numbers: [3, 2, 59] Generated Node #0,4: 27:[3, 2, 59] Operation: 88-29=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[3, 29, 44], Operations: ['88/2=44'] Exploring Operation: 44-3=41, Resulting Numbers: [29, 41] Generated Node #0,0,0: 27:[29, 41] Operation: 44-3=41 Exploring Operation: 29-3=26, Resulting Numbers: [44, 26] Generated Node #0,0,1: 27:[44, 26] Operation: 29-3=26 Exploring Operation: 3+44=47, Resulting Numbers: [29, 47] Generated Node #0,0,2: 27:[29, 47] Operation: 3+44=47 Exploring Operation: 3+29=32, Resulting Numbers: [44, 32] Generated Node #0,0,3: 27:[44, 32] Operation: 3+29=32 Exploring Operation: 44-29=15, Resulting Numbers: [3, 15] Generated Node #0,0,4: 27:[3, 15] Operation: 44-29=15 Moving to Node #0,0,4 Current State: 27:[3, 15], Operations: ['88/2=44', '44-29=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,27 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[29, 41], Operations: ['88/2=44', '44-3=41'] Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,27 unequal: No Solution 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 Moving to Node #0,0,1 Current State: 27:[44, 26], Operations: ['88/2=44', '29-3=26'] Exploring Operation: 44+26=70, Resulting Numbers: [70] 70,27 unequal: No Solution Exploring Operation: 44*26=1144, Resulting Numbers: [1144] 1144,27 unequal: No Solution Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[29, 47], Operations: ['88/2=44', '3+44=47'] Exploring Operation: 29*47=1363, Resulting Numbers: [1363] 1363,27 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 29+47=76, Resulting Numbers: [76] 76,27 unequal: No Solution Moving to Node #0,0,3 Current State: 27:[44, 32], Operations: ['88/2=44', '3+29=32'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 44+32=76, Resulting Numbers: [76] 76,27 unequal: No Solution Exploring Operation: 44*32=1408, Resulting Numbers: [1408] 1408,27 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 Current State: 27:[3, 2, 59], Operations: ['88-29=59'] Exploring Operation: 59-2=57, Resulting Numbers: [3, 57] Generated Node #0,4,0: 27:[3, 57] Operation: 59-2=57 Exploring Operation: 2+59=61, Resulting Numbers: [3, 61] Generated Node #0,4,1: 27:[3, 61] Operation: 2+59=61 Exploring Operation: 3-2=1, Resulting Numbers: [59, 1] Generated Node #0,4,2: 27:[59, 1] Operation: 3-2=1 Exploring Operation: 3+2=5, Resulting Numbers: [59, 5] Generated Node #0,4,3: 27:[59, 5] Operation: 3+2=5 Exploring Operation: 59-3=56, Resulting Numbers: [2, 56] Generated Node #0,4,4: 27:[2, 56] Operation: 59-3=56 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 27:[3, 57], Operations: ['88-29=59', '59-2=57'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,27 unequal: No Solution Exploring Operation: 3*57=171, Resulting Numbers: [171] 171,27 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,27 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 #0,4,4 Current State: 27:[2, 56], Operations: ['88-29=59', '59-3=56'] Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,27 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 #0,4,1 Current State: 27:[3, 61], Operations: ['88-29=59', '2+59=61'] Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,27 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,27 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 #0,4,2 Current State: 27:[59, 1], Operations: ['88-29=59', '3-2=1'] Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,27 unequal: No Solution Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,27 unequal: No Solution Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,27 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 #0,4,3 Current State: 27:[59, 5], Operations: ['88-29=59', '3+2=5'] Exploring Operation: 59+5=64, Resulting Numbers: [64] 64,27 unequal: No Solution Exploring Operation: 59*5=295, Resulting Numbers: [295] 295,27 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,27 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 #0,1 Current State: 27:[3, 88, 27], Operations: ['29-2=27'] Exploring Operation: 3+88=91, Resulting Numbers: [27, 91] Generated Node #0,1,0: 27:[27, 91] Operation: 3+88=91 Exploring Operation: 88-27=61, Resulting Numbers: [3, 61] Generated Node #0,1,1: 27:[3, 61] Operation: 88-27=61 Exploring Operation: 3+27=30, Resulting Numbers: [88, 30] Generated Node #0,1,2: 27:[88, 30] Operation: 3+27=30 Exploring Operation: 88-3=85, Resulting Numbers: [27, 85] Generated Node #0,1,3: 27:[27, 85] Operation: 88-3=85 Exploring Operation: 27/3=9, Resulting Numbers: [88, 9] Generated Node #0,1,4: 27:[88, 9] Operation: 27/3=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 27:[3, 61], Operations: ['29-2=27', '88-27=61'] Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,27 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,27 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 #0,1,3 Current State: 27:[27, 85], Operations: ['29-2=27', '88-3=85'] Exploring Operation: 27*85=2295, Resulting Numbers: [2295] 2295,27 unequal: No Solution Exploring Operation: 27+85=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 85-27=58, Resulting Numbers: [58] 58,27 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 #0,1,4 Current State: 27:[88, 9], Operations: ['29-2=27', '27/3=9'] Exploring Operation: 88*9=792, Resulting Numbers: [792] 792,27 unequal: No Solution Exploring Operation: 88-9=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 88+9=97, Resulting Numbers: [97] 97,27 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 #0,1,0 Current State: 27:[27, 91], Operations: ['29-2=27', '3+88=91'] Exploring Operation: 91-27=64, Resulting Numbers: [64] 64,27 unequal: No Solution Exploring Operation: 27*91=2457, Resulting Numbers: [2457] 2457,27 unequal: No Solution Exploring Operation: 27+91=118, Resulting Numbers: [118] 118,27 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 #0,1,2 Current State: 27:[88, 30], Operations: ['29-2=27', '3+27=30'] Exploring Operation: 88*30=2640, Resulting Numbers: [2640] 2640,27 unequal: No Solution Exploring Operation: 88-30=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 88+30=118, Resulting Numbers: [118] 118,27 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:[29, 2, 85], Operations: ['88-3=85'] Exploring Operation: 29-2=27, Resulting Numbers: [85, 27] Generated Node #0,2,0: 27:[85, 27] Operation: 29-2=27 Exploring Operation: 2+85=87, Resulting Numbers: [29, 87] Generated Node #0,2,1: 27:[29, 87] Operation: 2+85=87 Exploring Operation: 85-2=83, Resulting Numbers: [29, 83] Generated Node #0,2,2: 27:[29, 83] Operation: 85-2=83 Exploring Operation: 85-29=56, Resulting Numbers: [2, 56] Generated Node #0,2,3: 27:[2, 56] Operation: 85-29=56 Exploring Operation: 29+2=31, Resulting Numbers: [85, 31] Generated Node #0,2,4: 27:[85, 31] Operation: 29+2=31 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 27:[2, 56], Operations: ['88-3=85', '85-29=56'] Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,27 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 #0,2,0 Current State: 27:[85, 27], Operations: ['88-3=85', '29-2=27'] Exploring Operation: 85-27=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 85+27=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 85*27=2295, Resulting Numbers: [2295] 2295,27 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 #0,2,2 Current State: 27:[29, 83], Operations: ['88-3=85', '85-2=83'] Exploring Operation: 29+83=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 29*83=2407, Resulting Numbers: [2407] 2407,27 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 #0,2,1 Current State: 27:[29, 87], Operations: ['88-3=85', '2+85=87'] Exploring Operation: 29+87=116, Resulting Numbers: [116] 116,27 unequal: No Solution Exploring Operation: 29*87=2523, Resulting Numbers: [2523] 2523,27 unequal: No Solution Exploring Operation: 87-29=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 87/29=3, Resulting Numbers: [3] 3,27 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 #0,2,4 Current State: 27:[85, 31], Operations: ['88-3=85', '29+2=31'] Exploring Operation: 85+31=116, Resulting Numbers: [116] 116,27 unequal: No Solution Exploring Operation: 85-31=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 85*31=2635, Resulting Numbers: [2635] 2635,27 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 #0,3 Current State: 27:[3, 29, 86], Operations: ['88-2=86'] Exploring Operation: 3+29=32, Resulting Numbers: [86, 32] Generated Node #0,3,0: 27:[86, 32] Operation: 3+29=32 Exploring Operation: 86-3=83, Resulting Numbers: [29, 83] Generated Node #0,3,1: 27:[29, 83] Operation: 86-3=83 Exploring Operation: 29-3=26, Resulting Numbers: [86, 26] Generated Node #0,3,2: 27:[86, 26] Operation: 29-3=26 Exploring Operation: 86-29=57, Resulting Numbers: [3, 57] Generated Node #0,3,3: 27:[3, 57] Operation: 86-29=57 Exploring Operation: 3+86=89, Resulting Numbers: [29, 89] Generated Node #0,3,4: 27:[29, 89] Operation: 3+86=89 Moving to Node #0,3,3 Current State: 27:[3, 57], Operations: ['88-2=86', '86-29=57'] Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,27 unequal: No Solution Exploring Operation: 3*57=171, Resulting Numbers: [171] 171,27 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,27 unequal: No Solution Moving to Node #0,3,1 Current State: 27:[29, 83], Operations: ['88-2=86', '86-3=83'] Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 29*83=2407, Resulting Numbers: [2407] 2407,27 unequal: No Solution Exploring Operation: 29+83=112, Resulting Numbers: [112] 112,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[86, 26], Operations: ['88-2=86', '29-3=26'] Exploring Operation: 86*26=2236, Resulting Numbers: [2236] 2236,27 unequal: No Solution Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,27 unequal: No Solution Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,27 unequal: No Solution Moving to Node #0,3,0 Current State: 27:[86, 32], Operations: ['88-2=86', '3+29=32'] Exploring Operation: 86-32=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 86*32=2752, Resulting Numbers: [2752] 2752,27 unequal: No Solution Exploring Operation: 86+32=118, Resulting Numbers: [118] 118,27 unequal: No Solution Moving to Node #0,3,4 Current State: 27:[29, 89], Operations: ['88-2=86', '3+86=89'] Exploring Operation: 89-29=60, Resulting Numbers: [60] 60,27 unequal: No Solution Exploring Operation: 29*89=2581, Resulting Numbers: [2581] 2581,27 unequal: No Solution Exploring Operation: 29+89=118, Resulting Numbers: [118] 118,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 22, 67, 88, 65 ]
33
[ "88-22=66", "67-65=2", "66/2=33" ]
Current State: 33:[22, 67, 88, 65], Operations: [] Exploring Operation: 88-22=66, Resulting Numbers: [67, 65, 66] Generated Node #2: [67, 65, 66] from Operation: 88-22=66 Current State: 33:[67, 65, 66], Operations: ['88-22=66'] Exploring Operation: 67-65=2, Resulting Numbers: [66, 2] Generated Node #3: [66, 2] from Operation: 67-65=2 Current State: 33:[66, 2], Operations: ['88-22=66', '67-65=2'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[22, 67, 88, 65], Operations: [] Exploring Operation: 88-67=21, Resulting Numbers: [22, 65, 21] Generated Node #0,0: 33:[22, 65, 21] Operation: 88-67=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[22, 65, 21], Operations: ['88-67=21'] Exploring Operation: 65-22=43, Resulting Numbers: [21, 43] Generated Node #0,0,0: 33:[21, 43] Operation: 65-22=43 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[21, 43], Operations: ['88-67=21', '65-22=43'] Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 41, 11, 98, 49 ]
54
[ "41+11=52", "98/49=2", "52+2=54" ]
Current State: 54:[41, 11, 98, 49], Operations: [] Exploring Operation: 41+11=52, Resulting Numbers: [98, 49, 52] Generated Node #2: [98, 49, 52] from Operation: 41+11=52 Current State: 54:[98, 49, 52], Operations: ['41+11=52'] Exploring Operation: 98/49=2, Resulting Numbers: [52, 2] Generated Node #3: [52, 2] from Operation: 98/49=2 Current State: 54:[52, 2], Operations: ['41+11=52', '98/49=2'] Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[41, 11, 98, 49], Operations: [] Exploring Operation: 98-41=57, Resulting Numbers: [11, 49, 57] Generated Node #0,0: 54:[11, 49, 57] Operation: 98-41=57 Exploring Operation: 41+11=52, Resulting Numbers: [98, 49, 52] Generated Node #0,1: 54:[98, 49, 52] Operation: 41+11=52 Exploring Operation: 49-41=8, Resulting Numbers: [11, 98, 8] Generated Node #0,2: 54:[11, 98, 8] Operation: 49-41=8 Exploring Operation: 98/49=2, Resulting Numbers: [41, 11, 2] Generated Node #0,3: 54:[41, 11, 2] Operation: 98/49=2 Exploring Operation: 98-49=49, Resulting Numbers: [41, 11, 49] Generated Node #0,4: 54:[41, 11, 49] Operation: 98-49=49 Moving to Node #0,0 Current State: 54:[11, 49, 57], Operations: ['98-41=57'] Exploring Operation: 11+57=68, Resulting Numbers: [49, 68] Generated Node #0,0,0: 54:[49, 68] Operation: 11+57=68 Exploring Operation: 11+49=60, Resulting Numbers: [57, 60] Generated Node #0,0,1: 54:[57, 60] Operation: 11+49=60 Exploring Operation: 49-11=38, Resulting Numbers: [57, 38] Generated Node #0,0,2: 54:[57, 38] Operation: 49-11=38 Exploring Operation: 57-11=46, Resulting Numbers: [49, 46] Generated Node #0,0,3: 54:[49, 46] Operation: 57-11=46 Exploring Operation: 57-49=8, Resulting Numbers: [11, 8] Generated Node #0,0,4: 54:[11, 8] Operation: 57-49=8 Moving to Node #0,3 Current State: 54:[41, 11, 2], Operations: ['98/49=2'] Exploring Operation: 41+2=43, Resulting Numbers: [11, 43] Generated Node #0,3,0: 54:[11, 43] Operation: 41+2=43 Exploring Operation: 11-2=9, Resulting Numbers: [41, 9] Generated Node #0,3,1: 54:[41, 9] Operation: 11-2=9 Exploring Operation: 41+11=52, Resulting Numbers: [2, 52] Generated Node #0,3,2: 54:[2, 52] Operation: 41+11=52 Exploring Operation: 41-2=39, Resulting Numbers: [11, 39] Generated Node #0,3,3: 54:[11, 39] Operation: 41-2=39 Exploring Operation: 41-11=30, Resulting Numbers: [2, 30] Generated Node #0,3,4: 54:[2, 30] Operation: 41-11=30 Moving to Node #0,4 Current State: 54:[41, 11, 49], Operations: ['98-49=49'] Exploring Operation: 49-41=8, Resulting Numbers: [11, 8] Generated Node #0,4,0: 54:[11, 8] Operation: 49-41=8 Exploring Operation: 41-11=30, Resulting Numbers: [49, 30] Generated Node #0,4,1: 54:[49, 30] Operation: 41-11=30 Exploring Operation: 49-11=38, Resulting Numbers: [41, 38] Generated Node #0,4,2: 54:[41, 38] Operation: 49-11=38 Exploring Operation: 11+49=60, Resulting Numbers: [41, 60] Generated Node #0,4,3: 54:[41, 60] Operation: 11+49=60 Exploring Operation: 41+11=52, Resulting Numbers: [49, 52] Generated Node #0,4,4: 54:[49, 52] Operation: 41+11=52 Moving to Node #0,2 Current State: 54:[11, 98, 8], Operations: ['49-41=8'] Exploring Operation: 98-11=87, Resulting Numbers: [8, 87] Generated Node #0,2,0: 54:[8, 87] Operation: 98-11=87 Exploring Operation: 98-8=90, Resulting Numbers: [11, 90] Generated Node #0,2,1: 54:[11, 90] Operation: 98-8=90 Exploring Operation: 11+8=19, Resulting Numbers: [98, 19] Generated Node #0,2,2: 54:[98, 19] Operation: 11+8=19 Exploring Operation: 11-8=3, Resulting Numbers: [98, 3] Generated Node #0,2,3: 54:[98, 3] Operation: 11-8=3 Exploring Operation: 98+8=106, Resulting Numbers: [11, 106] Generated Node #0,2,4: 54:[11, 106] Operation: 98+8=106 Moving to Node #0,1 Current State: 54:[98, 49, 52], Operations: ['41+11=52'] Exploring Operation: 98-52=46, Resulting Numbers: [49, 46] Generated Node #0,1,0: 54:[49, 46] Operation: 98-52=46 Exploring Operation: 52-49=3, Resulting Numbers: [98, 3] Generated Node #0,1,1: 54:[98, 3] Operation: 52-49=3 Exploring Operation: 49+52=101, Resulting Numbers: [98, 101] Generated Node #0,1,2: 54:[98, 101] Operation: 49+52=101 Exploring Operation: 98-49=49, Resulting Numbers: [52, 49] Generated Node #0,1,3: 54:[52, 49] Operation: 98-49=49 Exploring Operation: 98/49=2, Resulting Numbers: [52, 2] Generated Node #0,1,4: 54:[52, 2] Operation: 98/49=2 Moving to Node #0,3,2 Current State: 54:[2, 52], Operations: ['98/49=2', '41+11=52'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,54 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[41, 11, 98, 49], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [41, 11, 2] Generated Node #0,3: 54:[41, 11, 2] Operation: 98/49=2 Moving to Node #0,3 Current State: 54:[41, 11, 2], Operations: ['98/49=2'] Exploring Operation: 41+11=52, Resulting Numbers: [2, 52] Generated Node #0,3,2: 54:[2, 52] Operation: 41+11=52 Moving to Node #0,3,2 Current State: 54:[2, 52], Operations: ['98/49=2', '41+11=52'] Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.967882
hs_5
sum_heuristic
[ 49, 33, 13, 80 ]
15
[ "49+33=82", "80-13=67", "82-67=15" ]
Current State: 15:[49, 33, 13, 80], Operations: [] Exploring Operation: 49+33=82, Resulting Numbers: [13, 80, 82] Generated Node #2: [13, 80, 82] from Operation: 49+33=82 Current State: 15:[13, 80, 82], Operations: ['49+33=82'] Exploring Operation: 80-13=67, Resulting Numbers: [82, 67] Generated Node #3: [82, 67] from Operation: 80-13=67 Current State: 15:[82, 67], Operations: ['49+33=82', '80-13=67'] Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[49, 33, 13, 80], Operations: [] Exploring Operation: 80-49=31, Resulting Numbers: [33, 13, 31] Generated Node #0,0: 15:[33, 13, 31] Operation: 80-49=31 Moving to Node #0,0 Current State: 15:[33, 13, 31], Operations: ['80-49=31'] Exploring Operation: 33-31=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 15:[13, 2] Operation: 33-31=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[13, 2], Operations: ['80-49=31', '33-31=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[49, 33, 13, 80], Operations: [] Exploring Operation: 80-49=31, Resulting Numbers: [33, 13, 31] Generated Node #0,0: 15:[33, 13, 31] Operation: 80-49=31 Moving to Node #0,0 Current State: 15:[33, 13, 31], Operations: ['80-49=31'] Exploring Operation: 33-31=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 15:[13, 2] Operation: 33-31=2 Moving to Node #0,0,0 Current State: 15:[13, 2], Operations: ['80-49=31', '33-31=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 57, 10, 89, 73 ]
63
[ "57-10=47", "89-73=16", "47+16=63" ]
Current State: 63:[57, 10, 89, 73], Operations: [] Exploring Operation: 57-10=47, Resulting Numbers: [89, 73, 47] Generated Node #2: [89, 73, 47] from Operation: 57-10=47 Current State: 63:[89, 73, 47], Operations: ['57-10=47'] Exploring Operation: 89-73=16, Resulting Numbers: [47, 16] Generated Node #3: [47, 16] from Operation: 89-73=16 Current State: 63:[47, 16], Operations: ['57-10=47', '89-73=16'] Exploring Operation: 47+16=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[57, 10, 89, 73], Operations: [] Exploring Operation: 89-73=16, Resulting Numbers: [57, 10, 16] Generated Node #0,0: 63:[57, 10, 16] Operation: 89-73=16 Exploring Operation: 73-57=16, Resulting Numbers: [10, 89, 16] Generated Node #0,1: 63:[10, 89, 16] Operation: 73-57=16 Exploring Operation: 89-57=32, Resulting Numbers: [10, 73, 32] Generated Node #0,2: 63:[10, 73, 32] Operation: 89-57=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[57, 10, 16], Operations: ['89-73=16'] Exploring Operation: 16-10=6, Resulting Numbers: [57, 6] Generated Node #0,0,0: 63:[57, 6] Operation: 16-10=6 Exploring Operation: 57+10=67, Resulting Numbers: [16, 67] Generated Node #0,0,1: 63:[16, 67] Operation: 57+10=67 Exploring Operation: 57+16=73, Resulting Numbers: [10, 73] Generated Node #0,0,2: 63:[10, 73] Operation: 57+16=73 Moving to Node #0,0,0 Current State: 63:[57, 6], Operations: ['89-73=16', '16-10=6'] Exploring Operation: 57*6=342, Resulting Numbers: [342] 342,63 unequal: No Solution Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[57, 10, 89, 73], Operations: [] Exploring Operation: 89-73=16, Resulting Numbers: [57, 10, 16] Generated Node #0,0: 63:[57, 10, 16] Operation: 89-73=16 Moving to Node #0,0 Current State: 63:[57, 10, 16], Operations: ['89-73=16'] Exploring Operation: 16-10=6, Resulting Numbers: [57, 6] Generated Node #0,0,0: 63:[57, 6] Operation: 16-10=6 Moving to Node #0,0,0 Current State: 63:[57, 6], Operations: ['89-73=16', '16-10=6'] Exploring Operation: 57+6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 20, 55, 26, 70 ]
75
[ "55*26=1430", "70+1430=1500", "1500/20=75" ]
Current State: 75:[20, 55, 26, 70], Operations: [] Exploring Operation: 55*26=1430, Resulting Numbers: [20, 70, 1430] Generated Node #2: [20, 70, 1430] from Operation: 55*26=1430 Current State: 75:[20, 70, 1430], Operations: ['55*26=1430'] Exploring Operation: 70+1430=1500, Resulting Numbers: [20, 1500] Generated Node #3: [20, 1500] from Operation: 70+1430=1500 Current State: 75:[20, 1500], Operations: ['55*26=1430', '70+1430=1500'] Exploring Operation: 1500/20=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[20, 55, 26, 70], Operations: [] Exploring Operation: 20+55=75, Resulting Numbers: [26, 70, 75] Generated Node #0,0: 75:[26, 70, 75] Operation: 20+55=75 Moving to Node #0,0 Current State: 75:[26, 70, 75], Operations: ['20+55=75'] Exploring Operation: 75-70=5, Resulting Numbers: [26, 5] Generated Node #0,0,0: 75:[26, 5] Operation: 75-70=5 Moving to Node #0,0,0 Current State: 75:[26, 5], Operations: ['20+55=75', '75-70=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,75 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 42, 32, 15, 20 ]
88
[ "42*20=840", "840/15=56", "32+56=88" ]
Current State: 88:[42, 32, 15, 20], Operations: [] Exploring Operation: 42*20=840, Resulting Numbers: [32, 15, 840] Generated Node #2: [32, 15, 840] from Operation: 42*20=840 Current State: 88:[32, 15, 840], Operations: ['42*20=840'] Exploring Operation: 840/15=56, Resulting Numbers: [32, 56] Generated Node #3: [32, 56] from Operation: 840/15=56 Current State: 88:[32, 56], Operations: ['42*20=840', '840/15=56'] Exploring Operation: 32+56=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[42, 32, 15, 20], Operations: [] Exploring Operation: 32-15=17, Resulting Numbers: [42, 20, 17] Generated Node #0,0: 88:[42, 20, 17] Operation: 32-15=17 Exploring Operation: 32-20=12, Resulting Numbers: [42, 15, 12] Generated Node #0,1: 88:[42, 15, 12] Operation: 32-20=12 Exploring Operation: 20-15=5, Resulting Numbers: [42, 32, 5] Generated Node #0,2: 88:[42, 32, 5] Operation: 20-15=5 Exploring Operation: 32+15=47, Resulting Numbers: [42, 20, 47] Generated Node #0,3: 88:[42, 20, 47] Operation: 32+15=47 Exploring Operation: 42-32=10, Resulting Numbers: [15, 20, 10] Generated Node #0,4: 88:[15, 20, 10] Operation: 42-32=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[42, 15, 12], Operations: ['32-20=12'] Exploring Operation: 42-15=27, Resulting Numbers: [12, 27] Generated Node #0,1,0: 88:[12, 27] Operation: 42-15=27 Exploring Operation: 15-12=3, Resulting Numbers: [42, 3] Generated Node #0,1,1: 88:[42, 3] Operation: 15-12=3 Exploring Operation: 42+15=57, Resulting Numbers: [12, 57] Generated Node #0,1,2: 88:[12, 57] Operation: 42+15=57 Exploring Operation: 42-12=30, Resulting Numbers: [15, 30] Generated Node #0,1,3: 88:[15, 30] Operation: 42-12=30 Exploring Operation: 15+12=27, Resulting Numbers: [42, 27] Generated Node #0,1,4: 88:[42, 27] Operation: 15+12=27 Moving to Node #0,1,1 Current State: 88:[42, 3], Operations: ['32-20=12', '15-12=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,88 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[12, 27], Operations: ['32-20=12', '42-15=27'] Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,88 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,88 unequal: No Solution Moving to Node #0,1,4 Current State: 88:[42, 27], Operations: ['32-20=12', '15+12=27'] Exploring Operation: 42*27=1134, Resulting Numbers: [1134] 1134,88 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 42+27=69, Resulting Numbers: [69] 69,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[15, 30], Operations: ['32-20=12', '42-12=30'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[12, 57], Operations: ['32-20=12', '42+15=57'] Exploring Operation: 12*57=684, Resulting Numbers: [684] 684,88 unequal: No Solution Exploring Operation: 57-12=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 12+57=69, Resulting Numbers: [69] 69,88 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 Current State: 88:[42, 20, 47], Operations: ['32+15=47'] Exploring Operation: 42+20=62, Resulting Numbers: [47, 62] Generated Node #0,3,0: 88:[47, 62] Operation: 42+20=62 Exploring Operation: 42+47=89, Resulting Numbers: [20, 89] Generated Node #0,3,1: 88:[20, 89] Operation: 42+47=89 Exploring Operation: 47-42=5, Resulting Numbers: [20, 5] Generated Node #0,3,2: 88:[20, 5] Operation: 47-42=5 Exploring Operation: 42-20=22, Resulting Numbers: [47, 22] Generated Node #0,3,3: 88:[47, 22] Operation: 42-20=22 Exploring Operation: 47-20=27, Resulting Numbers: [42, 27] Generated Node #0,3,4: 88:[42, 27] Operation: 47-20=27 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 88:[20, 89], Operations: ['32+15=47', '42+47=89'] Exploring Operation: 20*89=1780, Resulting Numbers: [1780] 1780,88 unequal: No Solution Exploring Operation: 89-20=69, Resulting Numbers: [69] 69,88 unequal: No Solution Exploring Operation: 20+89=109, Resulting Numbers: [109] 109,88 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 #0,3,2 Current State: 88:[20, 5], Operations: ['32+15=47', '47-42=5'] Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,88 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,88 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 #0,3,3 Current State: 88:[47, 22], Operations: ['32+15=47', '42-20=22'] Exploring Operation: 47*22=1034, Resulting Numbers: [1034] 1034,88 unequal: No Solution Exploring Operation: 47+22=69, Resulting Numbers: [69] 69,88 unequal: No Solution Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,88 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 #0,3,4 Current State: 88:[42, 27], Operations: ['32+15=47', '47-20=27'] Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 42*27=1134, Resulting Numbers: [1134] 1134,88 unequal: No Solution Exploring Operation: 42+27=69, Resulting Numbers: [69] 69,88 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 #0,3,0 Current State: 88:[47, 62], Operations: ['32+15=47', '42+20=62'] Exploring Operation: 47+62=109, Resulting Numbers: [109] 109,88 unequal: No Solution Exploring Operation: 62-47=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 47*62=2914, Resulting Numbers: [2914] 2914,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 88:[15, 20, 10], Operations: ['42-32=10'] Exploring Operation: 20/10=2, Resulting Numbers: [15, 2] Generated Node #0,4,0: 88:[15, 2] Operation: 20/10=2 Exploring Operation: 20-15=5, Resulting Numbers: [10, 5] Generated Node #0,4,1: 88:[10, 5] Operation: 20-15=5 Exploring Operation: 15+10=25, Resulting Numbers: [20, 25] Generated Node #0,4,2: 88:[20, 25] Operation: 15+10=25 Exploring Operation: 20-10=10, Resulting Numbers: [15, 10] Generated Node #0,4,3: 88:[15, 10] Operation: 20-10=10 Exploring Operation: 15-10=5, Resulting Numbers: [20, 5] Generated Node #0,4,4: 88:[20, 5] Operation: 15-10=5 Moving to Node #0,4,1 Current State: 88:[10, 5], Operations: ['42-32=10', '20-15=5'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[20, 5], Operations: ['42-32=10', '15-10=5'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,88 unequal: No Solution Moving to Node #0,4,0 Current State: 88:[15, 2], Operations: ['42-32=10', '20/10=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,88 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[20, 25], Operations: ['42-32=10', '15+10=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,88 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,88 unequal: No Solution Moving to Node #0,4,3 Current State: 88:[15, 10], Operations: ['42-32=10', '20-10=10'] Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,88 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,88 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 Current State: 88:[42, 20, 17], Operations: ['32-15=17'] Exploring Operation: 20-17=3, Resulting Numbers: [42, 3] Generated Node #0,0,0: 88:[42, 3] Operation: 20-17=3 Exploring Operation: 42-20=22, Resulting Numbers: [17, 22] Generated Node #0,0,1: 88:[17, 22] Operation: 42-20=22 Exploring Operation: 42-17=25, Resulting Numbers: [20, 25] Generated Node #0,0,2: 88:[20, 25] Operation: 42-17=25 Exploring Operation: 42+17=59, Resulting Numbers: [20, 59] Generated Node #0,0,3: 88:[20, 59] Operation: 42+17=59 Exploring Operation: 20+17=37, Resulting Numbers: [42, 37] Generated Node #0,0,4: 88:[42, 37] Operation: 20+17=37 Moving to Node #0,0,0 Current State: 88:[42, 3], Operations: ['32-15=17', '20-17=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,88 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[20, 25], Operations: ['32-15=17', '42-17=25'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,88 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[17, 22], Operations: ['32-15=17', '42-20=22'] Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,88 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,88 unequal: No Solution Moving to Node #0,0,4 Current State: 88:[42, 37], Operations: ['32-15=17', '20+17=37'] Exploring Operation: 42+37=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 42*37=1554, Resulting Numbers: [1554] 1554,88 unequal: No Solution Moving to Node #0,0,3 Current State: 88:[20, 59], Operations: ['32-15=17', '42+17=59'] Exploring Operation: 20+59=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 59-20=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 20*59=1180, Resulting Numbers: [1180] 1180,88 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 Current State: 88:[42, 32, 5], Operations: ['20-15=5'] Exploring Operation: 42+32=74, Resulting Numbers: [5, 74] Generated Node #0,2,0: 88:[5, 74] Operation: 42+32=74 Exploring Operation: 42-32=10, Resulting Numbers: [5, 10] Generated Node #0,2,1: 88:[5, 10] Operation: 42-32=10 Exploring Operation: 32-5=27, Resulting Numbers: [42, 27] Generated Node #0,2,2: 88:[42, 27] Operation: 32-5=27 Exploring Operation: 32+5=37, Resulting Numbers: [42, 37] Generated Node #0,2,3: 88:[42, 37] Operation: 32+5=37 Exploring Operation: 42+5=47, Resulting Numbers: [32, 47] Generated Node #0,2,4: 88:[32, 47] Operation: 42+5=47 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 88:[5, 10], Operations: ['20-15=5', '42-32=10'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,88 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:[42, 27], Operations: ['20-15=5', '32-5=27'] Exploring Operation: 42*27=1134, Resulting Numbers: [1134] 1134,88 unequal: No Solution Exploring Operation: 42+27=69, Resulting Numbers: [69] 69,88 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,88 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 #0,2,3 Current State: 88:[42, 37], Operations: ['20-15=5', '32+5=37'] Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 42*37=1554, Resulting Numbers: [1554] 1554,88 unequal: No Solution Exploring Operation: 42+37=79, Resulting Numbers: [79] 79,88 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 #0,2,4 Current State: 88:[32, 47], Operations: ['20-15=5', '42+5=47'] Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 32*47=1504, Resulting Numbers: [1504] 1504,88 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 #0,2,0 Current State: 88:[5, 74], Operations: ['20-15=5', '42+32=74'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,88 unequal: No Solution Exploring Operation: 5*74=370, Resulting Numbers: [370] 370,88 unequal: No Solution Exploring Operation: 5+74=79, Resulting Numbers: [79] 79,88 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
[ 89, 6, 92, 80 ]
17
[ "92-80=12", "6*12=72", "89-72=17" ]
Current State: 17:[89, 6, 92, 80], Operations: [] Exploring Operation: 92-80=12, Resulting Numbers: [89, 6, 12] Generated Node #2: [89, 6, 12] from Operation: 92-80=12 Current State: 17:[89, 6, 12], Operations: ['92-80=12'] Exploring Operation: 6*12=72, Resulting Numbers: [89, 72] Generated Node #3: [89, 72] from Operation: 6*12=72 Current State: 17:[89, 72], Operations: ['92-80=12', '6*12=72'] Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[89, 6, 92, 80], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [6, 80, 3] Generated Node #0,0: 17:[6, 80, 3] Operation: 92-89=3 Moving to Node #0,0 Current State: 17:[6, 80, 3], Operations: ['92-89=3'] Exploring Operation: 6*3=18, Resulting Numbers: [80, 18] Generated Node #0,0,0: 17:[80, 18] Operation: 6*3=18 Moving to Node #0,0,0 Current State: 17:[80, 18], Operations: ['92-89=3', '6*3=18'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,17 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 6, 52, 10, 56 ]
27
[ "10-6=4", "52+56=108", "108/4=27" ]
Current State: 27:[6, 52, 10, 56], Operations: [] Exploring Operation: 10-6=4, Resulting Numbers: [52, 56, 4] Generated Node #2: [52, 56, 4] from Operation: 10-6=4 Current State: 27:[52, 56, 4], Operations: ['10-6=4'] Exploring Operation: 52+56=108, Resulting Numbers: [4, 108] Generated Node #3: [4, 108] from Operation: 52+56=108 Current State: 27:[4, 108], Operations: ['10-6=4', '52+56=108'] Exploring Operation: 108/4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[6, 52, 10, 56], Operations: [] Exploring Operation: 52-10=42, Resulting Numbers: [6, 56, 42] Generated Node #0,0: 27:[6, 56, 42] Operation: 52-10=42 Exploring Operation: 56-10=46, Resulting Numbers: [6, 52, 46] Generated Node #0,1: 27:[6, 52, 46] Operation: 56-10=46 Exploring Operation: 56-52=4, Resulting Numbers: [6, 10, 4] Generated Node #0,2: 27:[6, 10, 4] Operation: 56-52=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[6, 10, 4], Operations: ['56-52=4'] Exploring Operation: 10-6=4, Resulting Numbers: [4, 4] Generated Node #0,2,0: 27:[4, 4] Operation: 10-6=4 Exploring Operation: 6+4=10, Resulting Numbers: [10, 10] Generated Node #0,2,1: 27:[10, 10] Operation: 6+4=10 Exploring Operation: 6-4=2, Resulting Numbers: [10, 2] Generated Node #0,2,2: 27:[10, 2] Operation: 6-4=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 27:[4, 4], Operations: ['56-52=4', '10-6=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,27 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 #0,2,1 Current State: 27:[10, 10], Operations: ['56-52=4', '6+4=10'] Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 10-10=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,27 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 #0,2,2 Current State: 27:[10, 2], Operations: ['56-52=4', '6-4=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,27 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 #0,0 Current State: 27:[6, 56, 42], Operations: ['52-10=42'] Exploring Operation: 42/6=7, Resulting Numbers: [56, 7] Generated Node #0,0,0: 27:[56, 7] Operation: 42/6=7 Exploring Operation: 56-42=14, Resulting Numbers: [6, 14] Generated Node #0,0,1: 27:[6, 14] Operation: 56-42=14 Exploring Operation: 56-6=50, Resulting Numbers: [42, 50] Generated Node #0,0,2: 27:[42, 50] Operation: 56-6=50 Moving to Node #0,0,1 Current State: 27:[6, 14], Operations: ['52-10=42', '56-42=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[56, 7], Operations: ['52-10=42', '42/6=7'] Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,27 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,27 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[42, 50], Operations: ['52-10=42', '56-6=50'] Exploring Operation: 42*50=2100, Resulting Numbers: [2100] 2100,27 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 42+50=92, Resulting Numbers: [92] 92,27 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 #0,1 Current State: 27:[6, 52, 46], Operations: ['56-10=46'] Exploring Operation: 46-6=40, Resulting Numbers: [52, 40] Generated Node #0,1,0: 27:[52, 40] Operation: 46-6=40 Exploring Operation: 52-46=6, Resulting Numbers: [6, 6] Generated Node #0,1,1: 27:[6, 6] Operation: 52-46=6 Exploring Operation: 52-6=46, Resulting Numbers: [46, 46] Generated Node #0,1,2: 27:[46, 46] Operation: 52-6=46 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 27:[6, 6], Operations: ['56-10=46', '52-46=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,27 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 #0,1,0 Current State: 27:[52, 40], Operations: ['56-10=46', '46-6=40'] Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,27 unequal: No Solution Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,27 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 #0,1,2 Current State: 27:[46, 46], Operations: ['56-10=46', '52-6=46'] Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,27 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 No solution found.
0
hs_3
mult_heuristic
[ 94, 29, 5, 58 ]
84
[ "58/29=2", "5*2=10", "94-10=84" ]
Current State: 84:[94, 29, 5, 58], Operations: [] Exploring Operation: 58/29=2, Resulting Numbers: [94, 5, 2] Generated Node #2: [94, 5, 2] from Operation: 58/29=2 Current State: 84:[94, 5, 2], Operations: ['58/29=2'] Exploring Operation: 5*2=10, Resulting Numbers: [94, 10] Generated Node #3: [94, 10] from Operation: 5*2=10 Current State: 84:[94, 10], Operations: ['58/29=2', '5*2=10'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[94, 29, 5, 58], Operations: [] Exploring Operation: 29+58=87, Resulting Numbers: [94, 5, 87] Generated Node #0,0: 84:[94, 5, 87] Operation: 29+58=87 Exploring Operation: 58/29=2, Resulting Numbers: [94, 5, 2] Generated Node #0,1: 84:[94, 5, 2] Operation: 58/29=2 Exploring Operation: 94-58=36, Resulting Numbers: [29, 5, 36] Generated Node #0,2: 84:[29, 5, 36] Operation: 94-58=36 Exploring Operation: 58-29=29, Resulting Numbers: [94, 5, 29] Generated Node #0,3: 84:[94, 5, 29] Operation: 58-29=29 Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[29, 5, 36], Operations: ['94-58=36'] Exploring Operation: 36-29=7, Resulting Numbers: [5, 7] Generated Node #0,2,0: 84:[5, 7] Operation: 36-29=7 Exploring Operation: 5+36=41, Resulting Numbers: [29, 41] Generated Node #0,2,1: 84:[29, 41] Operation: 5+36=41 Exploring Operation: 36-5=31, Resulting Numbers: [29, 31] Generated Node #0,2,2: 84:[29, 31] Operation: 36-5=31 Exploring Operation: 29-5=24, Resulting Numbers: [36, 24] Generated Node #0,2,3: 84:[36, 24] Operation: 29-5=24 Moving to Node #0,2,0 Current State: 84:[5, 7], Operations: ['94-58=36', '36-29=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[29, 41], Operations: ['94-58=36', '5+36=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[29, 31], Operations: ['94-58=36', '36-5=31'] Exploring Operation: 29*31=899, Resulting Numbers: [899] 899,84 unequal: No Solution Exploring Operation: 29+31=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,84 unequal: No Solution Moving to Node #0,2,3 Current State: 84:[36, 24], Operations: ['94-58=36', '29-5=24'] Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 36*24=864, Resulting Numbers: [864] 864,84 unequal: No Solution Exploring Operation: 36+24=60, Resulting Numbers: [60] 60,84 unequal: No Solution No 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: 84:[94, 5, 2], Operations: ['58/29=2'] Exploring Operation: 94-5=89, Resulting Numbers: [2, 89] Generated Node #0,1,0: 84:[2, 89] Operation: 94-5=89 Exploring Operation: 5+2=7, Resulting Numbers: [94, 7] Generated Node #0,1,1: 84:[94, 7] Operation: 5+2=7 Exploring Operation: 94/2=47, Resulting Numbers: [5, 47] Generated Node #0,1,2: 84:[5, 47] Operation: 94/2=47 Exploring Operation: 94-2=92, Resulting Numbers: [5, 92] Generated Node #0,1,3: 84:[5, 92] Operation: 94-2=92 Moving to Node #0,1,0 Current State: 84:[2, 89], Operations: ['58/29=2', '94-5=89'] Exploring Operation: 2*89=178, Resulting Numbers: [178] 178,84 unequal: No Solution Exploring Operation: 2+89=91, Resulting Numbers: [91] 91,84 unequal: No Solution Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[5, 47], Operations: ['58/29=2', '94/2=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,84 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[5, 92], Operations: ['58/29=2', '94-2=92'] Exploring Operation: 92-5=87, Resulting Numbers: [87] 87,84 unequal: No Solution Exploring Operation: 5*92=460, Resulting Numbers: [460] 460,84 unequal: No Solution Exploring Operation: 5+92=97, Resulting Numbers: [97] 97,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[94, 7], Operations: ['58/29=2', '5+2=7'] Exploring Operation: 94*7=658, Resulting Numbers: [658] 658,84 unequal: No Solution Exploring Operation: 94-7=87, Resulting Numbers: [87] 87,84 unequal: No Solution Exploring Operation: 94+7=101, Resulting Numbers: [101] 101,84 unequal: No Solution No 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: 84:[94, 5, 29], Operations: ['58-29=29'] Exploring Operation: 94+5=99, Resulting Numbers: [29, 99] Generated Node #0,3,0: 84:[29, 99] Operation: 94+5=99 Exploring Operation: 5+29=34, Resulting Numbers: [94, 34] Generated Node #0,3,1: 84:[94, 34] Operation: 5+29=34 Exploring Operation: 29-5=24, Resulting Numbers: [94, 24] Generated Node #0,3,2: 84:[94, 24] Operation: 29-5=24 Exploring Operation: 94-5=89, Resulting Numbers: [29, 89] Generated Node #0,3,3: 84:[29, 89] Operation: 94-5=89 Moving to Node #0,3,3 Current State: 84:[29, 89], Operations: ['58-29=29', '94-5=89'] Exploring Operation: 29+89=118, Resulting Numbers: [118] 118,84 unequal: No Solution Exploring Operation: 89-29=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 29*89=2581, Resulting Numbers: [2581] 2581,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[94, 24], Operations: ['58-29=29', '29-5=24'] Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 94*24=2256, Resulting Numbers: [2256] 2256,84 unequal: No Solution Exploring Operation: 94+24=118, Resulting Numbers: [118] 118,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[94, 34], Operations: ['58-29=29', '5+29=34'] Exploring Operation: 94+34=128, Resulting Numbers: [128] 128,84 unequal: No Solution Exploring Operation: 94-34=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 94*34=3196, Resulting Numbers: [3196] 3196,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[29, 99], Operations: ['58-29=29', '94+5=99'] Exploring Operation: 99-29=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 29+99=128, Resulting Numbers: [128] 128,84 unequal: No Solution Exploring Operation: 29*99=2871, Resulting Numbers: [2871] 2871,84 unequal: No Solution No 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: 84:[94, 5, 87], Operations: ['29+58=87'] Exploring Operation: 94-5=89, Resulting Numbers: [87, 89] Generated Node #0,0,0: 84:[87, 89] Operation: 94-5=89 Exploring Operation: 87-5=82, Resulting Numbers: [94, 82] Generated Node #0,0,1: 84:[94, 82] Operation: 87-5=82 Exploring Operation: 94-87=7, Resulting Numbers: [5, 7] Generated Node #0,0,2: 84:[5, 7] Operation: 94-87=7 Exploring Operation: 94+5=99, Resulting Numbers: [87, 99] Generated Node #0,0,3: 84:[87, 99] Operation: 94+5=99 Moving to Node #0,0,2 Current State: 84:[5, 7], Operations: ['29+58=87', '94-87=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[87, 89], Operations: ['29+58=87', '94-5=89'] Exploring Operation: 87*89=7743, Resulting Numbers: [7743] 7743,84 unequal: No Solution Exploring Operation: 87+89=176, Resulting Numbers: [176] 176,84 unequal: No Solution Exploring Operation: 89-87=2, Resulting Numbers: [2] 2,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[94, 82], Operations: ['29+58=87', '87-5=82'] Exploring Operation: 94+82=176, Resulting Numbers: [176] 176,84 unequal: No Solution Exploring Operation: 94*82=7708, Resulting Numbers: [7708] 7708,84 unequal: No Solution Exploring Operation: 94-82=12, Resulting Numbers: [12] 12,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[87, 99], Operations: ['29+58=87', '94+5=99'] Exploring Operation: 87+99=186, Resulting Numbers: [186] 186,84 unequal: No Solution Exploring Operation: 99-87=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 87*99=8613, Resulting Numbers: [8613] 8613,84 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
[ 10, 63, 13, 1 ]
40
[ "63-10=53", "13*1=13", "53-13=40" ]
Current State: 40:[10, 63, 13, 1], Operations: [] Exploring Operation: 63-10=53, Resulting Numbers: [13, 1, 53] Generated Node #2: [13, 1, 53] from Operation: 63-10=53 Current State: 40:[13, 1, 53], Operations: ['63-10=53'] Exploring Operation: 13*1=13, Resulting Numbers: [53, 13] Generated Node #3: [53, 13] from Operation: 13*1=13 Current State: 40:[53, 13], Operations: ['63-10=53', '13*1=13'] Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[10, 63, 13, 1], Operations: [] Exploring Operation: 63-1=62, Resulting Numbers: [10, 13, 62] Generated Node #0,0: 40:[10, 13, 62] Operation: 63-1=62 Exploring Operation: 13-10=3, Resulting Numbers: [63, 1, 3] Generated Node #0,1: 40:[63, 1, 3] Operation: 13-10=3 Exploring Operation: 63-13=50, Resulting Numbers: [10, 1, 50] Generated Node #0,2: 40:[10, 1, 50] Operation: 63-13=50 Exploring Operation: 13-1=12, Resulting Numbers: [10, 63, 12] Generated Node #0,3: 40:[10, 63, 12] Operation: 13-1=12 Exploring Operation: 63-10=53, Resulting Numbers: [13, 1, 53] Generated Node #0,4: 40:[13, 1, 53] Operation: 63-10=53 Moving to Node #0,2 Current State: 40:[10, 1, 50], Operations: ['63-13=50'] Exploring Operation: 10/1=10, Resulting Numbers: [50, 10] Generated Node #0,2,0: 40:[50, 10] Operation: 10/1=10 Exploring Operation: 50/10=5, Resulting Numbers: [1, 5] Generated Node #0,2,1: 40:[1, 5] Operation: 50/10=5 Exploring Operation: 50-1=49, Resulting Numbers: [10, 49] Generated Node #0,2,2: 40:[10, 49] Operation: 50-1=49 Exploring Operation: 50-10=40, Resulting Numbers: [1, 40] Generated Node #0,2,3: 40:[1, 40] Operation: 50-10=40 Exploring Operation: 10*1=10, Resulting Numbers: [50, 10] Generated Node #0,2,4: 40:[50, 10] Operation: 10*1=10 Moving to Node #0,4 Current State: 40:[13, 1, 53], Operations: ['63-10=53'] Exploring Operation: 13-1=12, Resulting Numbers: [53, 12] Generated Node #0,4,0: 40:[53, 12] Operation: 13-1=12 Exploring Operation: 13*1=13, Resulting Numbers: [53, 13] Generated Node #0,4,1: 40:[53, 13] Operation: 13*1=13 Exploring Operation: 53-1=52, Resulting Numbers: [13, 52] Generated Node #0,4,2: 40:[13, 52] Operation: 53-1=52 Exploring Operation: 13/1=13, Resulting Numbers: [53, 13] Generated Node #0,4,3: 40:[53, 13] Operation: 13/1=13 Exploring Operation: 53-13=40, Resulting Numbers: [1, 40] Generated Node #0,4,4: 40:[1, 40] Operation: 53-13=40 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 40:[1, 40], Operations: ['63-10=53', '53-13=40'] Exploring Operation: 1+40=41, Resulting Numbers: [41] 41,40 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,40 unequal: No Solution Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[10, 63, 13, 1], Operations: [] Exploring Operation: 63-10=53, Resulting Numbers: [13, 1, 53] Generated Node #0,4: 40:[13, 1, 53] Operation: 63-10=53 Moving to Node #0,4 Current State: 40:[13, 1, 53], Operations: ['63-10=53'] Exploring Operation: 53-13=40, Resulting Numbers: [1, 40] Generated Node #0,4,4: 40:[1, 40] Operation: 53-13=40 Moving to Node #0,4,4 Current State: 40:[1, 40], Operations: ['63-10=53', '53-13=40'] Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 47, 27, 28, 46 ]
94
[ "47-27=20", "28+46=74", "20+74=94" ]
Current State: 94:[47, 27, 28, 46], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [28, 46, 20] Generated Node #2: [28, 46, 20] from Operation: 47-27=20 Current State: 94:[28, 46, 20], Operations: ['47-27=20'] Exploring Operation: 28+46=74, Resulting Numbers: [20, 74] Generated Node #3: [20, 74] from Operation: 28+46=74 Current State: 94:[20, 74], Operations: ['47-27=20', '28+46=74'] Exploring Operation: 20+74=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[47, 27, 28, 46], Operations: [] Exploring Operation: 28-27=1, Resulting Numbers: [47, 46, 1] Generated Node #0,0: 94:[47, 46, 1] Operation: 28-27=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[47, 46, 1], Operations: ['28-27=1'] Exploring Operation: 46+1=47, Resulting Numbers: [47, 47] Generated Node #0,0,0: 94:[47, 47] Operation: 46+1=47 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[47, 47], Operations: ['28-27=1', '46+1=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[47, 27, 28, 46], Operations: [] Exploring Operation: 28-27=1, Resulting Numbers: [47, 46, 1] Generated Node #0,0: 94:[47, 46, 1] Operation: 28-27=1 Moving to Node #0,0 Current State: 94:[47, 46, 1], Operations: ['28-27=1'] Exploring Operation: 46+1=47, Resulting Numbers: [47, 47] Generated Node #0,0,0: 94:[47, 47] Operation: 46+1=47 Moving to Node #0,0,0 Current State: 94:[47, 47], Operations: ['28-27=1', '46+1=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 68, 5, 40, 33 ]
15
[ "68+40=108", "108-33=75", "75/5=15" ]
Current State: 15:[68, 5, 40, 33], Operations: [] Exploring Operation: 68+40=108, Resulting Numbers: [5, 33, 108] Generated Node #2: [5, 33, 108] from Operation: 68+40=108 Current State: 15:[5, 33, 108], Operations: ['68+40=108'] Exploring Operation: 108-33=75, Resulting Numbers: [5, 75] Generated Node #3: [5, 75] from Operation: 108-33=75 Current State: 15:[5, 75], Operations: ['68+40=108', '108-33=75'] Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[68, 5, 40, 33], Operations: [] Exploring Operation: 68-40=28, Resulting Numbers: [5, 33, 28] Generated Node #0,0: 15:[5, 33, 28] Operation: 68-40=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[5, 33, 28], Operations: ['68-40=28'] Exploring Operation: 33-28=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 15:[5, 5] Operation: 33-28=5 Moving to Node #0,0,0 Current State: 15:[5, 5], Operations: ['68-40=28', '33-28=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,15 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
[ 66, 22, 57, 47 ]
16
[ "66+22=88", "57+47=104", "104-88=16" ]
Current State: 16:[66, 22, 57, 47], Operations: [] Exploring Operation: 66+22=88, Resulting Numbers: [57, 47, 88] Generated Node #2: [57, 47, 88] from Operation: 66+22=88 Current State: 16:[57, 47, 88], Operations: ['66+22=88'] Exploring Operation: 57+47=104, Resulting Numbers: [88, 104] Generated Node #3: [88, 104] from Operation: 57+47=104 Current State: 16:[88, 104], Operations: ['66+22=88', '57+47=104'] Exploring Operation: 104-88=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[66, 22, 57, 47], Operations: [] Exploring Operation: 66/22=3, Resulting Numbers: [57, 47, 3] Generated Node #0,0: 16:[57, 47, 3] Operation: 66/22=3 Exploring Operation: 57-47=10, Resulting Numbers: [66, 22, 10] Generated Node #0,1: 16:[66, 22, 10] Operation: 57-47=10 Exploring Operation: 66-57=9, Resulting Numbers: [22, 47, 9] Generated Node #0,2: 16:[22, 47, 9] Operation: 66-57=9 Exploring Operation: 66-47=19, Resulting Numbers: [22, 57, 19] Generated Node #0,3: 16:[22, 57, 19] Operation: 66-47=19 Moving to Node #0,2 Current State: 16:[22, 47, 9], Operations: ['66-57=9'] Exploring Operation: 47-9=38, Resulting Numbers: [22, 38] Generated Node #0,2,0: 16:[22, 38] Operation: 47-9=38 Exploring Operation: 22-9=13, Resulting Numbers: [47, 13] Generated Node #0,2,1: 16:[47, 13] Operation: 22-9=13 Exploring Operation: 47-22=25, Resulting Numbers: [9, 25] Generated Node #0,2,2: 16:[9, 25] Operation: 47-22=25 Exploring Operation: 22+9=31, Resulting Numbers: [47, 31] Generated Node #0,2,3: 16:[47, 31] Operation: 22+9=31 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 16:[9, 25], Operations: ['66-57=9', '47-22=25'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[66, 22, 57, 47], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [22, 47, 9] Generated Node #0,2: 16:[22, 47, 9] Operation: 66-57=9 Moving to Node #0,2 Current State: 16:[22, 47, 9], Operations: ['66-57=9'] Exploring Operation: 47-22=25, Resulting Numbers: [9, 25] Generated Node #0,2,2: 16:[9, 25] Operation: 47-22=25 Moving to Node #0,2,2 Current State: 16:[9, 25], Operations: ['66-57=9', '47-22=25'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 88, 50, 28, 17 ]
68
[ "88*17=1496", "50-28=22", "1496/22=68" ]
Current State: 68:[88, 50, 28, 17], Operations: [] Exploring Operation: 88*17=1496, Resulting Numbers: [50, 28, 1496] Generated Node #2: [50, 28, 1496] from Operation: 88*17=1496 Current State: 68:[50, 28, 1496], Operations: ['88*17=1496'] Exploring Operation: 50-28=22, Resulting Numbers: [1496, 22] Generated Node #3: [1496, 22] from Operation: 50-28=22 Current State: 68:[1496, 22], Operations: ['88*17=1496', '50-28=22'] Exploring Operation: 1496/22=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[88, 50, 28, 17], Operations: [] Exploring Operation: 88-17=71, Resulting Numbers: [50, 28, 71] Generated Node #0,0: 68:[50, 28, 71] Operation: 88-17=71 Exploring Operation: 88-28=60, Resulting Numbers: [50, 17, 60] Generated Node #0,1: 68:[50, 17, 60] Operation: 88-28=60 Exploring Operation: 88-50=38, Resulting Numbers: [28, 17, 38] Generated Node #0,2: 68:[28, 17, 38] Operation: 88-50=38 Moving to Node #0,2 Current State: 68:[28, 17, 38], Operations: ['88-50=38'] Exploring Operation: 28-17=11, Resulting Numbers: [38, 11] Generated Node #0,2,0: 68:[38, 11] Operation: 28-17=11 Exploring Operation: 38-28=10, Resulting Numbers: [17, 10] Generated Node #0,2,1: 68:[17, 10] Operation: 38-28=10 Exploring Operation: 28+38=66, Resulting Numbers: [17, 66] Generated Node #0,2,2: 68:[17, 66] Operation: 28+38=66 Moving to Node #0,1 Current State: 68:[50, 17, 60], Operations: ['88-28=60'] Exploring Operation: 60-50=10, Resulting Numbers: [17, 10] Generated Node #0,1,0: 68:[17, 10] Operation: 60-50=10 Exploring Operation: 50-17=33, Resulting Numbers: [60, 33] Generated Node #0,1,1: 68:[60, 33] Operation: 50-17=33 Exploring Operation: 50+17=67, Resulting Numbers: [60, 67] Generated Node #0,1,2: 68:[60, 67] Operation: 50+17=67 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[17, 10], Operations: ['88-28=60', '60-50=10'] Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,68 unequal: No Solution Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[60, 33], Operations: ['88-28=60', '50-17=33'] Exploring Operation: 60+33=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 60*33=1980, Resulting Numbers: [1980] 1980,68 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 68:[60, 67], Operations: ['88-28=60', '50+17=67'] Exploring Operation: 67-60=7, Resulting Numbers: [7] 7,68 unequal: No Solution Exploring Operation: 60+67=127, Resulting Numbers: [127] 127,68 unequal: No Solution Exploring Operation: 60*67=4020, Resulting Numbers: [4020] 4020,68 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: 68:[50, 28, 71], Operations: ['88-17=71'] Exploring Operation: 50-28=22, Resulting Numbers: [71, 22] Generated Node #0,0,0: 68:[71, 22] Operation: 50-28=22 Exploring Operation: 50+28=78, Resulting Numbers: [71, 78] Generated Node #0,0,1: 68:[71, 78] Operation: 50+28=78 Exploring Operation: 71-50=21, Resulting Numbers: [28, 21] Generated Node #0,0,2: 68:[28, 21] Operation: 71-50=21 Moving to Node #0,2,2 Current State: 68:[17, 66], Operations: ['88-50=38', '28+38=66'] Exploring Operation: 17+66=83, Resulting Numbers: [83] 83,68 unequal: No Solution Exploring Operation: 17*66=1122, Resulting Numbers: [1122] 1122,68 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[17, 10], Operations: ['88-50=38', '38-28=10'] Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,68 unequal: No Solution Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[71, 22], Operations: ['88-17=71', '50-28=22'] Exploring Operation: 71*22=1562, Resulting Numbers: [1562] 1562,68 unequal: No Solution Exploring Operation: 71+22=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 71-22=49, Resulting Numbers: [49] 49,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[38, 11], Operations: ['88-50=38', '28-17=11'] Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 38+11=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 38*11=418, Resulting Numbers: [418] 418,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[28, 21], Operations: ['88-17=71', '71-50=21'] Exploring Operation: 28*21=588, Resulting Numbers: [588] 588,68 unequal: No Solution Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[71, 78], Operations: ['88-17=71', '50+28=78'] Exploring Operation: 71*78=5538, Resulting Numbers: [5538] 5538,68 unequal: No Solution Exploring Operation: 78-71=7, Resulting Numbers: [7] 7,68 unequal: No Solution Exploring Operation: 71+78=149, Resulting Numbers: [149] 149,68 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 22, 8, 11, 73 ]
92
[ "22+8=30", "73-11=62", "30+62=92" ]
Current State: 92:[22, 8, 11, 73], Operations: [] Exploring Operation: 22+8=30, Resulting Numbers: [11, 73, 30] Generated Node #2: [11, 73, 30] from Operation: 22+8=30 Current State: 92:[11, 73, 30], Operations: ['22+8=30'] Exploring Operation: 73-11=62, Resulting Numbers: [30, 62] Generated Node #3: [30, 62] from Operation: 73-11=62 Current State: 92:[30, 62], Operations: ['22+8=30', '73-11=62'] Exploring Operation: 30+62=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[22, 8, 11, 73], Operations: [] Exploring Operation: 11+73=84, Resulting Numbers: [22, 8, 84] Generated Node #0,0: 92:[22, 8, 84] Operation: 11+73=84 Moving to Node #0,0 Current State: 92:[22, 8, 84], Operations: ['11+73=84'] Exploring Operation: 8+84=92, Resulting Numbers: [22, 92] Generated Node #0,0,0: 92:[22, 92] Operation: 8+84=92 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[22, 92], Operations: ['11+73=84', '8+84=92'] Exploring Operation: 22+92=114, Resulting Numbers: [114] 114,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 36, 95, 45, 78 ]
26
[ "95-36=59", "78-45=33", "59-33=26" ]
Current State: 26:[36, 95, 45, 78], Operations: [] Exploring Operation: 95-36=59, Resulting Numbers: [45, 78, 59] Generated Node #2: [45, 78, 59] from Operation: 95-36=59 Current State: 26:[45, 78, 59], Operations: ['95-36=59'] Exploring Operation: 78-45=33, Resulting Numbers: [59, 33] Generated Node #3: [59, 33] from Operation: 78-45=33 Current State: 26:[59, 33], Operations: ['95-36=59', '78-45=33'] Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[36, 95, 45, 78], Operations: [] Exploring Operation: 95-36=59, Resulting Numbers: [45, 78, 59] Generated Node #0,0: 26:[45, 78, 59] Operation: 95-36=59 Exploring Operation: 95-78=17, Resulting Numbers: [36, 45, 17] Generated Node #0,1: 26:[36, 45, 17] Operation: 95-78=17 Exploring Operation: 95-45=50, Resulting Numbers: [36, 78, 50] Generated Node #0,2: 26:[36, 78, 50] Operation: 95-45=50 Exploring Operation: 78-45=33, Resulting Numbers: [36, 95, 33] Generated Node #0,3: 26:[36, 95, 33] Operation: 78-45=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[36, 45, 17], Operations: ['95-78=17'] Exploring Operation: 45-17=28, Resulting Numbers: [36, 28] Generated Node #0,1,0: 26:[36, 28] Operation: 45-17=28 Exploring Operation: 45-36=9, Resulting Numbers: [17, 9] Generated Node #0,1,1: 26:[17, 9] Operation: 45-36=9 Exploring Operation: 36+17=53, Resulting Numbers: [45, 53] Generated Node #0,1,2: 26:[45, 53] Operation: 36+17=53 Exploring Operation: 36-17=19, Resulting Numbers: [45, 19] Generated Node #0,1,3: 26:[45, 19] Operation: 36-17=19 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 26:[17, 9], Operations: ['95-78=17', '45-36=9'] Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,26 unequal: No Solution Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[36, 95, 45, 78], Operations: [] Exploring Operation: 95-78=17, Resulting Numbers: [36, 45, 17] Generated Node #0,1: 26:[36, 45, 17] Operation: 95-78=17 Moving to Node #0,1 Current State: 26:[36, 45, 17], Operations: ['95-78=17'] Exploring Operation: 45-36=9, Resulting Numbers: [17, 9] Generated Node #0,1,1: 26:[17, 9] Operation: 45-36=9 Moving to Node #0,1,1 Current State: 26:[17, 9], Operations: ['95-78=17', '45-36=9'] Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 60, 17, 71, 20 ]
85
[ "60/20=3", "17+71=88", "88-3=85" ]
Current State: 85:[60, 17, 71, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [17, 71, 3] Generated Node #2: [17, 71, 3] from Operation: 60/20=3 Current State: 85:[17, 71, 3], Operations: ['60/20=3'] Exploring Operation: 17+71=88, Resulting Numbers: [3, 88] Generated Node #3: [3, 88] from Operation: 17+71=88 Current State: 85:[3, 88], Operations: ['60/20=3', '17+71=88'] Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[60, 17, 71, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [17, 71, 3] Generated Node #0,0: 85:[17, 71, 3] Operation: 60/20=3 Exploring Operation: 71-60=11, Resulting Numbers: [17, 20, 11] Generated Node #0,1: 85:[17, 20, 11] Operation: 71-60=11 Moving to Node #0,1 Current State: 85:[17, 20, 11], Operations: ['71-60=11'] Exploring Operation: 17-11=6, Resulting Numbers: [20, 6] Generated Node #0,1,0: 85:[20, 6] Operation: 17-11=6 Exploring Operation: 20-11=9, Resulting Numbers: [17, 9] Generated Node #0,1,1: 85:[17, 9] Operation: 20-11=9 Moving to Node #0,0 Current State: 85:[17, 71, 3], Operations: ['60/20=3'] Exploring Operation: 71+3=74, Resulting Numbers: [17, 74] Generated Node #0,0,0: 85:[17, 74] Operation: 71+3=74 Exploring Operation: 17+71=88, Resulting Numbers: [3, 88] Generated Node #0,0,1: 85:[3, 88] Operation: 17+71=88 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[3, 88], Operations: ['60/20=3', '17+71=88'] Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[60, 17, 71, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [17, 71, 3] Generated Node #0,0: 85:[17, 71, 3] Operation: 60/20=3 Moving to Node #0,0 Current State: 85:[17, 71, 3], Operations: ['60/20=3'] Exploring Operation: 17+71=88, Resulting Numbers: [3, 88] Generated Node #0,0,1: 85:[3, 88] Operation: 17+71=88 Moving to Node #0,0,1 Current State: 85:[3, 88], Operations: ['60/20=3', '17+71=88'] Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 46, 86, 22, 29 ]
47
[ "86-46=40", "29-22=7", "40+7=47" ]
Current State: 47:[46, 86, 22, 29], Operations: [] Exploring Operation: 86-46=40, Resulting Numbers: [22, 29, 40] Generated Node #2: [22, 29, 40] from Operation: 86-46=40 Current State: 47:[22, 29, 40], Operations: ['86-46=40'] Exploring Operation: 29-22=7, Resulting Numbers: [40, 7] Generated Node #3: [40, 7] from Operation: 29-22=7 Current State: 47:[40, 7], Operations: ['86-46=40', '29-22=7'] Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[46, 86, 22, 29], Operations: [] Exploring Operation: 86-29=57, Resulting Numbers: [46, 22, 57] Generated Node #0,0: 47:[46, 22, 57] Operation: 86-29=57 Exploring Operation: 86-22=64, Resulting Numbers: [46, 29, 64] Generated Node #0,1: 47:[46, 29, 64] Operation: 86-22=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[46, 22, 57], Operations: ['86-29=57'] Exploring Operation: 46+22=68, Resulting Numbers: [57, 68] Generated Node #0,0,0: 47:[57, 68] Operation: 46+22=68 Exploring Operation: 57-22=35, Resulting Numbers: [46, 35] Generated Node #0,0,1: 47:[46, 35] Operation: 57-22=35 Moving to Node #0,0,1 Current State: 47:[46, 35], Operations: ['86-29=57', '57-22=35'] Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,47 unequal: No Solution Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[57, 68], Operations: ['86-29=57', '46+22=68'] Exploring Operation: 68-57=11, Resulting Numbers: [11] 11,47 unequal: No Solution Exploring Operation: 57+68=125, Resulting Numbers: [125] 125,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[46, 29, 64], Operations: ['86-22=64'] Exploring Operation: 46+29=75, Resulting Numbers: [64, 75] Generated Node #0,1,0: 47:[64, 75] Operation: 46+29=75 Exploring Operation: 64-29=35, Resulting Numbers: [46, 35] Generated Node #0,1,1: 47:[46, 35] Operation: 64-29=35 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 47:[46, 35], Operations: ['86-22=64', '64-29=35'] Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,47 unequal: No Solution Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[64, 75], Operations: ['86-22=64', '46+29=75'] Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,47 unequal: No Solution Exploring Operation: 64+75=139, Resulting Numbers: [139] 139,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 22, 85, 85, 87 ]
74
[ "87-85=2", "22/2=11", "85-11=74" ]
Current State: 74:[22, 85, 85, 87], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [22, 2] Generated Node #2: [22, 2] from Operation: 87-85=2 Current State: 74:[22, 2], Operations: ['87-85=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,74 equal: Goal Reached Exploring Operation: 85-11=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[22, 85, 85, 87], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [22, 85, 2] Generated Node #0,0: 74:[22, 85, 2] Operation: 87-85=2 Exploring Operation: 85/85=1, Resulting Numbers: [22, 87, 1] Generated Node #0,1: 74:[22, 87, 1] Operation: 85/85=1 Exploring Operation: 87-85=2, Resulting Numbers: [22, 85, 2] Generated Node #0,2: 74:[22, 85, 2] Operation: 87-85=2 Moving to Node #0,0 Current State: 74:[22, 85, 2], Operations: ['87-85=2'] Exploring Operation: 22*2=44, Resulting Numbers: [85, 44] Generated Node #0,0,0: 74:[85, 44] Operation: 22*2=44 Exploring Operation: 22/2=11, Resulting Numbers: [85, 11] Generated Node #0,0,1: 74:[85, 11] Operation: 22/2=11 Exploring Operation: 85-22=63, Resulting Numbers: [2, 63] Generated Node #0,0,2: 74:[2, 63] Operation: 85-22=63 Moving to Node #0,2 Current State: 74:[22, 85, 2], Operations: ['87-85=2'] Exploring Operation: 22*2=44, Resulting Numbers: [85, 44] Generated Node #0,2,0: 74:[85, 44] Operation: 22*2=44 Exploring Operation: 22/2=11, Resulting Numbers: [85, 11] Generated Node #0,2,1: 74:[85, 11] Operation: 22/2=11 Exploring Operation: 85-22=63, Resulting Numbers: [2, 63] Generated Node #0,2,2: 74:[2, 63] Operation: 85-22=63 Moving to Node #0,1 Current State: 74:[22, 87, 1], Operations: ['85/85=1'] Exploring Operation: 87-22=65, Resulting Numbers: [1, 65] Generated Node #0,1,0: 74:[1, 65] Operation: 87-22=65 Exploring Operation: 87-1=86, Resulting Numbers: [22, 86] Generated Node #0,1,1: 74:[22, 86] Operation: 87-1=86 Exploring Operation: 22+1=23, Resulting Numbers: [87, 23] Generated Node #0,1,2: 74:[87, 23] Operation: 22+1=23 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[1, 65], Operations: ['85/85=1', '87-22=65'] Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,74 unequal: No Solution Exploring Operation: 1+65=66, Resulting Numbers: [66] 66,74 unequal: No Solution Exploring Operation: 1*65=65, Resulting Numbers: [65] 65,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 74:[22, 86], Operations: ['85/85=1', '87-1=86'] Exploring Operation: 22*86=1892, Resulting Numbers: [1892] 1892,74 unequal: No Solution Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,74 unequal: No Solution Exploring Operation: 22+86=108, Resulting Numbers: [108] 108,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 74:[87, 23], Operations: ['85/85=1', '22+1=23'] Exploring Operation: 87*23=2001, Resulting Numbers: [2001] 2001,74 unequal: No Solution Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,74 unequal: No Solution Exploring Operation: 87+23=110, Resulting Numbers: [110] 110,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 74:[2, 63], Operations: ['87-85=2', '85-22=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,74 unequal: No Solution Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,74 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,74 unequal: No Solution Moving to Node #0,2,2 Current State: 74:[2, 63], Operations: ['87-85=2', '85-22=63'] Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,74 unequal: No Solution Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,74 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,74 unequal: No Solution Moving to Node #0,2,0 Current State: 74:[85, 44], Operations: ['87-85=2', '22*2=44'] Exploring Operation: 85+44=129, Resulting Numbers: [129] 129,74 unequal: No Solution Exploring Operation: 85-44=41, Resulting Numbers: [41] 41,74 unequal: No Solution Exploring Operation: 85*44=3740, Resulting Numbers: [3740] 3740,74 unequal: No Solution Moving to Node #0,0,0 Current State: 74:[85, 44], Operations: ['87-85=2', '22*2=44'] Exploring Operation: 85+44=129, Resulting Numbers: [129] 129,74 unequal: No Solution Exploring Operation: 85-44=41, Resulting Numbers: [41] 41,74 unequal: No Solution Exploring Operation: 85*44=3740, Resulting Numbers: [3740] 3740,74 unequal: No Solution Moving to Node #0,2,1 Current State: 74:[85, 11], Operations: ['87-85=2', '22/2=11'] Exploring Operation: 85-11=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[22, 85, 85, 87], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [22, 85, 2] Generated Node #0,2: 74:[22, 85, 2] Operation: 87-85=2 Moving to Node #0,2 Current State: 74:[22, 85, 2], Operations: ['87-85=2'] Exploring Operation: 22/2=11, Resulting Numbers: [85, 11] Generated Node #0,2,1: 74:[85, 11] Operation: 22/2=11 Moving to Node #0,2,1 Current State: 74:[85, 11], Operations: ['87-85=2', '22/2=11'] Exploring Operation: 85-11=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
0.967014
hs_3
mult_heuristic
[ 37, 33, 23, 8 ]
84
[ "37-33=4", "23*4=92", "92-8=84" ]
Current State: 84:[37, 33, 23, 8], Operations: [] Exploring Operation: 37-33=4, Resulting Numbers: [23, 8, 4] Generated Node #2: [23, 8, 4] from Operation: 37-33=4 Current State: 84:[23, 8, 4], Operations: ['37-33=4'] Exploring Operation: 23*4=92, Resulting Numbers: [8, 92] Generated Node #3: [8, 92] from Operation: 23*4=92 Current State: 84:[8, 92], Operations: ['37-33=4', '23*4=92'] Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[37, 33, 23, 8], Operations: [] Exploring Operation: 37-33=4, Resulting Numbers: [23, 8, 4] Generated Node #0,0: 84:[23, 8, 4] Operation: 37-33=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[23, 8, 4], Operations: ['37-33=4'] Exploring Operation: 23-8=15, Resulting Numbers: [4, 15] Generated Node #0,0,0: 84:[4, 15] Operation: 23-8=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 84:[4, 15], Operations: ['37-33=4', '23-8=15'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,84 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
[ 35, 7, 20, 26 ]
34
[ "35-7=28", "26-20=6", "28+6=34" ]
Current State: 34:[35, 7, 20, 26], Operations: [] Exploring Operation: 35-7=28, Resulting Numbers: [20, 26, 28] Generated Node #2: [20, 26, 28] from Operation: 35-7=28 Current State: 34:[20, 26, 28], Operations: ['35-7=28'] Exploring Operation: 26-20=6, Resulting Numbers: [28, 6] Generated Node #3: [28, 6] from Operation: 26-20=6 Current State: 34:[28, 6], Operations: ['35-7=28', '26-20=6'] Exploring Operation: 28+6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[35, 7, 20, 26], Operations: [] Exploring Operation: 7+26=33, Resulting Numbers: [35, 20, 33] Generated Node #0,0: 34:[35, 20, 33] Operation: 7+26=33 Moving to Node #0,0 Current State: 34:[35, 20, 33], Operations: ['7+26=33'] Exploring Operation: 35-20=15, Resulting Numbers: [33, 15] Generated Node #0,0,0: 34:[33, 15] Operation: 35-20=15 Moving to Node #0,0,0 Current State: 34:[33, 15], Operations: ['7+26=33', '35-20=15'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,34 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 39, 13, 77, 29 ]
100
[ "39+13=52", "77-29=48", "52+48=100" ]
Current State: 100:[39, 13, 77, 29], Operations: [] Exploring Operation: 39+13=52, Resulting Numbers: [77, 29, 52] Generated Node #2: [77, 29, 52] from Operation: 39+13=52 Current State: 100:[77, 29, 52], Operations: ['39+13=52'] Exploring Operation: 77-29=48, Resulting Numbers: [52, 48] Generated Node #3: [52, 48] from Operation: 77-29=48 Current State: 100:[52, 48], Operations: ['39+13=52', '77-29=48'] Exploring Operation: 52+48=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[39, 13, 77, 29], Operations: [] Exploring Operation: 39+77=116, Resulting Numbers: [13, 29, 116] Generated Node #0,0: 100:[13, 29, 116] Operation: 39+77=116 Exploring Operation: 13+77=90, Resulting Numbers: [39, 29, 90] Generated Node #0,1: 100:[39, 29, 90] Operation: 13+77=90 Exploring Operation: 77-39=38, Resulting Numbers: [13, 29, 38] Generated Node #0,2: 100:[13, 29, 38] Operation: 77-39=38 Exploring Operation: 77+29=106, Resulting Numbers: [39, 13, 106] Generated Node #0,3: 100:[39, 13, 106] Operation: 77+29=106 Exploring Operation: 77-29=48, Resulting Numbers: [39, 13, 48] Generated Node #0,4: 100:[39, 13, 48] Operation: 77-29=48 Start Sub Search at level 1: Moving to Node #0,4 Current State: 100:[39, 13, 48], Operations: ['77-29=48'] Exploring Operation: 39-13=26, Resulting Numbers: [48, 26] Generated Node #0,4,0: 100:[48, 26] Operation: 39-13=26 Exploring Operation: 39/13=3, Resulting Numbers: [48, 3] Generated Node #0,4,1: 100:[48, 3] Operation: 39/13=3 Exploring Operation: 39+13=52, Resulting Numbers: [48, 52] Generated Node #0,4,2: 100:[48, 52] Operation: 39+13=52 Exploring Operation: 39+48=87, Resulting Numbers: [13, 87] Generated Node #0,4,3: 100:[13, 87] Operation: 39+48=87 Exploring Operation: 48-39=9, Resulting Numbers: [13, 9] Generated Node #0,4,4: 100:[13, 9] Operation: 48-39=9 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 100:[48, 26], Operations: ['77-29=48', '39-13=26'] Exploring Operation: 48+26=74, Resulting Numbers: [74] 74,100 unequal: No Solution Exploring Operation: 48*26=1248, Resulting Numbers: [1248] 1248,100 unequal: No Solution Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 100:[48, 3], Operations: ['77-29=48', '39/13=3'] Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,100 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 100:[48, 52], Operations: ['77-29=48', '39+13=52'] Exploring Operation: 48*52=2496, Resulting Numbers: [2496] 2496,100 unequal: No Solution Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[39, 13, 77, 29], Operations: [] Exploring Operation: 77-29=48, Resulting Numbers: [39, 13, 48] Generated Node #0,4: 100:[39, 13, 48] Operation: 77-29=48 Moving to Node #0,4 Current State: 100:[39, 13, 48], Operations: ['77-29=48'] Exploring Operation: 39+13=52, Resulting Numbers: [48, 52] Generated Node #0,4,2: 100:[48, 52] Operation: 39+13=52 Moving to Node #0,4,2 Current State: 100:[48, 52], Operations: ['77-29=48', '39+13=52'] Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 43, 9, 75, 11 ]
64
[ "75-43=32", "11-9=2", "32*2=64" ]
Current State: 64:[43, 9, 75, 11], Operations: [] Exploring Operation: 75-43=32, Resulting Numbers: [9, 11, 32] Generated Node #2: [9, 11, 32] from Operation: 75-43=32 Current State: 64:[9, 11, 32], Operations: ['75-43=32'] Exploring Operation: 11-9=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 11-9=2 Current State: 64:[32, 2], Operations: ['75-43=32', '11-9=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[43, 9, 75, 11], Operations: [] Exploring Operation: 75-43=32, Resulting Numbers: [9, 11, 32] Generated Node #0,0: 64:[9, 11, 32] Operation: 75-43=32 Moving to Node #0,0 Current State: 64:[9, 11, 32], Operations: ['75-43=32'] Exploring Operation: 11-9=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 64:[32, 2] Operation: 11-9=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[32, 2], Operations: ['75-43=32', '11-9=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[43, 9, 75, 11], Operations: [] Exploring Operation: 75-43=32, Resulting Numbers: [9, 11, 32] Generated Node #0,0: 64:[9, 11, 32] Operation: 75-43=32 Moving to Node #0,0 Current State: 64:[9, 11, 32], Operations: ['75-43=32'] Exploring Operation: 11-9=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 64:[32, 2] Operation: 11-9=2 Moving to Node #0,0,0 Current State: 64:[32, 2], Operations: ['75-43=32', '11-9=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 58, 94, 94, 41 ]
89
[ "94-58=36", "94-41=53", "36+53=89" ]
Current State: 89:[58, 94, 94, 41], Operations: [] Exploring Operation: 94-58=36, Resulting Numbers: [41, 36] Generated Node #2: [41, 36] from Operation: 94-58=36 Current State: 89:[41, 36], Operations: ['94-58=36'] Exploring Operation: 94-41=53, Resulting Numbers: [36, 53] Generated Node #3: [36, 53] from Operation: 94-41=53 Current State: 89:[36, 53], Operations: ['94-58=36', '94-41=53'] Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[58, 94, 94, 41], Operations: [] Exploring Operation: 94-41=53, Resulting Numbers: [58, 94, 53] Generated Node #0,0: 89:[58, 94, 53] Operation: 94-41=53 Exploring Operation: 94-41=53, Resulting Numbers: [58, 94, 53] Generated Node #0,1: 89:[58, 94, 53] Operation: 94-41=53 Exploring Operation: 58+41=99, Resulting Numbers: [94, 94, 99] Generated Node #0,2: 89:[94, 94, 99] Operation: 58+41=99 Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[94, 94, 99], Operations: ['58+41=99'] Exploring Operation: 94/94=1, Resulting Numbers: [99, 1] Generated Node #0,2,0: 89:[99, 1] Operation: 94/94=1 Exploring Operation: 99-94=5, Resulting Numbers: [94, 5] Generated Node #0,2,1: 89:[94, 5] Operation: 99-94=5 Exploring Operation: 99-94=5, Resulting Numbers: [94, 5] Generated Node #0,2,2: 89:[94, 5] Operation: 99-94=5 Moving to Node #0,2,1 Current State: 89:[94, 5], Operations: ['58+41=99', '99-94=5'] Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[58, 94, 94, 41], Operations: [] Exploring Operation: 58+41=99, Resulting Numbers: [94, 94, 99] Generated Node #0,2: 89:[94, 94, 99] Operation: 58+41=99 Moving to Node #0,2 Current State: 89:[94, 94, 99], Operations: ['58+41=99'] Exploring Operation: 99-94=5, Resulting Numbers: [94, 5] Generated Node #0,2,1: 89:[94, 5] Operation: 99-94=5 Moving to Node #0,2,1 Current State: 89:[94, 5], Operations: ['58+41=99', '99-94=5'] Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 26, 54, 47, 58 ]
84
[ "47-26=21", "58-54=4", "21*4=84" ]
Current State: 84:[26, 54, 47, 58], Operations: [] Exploring Operation: 47-26=21, Resulting Numbers: [54, 58, 21] Generated Node #2: [54, 58, 21] from Operation: 47-26=21 Current State: 84:[54, 58, 21], Operations: ['47-26=21'] Exploring Operation: 58-54=4, Resulting Numbers: [21, 4] Generated Node #3: [21, 4] from Operation: 58-54=4 Current State: 84:[21, 4], Operations: ['47-26=21', '58-54=4'] Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[26, 54, 47, 58], Operations: [] Exploring Operation: 26+58=84, Resulting Numbers: [54, 47, 84] Generated Node #0,0: 84:[54, 47, 84] Operation: 26+58=84 Exploring Operation: 58-47=11, Resulting Numbers: [26, 54, 11] Generated Node #0,1: 84:[26, 54, 11] Operation: 58-47=11 Exploring Operation: 58-54=4, Resulting Numbers: [26, 47, 4] Generated Node #0,2: 84:[26, 47, 4] Operation: 58-54=4 Exploring Operation: 54-47=7, Resulting Numbers: [26, 58, 7] Generated Node #0,3: 84:[26, 58, 7] Operation: 54-47=7 Moving to Node #0,2 Current State: 84:[26, 47, 4], Operations: ['58-54=4'] Exploring Operation: 47-26=21, Resulting Numbers: [4, 21] Generated Node #0,2,0: 84:[4, 21] Operation: 47-26=21 Exploring Operation: 47-4=43, Resulting Numbers: [26, 43] Generated Node #0,2,1: 84:[26, 43] Operation: 47-4=43 Exploring Operation: 26+4=30, Resulting Numbers: [47, 30] Generated Node #0,2,2: 84:[47, 30] Operation: 26+4=30 Exploring Operation: 26-4=22, Resulting Numbers: [47, 22] Generated Node #0,2,3: 84:[47, 22] Operation: 26-4=22 Moving to Node #0,1 Current State: 84:[26, 54, 11], Operations: ['58-47=11'] Exploring Operation: 26+54=80, Resulting Numbers: [11, 80] Generated Node #0,1,0: 84:[11, 80] Operation: 26+54=80 Exploring Operation: 54-11=43, Resulting Numbers: [26, 43] Generated Node #0,1,1: 84:[26, 43] Operation: 54-11=43 Exploring Operation: 26-11=15, Resulting Numbers: [54, 15] Generated Node #0,1,2: 84:[54, 15] Operation: 26-11=15 Exploring Operation: 54-26=28, Resulting Numbers: [11, 28] Generated Node #0,1,3: 84:[11, 28] Operation: 54-26=28 Moving to Node #0,0 Current State: 84:[54, 47, 84], Operations: ['26+58=84'] Exploring Operation: 84-54=30, Resulting Numbers: [47, 30] Generated Node #0,0,0: 84:[47, 30] Operation: 84-54=30 Exploring Operation: 54+47=101, Resulting Numbers: [84, 101] Generated Node #0,0,1: 84:[84, 101] Operation: 54+47=101 Exploring Operation: 54-47=7, Resulting Numbers: [84, 7] Generated Node #0,0,2: 84:[84, 7] Operation: 54-47=7 Exploring Operation: 84-47=37, Resulting Numbers: [54, 37] Generated Node #0,0,3: 84:[54, 37] Operation: 84-47=37 Moving to Node #0,3 Current State: 84:[26, 58, 7], Operations: ['54-47=7'] Exploring Operation: 58-7=51, Resulting Numbers: [26, 51] Generated Node #0,3,0: 84:[26, 51] Operation: 58-7=51 Exploring Operation: 26+58=84, Resulting Numbers: [7, 84] Generated Node #0,3,1: 84:[7, 84] Operation: 26+58=84 Exploring Operation: 26-7=19, Resulting Numbers: [58, 19] Generated Node #0,3,2: 84:[58, 19] Operation: 26-7=19 Exploring Operation: 58-26=32, Resulting Numbers: [7, 32] Generated Node #0,3,3: 84:[7, 32] Operation: 58-26=32 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[7, 84], Operations: ['54-47=7', '26+58=84'] Exploring Operation: 7*84=588, Resulting Numbers: [588] 588,84 unequal: No Solution Exploring Operation: 7+84=91, Resulting Numbers: [91] 91,84 unequal: No Solution Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,84 unequal: No Solution Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,84 unequal: No Solution No 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: 84:[7, 32], Operations: ['54-47=7', '58-26=32'] Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,84 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,84 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,84 unequal: No Solution No 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: 84:[26, 51], Operations: ['54-47=7', '58-7=51'] Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 26+51=77, Resulting Numbers: [77] 77,84 unequal: No Solution Exploring Operation: 26*51=1326, Resulting Numbers: [1326] 1326,84 unequal: No Solution No 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: 84:[58, 19], Operations: ['54-47=7', '26-7=19'] Exploring Operation: 58*19=1102, Resulting Numbers: [1102] 1102,84 unequal: No Solution Exploring Operation: 58+19=77, Resulting Numbers: [77] 77,84 unequal: No Solution Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,84 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: 84:[4, 21], Operations: ['58-54=4', '47-26=21'] Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[26, 54, 47, 58], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [26, 47, 4] Generated Node #0,2: 84:[26, 47, 4] Operation: 58-54=4 Moving to Node #0,2 Current State: 84:[26, 47, 4], Operations: ['58-54=4'] Exploring Operation: 47-26=21, Resulting Numbers: [4, 21] Generated Node #0,2,0: 84:[4, 21] Operation: 47-26=21 Moving to Node #0,2,0 Current State: 84:[4, 21], Operations: ['58-54=4', '47-26=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.965278
hs_4
mult_heuristic
[ 52, 2, 57, 1 ]
47
[ "52*2=104", "57*1=57", "104-57=47" ]
Current State: 47:[52, 2, 57, 1], Operations: [] Exploring Operation: 52*2=104, Resulting Numbers: [57, 1, 104] Generated Node #2: [57, 1, 104] from Operation: 52*2=104 Current State: 47:[57, 1, 104], Operations: ['52*2=104'] Exploring Operation: 57*1=57, Resulting Numbers: [104, 57] Generated Node #3: [104, 57] from Operation: 57*1=57 Current State: 47:[104, 57], Operations: ['52*2=104', '57*1=57'] Exploring Operation: 104-57=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[52, 2, 57, 1], Operations: [] Exploring Operation: 52-2=50, Resulting Numbers: [57, 1, 50] Generated Node #0,0: 47:[57, 1, 50] Operation: 52-2=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[57, 1, 50], Operations: ['52-2=50'] Exploring Operation: 57-1=56, Resulting Numbers: [50, 56] Generated Node #0,0,0: 47:[50, 56] Operation: 57-1=56 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[50, 56], Operations: ['52-2=50', '57-1=56'] Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 43, 9, 7, 36 ]
77
[ "43-9=34", "7+36=43", "34+43=77" ]
Current State: 77:[43, 9, 7, 36], Operations: [] Exploring Operation: 43-9=34, Resulting Numbers: [7, 36, 34] Generated Node #2: [7, 36, 34] from Operation: 43-9=34 Current State: 77:[7, 36, 34], Operations: ['43-9=34'] Exploring Operation: 7+36=43, Resulting Numbers: [34, 43] Generated Node #3: [34, 43] from Operation: 7+36=43 Current State: 77:[34, 43], Operations: ['43-9=34', '7+36=43'] Exploring Operation: 34+43=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[43, 9, 7, 36], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [9, 7, 7] Generated Node #0,0: 77:[9, 7, 7] Operation: 43-36=7 Exploring Operation: 43+36=79, Resulting Numbers: [9, 7, 79] Generated Node #0,1: 77:[9, 7, 79] Operation: 43+36=79 Exploring Operation: 36/9=4, Resulting Numbers: [43, 7, 4] Generated Node #0,2: 77:[43, 7, 4] Operation: 36/9=4 Moving to Node #0,0 Current State: 77:[9, 7, 7], Operations: ['43-36=7'] Exploring Operation: 9+7=16, Resulting Numbers: [7, 16] Generated Node #0,0,0: 77:[7, 16] Operation: 9+7=16 Exploring Operation: 9-7=2, Resulting Numbers: [7, 2] Generated Node #0,0,1: 77:[7, 2] Operation: 9-7=2 Exploring Operation: 9+7=16, Resulting Numbers: [7, 16] Generated Node #0,0,2: 77:[7, 16] Operation: 9+7=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[7, 16], Operations: ['43-36=7', '9+7=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,77 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,77 unequal: No Solution No 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: 77:[7, 2], Operations: ['43-36=7', '9-7=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,77 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,77 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,77 unequal: No Solution No 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: 77:[7, 16], Operations: ['43-36=7', '9+7=16'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,77 unequal: No Solution Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,77 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: 77:[9, 7, 79], Operations: ['43+36=79'] Exploring Operation: 9-7=2, Resulting Numbers: [79, 2] Generated Node #0,1,0: 77:[79, 2] Operation: 9-7=2 Exploring Operation: 9+7=16, Resulting Numbers: [79, 16] Generated Node #0,1,1: 77:[79, 16] Operation: 9+7=16 Exploring Operation: 79-9=70, Resulting Numbers: [7, 70] Generated Node #0,1,2: 77:[7, 70] Operation: 79-9=70 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[79, 2], Operations: ['43+36=79', '9-7=2'] Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,77 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[43, 9, 7, 36], Operations: [] Exploring Operation: 43+36=79, Resulting Numbers: [9, 7, 79] Generated Node #0,1: 77:[9, 7, 79] Operation: 43+36=79 Moving to Node #0,1 Current State: 77:[9, 7, 79], Operations: ['43+36=79'] Exploring Operation: 9-7=2, Resulting Numbers: [79, 2] Generated Node #0,1,0: 77:[79, 2] Operation: 9-7=2 Moving to Node #0,1,0 Current State: 77:[79, 2], Operations: ['43+36=79', '9-7=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 24, 10, 60, 23 ]
51
[ "24-10=14", "60-23=37", "14+37=51" ]
Current State: 51:[24, 10, 60, 23], Operations: [] Exploring Operation: 24-10=14, Resulting Numbers: [60, 23, 14] Generated Node #2: [60, 23, 14] from Operation: 24-10=14 Current State: 51:[60, 23, 14], Operations: ['24-10=14'] Exploring Operation: 60-23=37, Resulting Numbers: [14, 37] Generated Node #3: [14, 37] from Operation: 60-23=37 Current State: 51:[14, 37], Operations: ['24-10=14', '60-23=37'] Exploring Operation: 14+37=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[24, 10, 60, 23], Operations: [] Exploring Operation: 24-10=14, Resulting Numbers: [60, 23, 14] Generated Node #0,0: 51:[60, 23, 14] Operation: 24-10=14 Exploring Operation: 60/10=6, Resulting Numbers: [24, 23, 6] Generated Node #0,1: 51:[24, 23, 6] Operation: 60/10=6 Exploring Operation: 24-23=1, Resulting Numbers: [10, 60, 1] Generated Node #0,2: 51:[10, 60, 1] Operation: 24-23=1 Exploring Operation: 60-10=50, Resulting Numbers: [24, 23, 50] Generated Node #0,3: 51:[24, 23, 50] Operation: 60-10=50 Moving to Node #0,3 Current State: 51:[24, 23, 50], Operations: ['60-10=50'] Exploring Operation: 24+23=47, Resulting Numbers: [50, 47] Generated Node #0,3,0: 51:[50, 47] Operation: 24+23=47 Exploring Operation: 50-23=27, Resulting Numbers: [24, 27] Generated Node #0,3,1: 51:[24, 27] Operation: 50-23=27 Exploring Operation: 50-24=26, Resulting Numbers: [23, 26] Generated Node #0,3,2: 51:[23, 26] Operation: 50-24=26 Exploring Operation: 24-23=1, Resulting Numbers: [50, 1] Generated Node #0,3,3: 51:[50, 1] Operation: 24-23=1 Moving to Node #0,1 Current State: 51:[24, 23, 6], Operations: ['60/10=6'] Exploring Operation: 24/6=4, Resulting Numbers: [23, 4] Generated Node #0,1,0: 51:[23, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [23, 18] Generated Node #0,1,1: 51:[23, 18] Operation: 24-6=18 Exploring Operation: 24+23=47, Resulting Numbers: [6, 47] Generated Node #0,1,2: 51:[6, 47] Operation: 24+23=47 Exploring Operation: 24-23=1, Resulting Numbers: [6, 1] Generated Node #0,1,3: 51:[6, 1] Operation: 24-23=1 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 51:[6, 1], Operations: ['60/10=6', '24-23=1'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,51 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,51 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:[23, 4], Operations: ['60/10=6', '24/6=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,51 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 23+4=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 #0,1,1 Current State: 51:[23, 18], Operations: ['60/10=6', '24-6=18'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 23*18=414, Resulting Numbers: [414] 414,51 unequal: No Solution Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,51 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 #0,1,2 Current State: 51:[6, 47], Operations: ['60/10=6', '24+23=47'] Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,51 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,51 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: 51:[10, 60, 1], Operations: ['24-23=1'] Exploring Operation: 60-10=50, Resulting Numbers: [1, 50] Generated Node #0,2,0: 51:[1, 50] Operation: 60-10=50 Exploring Operation: 60/10=6, Resulting Numbers: [1, 6] Generated Node #0,2,1: 51:[1, 6] Operation: 60/10=6 Exploring Operation: 10-1=9, Resulting Numbers: [60, 9] Generated Node #0,2,2: 51:[60, 9] Operation: 10-1=9 Exploring Operation: 10+1=11, Resulting Numbers: [60, 11] Generated Node #0,2,3: 51:[60, 11] Operation: 10+1=11 Moving to Node #0,0 Current State: 51:[60, 23, 14], Operations: ['24-10=14'] Exploring Operation: 23+14=37, Resulting Numbers: [60, 37] Generated Node #0,0,0: 51:[60, 37] Operation: 23+14=37 Exploring Operation: 23-14=9, Resulting Numbers: [60, 9] Generated Node #0,0,1: 51:[60, 9] Operation: 23-14=9 Exploring Operation: 60-14=46, Resulting Numbers: [23, 46] Generated Node #0,0,2: 51:[23, 46] Operation: 60-14=46 Exploring Operation: 60-23=37, Resulting Numbers: [14, 37] Generated Node #0,0,3: 51:[14, 37] Operation: 60-23=37 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 51:[23, 46], Operations: ['24-10=14', '60-14=46'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 23+46=69, Resulting Numbers: [69] 69,51 unequal: No Solution Exploring Operation: 23*46=1058, Resulting Numbers: [1058] 1058,51 unequal: No Solution Exploring Operation: 46/23=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 #0,0,1 Current State: 51:[60, 9], Operations: ['24-10=14', '23-14=9'] Exploring Operation: 60+9=69, Resulting Numbers: [69] 69,51 unequal: No Solution Exploring Operation: 60*9=540, Resulting Numbers: [540] 540,51 unequal: No Solution Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[24, 10, 60, 23], Operations: [] Exploring Operation: 24-10=14, Resulting Numbers: [60, 23, 14] Generated Node #0,0: 51:[60, 23, 14] Operation: 24-10=14 Moving to Node #0,0 Current State: 51:[60, 23, 14], Operations: ['24-10=14'] Exploring Operation: 23-14=9, Resulting Numbers: [60, 9] Generated Node #0,0,1: 51:[60, 9] Operation: 23-14=9 Moving to Node #0,0,1 Current State: 51:[60, 9], Operations: ['24-10=14', '23-14=9'] Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.961806
hs_4
sum_heuristic
[ 53, 11, 51, 3 ]
65
[ "53-11=42", "42/3=14", "51+14=65" ]
Current State: 65:[53, 11, 51, 3], Operations: [] Exploring Operation: 53-11=42, Resulting Numbers: [51, 3, 42] Generated Node #2: [51, 3, 42] from Operation: 53-11=42 Current State: 65:[51, 3, 42], Operations: ['53-11=42'] Exploring Operation: 42/3=14, Resulting Numbers: [51, 14] Generated Node #3: [51, 14] from Operation: 42/3=14 Current State: 65:[51, 14], Operations: ['53-11=42', '42/3=14'] Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[53, 11, 51, 3], Operations: [] Exploring Operation: 53+11=64, Resulting Numbers: [51, 3, 64] Generated Node #0,0: 65:[51, 3, 64] Operation: 53+11=64 Exploring Operation: 53-51=2, Resulting Numbers: [11, 3, 2] Generated Node #0,1: 65:[11, 3, 2] Operation: 53-51=2 Moving to Node #0,1 Current State: 65:[11, 3, 2], Operations: ['53-51=2'] Exploring Operation: 11+2=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 65:[3, 13] Operation: 11+2=13 Exploring Operation: 3+2=5, Resulting Numbers: [11, 5] Generated Node #0,1,1: 65:[11, 5] Operation: 3+2=5 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[3, 13], Operations: ['53-51=2', '11+2=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,65 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,65 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 #0,1,1 Current State: 65:[11, 5], Operations: ['53-51=2', '3+2=5'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,65 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: 65:[51, 3, 64], Operations: ['53+11=64'] Exploring Operation: 51/3=17, Resulting Numbers: [64, 17] Generated Node #0,0,0: 65:[64, 17] Operation: 51/3=17 Exploring Operation: 64-51=13, Resulting Numbers: [3, 13] Generated Node #0,0,1: 65:[3, 13] Operation: 64-51=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[3, 13], Operations: ['53+11=64', '64-51=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,65 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 #0,0,0 Current State: 65:[64, 17], Operations: ['53+11=64', '51/3=17'] Exploring Operation: 64+17=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 8, 44, 57, 3 ]
65
[ "8-3=5", "57-44=13", "5*13=65" ]
Current State: 65:[8, 44, 57, 3], Operations: [] Exploring Operation: 8-3=5, Resulting Numbers: [44, 57, 5] Generated Node #2: [44, 57, 5] from Operation: 8-3=5 Current State: 65:[44, 57, 5], Operations: ['8-3=5'] Exploring Operation: 57-44=13, Resulting Numbers: [5, 13] Generated Node #3: [5, 13] from Operation: 57-44=13 Current State: 65:[5, 13], Operations: ['8-3=5', '57-44=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[8, 44, 57, 3], Operations: [] Exploring Operation: 8+57=65, Resulting Numbers: [44, 3, 65] Generated Node #0,0: 65:[44, 3, 65] Operation: 8+57=65 Exploring Operation: 8+44=52, Resulting Numbers: [57, 3, 52] Generated Node #0,1: 65:[57, 3, 52] Operation: 8+44=52 Exploring Operation: 57-44=13, Resulting Numbers: [8, 3, 13] Generated Node #0,2: 65:[8, 3, 13] Operation: 57-44=13 Moving to Node #0,2 Current State: 65:[8, 3, 13], Operations: ['57-44=13'] Exploring Operation: 13-8=5, Resulting Numbers: [3, 5] Generated Node #0,2,0: 65:[3, 5] Operation: 13-8=5 Exploring Operation: 8-3=5, Resulting Numbers: [13, 5] Generated Node #0,2,1: 65:[13, 5] Operation: 8-3=5 Exploring Operation: 8+3=11, Resulting Numbers: [13, 11] Generated Node #0,2,2: 65:[13, 11] Operation: 8+3=11 Moving to Node #0,0 Current State: 65:[44, 3, 65], Operations: ['8+57=65'] Exploring Operation: 65-44=21, Resulting Numbers: [3, 21] Generated Node #0,0,0: 65:[3, 21] Operation: 65-44=21 Exploring Operation: 44+3=47, Resulting Numbers: [65, 47] Generated Node #0,0,1: 65:[65, 47] Operation: 44+3=47 Exploring Operation: 44-3=41, Resulting Numbers: [65, 41] Generated Node #0,0,2: 65:[65, 41] Operation: 44-3=41 Moving to Node #0,1 Current State: 65:[57, 3, 52], Operations: ['8+44=52'] Exploring Operation: 57+3=60, Resulting Numbers: [52, 60] Generated Node #0,1,0: 65:[52, 60] Operation: 57+3=60 Exploring Operation: 3+52=55, Resulting Numbers: [57, 55] Generated Node #0,1,1: 65:[57, 55] Operation: 3+52=55 Exploring Operation: 57-52=5, Resulting Numbers: [3, 5] Generated Node #0,1,2: 65:[3, 5] Operation: 57-52=5 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[3, 5], Operations: ['8+44=52', '57-52=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,65 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 #0,1,0 Current State: 65:[52, 60], Operations: ['8+44=52', '57+3=60'] Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,65 unequal: No Solution Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,65 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 #0,1,1 Current State: 65:[57, 55], Operations: ['8+44=52', '3+52=55'] Exploring Operation: 57-55=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 57*55=3135, Resulting Numbers: [3135] 3135,65 unequal: No Solution Exploring Operation: 57+55=112, Resulting Numbers: [112] 112,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 65:[13, 5], Operations: ['57-44=13', '8-3=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[8, 44, 57, 3], Operations: [] Exploring Operation: 57-44=13, Resulting Numbers: [8, 3, 13] Generated Node #0,2: 65:[8, 3, 13] Operation: 57-44=13 Moving to Node #0,2 Current State: 65:[8, 3, 13], Operations: ['57-44=13'] Exploring Operation: 8-3=5, Resulting Numbers: [13, 5] Generated Node #0,2,1: 65:[13, 5] Operation: 8-3=5 Moving to Node #0,2,1 Current State: 65:[13, 5], Operations: ['57-44=13', '8-3=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 46, 92, 56, 72 ]
32
[ "92/46=2", "72-56=16", "2*16=32" ]
Current State: 32:[46, 92, 56, 72], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [56, 72, 2] Generated Node #2: [56, 72, 2] from Operation: 92/46=2 Current State: 32:[56, 72, 2], Operations: ['92/46=2'] Exploring Operation: 72-56=16, Resulting Numbers: [2, 16] Generated Node #3: [2, 16] from Operation: 72-56=16 Current State: 32:[2, 16], Operations: ['92/46=2', '72-56=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[46, 92, 56, 72], Operations: [] Exploring Operation: 92-56=36, Resulting Numbers: [46, 72, 36] Generated Node #0,0: 32:[46, 72, 36] Operation: 92-56=36 Exploring Operation: 92/46=2, Resulting Numbers: [56, 72, 2] Generated Node #0,1: 32:[56, 72, 2] Operation: 92/46=2 Exploring Operation: 92-72=20, Resulting Numbers: [46, 56, 20] Generated Node #0,2: 32:[46, 56, 20] Operation: 92-72=20 Moving to Node #0,2 Current State: 32:[46, 56, 20], Operations: ['92-72=20'] Exploring Operation: 56-20=36, Resulting Numbers: [46, 36] Generated Node #0,2,0: 32:[46, 36] Operation: 56-20=36 Exploring Operation: 56-46=10, Resulting Numbers: [20, 10] Generated Node #0,2,1: 32:[20, 10] Operation: 56-46=10 Exploring Operation: 46-20=26, Resulting Numbers: [56, 26] Generated Node #0,2,2: 32:[56, 26] Operation: 46-20=26 Moving to Node #0,0 Current State: 32:[46, 72, 36], Operations: ['92-56=36'] Exploring Operation: 72-36=36, Resulting Numbers: [46, 36] Generated Node #0,0,0: 32:[46, 36] Operation: 72-36=36 Exploring Operation: 72-46=26, Resulting Numbers: [36, 26] Generated Node #0,0,1: 32:[36, 26] Operation: 72-46=26 Exploring Operation: 72/36=2, Resulting Numbers: [46, 2] Generated Node #0,0,2: 32:[46, 2] Operation: 72/36=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[36, 26], Operations: ['92-56=36', '72-46=26'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 36+26=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 36*26=936, Resulting Numbers: [936] 936,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[46, 2], Operations: ['92-56=36', '72/36=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,32 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[46, 36], Operations: ['92-56=36', '72-36=36'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,32 unequal: No Solution Exploring Operation: 46*36=1656, Resulting Numbers: [1656] 1656,32 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: 32:[56, 72, 2], Operations: ['92/46=2'] Exploring Operation: 72/2=36, Resulting Numbers: [56, 36] Generated Node #0,1,0: 32:[56, 36] Operation: 72/2=36 Exploring Operation: 56/2=28, Resulting Numbers: [72, 28] Generated Node #0,1,1: 32:[72, 28] Operation: 56/2=28 Exploring Operation: 72-56=16, Resulting Numbers: [2, 16] Generated Node #0,1,2: 32:[2, 16] Operation: 72-56=16 Moving to Node #0,1,2 Current State: 32:[2, 16], Operations: ['92/46=2', '72-56=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[46, 92, 56, 72], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [56, 72, 2] Generated Node #0,1: 32:[56, 72, 2] Operation: 92/46=2 Moving to Node #0,1 Current State: 32:[56, 72, 2], Operations: ['92/46=2'] Exploring Operation: 72-56=16, Resulting Numbers: [2, 16] Generated Node #0,1,2: 32:[2, 16] Operation: 72-56=16 Moving to Node #0,1,2 Current State: 32:[2, 16], Operations: ['92/46=2', '72-56=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 30, 8, 83, 70 ]
51
[ "30+8=38", "83-70=13", "38+13=51" ]
Current State: 51:[30, 8, 83, 70], Operations: [] Exploring Operation: 30+8=38, Resulting Numbers: [83, 70, 38] Generated Node #2: [83, 70, 38] from Operation: 30+8=38 Current State: 51:[83, 70, 38], Operations: ['30+8=38'] Exploring Operation: 83-70=13, Resulting Numbers: [38, 13] Generated Node #3: [38, 13] from Operation: 83-70=13 Current State: 51:[38, 13], Operations: ['30+8=38', '83-70=13'] Exploring Operation: 38+13=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[30, 8, 83, 70], Operations: [] Exploring Operation: 83-30=53, Resulting Numbers: [8, 70, 53] Generated Node #0,0: 51:[8, 70, 53] Operation: 83-30=53 Exploring Operation: 83-70=13, Resulting Numbers: [30, 8, 13] Generated Node #0,1: 51:[30, 8, 13] Operation: 83-70=13 Exploring Operation: 70-30=40, Resulting Numbers: [8, 83, 40] Generated Node #0,2: 51:[8, 83, 40] Operation: 70-30=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[30, 8, 13], Operations: ['83-70=13'] Exploring Operation: 30-8=22, Resulting Numbers: [13, 22] Generated Node #0,1,0: 51:[13, 22] Operation: 30-8=22 Exploring Operation: 30-13=17, Resulting Numbers: [8, 17] Generated Node #0,1,1: 51:[8, 17] Operation: 30-13=17 Exploring Operation: 30+13=43, Resulting Numbers: [8, 43] Generated Node #0,1,2: 51:[8, 43] Operation: 30+13=43 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[8, 17], Operations: ['83-70=13', '30-13=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 8*17=136, Resulting Numbers: [136] 136,51 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,51 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:[13, 22], Operations: ['83-70=13', '30-8=22'] Exploring Operation: 13+22=35, Resulting Numbers: [35] 35,51 unequal: No Solution Exploring Operation: 13*22=286, Resulting Numbers: [286] 286,51 unequal: No Solution Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,51 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 #0,1,2 Current State: 51:[8, 43], Operations: ['83-70=13', '30+13=43'] Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,51 unequal: No Solution Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[30, 8, 83, 70], Operations: [] Exploring Operation: 83-70=13, Resulting Numbers: [30, 8, 13] Generated Node #0,1: 51:[30, 8, 13] Operation: 83-70=13 Moving to Node #0,1 Current State: 51:[30, 8, 13], Operations: ['83-70=13'] Exploring Operation: 30+13=43, Resulting Numbers: [8, 43] Generated Node #0,1,2: 51:[8, 43] Operation: 30+13=43 Moving to Node #0,1,2 Current State: 51:[8, 43], Operations: ['83-70=13', '30+13=43'] Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 63, 31, 92, 42 ]
84
[ "63+31=94", "94-92=2", "42*2=84" ]
Current State: 84:[63, 31, 92, 42], Operations: [] Exploring Operation: 63+31=94, Resulting Numbers: [92, 42, 94] Generated Node #2: [92, 42, 94] from Operation: 63+31=94 Current State: 84:[92, 42, 94], Operations: ['63+31=94'] Exploring Operation: 94-92=2, Resulting Numbers: [42, 2] Generated Node #3: [42, 2] from Operation: 94-92=2 Current State: 84:[42, 2], Operations: ['63+31=94', '94-92=2'] Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[63, 31, 92, 42], Operations: [] Exploring Operation: 63-42=21, Resulting Numbers: [31, 92, 21] Generated Node #0,0: 84:[31, 92, 21] Operation: 63-42=21 Exploring Operation: 42-31=11, Resulting Numbers: [63, 92, 11] Generated Node #0,1: 84:[63, 92, 11] Operation: 42-31=11 Exploring Operation: 63+31=94, Resulting Numbers: [92, 42, 94] Generated Node #0,2: 84:[92, 42, 94] Operation: 63+31=94 Exploring Operation: 92-63=29, Resulting Numbers: [31, 42, 29] Generated Node #0,3: 84:[31, 42, 29] Operation: 92-63=29 Exploring Operation: 63-31=32, Resulting Numbers: [92, 42, 32] Generated Node #0,4: 84:[92, 42, 32] Operation: 63-31=32 Moving to Node #0,3 Current State: 84:[31, 42, 29], Operations: ['92-63=29'] Exploring Operation: 42-31=11, Resulting Numbers: [29, 11] Generated Node #0,3,0: 84:[29, 11] Operation: 42-31=11 Exploring Operation: 31-29=2, Resulting Numbers: [42, 2] Generated Node #0,3,1: 84:[42, 2] Operation: 31-29=2 Exploring Operation: 42-29=13, Resulting Numbers: [31, 13] Generated Node #0,3,2: 84:[31, 13] Operation: 42-29=13 Exploring Operation: 42+29=71, Resulting Numbers: [31, 71] Generated Node #0,3,3: 84:[31, 71] Operation: 42+29=71 Exploring Operation: 31+42=73, Resulting Numbers: [29, 73] Generated Node #0,3,4: 84:[29, 73] Operation: 31+42=73 Moving to Node #0,0 Current State: 84:[31, 92, 21], Operations: ['63-42=21'] Exploring Operation: 92+21=113, Resulting Numbers: [31, 113] Generated Node #0,0,0: 84:[31, 113] Operation: 92+21=113 Exploring Operation: 31-21=10, Resulting Numbers: [92, 10] Generated Node #0,0,1: 84:[92, 10] Operation: 31-21=10 Exploring Operation: 92-31=61, Resulting Numbers: [21, 61] Generated Node #0,0,2: 84:[21, 61] Operation: 92-31=61 Exploring Operation: 31+21=52, Resulting Numbers: [92, 52] Generated Node #0,0,3: 84:[92, 52] Operation: 31+21=52 Exploring Operation: 92-21=71, Resulting Numbers: [31, 71] Generated Node #0,0,4: 84:[31, 71] Operation: 92-21=71 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[92, 10], Operations: ['63-42=21', '31-21=10'] Exploring Operation: 92-10=82, Resulting Numbers: [82] 82,84 unequal: No Solution Exploring Operation: 92*10=920, Resulting Numbers: [920] 920,84 unequal: No Solution Exploring Operation: 92+10=102, Resulting Numbers: [102] 102,84 unequal: No Solution No 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: 84:[31, 71], Operations: ['63-42=21', '92-21=71'] Exploring Operation: 31+71=102, Resulting Numbers: [102] 102,84 unequal: No Solution Exploring Operation: 31*71=2201, Resulting Numbers: [2201] 2201,84 unequal: No Solution Exploring Operation: 71-31=40, Resulting Numbers: [40] 40,84 unequal: No Solution No 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: 84:[92, 52], Operations: ['63-42=21', '31+21=52'] Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 92*52=4784, Resulting Numbers: [4784] 4784,84 unequal: No Solution Exploring Operation: 92+52=144, Resulting Numbers: [144] 144,84 unequal: No Solution No 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: 84:[21, 61], Operations: ['63-42=21', '92-31=61'] Exploring Operation: 21*61=1281, Resulting Numbers: [1281] 1281,84 unequal: No Solution Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 21+61=82, Resulting Numbers: [82] 82,84 unequal: No Solution No 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: 84:[31, 113], Operations: ['63-42=21', '92+21=113'] Exploring Operation: 31*113=3503, Resulting Numbers: [3503] 3503,84 unequal: No Solution Exploring Operation: 31+113=144, Resulting Numbers: [144] 144,84 unequal: No Solution Exploring Operation: 113-31=82, Resulting Numbers: [82] 82,84 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: 84:[92, 42, 32], Operations: ['63-31=32'] Exploring Operation: 42+32=74, Resulting Numbers: [92, 74] Generated Node #0,4,0: 84:[92, 74] Operation: 42+32=74 Exploring Operation: 92-42=50, Resulting Numbers: [32, 50] Generated Node #0,4,1: 84:[32, 50] Operation: 92-42=50 Exploring Operation: 92+32=124, Resulting Numbers: [42, 124] Generated Node #0,4,2: 84:[42, 124] Operation: 92+32=124 Exploring Operation: 42-32=10, Resulting Numbers: [92, 10] Generated Node #0,4,3: 84:[92, 10] Operation: 42-32=10 Exploring Operation: 92-32=60, Resulting Numbers: [42, 60] Generated Node #0,4,4: 84:[42, 60] Operation: 92-32=60 Moving to Node #0,2 Current State: 84:[92, 42, 94], Operations: ['63+31=94'] Exploring Operation: 92+42=134, Resulting Numbers: [94, 134] Generated Node #0,2,0: 84:[94, 134] Operation: 92+42=134 Exploring Operation: 94-42=52, Resulting Numbers: [92, 52] Generated Node #0,2,1: 84:[92, 52] Operation: 94-42=52 Exploring Operation: 42+94=136, Resulting Numbers: [92, 136] Generated Node #0,2,2: 84:[92, 136] Operation: 42+94=136 Exploring Operation: 94-92=2, Resulting Numbers: [42, 2] Generated Node #0,2,3: 84:[42, 2] Operation: 94-92=2 Exploring Operation: 92-42=50, Resulting Numbers: [94, 50] Generated Node #0,2,4: 84:[94, 50] Operation: 92-42=50 Moving to Node #0,1 Current State: 84:[63, 92, 11], Operations: ['42-31=11'] Exploring Operation: 63-11=52, Resulting Numbers: [92, 52] Generated Node #0,1,0: 84:[92, 52] Operation: 63-11=52 Exploring Operation: 63+11=74, Resulting Numbers: [92, 74] Generated Node #0,1,1: 84:[92, 74] Operation: 63+11=74 Exploring Operation: 92-63=29, Resulting Numbers: [11, 29] Generated Node #0,1,2: 84:[11, 29] Operation: 92-63=29 Exploring Operation: 92-11=81, Resulting Numbers: [63, 81] Generated Node #0,1,3: 84:[63, 81] Operation: 92-11=81 Exploring Operation: 92+11=103, Resulting Numbers: [63, 103] Generated Node #0,1,4: 84:[63, 103] Operation: 92+11=103 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[11, 29], Operations: ['42-31=11', '92-63=29'] Exploring Operation: 11+29=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 11*29=319, Resulting Numbers: [319] 319,84 unequal: No Solution No 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: 84:[92, 52], Operations: ['42-31=11', '63-11=52'] Exploring Operation: 92*52=4784, Resulting Numbers: [4784] 4784,84 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 92+52=144, Resulting Numbers: [144] 144,84 unequal: No Solution No 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: 84:[92, 74], Operations: ['42-31=11', '63+11=74'] Exploring Operation: 92+74=166, Resulting Numbers: [166] 166,84 unequal: No Solution Exploring Operation: 92*74=6808, Resulting Numbers: [6808] 6808,84 unequal: No Solution Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,84 unequal: No Solution No 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: 84:[63, 81], Operations: ['42-31=11', '92-11=81'] Exploring Operation: 81-63=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 63+81=144, Resulting Numbers: [144] 144,84 unequal: No Solution Exploring Operation: 63*81=5103, Resulting Numbers: [5103] 5103,84 unequal: No Solution No 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: 84:[63, 103], Operations: ['42-31=11', '92+11=103'] Exploring Operation: 63*103=6489, Resulting Numbers: [6489] 6489,84 unequal: No Solution Exploring Operation: 103-63=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 63+103=166, Resulting Numbers: [166] 166,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 84:[42, 2], Operations: ['92-63=29', '31-29=2'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,84 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[63, 31, 92, 42], Operations: [] Exploring Operation: 92-63=29, Resulting Numbers: [31, 42, 29] Generated Node #0,3: 84:[31, 42, 29] Operation: 92-63=29 Moving to Node #0,3 Current State: 84:[31, 42, 29], Operations: ['92-63=29'] Exploring Operation: 31-29=2, Resulting Numbers: [42, 2] Generated Node #0,3,1: 84:[42, 2] Operation: 31-29=2 Moving to Node #0,3,1 Current State: 84:[42, 2], Operations: ['92-63=29', '31-29=2'] Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.940972
hs_5
sum_heuristic
[ 19, 3, 40, 17 ]
17
[ "19-17=2", "40/2=20", "20-3=17" ]
Current State: 17:[19, 3, 40, 17], Operations: [] Exploring Operation: 19-17=2, Resulting Numbers: [3, 40, 2] Generated Node #2: [3, 40, 2] from Operation: 19-17=2 Current State: 17:[3, 40, 2], Operations: ['19-17=2'] Exploring Operation: 40/2=20, Resulting Numbers: [3, 20] Generated Node #3: [3, 20] from Operation: 40/2=20 Current State: 17:[3, 20], Operations: ['19-17=2', '40/2=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[19, 3, 40, 17], Operations: [] Exploring Operation: 40-19=21, Resulting Numbers: [3, 17, 21] Generated Node #0,0: 17:[3, 17, 21] Operation: 40-19=21 Exploring Operation: 40-17=23, Resulting Numbers: [19, 3, 23] Generated Node #0,1: 17:[19, 3, 23] Operation: 40-17=23 Exploring Operation: 40-3=37, Resulting Numbers: [19, 17, 37] Generated Node #0,2: 17:[19, 17, 37] Operation: 40-3=37 Moving to Node #0,0 Current State: 17:[3, 17, 21], Operations: ['40-19=21'] Exploring Operation: 3+17=20, Resulting Numbers: [21, 20] Generated Node #0,0,0: 17:[21, 20] Operation: 3+17=20 Exploring Operation: 17-3=14, Resulting Numbers: [21, 14] Generated Node #0,0,1: 17:[21, 14] Operation: 17-3=14 Exploring Operation: 21-3=18, Resulting Numbers: [17, 18] Generated Node #0,0,2: 17:[17, 18] Operation: 21-3=18 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 17:[17, 18], Operations: ['40-19=21', '21-3=18'] Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,17 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,17 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[21, 20], Operations: ['40-19=21', '3+17=20'] Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,17 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 17:[21, 14], Operations: ['40-19=21', '17-3=14'] Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,17 unequal: No Solution Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,17 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: 17:[19, 3, 23], Operations: ['40-17=23'] Exploring Operation: 19-3=16, Resulting Numbers: [23, 16] Generated Node #0,1,0: 17:[23, 16] Operation: 19-3=16 Exploring Operation: 23-3=20, Resulting Numbers: [19, 20] Generated Node #0,1,1: 17:[19, 20] Operation: 23-3=20 Exploring Operation: 19+3=22, Resulting Numbers: [23, 22] Generated Node #0,1,2: 17:[23, 22] Operation: 19+3=22 Moving to Node #0,2 Current State: 17:[19, 17, 37], Operations: ['40-3=37'] Exploring Operation: 37-17=20, Resulting Numbers: [19, 20] Generated Node #0,2,0: 17:[19, 20] Operation: 37-17=20 Exploring Operation: 19-17=2, Resulting Numbers: [37, 2] Generated Node #0,2,1: 17:[37, 2] Operation: 19-17=2 Exploring Operation: 37-19=18, Resulting Numbers: [17, 18] Generated Node #0,2,2: 17:[17, 18] Operation: 37-19=18 Moving to Node #0,2,2 Current State: 17:[17, 18], Operations: ['40-3=37', '37-19=18'] Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,17 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[19, 20], Operations: ['40-17=23', '23-3=20'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,17 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[19, 20], Operations: ['40-3=37', '37-17=20'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,17 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[23, 16], Operations: ['40-17=23', '19-3=16'] Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,17 unequal: No Solution Exploring Operation: 23*16=368, Resulting Numbers: [368] 368,17 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[23, 22], Operations: ['40-17=23', '19+3=22'] Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,17 unequal: No Solution Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[37, 2], Operations: ['40-3=37', '19-17=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,17 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,17 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,17 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 72, 31, 39, 65 ]
52
[ "31+65=96", "39*96=3744", "3744/72=52" ]
Current State: 52:[72, 31, 39, 65], Operations: [] Exploring Operation: 31+65=96, Resulting Numbers: [72, 39, 96] Generated Node #2: [72, 39, 96] from Operation: 31+65=96 Current State: 52:[72, 39, 96], Operations: ['31+65=96'] Exploring Operation: 39*96=3744, Resulting Numbers: [72, 3744] Generated Node #3: [72, 3744] from Operation: 39*96=3744 Current State: 52:[72, 3744], Operations: ['31+65=96', '39*96=3744'] Exploring Operation: 3744/72=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[72, 31, 39, 65], Operations: [] Exploring Operation: 72-31=41, Resulting Numbers: [39, 65, 41] Generated Node #0,0: 52:[39, 65, 41] Operation: 72-31=41 Exploring Operation: 65-39=26, Resulting Numbers: [72, 31, 26] Generated Node #0,1: 52:[72, 31, 26] Operation: 65-39=26 Exploring Operation: 39-31=8, Resulting Numbers: [72, 65, 8] Generated Node #0,2: 52:[72, 65, 8] Operation: 39-31=8 Exploring Operation: 72-39=33, Resulting Numbers: [31, 65, 33] Generated Node #0,3: 52:[31, 65, 33] Operation: 72-39=33 Exploring Operation: 72-65=7, Resulting Numbers: [31, 39, 7] Generated Node #0,4: 52:[31, 39, 7] Operation: 72-65=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 52:[31, 39, 7], Operations: ['72-65=7'] Exploring Operation: 31+39=70, Resulting Numbers: [7, 70] Generated Node #0,4,0: 52:[7, 70] Operation: 31+39=70 Exploring Operation: 31-7=24, Resulting Numbers: [39, 24] Generated Node #0,4,1: 52:[39, 24] Operation: 31-7=24 Exploring Operation: 39-7=32, Resulting Numbers: [31, 32] Generated Node #0,4,2: 52:[31, 32] Operation: 39-7=32 Exploring Operation: 39+7=46, Resulting Numbers: [31, 46] Generated Node #0,4,3: 52:[31, 46] Operation: 39+7=46 Exploring Operation: 39-31=8, Resulting Numbers: [7, 8] Generated Node #0,4,4: 52:[7, 8] Operation: 39-31=8 Moving to Node #0,4,4 Current State: 52:[7, 8], Operations: ['72-65=7', '39-31=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,52 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,52 unequal: No Solution Moving to Node #0,4,3 Current State: 52:[31, 46], Operations: ['72-65=7', '39+7=46'] Exploring Operation: 31+46=77, Resulting Numbers: [77] 77,52 unequal: No Solution Exploring Operation: 31*46=1426, Resulting Numbers: [1426] 1426,52 unequal: No Solution Exploring Operation: 46-31=15, Resulting Numbers: [15] 15,52 unequal: No Solution Moving to Node #0,4,2 Current State: 52:[31, 32], Operations: ['72-65=7', '39-7=32'] Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,52 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,52 unequal: No Solution Moving to Node #0,4,1 Current State: 52:[39, 24], Operations: ['72-65=7', '31-7=24'] Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,52 unequal: No Solution Moving to Node #0,4,0 Current State: 52:[7, 70], Operations: ['72-65=7', '31+39=70'] Exploring Operation: 7*70=490, Resulting Numbers: [490] 490,52 unequal: No Solution Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,52 unequal: No Solution Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[72, 31, 26], Operations: ['65-39=26'] Exploring Operation: 31+26=57, Resulting Numbers: [72, 57] Generated Node #0,1,0: 52:[72, 57] Operation: 31+26=57 Exploring Operation: 72-26=46, Resulting Numbers: [31, 46] Generated Node #0,1,1: 52:[31, 46] Operation: 72-26=46 Exploring Operation: 31-26=5, Resulting Numbers: [72, 5] Generated Node #0,1,2: 52:[72, 5] Operation: 31-26=5 Exploring Operation: 72-31=41, Resulting Numbers: [26, 41] Generated Node #0,1,3: 52:[26, 41] Operation: 72-31=41 Exploring Operation: 72+31=103, Resulting Numbers: [26, 103] Generated Node #0,1,4: 52:[26, 103] Operation: 72+31=103 Moving to Node #0,1,1 Current State: 52:[31, 46], Operations: ['65-39=26', '72-26=46'] Exploring Operation: 46-31=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 31*46=1426, Resulting Numbers: [1426] 1426,52 unequal: No Solution Exploring Operation: 31+46=77, Resulting Numbers: [77] 77,52 unequal: No Solution Moving to Node #0,1,3 Current State: 52:[26, 41], Operations: ['65-39=26', '72-31=41'] Exploring Operation: 26+41=67, Resulting Numbers: [67] 67,52 unequal: No Solution Exploring Operation: 26*41=1066, Resulting Numbers: [1066] 1066,52 unequal: No Solution Exploring Operation: 41-26=15, Resulting Numbers: [15] 15,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[72, 5], Operations: ['65-39=26', '31-26=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,52 unequal: No Solution Exploring Operation: 72*5=360, Resulting Numbers: [360] 360,52 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[72, 57], Operations: ['65-39=26', '31+26=57'] Exploring Operation: 72+57=129, Resulting Numbers: [129] 129,52 unequal: No Solution Exploring Operation: 72*57=4104, Resulting Numbers: [4104] 4104,52 unequal: No Solution Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,52 unequal: No Solution Moving to Node #0,1,4 Current State: 52:[26, 103], Operations: ['65-39=26', '72+31=103'] Exploring Operation: 26*103=2678, Resulting Numbers: [2678] 2678,52 unequal: No Solution Exploring Operation: 26+103=129, Resulting Numbers: [129] 129,52 unequal: No Solution Exploring Operation: 103-26=77, Resulting Numbers: [77] 77,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[31, 65, 33], Operations: ['72-39=33'] Exploring Operation: 31+65=96, Resulting Numbers: [33, 96] Generated Node #0,3,0: 52:[33, 96] Operation: 31+65=96 Exploring Operation: 65-31=34, Resulting Numbers: [33, 34] Generated Node #0,3,1: 52:[33, 34] Operation: 65-31=34 Exploring Operation: 65-33=32, Resulting Numbers: [31, 32] Generated Node #0,3,2: 52:[31, 32] Operation: 65-33=32 Exploring Operation: 33-31=2, Resulting Numbers: [65, 2] Generated Node #0,3,3: 52:[65, 2] Operation: 33-31=2 Exploring Operation: 31+33=64, Resulting Numbers: [65, 64] Generated Node #0,3,4: 52:[65, 64] Operation: 31+33=64 Moving to Node #0,3,2 Current State: 52:[31, 32], Operations: ['72-39=33', '65-33=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,52 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[65, 2], Operations: ['72-39=33', '33-31=2'] Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,52 unequal: No Solution Exploring Operation: 65*2=130, Resulting Numbers: [130] 130,52 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[33, 34], Operations: ['72-39=33', '65-31=34'] Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,52 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,52 unequal: No Solution Moving to Node #0,3,4 Current State: 52:[65, 64], Operations: ['72-39=33', '31+33=64'] Exploring Operation: 65+64=129, Resulting Numbers: [129] 129,52 unequal: No Solution Exploring Operation: 65*64=4160, Resulting Numbers: [4160] 4160,52 unequal: No Solution Exploring Operation: 65-64=1, Resulting Numbers: [1] 1,52 unequal: No Solution Moving to Node #0,3,0 Current State: 52:[33, 96], Operations: ['72-39=33', '31+65=96'] Exploring Operation: 96-33=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 33+96=129, Resulting Numbers: [129] 129,52 unequal: No Solution Exploring Operation: 33*96=3168, Resulting Numbers: [3168] 3168,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[39, 65, 41], Operations: ['72-31=41'] Exploring Operation: 65-39=26, Resulting Numbers: [41, 26] Generated Node #0,0,0: 52:[41, 26] Operation: 65-39=26 Exploring Operation: 39+41=80, Resulting Numbers: [65, 80] Generated Node #0,0,1: 52:[65, 80] Operation: 39+41=80 Exploring Operation: 65-41=24, Resulting Numbers: [39, 24] Generated Node #0,0,2: 52:[39, 24] Operation: 65-41=24 Exploring Operation: 41-39=2, Resulting Numbers: [65, 2] Generated Node #0,0,3: 52:[65, 2] Operation: 41-39=2 Exploring Operation: 39+65=104, Resulting Numbers: [41, 104] Generated Node #0,0,4: 52:[41, 104] Operation: 39+65=104 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[41, 26], Operations: ['72-31=41', '65-39=26'] Exploring Operation: 41-26=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 41+26=67, Resulting Numbers: [67] 67,52 unequal: No Solution Exploring Operation: 41*26=1066, Resulting Numbers: [1066] 1066,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 52:[65, 2], Operations: ['72-31=41', '41-39=2'] Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,52 unequal: No Solution Exploring Operation: 65*2=130, Resulting Numbers: [130] 130,52 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[39, 24], Operations: ['72-31=41', '65-41=24'] Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,52 unequal: No Solution Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[65, 80], Operations: ['72-31=41', '39+41=80'] Exploring Operation: 65+80=145, Resulting Numbers: [145] 145,52 unequal: No Solution Exploring Operation: 65*80=5200, Resulting Numbers: [5200] 5200,52 unequal: No Solution Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 52:[41, 104], Operations: ['72-31=41', '39+65=104'] Exploring Operation: 41*104=4264, Resulting Numbers: [4264] 4264,52 unequal: No Solution Exploring Operation: 41+104=145, Resulting Numbers: [145] 145,52 unequal: No Solution Exploring Operation: 104-41=63, Resulting Numbers: [63] 63,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[72, 65, 8], Operations: ['39-31=8'] Exploring Operation: 72/8=9, Resulting Numbers: [65, 9] Generated Node #0,2,0: 52:[65, 9] Operation: 72/8=9 Exploring Operation: 72-8=64, Resulting Numbers: [65, 64] Generated Node #0,2,1: 52:[65, 64] Operation: 72-8=64 Exploring Operation: 65-8=57, Resulting Numbers: [72, 57] Generated Node #0,2,2: 52:[72, 57] Operation: 65-8=57 Exploring Operation: 72-65=7, Resulting Numbers: [8, 7] Generated Node #0,2,3: 52:[8, 7] Operation: 72-65=7 Exploring Operation: 72+8=80, Resulting Numbers: [65, 80] Generated Node #0,2,4: 52:[65, 80] Operation: 72+8=80 Moving to Node #0,2,3 Current State: 52:[8, 7], Operations: ['39-31=8', '72-65=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,52 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[65, 9], Operations: ['39-31=8', '72/8=9'] Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,52 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,52 unequal: No Solution Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,52 unequal: No Solution Moving to Node #0,2,1 Current State: 52:[65, 64], Operations: ['39-31=8', '72-8=64'] Exploring Operation: 65+64=129, Resulting Numbers: [129] 129,52 unequal: No Solution Exploring Operation: 65*64=4160, Resulting Numbers: [4160] 4160,52 unequal: No Solution Exploring Operation: 65-64=1, Resulting Numbers: [1] 1,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[72, 57], Operations: ['39-31=8', '65-8=57'] Exploring Operation: 72+57=129, Resulting Numbers: [129] 129,52 unequal: No Solution Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 72*57=4104, Resulting Numbers: [4104] 4104,52 unequal: No Solution Moving to Node #0,2,4 Current State: 52:[65, 80], Operations: ['39-31=8', '72+8=80'] Exploring Operation: 65*80=5200, Resulting Numbers: [5200] 5200,52 unequal: No Solution Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 65+80=145, Resulting Numbers: [145] 145,52 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
[ 20, 40, 2, 77 ]
55
[ "40-20=20", "77-2=75", "75-20=55" ]
Current State: 55:[20, 40, 2, 77], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [2, 77, 20] Generated Node #2: [2, 77, 20] from Operation: 40-20=20 Current State: 55:[2, 77, 20], Operations: ['40-20=20'] Exploring Operation: 77-2=75, Resulting Numbers: [20, 75] Generated Node #3: [20, 75] from Operation: 77-2=75 Current State: 55:[20, 75], Operations: ['40-20=20', '77-2=75'] Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[20, 40, 2, 77], Operations: [] Exploring Operation: 77-20=57, Resulting Numbers: [40, 2, 57] Generated Node #0,0: 55:[40, 2, 57] Operation: 77-20=57 Exploring Operation: 40/20=2, Resulting Numbers: [2, 77, 2] Generated Node #0,1: 55:[2, 77, 2] Operation: 40/20=2 Moving to Node #0,0 Current State: 55:[40, 2, 57], Operations: ['77-20=57'] Exploring Operation: 40/2=20, Resulting Numbers: [57, 20] Generated Node #0,0,0: 55:[57, 20] Operation: 40/2=20 Exploring Operation: 57-40=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 55:[2, 17] Operation: 57-40=17 Moving to Node #0,1 Current State: 55:[2, 77, 2], Operations: ['40/20=2'] Exploring Operation: 77-2=75, Resulting Numbers: [2, 75] Generated Node #0,1,0: 55:[2, 75] Operation: 77-2=75 Exploring Operation: 2+2=4, Resulting Numbers: [77, 4] Generated Node #0,1,1: 55:[77, 4] Operation: 2+2=4 Moving to Node #0,0,1 Current State: 55:[2, 17], Operations: ['77-20=57', '57-40=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[57, 20], Operations: ['77-20=57', '40/2=20'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,55 unequal: No Solution Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[77, 4], Operations: ['40/20=2', '2+2=4'] Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,55 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[2, 75], Operations: ['40/20=2', '77-2=75'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,55 unequal: No Solution Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,55 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 25, 2, 16, 38 ]
42
[ "38-25=13", "2*13=26", "16+26=42" ]
Current State: 42:[25, 2, 16, 38], Operations: [] Exploring Operation: 38-25=13, Resulting Numbers: [2, 16, 13] Generated Node #2: [2, 16, 13] from Operation: 38-25=13 Current State: 42:[2, 16, 13], Operations: ['38-25=13'] Exploring Operation: 2*13=26, Resulting Numbers: [16, 26] Generated Node #3: [16, 26] from Operation: 2*13=26 Current State: 42:[16, 26], Operations: ['38-25=13', '2*13=26'] Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[25, 2, 16, 38], Operations: [] Exploring Operation: 38-25=13, Resulting Numbers: [2, 16, 13] Generated Node #0,0: 42:[2, 16, 13] Operation: 38-25=13 Exploring Operation: 38-16=22, Resulting Numbers: [25, 2, 22] Generated Node #0,1: 42:[25, 2, 22] Operation: 38-16=22 Exploring Operation: 25+16=41, Resulting Numbers: [2, 38, 41] Generated Node #0,2: 42:[2, 38, 41] Operation: 25+16=41 Moving to Node #0,0 Current State: 42:[2, 16, 13], Operations: ['38-25=13'] Exploring Operation: 16-2=14, Resulting Numbers: [13, 14] Generated Node #0,0,0: 42:[13, 14] Operation: 16-2=14 Exploring Operation: 16/2=8, Resulting Numbers: [13, 8] Generated Node #0,0,1: 42:[13, 8] Operation: 16/2=8 Exploring Operation: 16-13=3, Resulting Numbers: [2, 3] Generated Node #0,0,2: 42:[2, 3] Operation: 16-13=3 Moving to Node #0,1 Current State: 42:[25, 2, 22], Operations: ['38-16=22'] Exploring Operation: 25-2=23, Resulting Numbers: [22, 23] Generated Node #0,1,0: 42:[22, 23] Operation: 25-2=23 Exploring Operation: 25-22=3, Resulting Numbers: [2, 3] Generated Node #0,1,1: 42:[2, 3] Operation: 25-22=3 Exploring Operation: 25+22=47, Resulting Numbers: [2, 47] Generated Node #0,1,2: 42:[2, 47] Operation: 25+22=47 Moving to Node #0,2 Current State: 42:[2, 38, 41], Operations: ['25+16=41'] Exploring Operation: 41-38=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 42:[2, 3] Operation: 41-38=3 Exploring Operation: 2+38=40, Resulting Numbers: [41, 40] Generated Node #0,2,1: 42:[41, 40] Operation: 2+38=40 Exploring Operation: 38/2=19, Resulting Numbers: [41, 19] Generated Node #0,2,2: 42:[41, 19] Operation: 38/2=19 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[2, 3], Operations: ['25+16=41', '41-38=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,42 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:[41, 40], Operations: ['25+16=41', '2+38=40'] Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,42 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,42 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,42 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:[41, 19], Operations: ['25+16=41', '38/2=19'] Exploring Operation: 41*19=779, Resulting Numbers: [779] 779,42 unequal: No Solution Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 41+19=60, Resulting Numbers: [60] 60,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 42:[2, 3], Operations: ['38-25=13', '16-13=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[2, 3], Operations: ['38-16=22', '25-22=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[13, 14], Operations: ['38-25=13', '16-2=14'] Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,42 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[13, 8], Operations: ['38-25=13', '16/2=8'] Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,42 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[22, 23], Operations: ['38-16=22', '25-2=23'] Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,42 unequal: No Solution Exploring Operation: 22*23=506, Resulting Numbers: [506] 506,42 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[2, 47], Operations: ['38-16=22', '25+22=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,42 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,42 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,42 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 56, 34, 22, 2 ]
28
[ "56/2=28", "34+22=56", "56-28=28" ]
Current State: 28:[56, 34, 22, 2], Operations: [] Exploring Operation: 56/2=28, Resulting Numbers: [34, 22, 28] Generated Node #2: [34, 22, 28] from Operation: 56/2=28 Current State: 28:[34, 22, 28], Operations: ['56/2=28'] Exploring Operation: 34+22=56, Resulting Numbers: [28, 56] Generated Node #3: [28, 56] from Operation: 34+22=56 Current State: 28:[28, 56], Operations: ['56/2=28', '34+22=56'] Exploring Operation: 56-28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[56, 34, 22, 2], Operations: [] Exploring Operation: 56-34=22, Resulting Numbers: [22, 2, 22] Generated Node #0,0: 28:[22, 2, 22] Operation: 56-34=22 Exploring Operation: 56-22=34, Resulting Numbers: [34, 2, 34] Generated Node #0,1: 28:[34, 2, 34] Operation: 56-22=34 Exploring Operation: 56/2=28, Resulting Numbers: [34, 22, 28] Generated Node #0,2: 28:[34, 22, 28] Operation: 56/2=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[22, 2, 22], Operations: ['56-34=22'] Exploring Operation: 22/2=11, Resulting Numbers: [22, 11] Generated Node #0,0,0: 28:[22, 11] Operation: 22/2=11 Exploring Operation: 22/22=1, Resulting Numbers: [2, 1] Generated Node #0,0,1: 28:[2, 1] Operation: 22/22=1 Exploring Operation: 22-22=0, Resulting Numbers: [2, 0] Generated Node #0,0,2: 28:[2, 0] Operation: 22-22=0 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[2, 1], Operations: ['56-34=22', '22/22=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,28 unequal: No Solution No 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: 28:[2, 0], Operations: ['56-34=22', '22-22=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,28 unequal: No Solution No 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: 28:[22, 11], Operations: ['56-34=22', '22/2=11'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,28 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: 28:[34, 2, 34], Operations: ['56-22=34'] Exploring Operation: 34/2=17, Resulting Numbers: [34, 17] Generated Node #0,1,0: 28:[34, 17] Operation: 34/2=17 Exploring Operation: 34/34=1, Resulting Numbers: [2, 1] Generated Node #0,1,1: 28:[2, 1] Operation: 34/34=1 Exploring Operation: 34-34=0, Resulting Numbers: [2, 0] Generated Node #0,1,2: 28:[2, 0] Operation: 34-34=0 Moving to Node #0,1,1 Current State: 28:[2, 1], Operations: ['56-22=34', '34/34=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,28 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,28 unequal: No Solution Moving to Node #0,1,2 Current State: 28:[2, 0], Operations: ['56-22=34', '34-34=0'] Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[34, 17], Operations: ['56-22=34', '34/2=17'] Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,28 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,28 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 #0,2 Current State: 28:[34, 22, 28], Operations: ['56/2=28'] Exploring Operation: 28-22=6, Resulting Numbers: [34, 6] Generated Node #0,2,0: 28:[34, 6] Operation: 28-22=6 Exploring Operation: 34-28=6, Resulting Numbers: [22, 6] Generated Node #0,2,1: 28:[22, 6] Operation: 34-28=6 Exploring Operation: 34-22=12, Resulting Numbers: [28, 12] Generated Node #0,2,2: 28:[28, 12] Operation: 34-22=12 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 28:[28, 12], Operations: ['56/2=28', '34-22=12'] Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,28 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,28 unequal: No Solution No 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: 28:[34, 6], Operations: ['56/2=28', '28-22=6'] Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,28 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[56, 34, 22, 2], Operations: [] Exploring Operation: 56/2=28, Resulting Numbers: [34, 22, 28] Generated Node #0,2: 28:[34, 22, 28] Operation: 56/2=28 Moving to Node #0,2 Current State: 28:[34, 22, 28], Operations: ['56/2=28'] Exploring Operation: 28-22=6, Resulting Numbers: [34, 6] Generated Node #0,2,0: 28:[34, 6] Operation: 28-22=6 Moving to Node #0,2,0 Current State: 28:[34, 6], Operations: ['56/2=28', '28-22=6'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.966146
hs_3
mult_heuristic
[ 27, 71, 86, 55 ]
99
[ "27*55=1485", "86-71=15", "1485/15=99" ]
Current State: 99:[27, 71, 86, 55], Operations: [] Exploring Operation: 27*55=1485, Resulting Numbers: [71, 86, 1485] Generated Node #2: [71, 86, 1485] from Operation: 27*55=1485 Current State: 99:[71, 86, 1485], Operations: ['27*55=1485'] Exploring Operation: 86-71=15, Resulting Numbers: [1485, 15] Generated Node #3: [1485, 15] from Operation: 86-71=15 Current State: 99:[1485, 15], Operations: ['27*55=1485', '86-71=15'] Exploring Operation: 1485/15=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[27, 71, 86, 55], Operations: [] Exploring Operation: 86-71=15, Resulting Numbers: [27, 55, 15] Generated Node #0,0: 99:[27, 55, 15] Operation: 86-71=15 Exploring Operation: 71-55=16, Resulting Numbers: [27, 86, 16] Generated Node #0,1: 99:[27, 86, 16] Operation: 71-55=16 Moving to Node #0,1 Current State: 99:[27, 86, 16], Operations: ['71-55=16'] Exploring Operation: 86+16=102, Resulting Numbers: [27, 102] Generated Node #0,1,0: 99:[27, 102] Operation: 86+16=102 Exploring Operation: 27-16=11, Resulting Numbers: [86, 11] Generated Node #0,1,1: 99:[86, 11] Operation: 27-16=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[27, 102], Operations: ['71-55=16', '86+16=102'] Exploring Operation: 102-27=75, Resulting Numbers: [75] 75,99 unequal: No Solution Exploring Operation: 27+102=129, Resulting Numbers: [129] 129,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[86, 11], Operations: ['71-55=16', '27-16=11'] Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,99 unequal: No Solution Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,99 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: 99:[27, 55, 15], Operations: ['86-71=15'] Exploring Operation: 55-15=40, Resulting Numbers: [27, 40] Generated Node #0,0,0: 99:[27, 40] Operation: 55-15=40 Exploring Operation: 55-27=28, Resulting Numbers: [15, 28] Generated Node #0,0,1: 99:[15, 28] Operation: 55-27=28 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[15, 28], Operations: ['86-71=15', '55-27=28'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,99 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[27, 40], Operations: ['86-71=15', '55-15=40'] Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,99 unequal: No Solution Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 2, 17, 4, 17 ]
85
[ "2+4=6", "17*6=102", "102-17=85" ]
Current State: 85:[2, 17, 4, 17], Operations: [] Exploring Operation: 2+4=6, Resulting Numbers: [17, 17, 6] Generated Node #2: [17, 17, 6] from Operation: 2+4=6 Current State: 85:[17, 17, 6], Operations: ['2+4=6'] Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,85 equal: Goal Reached Exploring Operation: 102-17=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[2, 17, 4, 17], Operations: [] Exploring Operation: 2+4=6, Resulting Numbers: [17, 17, 6] Generated Node #0,0: 85:[17, 17, 6] Operation: 2+4=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[17, 17, 6], Operations: ['2+4=6'] Exploring Operation: 17/17=1, Resulting Numbers: [6, 1] Generated Node #0,0,0: 85:[6, 1] Operation: 17/17=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[6, 1], Operations: ['2+4=6', '17/17=1'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 73, 34, 11, 6 ]
44
[ "73-34=39", "11-6=5", "39+5=44" ]
Current State: 44:[73, 34, 11, 6], Operations: [] Exploring Operation: 73-34=39, Resulting Numbers: [11, 6, 39] Generated Node #2: [11, 6, 39] from Operation: 73-34=39 Current State: 44:[11, 6, 39], Operations: ['73-34=39'] Exploring Operation: 11-6=5, Resulting Numbers: [39, 5] Generated Node #3: [39, 5] from Operation: 11-6=5 Current State: 44:[39, 5], Operations: ['73-34=39', '11-6=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[73, 34, 11, 6], Operations: [] Exploring Operation: 73-11=62, Resulting Numbers: [34, 6, 62] Generated Node #0,0: 44:[34, 6, 62] Operation: 73-11=62 Exploring Operation: 34+11=45, Resulting Numbers: [73, 6, 45] Generated Node #0,1: 44:[73, 6, 45] Operation: 34+11=45 Exploring Operation: 73-34=39, Resulting Numbers: [11, 6, 39] Generated Node #0,2: 44:[11, 6, 39] Operation: 73-34=39 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[11, 6, 39], Operations: ['73-34=39'] Exploring Operation: 6+39=45, Resulting Numbers: [11, 45] Generated Node #0,2,0: 44:[11, 45] Operation: 6+39=45 Exploring Operation: 11-6=5, Resulting Numbers: [39, 5] Generated Node #0,2,1: 44:[39, 5] Operation: 11-6=5 Exploring Operation: 11+39=50, Resulting Numbers: [6, 50] Generated Node #0,2,2: 44:[6, 50] Operation: 11+39=50 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[11, 45], Operations: ['73-34=39', '6+39=45'] Exploring Operation: 11*45=495, Resulting Numbers: [495] 495,44 unequal: No Solution Exploring Operation: 11+45=56, Resulting Numbers: [56] 56,44 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,44 unequal: No Solution No 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: 44:[39, 5], Operations: ['73-34=39', '11-6=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,44 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[73, 34, 11, 6], Operations: [] Exploring Operation: 73-34=39, Resulting Numbers: [11, 6, 39] Generated Node #0,2: 44:[11, 6, 39] Operation: 73-34=39 Moving to Node #0,2 Current State: 44:[11, 6, 39], Operations: ['73-34=39'] Exploring Operation: 11-6=5, Resulting Numbers: [39, 5] Generated Node #0,2,1: 44:[39, 5] Operation: 11-6=5 Moving to Node #0,2,1 Current State: 44:[39, 5], Operations: ['73-34=39', '11-6=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 80, 40, 67, 16 ]
53
[ "80/40=2", "67-16=51", "2+51=53" ]
Current State: 53:[80, 40, 67, 16], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [67, 16, 2] Generated Node #2: [67, 16, 2] from Operation: 80/40=2 Current State: 53:[67, 16, 2], Operations: ['80/40=2'] Exploring Operation: 67-16=51, Resulting Numbers: [2, 51] Generated Node #3: [2, 51] from Operation: 67-16=51 Current State: 53:[2, 51], Operations: ['80/40=2', '67-16=51'] Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[80, 40, 67, 16], Operations: [] Exploring Operation: 80-40=40, Resulting Numbers: [67, 16, 40] Generated Node #0,0: 53:[67, 16, 40] Operation: 80-40=40 Exploring Operation: 40+16=56, Resulting Numbers: [80, 67, 56] Generated Node #0,1: 53:[80, 67, 56] Operation: 40+16=56 Exploring Operation: 80-16=64, Resulting Numbers: [40, 67, 64] Generated Node #0,2: 53:[40, 67, 64] Operation: 80-16=64 Exploring Operation: 67-16=51, Resulting Numbers: [80, 40, 51] Generated Node #0,3: 53:[80, 40, 51] Operation: 67-16=51 Moving to Node #0,2 Current State: 53:[40, 67, 64], Operations: ['80-16=64'] Exploring Operation: 64-40=24, Resulting Numbers: [67, 24] Generated Node #0,2,0: 53:[67, 24] Operation: 64-40=24 Exploring Operation: 67-40=27, Resulting Numbers: [64, 27] Generated Node #0,2,1: 53:[64, 27] Operation: 67-40=27 Exploring Operation: 40+67=107, Resulting Numbers: [64, 107] Generated Node #0,2,2: 53:[64, 107] Operation: 40+67=107 Exploring Operation: 67-64=3, Resulting Numbers: [40, 3] Generated Node #0,2,3: 53:[40, 3] Operation: 67-64=3 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 53:[64, 27], Operations: ['80-16=64', '67-40=27'] Exploring Operation: 64+27=91, Resulting Numbers: [91] 91,53 unequal: No Solution Exploring Operation: 64*27=1728, Resulting Numbers: [1728] 1728,53 unequal: No Solution Exploring Operation: 64-27=37, Resulting Numbers: [37] 37,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 53:[67, 24], Operations: ['80-16=64', '64-40=24'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,53 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 53:[40, 3], Operations: ['80-16=64', '67-64=3'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,53 unequal: No Solution Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 53:[64, 107], Operations: ['80-16=64', '40+67=107'] Exploring Operation: 64*107=6848, Resulting Numbers: [6848] 6848,53 unequal: No Solution Exploring Operation: 107-64=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 64+107=171, Resulting Numbers: [171] 171,53 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: 53:[80, 40, 51], Operations: ['67-16=51'] Exploring Operation: 80/40=2, Resulting Numbers: [51, 2] Generated Node #0,3,0: 53:[51, 2] Operation: 80/40=2 Exploring Operation: 80-51=29, Resulting Numbers: [40, 29] Generated Node #0,3,1: 53:[40, 29] Operation: 80-51=29 Exploring Operation: 40+51=91, Resulting Numbers: [80, 91] Generated Node #0,3,2: 53:[80, 91] Operation: 40+51=91 Exploring Operation: 80-40=40, Resulting Numbers: [51, 40] Generated Node #0,3,3: 53:[51, 40] Operation: 80-40=40 Moving to Node #0,1 Current State: 53:[80, 67, 56], Operations: ['40+16=56'] Exploring Operation: 80-67=13, Resulting Numbers: [56, 13] Generated Node #0,1,0: 53:[56, 13] Operation: 80-67=13 Exploring Operation: 67-56=11, Resulting Numbers: [80, 11] Generated Node #0,1,1: 53:[80, 11] Operation: 67-56=11 Exploring Operation: 80+67=147, Resulting Numbers: [56, 147] Generated Node #0,1,2: 53:[56, 147] Operation: 80+67=147 Exploring Operation: 80-56=24, Resulting Numbers: [67, 24] Generated Node #0,1,3: 53:[67, 24] Operation: 80-56=24 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[56, 13], Operations: ['40+16=56', '80-67=13'] Exploring Operation: 56*13=728, Resulting Numbers: [728] 728,53 unequal: No Solution Exploring Operation: 56+13=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 56-13=43, Resulting Numbers: [43] 43,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 53:[67, 24], Operations: ['40+16=56', '80-56=24'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,53 unequal: No Solution Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[80, 11], Operations: ['40+16=56', '67-56=11'] Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,53 unequal: No Solution Exploring Operation: 80*11=880, Resulting Numbers: [880] 880,53 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[56, 147], Operations: ['40+16=56', '80+67=147'] Exploring Operation: 147-56=91, Resulting Numbers: [91] 91,53 unequal: No Solution Exploring Operation: 56*147=8232, Resulting Numbers: [8232] 8232,53 unequal: No Solution Exploring Operation: 56+147=203, Resulting Numbers: [203] 203,53 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: 53:[67, 16, 40], Operations: ['80-40=40'] Exploring Operation: 67-16=51, Resulting Numbers: [40, 51] Generated Node #0,0,0: 53:[40, 51] Operation: 67-16=51 Exploring Operation: 40-16=24, Resulting Numbers: [67, 24] Generated Node #0,0,1: 53:[67, 24] Operation: 40-16=24 Exploring Operation: 16+40=56, Resulting Numbers: [67, 56] Generated Node #0,0,2: 53:[67, 56] Operation: 16+40=56 Exploring Operation: 67+16=83, Resulting Numbers: [40, 83] Generated Node #0,0,3: 53:[40, 83] Operation: 67+16=83 Moving to Node #0,3,3 Current State: 53:[51, 40], Operations: ['67-16=51', '80-40=40'] Exploring Operation: 51*40=2040, Resulting Numbers: [2040] 2040,53 unequal: No Solution Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 51+40=91, Resulting Numbers: [91] 91,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[40, 51], Operations: ['80-40=40', '67-16=51'] Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,53 unequal: No Solution Exploring Operation: 40*51=2040, Resulting Numbers: [2040] 2040,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[67, 56], Operations: ['80-40=40', '16+40=56'] Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 67+56=123, Resulting Numbers: [123] 123,53 unequal: No Solution Exploring Operation: 67*56=3752, Resulting Numbers: [3752] 3752,53 unequal: No Solution Moving to Node #0,3,1 Current State: 53:[40, 29], Operations: ['67-16=51', '80-51=29'] Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 40*29=1160, Resulting Numbers: [1160] 1160,53 unequal: No Solution Exploring Operation: 40+29=69, Resulting Numbers: [69] 69,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[67, 24], Operations: ['80-40=40', '40-16=24'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,53 unequal: No Solution Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[40, 83], Operations: ['80-40=40', '67+16=83'] Exploring Operation: 40+83=123, Resulting Numbers: [123] 123,53 unequal: No Solution Exploring Operation: 83-40=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 40*83=3320, Resulting Numbers: [3320] 3320,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[51, 2], Operations: ['67-16=51', '80/40=2'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,53 unequal: No Solution Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,53 unequal: No Solution Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[80, 40, 67, 16], Operations: [] Exploring Operation: 67-16=51, Resulting Numbers: [80, 40, 51] Generated Node #0,3: 53:[80, 40, 51] Operation: 67-16=51 Moving to Node #0,3 Current State: 53:[80, 40, 51], Operations: ['67-16=51'] Exploring Operation: 80/40=2, Resulting Numbers: [51, 2] Generated Node #0,3,0: 53:[51, 2] Operation: 80/40=2 Moving to Node #0,3,0 Current State: 53:[51, 2], Operations: ['67-16=51', '80/40=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
0.940104
hs_4
mult_heuristic
[ 44, 92, 76, 21 ]
26
[ "92*21=1932", "44+1932=1976", "1976/76=26" ]
Current State: 26:[44, 92, 76, 21], Operations: [] Exploring Operation: 92*21=1932, Resulting Numbers: [44, 76, 1932] Generated Node #2: [44, 76, 1932] from Operation: 92*21=1932 Current State: 26:[44, 76, 1932], Operations: ['92*21=1932'] Exploring Operation: 44+1932=1976, Resulting Numbers: [76, 1976] Generated Node #3: [76, 1976] from Operation: 44+1932=1976 Current State: 26:[76, 1976], Operations: ['92*21=1932', '44+1932=1976'] Exploring Operation: 1976/76=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[44, 92, 76, 21], Operations: [] Exploring Operation: 76-44=32, Resulting Numbers: [92, 21, 32] Generated Node #0,0: 26:[92, 21, 32] Operation: 76-44=32 Exploring Operation: 92-44=48, Resulting Numbers: [76, 21, 48] Generated Node #0,1: 26:[76, 21, 48] Operation: 92-44=48 Exploring Operation: 92-76=16, Resulting Numbers: [44, 21, 16] Generated Node #0,2: 26:[44, 21, 16] Operation: 92-76=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[44, 21, 16], Operations: ['92-76=16'] Exploring Operation: 44-16=28, Resulting Numbers: [21, 28] Generated Node #0,2,0: 26:[21, 28] Operation: 44-16=28 Exploring Operation: 21-16=5, Resulting Numbers: [44, 5] Generated Node #0,2,1: 26:[44, 5] Operation: 21-16=5 Exploring Operation: 44-21=23, Resulting Numbers: [16, 23] Generated Node #0,2,2: 26:[16, 23] Operation: 44-21=23 Moving to Node #0,2,2 Current State: 26:[16, 23], Operations: ['92-76=16', '44-21=23'] Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 16*23=368, Resulting Numbers: [368] 368,26 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[21, 28], Operations: ['92-76=16', '44-16=28'] Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,26 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,26 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[44, 5], Operations: ['92-76=16', '21-16=5'] Exploring Operation: 44*5=220, Resulting Numbers: [220] 220,26 unequal: No Solution Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,26 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[92, 21, 32], Operations: ['76-44=32'] Exploring Operation: 92-21=71, Resulting Numbers: [32, 71] Generated Node #0,0,0: 26:[32, 71] Operation: 92-21=71 Exploring Operation: 92-32=60, Resulting Numbers: [21, 60] Generated Node #0,0,1: 26:[21, 60] Operation: 92-32=60 Exploring Operation: 32-21=11, Resulting Numbers: [92, 11] Generated Node #0,0,2: 26:[92, 11] Operation: 32-21=11 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 26:[21, 60], Operations: ['76-44=32', '92-32=60'] Exploring Operation: 21*60=1260, Resulting Numbers: [1260] 1260,26 unequal: No Solution Exploring Operation: 21+60=81, Resulting Numbers: [81] 81,26 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,26 unequal: No Solution No 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: 26:[32, 71], Operations: ['76-44=32', '92-21=71'] Exploring Operation: 32+71=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 71-32=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 32*71=2272, Resulting Numbers: [2272] 2272,26 unequal: No Solution No 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: 26:[92, 11], Operations: ['76-44=32', '32-21=11'] Exploring Operation: 92*11=1012, Resulting Numbers: [1012] 1012,26 unequal: No Solution Exploring Operation: 92+11=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,26 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: 26:[76, 21, 48], Operations: ['92-44=48'] Exploring Operation: 48-21=27, Resulting Numbers: [76, 27] Generated Node #0,1,0: 26:[76, 27] Operation: 48-21=27 Exploring Operation: 76-21=55, Resulting Numbers: [48, 55] Generated Node #0,1,1: 26:[48, 55] Operation: 76-21=55 Exploring Operation: 76-48=28, Resulting Numbers: [21, 28] Generated Node #0,1,2: 26:[21, 28] Operation: 76-48=28 Moving to Node #0,1,2 Current State: 26:[21, 28], Operations: ['92-44=48', '76-48=28'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,26 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[76, 27], Operations: ['92-44=48', '48-21=27'] Exploring Operation: 76*27=2052, Resulting Numbers: [2052] 2052,26 unequal: No Solution Exploring Operation: 76+27=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 76-27=49, Resulting Numbers: [49] 49,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[48, 55], Operations: ['92-44=48', '76-21=55'] Exploring Operation: 48+55=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 48*55=2640, Resulting Numbers: [2640] 2640,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 70, 77, 53, 91 ]
47
[ "70*53=3710", "3710-91=3619", "3619/77=47" ]
Current State: 47:[70, 77, 53, 91], Operations: [] Exploring Operation: 70*53=3710, Resulting Numbers: [77, 91, 3710] Generated Node #2: [77, 91, 3710] from Operation: 70*53=3710 Current State: 47:[77, 91, 3710], Operations: ['70*53=3710'] Exploring Operation: 3710-91=3619, Resulting Numbers: [77, 3619] Generated Node #3: [77, 3619] from Operation: 3710-91=3619 Current State: 47:[77, 3619], Operations: ['70*53=3710', '3710-91=3619'] Exploring Operation: 3619/77=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[70, 77, 53, 91], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [77, 53, 21] Generated Node #0,0: 47:[77, 53, 21] Operation: 91-70=21 Moving to Node #0,0 Current State: 47:[77, 53, 21], Operations: ['91-70=21'] Exploring Operation: 77-21=56, Resulting Numbers: [53, 56] Generated Node #0,0,0: 47:[53, 56] Operation: 77-21=56 Moving to Node #0,0,0 Current State: 47:[53, 56], Operations: ['91-70=21', '77-21=56'] Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,47 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 63, 31, 17, 22 ]
26
[ "63+22=85", "85/17=5", "31-5=26" ]
Current State: 26:[63, 31, 17, 22], Operations: [] Exploring Operation: 63+22=85, Resulting Numbers: [31, 17, 85] Generated Node #2: [31, 17, 85] from Operation: 63+22=85 Current State: 26:[31, 17, 85], Operations: ['63+22=85'] Exploring Operation: 85/17=5, Resulting Numbers: [31, 5] Generated Node #3: [31, 5] from Operation: 85/17=5 Current State: 26:[31, 5], Operations: ['63+22=85', '85/17=5'] Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[63, 31, 17, 22], Operations: [] Exploring Operation: 31-17=14, Resulting Numbers: [63, 22, 14] Generated Node #0,0: 26:[63, 22, 14] Operation: 31-17=14 Exploring Operation: 63-17=46, Resulting Numbers: [31, 22, 46] Generated Node #0,1: 26:[31, 22, 46] Operation: 63-17=46 Exploring Operation: 63-31=32, Resulting Numbers: [17, 22, 32] Generated Node #0,2: 26:[17, 22, 32] Operation: 63-31=32 Exploring Operation: 31-22=9, Resulting Numbers: [63, 17, 9] Generated Node #0,3: 26:[63, 17, 9] Operation: 31-22=9 Exploring Operation: 63-22=41, Resulting Numbers: [31, 17, 41] Generated Node #0,4: 26:[31, 17, 41] Operation: 63-22=41 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[17, 22, 32], Operations: ['63-31=32'] Exploring Operation: 32-22=10, Resulting Numbers: [17, 10] Generated Node #0,2,0: 26:[17, 10] Operation: 32-22=10 Exploring Operation: 17+22=39, Resulting Numbers: [32, 39] Generated Node #0,2,1: 26:[32, 39] Operation: 17+22=39 Exploring Operation: 22-17=5, Resulting Numbers: [32, 5] Generated Node #0,2,2: 26:[32, 5] Operation: 22-17=5 Exploring Operation: 17+32=49, Resulting Numbers: [22, 49] Generated Node #0,2,3: 26:[22, 49] Operation: 17+32=49 Exploring Operation: 32-17=15, Resulting Numbers: [22, 15] Generated Node #0,2,4: 26:[22, 15] Operation: 32-17=15 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 26:[22, 15], Operations: ['63-31=32', '32-17=15'] Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,26 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 26:[17, 10], Operations: ['63-31=32', '32-22=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,26 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,26 unequal: No Solution No 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: 26:[32, 5], Operations: ['63-31=32', '22-17=5'] Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,26 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,26 unequal: No Solution No 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: 26:[32, 39], Operations: ['63-31=32', '17+22=39'] Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 32*39=1248, Resulting Numbers: [1248] 1248,26 unequal: No Solution Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,26 unequal: No Solution No 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: 26:[22, 49], Operations: ['63-31=32', '17+32=49'] Exploring Operation: 22*49=1078, Resulting Numbers: [1078] 1078,26 unequal: No Solution Exploring Operation: 22+49=71, Resulting Numbers: [71] 71,26 unequal: No Solution Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 26:[31, 17, 41], Operations: ['63-22=41'] Exploring Operation: 31-17=14, Resulting Numbers: [41, 14] Generated Node #0,4,0: 26:[41, 14] Operation: 31-17=14 Exploring Operation: 41-31=10, Resulting Numbers: [17, 10] Generated Node #0,4,1: 26:[17, 10] Operation: 41-31=10 Exploring Operation: 17+41=58, Resulting Numbers: [31, 58] Generated Node #0,4,2: 26:[31, 58] Operation: 17+41=58 Exploring Operation: 41-17=24, Resulting Numbers: [31, 24] Generated Node #0,4,3: 26:[31, 24] Operation: 41-17=24 Exploring Operation: 31+17=48, Resulting Numbers: [41, 48] Generated Node #0,4,4: 26:[41, 48] Operation: 31+17=48 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 26:[17, 10], Operations: ['63-22=41', '41-31=10'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,26 unequal: No Solution No 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: 26:[31, 24], Operations: ['63-22=41', '41-17=24'] Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,26 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,26 unequal: No Solution No 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: 26:[41, 14], Operations: ['63-22=41', '31-17=14'] Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,26 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,26 unequal: No Solution No 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: 26:[31, 58], Operations: ['63-22=41', '17+41=58'] Exploring Operation: 31+58=89, Resulting Numbers: [89] 89,26 unequal: No Solution Exploring Operation: 31*58=1798, Resulting Numbers: [1798] 1798,26 unequal: No Solution Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,26 unequal: No Solution No 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: 26:[41, 48], Operations: ['63-22=41', '31+17=48'] Exploring Operation: 41*48=1968, Resulting Numbers: [1968] 1968,26 unequal: No Solution Exploring Operation: 41+48=89, Resulting Numbers: [89] 89,26 unequal: No Solution Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,26 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: 26:[31, 22, 46], Operations: ['63-17=46'] Exploring Operation: 22+46=68, Resulting Numbers: [31, 68] Generated Node #0,1,0: 26:[31, 68] Operation: 22+46=68 Exploring Operation: 46-31=15, Resulting Numbers: [22, 15] Generated Node #0,1,1: 26:[22, 15] Operation: 46-31=15 Exploring Operation: 31+22=53, Resulting Numbers: [46, 53] Generated Node #0,1,2: 26:[46, 53] Operation: 31+22=53 Exploring Operation: 46-22=24, Resulting Numbers: [31, 24] Generated Node #0,1,3: 26:[31, 24] Operation: 46-22=24 Exploring Operation: 31-22=9, Resulting Numbers: [46, 9] Generated Node #0,1,4: 26:[46, 9] Operation: 31-22=9 Moving to Node #0,1,1 Current State: 26:[22, 15], Operations: ['63-17=46', '46-31=15'] Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,26 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,26 unequal: No Solution Moving to Node #0,1,3 Current State: 26:[31, 24], Operations: ['63-17=46', '46-22=24'] Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,26 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,26 unequal: No Solution Moving to Node #0,1,4 Current State: 26:[46, 9], Operations: ['63-17=46', '31-22=9'] Exploring Operation: 46*9=414, Resulting Numbers: [414] 414,26 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[31, 68], Operations: ['63-17=46', '22+46=68'] Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 31+68=99, Resulting Numbers: [99] 99,26 unequal: No Solution Exploring Operation: 31*68=2108, Resulting Numbers: [2108] 2108,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[46, 53], Operations: ['63-17=46', '31+22=53'] Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,26 unequal: No Solution Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,26 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[63, 22, 14], Operations: ['31-17=14'] Exploring Operation: 22-14=8, Resulting Numbers: [63, 8] Generated Node #0,0,0: 26:[63, 8] Operation: 22-14=8 Exploring Operation: 63+14=77, Resulting Numbers: [22, 77] Generated Node #0,0,1: 26:[22, 77] Operation: 63+14=77 Exploring Operation: 22+14=36, Resulting Numbers: [63, 36] Generated Node #0,0,2: 26:[63, 36] Operation: 22+14=36 Exploring Operation: 63-22=41, Resulting Numbers: [14, 41] Generated Node #0,0,3: 26:[14, 41] Operation: 63-22=41 Exploring Operation: 63-14=49, Resulting Numbers: [22, 49] Generated Node #0,0,4: 26:[22, 49] Operation: 63-14=49 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 26:[14, 41], Operations: ['31-17=14', '63-22=41'] Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,26 unequal: No Solution No 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: 26:[22, 49], Operations: ['31-17=14', '63-14=49'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 22+49=71, Resulting Numbers: [71] 71,26 unequal: No Solution Exploring Operation: 22*49=1078, Resulting Numbers: [1078] 1078,26 unequal: No Solution No 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: 26:[63, 8], Operations: ['31-17=14', '22-14=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,26 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,26 unequal: No Solution No 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: 26:[63, 36], Operations: ['31-17=14', '22+14=36'] Exploring Operation: 63+36=99, Resulting Numbers: [99] 99,26 unequal: No Solution Exploring Operation: 63*36=2268, Resulting Numbers: [2268] 2268,26 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,26 unequal: No Solution No 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: 26:[22, 77], Operations: ['31-17=14', '63+14=77'] Exploring Operation: 22+77=99, Resulting Numbers: [99] 99,26 unequal: No Solution Exploring Operation: 22*77=1694, Resulting Numbers: [1694] 1694,26 unequal: No Solution Exploring Operation: 77-22=55, Resulting Numbers: [55] 55,26 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: 26:[63, 17, 9], Operations: ['31-22=9'] Exploring Operation: 17+9=26, Resulting Numbers: [63, 26] Generated Node #0,3,0: 26:[63, 26] Operation: 17+9=26 Exploring Operation: 63-17=46, Resulting Numbers: [9, 46] Generated Node #0,3,1: 26:[9, 46] Operation: 63-17=46 Exploring Operation: 63-9=54, Resulting Numbers: [17, 54] Generated Node #0,3,2: 26:[17, 54] Operation: 63-9=54 Exploring Operation: 63/9=7, Resulting Numbers: [17, 7] Generated Node #0,3,3: 26:[17, 7] Operation: 63/9=7 Exploring Operation: 17-9=8, Resulting Numbers: [63, 8] Generated Node #0,3,4: 26:[63, 8] Operation: 17-9=8 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 26:[17, 7], Operations: ['31-22=9', '63/9=7'] Exploring Operation: 17*7=119, Resulting Numbers: [119] 119,26 unequal: No Solution Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,26 unequal: No Solution No 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: 26:[9, 46], Operations: ['31-22=9', '63-17=46'] Exploring Operation: 9*46=414, Resulting Numbers: [414] 414,26 unequal: No Solution Exploring Operation: 9+46=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,26 unequal: No Solution No 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: 26:[17, 54], Operations: ['31-22=9', '63-9=54'] Exploring Operation: 17*54=918, Resulting Numbers: [918] 918,26 unequal: No Solution Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 17+54=71, Resulting Numbers: [71] 71,26 unequal: No Solution No 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: 26:[63, 26], Operations: ['31-22=9', '17+9=26'] Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,26 unequal: No Solution Exploring Operation: 63*26=1638, Resulting Numbers: [1638] 1638,26 unequal: No Solution No 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: 26:[63, 8], Operations: ['31-22=9', '17-9=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,26 unequal: No Solution Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,26 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
[ 74, 2, 22, 67 ]
17
[ "74-2=72", "22+67=89", "89-72=17" ]
Current State: 17:[74, 2, 22, 67], Operations: [] Exploring Operation: 74-2=72, Resulting Numbers: [22, 67, 72] Generated Node #2: [22, 67, 72] from Operation: 74-2=72 Current State: 17:[22, 67, 72], Operations: ['74-2=72'] Exploring Operation: 22+67=89, Resulting Numbers: [72, 89] Generated Node #3: [72, 89] from Operation: 22+67=89 Current State: 17:[72, 89], Operations: ['74-2=72', '22+67=89'] Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[74, 2, 22, 67], Operations: [] Exploring Operation: 74-67=7, Resulting Numbers: [2, 22, 7] Generated Node #0,0: 17:[2, 22, 7] Operation: 74-67=7 Exploring Operation: 74/2=37, Resulting Numbers: [22, 67, 37] Generated Node #0,1: 17:[22, 67, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[2, 22, 7], Operations: ['74-67=7'] Exploring Operation: 2*7=14, Resulting Numbers: [22, 14] Generated Node #0,0,0: 17:[22, 14] Operation: 2*7=14 Exploring Operation: 22-2=20, Resulting Numbers: [7, 20] Generated Node #0,0,1: 17:[7, 20] Operation: 22-2=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[22, 14], Operations: ['74-67=7', '2*7=14'] Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 17:[7, 20], Operations: ['74-67=7', '22-2=20'] Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,17 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[22, 67, 37], Operations: ['74/2=37'] Exploring Operation: 67-22=45, Resulting Numbers: [37, 45] Generated Node #0,1,0: 17:[37, 45] Operation: 67-22=45 Exploring Operation: 67-37=30, Resulting Numbers: [22, 30] Generated Node #0,1,1: 17:[22, 30] Operation: 67-37=30 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 17:[22, 30], Operations: ['74/2=37', '67-37=30'] Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 22+30=52, Resulting Numbers: [52] 52,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[37, 45], Operations: ['74/2=37', '67-22=45'] Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,17 unequal: No Solution Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 32, 13, 9, 34 ]
83
[ "32*34=1088", "1088-9=1079", "1079/13=83" ]
Current State: 83:[32, 13, 9, 34], Operations: [] Exploring Operation: 32*34=1088, Resulting Numbers: [13, 9, 1088] Generated Node #2: [13, 9, 1088] from Operation: 32*34=1088 Current State: 83:[13, 9, 1088], Operations: ['32*34=1088'] Exploring Operation: 1088-9=1079, Resulting Numbers: [13, 1079] Generated Node #3: [13, 1079] from Operation: 1088-9=1079 Current State: 83:[13, 1079], Operations: ['32*34=1088', '1088-9=1079'] Exploring Operation: 1079/13=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[32, 13, 9, 34], Operations: [] Exploring Operation: 13*9=117, Resulting Numbers: [32, 34, 117] Generated Node #0,0: 83:[32, 34, 117] Operation: 13*9=117 Moving to Node #0,0 Current State: 83:[32, 34, 117], Operations: ['13*9=117'] Exploring Operation: 32+34=66, Resulting Numbers: [117, 66] Generated Node #0,0,0: 83:[117, 66] Operation: 32+34=66 Moving to Node #0,0,0 Current State: 83:[117, 66], Operations: ['13*9=117', '32+34=66'] Exploring Operation: 117-66=51, Resulting Numbers: [51] 51,83 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 25, 39, 67, 23 ]
35
[ "25+67=92", "92/23=4", "39-4=35" ]
Current State: 35:[25, 39, 67, 23], Operations: [] Exploring Operation: 25+67=92, Resulting Numbers: [39, 23, 92] Generated Node #2: [39, 23, 92] from Operation: 25+67=92 Current State: 35:[39, 23, 92], Operations: ['25+67=92'] Exploring Operation: 92/23=4, Resulting Numbers: [39, 4] Generated Node #3: [39, 4] from Operation: 92/23=4 Current State: 35:[39, 4], Operations: ['25+67=92', '92/23=4'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[25, 39, 67, 23], Operations: [] Exploring Operation: 67-25=42, Resulting Numbers: [39, 23, 42] Generated Node #0,0: 35:[39, 23, 42] Operation: 67-25=42 Exploring Operation: 67-23=44, Resulting Numbers: [25, 39, 44] Generated Node #0,1: 35:[25, 39, 44] Operation: 67-23=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[39, 23, 42], Operations: ['67-25=42'] Exploring Operation: 39-23=16, Resulting Numbers: [42, 16] Generated Node #0,0,0: 35:[42, 16] Operation: 39-23=16 Exploring Operation: 42-39=3, Resulting Numbers: [23, 3] Generated Node #0,0,1: 35:[23, 3] Operation: 42-39=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[23, 3], Operations: ['67-25=42', '42-39=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,35 unequal: No Solution No 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: 35:[42, 16], Operations: ['67-25=42', '39-23=16'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,35 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: 35:[25, 39, 44], Operations: ['67-23=44'] Exploring Operation: 44-39=5, Resulting Numbers: [25, 5] Generated Node #0,1,0: 35:[25, 5] Operation: 44-39=5 Exploring Operation: 39-25=14, Resulting Numbers: [44, 14] Generated Node #0,1,1: 35:[44, 14] Operation: 39-25=14 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[25, 5], Operations: ['67-23=44', '44-39=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,35 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,35 unequal: No Solution No 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: 35:[44, 14], Operations: ['67-23=44', '39-25=14'] Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,35 unequal: No Solution Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,35 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
[ 43, 94, 36, 5 ]
59
[ "43-36=7", "5*7=35", "94-35=59" ]
Current State: 59:[43, 94, 36, 5], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [94, 5, 7] Generated Node #2: [94, 5, 7] from Operation: 43-36=7 Current State: 59:[94, 5, 7], Operations: ['43-36=7'] Exploring Operation: 5*7=35, Resulting Numbers: [94, 35] Generated Node #3: [94, 35] from Operation: 5*7=35 Current State: 59:[94, 35], Operations: ['43-36=7', '5*7=35'] Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[43, 94, 36, 5], Operations: [] Exploring Operation: 94-5=89, Resulting Numbers: [43, 36, 89] Generated Node #0,0: 59:[43, 36, 89] Operation: 94-5=89 Exploring Operation: 43+5=48, Resulting Numbers: [94, 36, 48] Generated Node #0,1: 59:[94, 36, 48] Operation: 43+5=48 Moving to Node #0,0 Current State: 59:[43, 36, 89], Operations: ['94-5=89'] Exploring Operation: 89-43=46, Resulting Numbers: [36, 46] Generated Node #0,0,0: 59:[36, 46] Operation: 89-43=46 Exploring Operation: 89-36=53, Resulting Numbers: [43, 53] Generated Node #0,0,1: 59:[43, 53] Operation: 89-36=53 Moving to Node #0,1 Current State: 59:[94, 36, 48], Operations: ['43+5=48'] Exploring Operation: 94-48=46, Resulting Numbers: [36, 46] Generated Node #0,1,0: 59:[36, 46] Operation: 94-48=46 Exploring Operation: 94-36=58, Resulting Numbers: [48, 58] Generated Node #0,1,1: 59:[48, 58] Operation: 94-36=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[48, 58], Operations: ['43+5=48', '94-36=58'] Exploring Operation: 58-48=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 48+58=106, Resulting Numbers: [106] 106,59 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 #0,1,0 Current State: 59:[36, 46], Operations: ['43+5=48', '94-48=46'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 36+46=82, Resulting Numbers: [82] 82,59 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: 59:[43, 53], Operations: ['94-5=89', '89-36=53'] Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 43+53=96, Resulting Numbers: [96] 96,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[36, 46], Operations: ['94-5=89', '89-43=46'] Exploring Operation: 36+46=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,59 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 45, 69, 35, 23 ]
34
[ "69-45=24", "35+23=58", "58-24=34" ]
Current State: 34:[45, 69, 35, 23], Operations: [] Exploring Operation: 69-45=24, Resulting Numbers: [35, 23, 24] Generated Node #2: [35, 23, 24] from Operation: 69-45=24 Current State: 34:[35, 23, 24], Operations: ['69-45=24'] Exploring Operation: 35+23=58, Resulting Numbers: [24, 58] Generated Node #3: [24, 58] from Operation: 35+23=58 Current State: 34:[24, 58], Operations: ['69-45=24', '35+23=58'] Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[45, 69, 35, 23], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [45, 35, 3] Generated Node #0,0: 34:[45, 35, 3] Operation: 69/23=3 Exploring Operation: 69-45=24, Resulting Numbers: [35, 23, 24] Generated Node #0,1: 34:[35, 23, 24] Operation: 69-45=24 Moving to Node #0,0 Current State: 34:[45, 35, 3], Operations: ['69/23=3'] Exploring Operation: 45/3=15, Resulting Numbers: [35, 15] Generated Node #0,0,0: 34:[35, 15] Operation: 45/3=15 Exploring Operation: 45-35=10, Resulting Numbers: [3, 10] Generated Node #0,0,1: 34:[3, 10] Operation: 45-35=10 Moving to Node #0,1 Current State: 34:[35, 23, 24], Operations: ['69-45=24'] Exploring Operation: 35-23=12, Resulting Numbers: [24, 12] Generated Node #0,1,0: 34:[24, 12] Operation: 35-23=12 Exploring Operation: 24-23=1, Resulting Numbers: [35, 1] Generated Node #0,1,1: 34:[35, 1] Operation: 24-23=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[35, 1], Operations: ['69-45=24', '24-23=1'] Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[45, 69, 35, 23], Operations: [] Exploring Operation: 69-45=24, Resulting Numbers: [35, 23, 24] Generated Node #0,1: 34:[35, 23, 24] Operation: 69-45=24 Moving to Node #0,1 Current State: 34:[35, 23, 24], Operations: ['69-45=24'] Exploring Operation: 24-23=1, Resulting Numbers: [35, 1] Generated Node #0,1,1: 34:[35, 1] Operation: 24-23=1 Moving to Node #0,1,1 Current State: 34:[35, 1], Operations: ['69-45=24', '24-23=1'] Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 34, 7, 13, 44 ]
16
[ "34+7=41", "13+44=57", "57-41=16" ]
Current State: 16:[34, 7, 13, 44], Operations: [] Exploring Operation: 34+7=41, Resulting Numbers: [13, 44, 41] Generated Node #2: [13, 44, 41] from Operation: 34+7=41 Current State: 16:[13, 44, 41], Operations: ['34+7=41'] Exploring Operation: 13+44=57, Resulting Numbers: [41, 57] Generated Node #3: [41, 57] from Operation: 13+44=57 Current State: 16:[41, 57], Operations: ['34+7=41', '13+44=57'] Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[34, 7, 13, 44], Operations: [] Exploring Operation: 44-34=10, Resulting Numbers: [7, 13, 10] Generated Node #0,0: 16:[7, 13, 10] Operation: 44-34=10 Exploring Operation: 34-13=21, Resulting Numbers: [7, 44, 21] Generated Node #0,1: 16:[7, 44, 21] Operation: 34-13=21 Moving to Node #0,0 Current State: 16:[7, 13, 10], Operations: ['44-34=10'] Exploring Operation: 13-10=3, Resulting Numbers: [7, 3] Generated Node #0,0,0: 16:[7, 3] Operation: 13-10=3 Exploring Operation: 13-7=6, Resulting Numbers: [10, 6] Generated Node #0,0,1: 16:[10, 6] Operation: 13-7=6 Moving to Node #0,1 Current State: 16:[7, 44, 21], Operations: ['34-13=21'] Exploring Operation: 44-21=23, Resulting Numbers: [7, 23] Generated Node #0,1,0: 16:[7, 23] Operation: 44-21=23 Exploring Operation: 44-7=37, Resulting Numbers: [21, 37] Generated Node #0,1,1: 16:[21, 37] Operation: 44-7=37 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[7, 23], Operations: ['34-13=21', '44-21=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[34, 7, 13, 44], Operations: [] Exploring Operation: 34-13=21, Resulting Numbers: [7, 44, 21] Generated Node #0,1: 16:[7, 44, 21] Operation: 34-13=21 Moving to Node #0,1 Current State: 16:[7, 44, 21], Operations: ['34-13=21'] Exploring Operation: 44-21=23, Resulting Numbers: [7, 23] Generated Node #0,1,0: 16:[7, 23] Operation: 44-21=23 Moving to Node #0,1,0 Current State: 16:[7, 23], Operations: ['34-13=21', '44-21=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 65, 67, 73, 70 ]
76
[ "67-65=2", "73*2=146", "146-70=76" ]
Current State: 76:[65, 67, 73, 70], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [73, 70, 2] Generated Node #2: [73, 70, 2] from Operation: 67-65=2 Current State: 76:[73, 70, 2], Operations: ['67-65=2'] Exploring Operation: 73*2=146, Resulting Numbers: [70, 146] Generated Node #3: [70, 146] from Operation: 73*2=146 Current State: 76:[70, 146], Operations: ['67-65=2', '73*2=146'] Exploring Operation: 146-70=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[65, 67, 73, 70], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [73, 70, 2] Generated Node #0,0: 76:[73, 70, 2] Operation: 67-65=2 Moving to Node #0,0 Current State: 76:[73, 70, 2], Operations: ['67-65=2'] Exploring Operation: 73-70=3, Resulting Numbers: [2, 3] Generated Node #0,0,0: 76:[2, 3] Operation: 73-70=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[2, 3], Operations: ['67-65=2', '73-70=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,76 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
[ 48, 12, 48, 92 ]
79
[ "48/48=1", "92-12=80", "80-1=79" ]
Current State: 79:[48, 12, 48, 92], Operations: [] Exploring Operation: 48/48=1, Resulting Numbers: [12, 92, 1] Generated Node #2: [12, 92, 1] from Operation: 48/48=1 Current State: 79:[12, 92, 1], Operations: ['48/48=1'] Exploring Operation: 92-12=80, Resulting Numbers: [1, 80] Generated Node #3: [1, 80] from Operation: 92-12=80 Current State: 79:[1, 80], Operations: ['48/48=1', '92-12=80'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[48, 12, 48, 92], Operations: [] Exploring Operation: 48-12=36, Resulting Numbers: [48, 92, 36] Generated Node #0,0: 79:[48, 92, 36] Operation: 48-12=36 Exploring Operation: 92-12=80, Resulting Numbers: [48, 48, 80] Generated Node #0,1: 79:[48, 48, 80] Operation: 92-12=80 Exploring Operation: 12+48=60, Resulting Numbers: [48, 92, 60] Generated Node #0,2: 79:[48, 92, 60] Operation: 12+48=60 Exploring Operation: 48+12=60, Resulting Numbers: [48, 92, 60] Generated Node #0,3: 79:[48, 92, 60] Operation: 48+12=60 Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[48, 48, 80], Operations: ['92-12=80'] Exploring Operation: 48+48=96, Resulting Numbers: [80, 96] Generated Node #0,1,0: 79:[80, 96] Operation: 48+48=96 Exploring Operation: 80-48=32, Resulting Numbers: [48, 32] Generated Node #0,1,1: 79:[48, 32] Operation: 80-48=32 Exploring Operation: 80-48=32, Resulting Numbers: [48, 32] Generated Node #0,1,2: 79:[48, 32] Operation: 80-48=32 Exploring Operation: 48/48=1, Resulting Numbers: [80, 1] Generated Node #0,1,3: 79:[80, 1] Operation: 48/48=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[80, 96], Operations: ['92-12=80', '48+48=96'] Exploring Operation: 80*96=7680, Resulting Numbers: [7680] 7680,79 unequal: No Solution Exploring Operation: 80+96=176, Resulting Numbers: [176] 176,79 unequal: No Solution Exploring Operation: 96-80=16, Resulting Numbers: [16] 16,79 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 #0,1,1 Current State: 79:[48, 32], Operations: ['92-12=80', '80-48=32'] Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,79 unequal: No Solution Exploring Operation: 48+32=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 48*32=1536, Resulting Numbers: [1536] 1536,79 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:[48, 32], Operations: ['92-12=80', '80-48=32'] Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,79 unequal: No Solution Exploring Operation: 48+32=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 48*32=1536, Resulting Numbers: [1536] 1536,79 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:[80, 1], Operations: ['92-12=80', '48/48=1'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[48, 12, 48, 92], Operations: [] Exploring Operation: 92-12=80, Resulting Numbers: [48, 48, 80] Generated Node #0,1: 79:[48, 48, 80] Operation: 92-12=80 Moving to Node #0,1 Current State: 79:[48, 48, 80], Operations: ['92-12=80'] Exploring Operation: 48/48=1, Resulting Numbers: [80, 1] Generated Node #0,1,3: 79:[80, 1] Operation: 48/48=1 Moving to Node #0,1,3 Current State: 79:[80, 1], Operations: ['92-12=80', '48/48=1'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 91, 9, 6, 95 ]
58
[ "95-91=4", "9*6=54", "4+54=58" ]
Current State: 58:[91, 9, 6, 95], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [9, 6, 4] Generated Node #2: [9, 6, 4] from Operation: 95-91=4 Current State: 58:[9, 6, 4], Operations: ['95-91=4'] Exploring Operation: 9*6=54, Resulting Numbers: [4, 54] Generated Node #3: [4, 54] from Operation: 9*6=54 Current State: 58:[4, 54], Operations: ['95-91=4', '9*6=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[91, 9, 6, 95], Operations: [] Exploring Operation: 95-9=86, Resulting Numbers: [91, 6, 86] Generated Node #0,0: 58:[91, 6, 86] Operation: 95-9=86 Exploring Operation: 91-9=82, Resulting Numbers: [6, 95, 82] Generated Node #0,1: 58:[6, 95, 82] Operation: 91-9=82 Exploring Operation: 95-91=4, Resulting Numbers: [9, 6, 4] Generated Node #0,2: 58:[9, 6, 4] Operation: 95-91=4 Moving to Node #0,2 Current State: 58:[9, 6, 4], Operations: ['95-91=4'] Exploring Operation: 9-4=5, Resulting Numbers: [6, 5] Generated Node #0,2,0: 58:[6, 5] Operation: 9-4=5 Exploring Operation: 9*6=54, Resulting Numbers: [4, 54] Generated Node #0,2,1: 58:[4, 54] Operation: 9*6=54 Exploring Operation: 9-6=3, Resulting Numbers: [4, 3] Generated Node #0,2,2: 58:[4, 3] Operation: 9-6=3 Moving to Node #0,0 Current State: 58:[91, 6, 86], Operations: ['95-9=86'] Exploring Operation: 86-6=80, Resulting Numbers: [91, 80] Generated Node #0,0,0: 58:[91, 80] Operation: 86-6=80 Exploring Operation: 91-6=85, Resulting Numbers: [86, 85] Generated Node #0,0,1: 58:[86, 85] Operation: 91-6=85 Exploring Operation: 91-86=5, Resulting Numbers: [6, 5] Generated Node #0,0,2: 58:[6, 5] Operation: 91-86=5 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 58:[6, 5], Operations: ['95-9=86', '91-86=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,58 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,58 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[91, 80], Operations: ['95-9=86', '86-6=80'] Exploring Operation: 91+80=171, Resulting Numbers: [171] 171,58 unequal: No Solution Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,58 unequal: No Solution Exploring Operation: 91*80=7280, Resulting Numbers: [7280] 7280,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 58:[86, 85], Operations: ['95-9=86', '91-6=85'] Exploring Operation: 86-85=1, Resulting Numbers: [1] 1,58 unequal: No Solution Exploring Operation: 86+85=171, Resulting Numbers: [171] 171,58 unequal: No Solution Exploring Operation: 86*85=7310, Resulting Numbers: [7310] 7310,58 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: 58:[6, 95, 82], Operations: ['91-9=82'] Exploring Operation: 95-82=13, Resulting Numbers: [6, 13] Generated Node #0,1,0: 58:[6, 13] Operation: 95-82=13 Exploring Operation: 82-6=76, Resulting Numbers: [95, 76] Generated Node #0,1,1: 58:[95, 76] Operation: 82-6=76 Exploring Operation: 95-6=89, Resulting Numbers: [82, 89] Generated Node #0,1,2: 58:[82, 89] Operation: 95-6=89 Moving to Node #0,2,2 Current State: 58:[4, 3], Operations: ['95-91=4', '9-6=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,58 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,58 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,58 unequal: No Solution Moving to Node #0,2,1 Current State: 58:[4, 54], Operations: ['95-91=4', '9*6=54'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,58 unequal: No Solution Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[91, 9, 6, 95], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [9, 6, 4] Generated Node #0,2: 58:[9, 6, 4] Operation: 95-91=4 Moving to Node #0,2 Current State: 58:[9, 6, 4], Operations: ['95-91=4'] Exploring Operation: 9*6=54, Resulting Numbers: [4, 54] Generated Node #0,2,1: 58:[4, 54] Operation: 9*6=54 Moving to Node #0,2,1 Current State: 58:[4, 54], Operations: ['95-91=4', '9*6=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.97309
hs_3
sum_heuristic
[ 35, 12, 14, 52 ]
89
[ "35-12=23", "14+52=66", "23+66=89" ]
Current State: 89:[35, 12, 14, 52], Operations: [] Exploring Operation: 35-12=23, Resulting Numbers: [14, 52, 23] Generated Node #2: [14, 52, 23] from Operation: 35-12=23 Current State: 89:[14, 52, 23], Operations: ['35-12=23'] Exploring Operation: 14+52=66, Resulting Numbers: [23, 66] Generated Node #3: [23, 66] from Operation: 14+52=66 Current State: 89:[23, 66], Operations: ['35-12=23', '14+52=66'] Exploring Operation: 23+66=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[35, 12, 14, 52], Operations: [] Exploring Operation: 35+14=49, Resulting Numbers: [12, 52, 49] Generated Node #0,0: 89:[12, 52, 49] Operation: 35+14=49 Exploring Operation: 35+52=87, Resulting Numbers: [12, 14, 87] Generated Node #0,1: 89:[12, 14, 87] Operation: 35+52=87 Exploring Operation: 35+12=47, Resulting Numbers: [14, 52, 47] Generated Node #0,2: 89:[14, 52, 47] Operation: 35+12=47 Moving to Node #0,0 Current State: 89:[12, 52, 49], Operations: ['35+14=49'] Exploring Operation: 12+49=61, Resulting Numbers: [52, 61] Generated Node #0,0,0: 89:[52, 61] Operation: 12+49=61 Exploring Operation: 12+52=64, Resulting Numbers: [49, 64] Generated Node #0,0,1: 89:[49, 64] Operation: 12+52=64 Exploring Operation: 52-12=40, Resulting Numbers: [49, 40] Generated Node #0,0,2: 89:[49, 40] Operation: 52-12=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[52, 61], Operations: ['35+14=49', '12+49=61'] Exploring Operation: 61-52=9, Resulting Numbers: [9] 9,89 unequal: No Solution Exploring Operation: 52*61=3172, Resulting Numbers: [3172] 3172,89 unequal: No Solution Exploring Operation: 52+61=113, Resulting Numbers: [113] 113,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[49, 64], Operations: ['35+14=49', '12+52=64'] Exploring Operation: 49*64=3136, Resulting Numbers: [3136] 3136,89 unequal: No Solution Exploring Operation: 49+64=113, Resulting Numbers: [113] 113,89 unequal: No Solution Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[49, 40], Operations: ['35+14=49', '52-12=40'] Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[35, 12, 14, 52], Operations: [] Exploring Operation: 35+14=49, Resulting Numbers: [12, 52, 49] Generated Node #0,0: 89:[12, 52, 49] Operation: 35+14=49 Moving to Node #0,0 Current State: 89:[12, 52, 49], Operations: ['35+14=49'] Exploring Operation: 52-12=40, Resulting Numbers: [49, 40] Generated Node #0,0,2: 89:[49, 40] Operation: 52-12=40 Moving to Node #0,0,2 Current State: 89:[49, 40], Operations: ['35+14=49', '52-12=40'] Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 34, 15, 45, 98 ]
72
[ "34-15=19", "98-45=53", "19+53=72" ]
Current State: 72:[34, 15, 45, 98], Operations: [] Exploring Operation: 34-15=19, Resulting Numbers: [45, 98, 19] Generated Node #2: [45, 98, 19] from Operation: 34-15=19 Current State: 72:[45, 98, 19], Operations: ['34-15=19'] Exploring Operation: 98-45=53, Resulting Numbers: [19, 53] Generated Node #3: [19, 53] from Operation: 98-45=53 Current State: 72:[19, 53], Operations: ['34-15=19', '98-45=53'] Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[34, 15, 45, 98], Operations: [] Exploring Operation: 45/15=3, Resulting Numbers: [34, 98, 3] Generated Node #0,0: 72:[34, 98, 3] Operation: 45/15=3 Exploring Operation: 45-34=11, Resulting Numbers: [15, 98, 11] Generated Node #0,1: 72:[15, 98, 11] Operation: 45-34=11 Exploring Operation: 98-45=53, Resulting Numbers: [34, 15, 53] Generated Node #0,2: 72:[34, 15, 53] Operation: 98-45=53 Exploring Operation: 98-15=83, Resulting Numbers: [34, 45, 83] Generated Node #0,3: 72:[34, 45, 83] Operation: 98-15=83 Exploring Operation: 98-34=64, Resulting Numbers: [15, 45, 64] Generated Node #0,4: 72:[15, 45, 64] Operation: 98-34=64 Start Sub Search at level 1: Moving to Node #0,4 Current State: 72:[15, 45, 64], Operations: ['98-34=64'] Exploring Operation: 64-45=19, Resulting Numbers: [15, 19] Generated Node #0,4,0: 72:[15, 19] Operation: 64-45=19 Exploring Operation: 45/15=3, Resulting Numbers: [64, 3] Generated Node #0,4,1: 72:[64, 3] Operation: 45/15=3 Exploring Operation: 15+64=79, Resulting Numbers: [45, 79] Generated Node #0,4,2: 72:[45, 79] Operation: 15+64=79 Exploring Operation: 15+45=60, Resulting Numbers: [64, 60] Generated Node #0,4,3: 72:[64, 60] Operation: 15+45=60 Exploring Operation: 45-15=30, Resulting Numbers: [64, 30] Generated Node #0,4,4: 72:[64, 30] Operation: 45-15=30 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 72:[15, 19], Operations: ['98-34=64', '64-45=19'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 72:[64, 3], Operations: ['98-34=64', '45/15=3'] Exploring Operation: 64+3=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 64*3=192, Resulting Numbers: [192] 192,72 unequal: No Solution Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 72:[64, 30], Operations: ['98-34=64', '45-15=30'] Exploring Operation: 64*30=1920, Resulting Numbers: [1920] 1920,72 unequal: No Solution Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 64+30=94, Resulting Numbers: [94] 94,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 72:[45, 79], Operations: ['98-34=64', '15+64=79'] Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 45*79=3555, Resulting Numbers: [3555] 3555,72 unequal: No Solution Exploring Operation: 45+79=124, Resulting Numbers: [124] 124,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 72:[64, 60], Operations: ['98-34=64', '15+45=60'] Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 64+60=124, Resulting Numbers: [124] 124,72 unequal: No Solution Exploring Operation: 64*60=3840, Resulting Numbers: [3840] 3840,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[34, 15, 53], Operations: ['98-45=53'] Exploring Operation: 53-34=19, Resulting Numbers: [15, 19] Generated Node #0,2,0: 72:[15, 19] Operation: 53-34=19 Exploring Operation: 34+53=87, Resulting Numbers: [15, 87] Generated Node #0,2,1: 72:[15, 87] Operation: 34+53=87 Exploring Operation: 34-15=19, Resulting Numbers: [53, 19] Generated Node #0,2,2: 72:[53, 19] Operation: 34-15=19 Exploring Operation: 15+53=68, Resulting Numbers: [34, 68] Generated Node #0,2,3: 72:[34, 68] Operation: 15+53=68 Exploring Operation: 53-15=38, Resulting Numbers: [34, 38] Generated Node #0,2,4: 72:[34, 38] Operation: 53-15=38 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[15, 19], Operations: ['98-45=53', '53-34=19'] Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,72 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 72:[34, 38], Operations: ['98-45=53', '53-15=38'] Exploring Operation: 34*38=1292, Resulting Numbers: [1292] 1292,72 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 34+38=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[34, 15, 45, 98], Operations: [] Exploring Operation: 98-45=53, Resulting Numbers: [34, 15, 53] Generated Node #0,2: 72:[34, 15, 53] Operation: 98-45=53 Moving to Node #0,2 Current State: 72:[34, 15, 53], Operations: ['98-45=53'] Exploring Operation: 53-15=38, Resulting Numbers: [34, 38] Generated Node #0,2,4: 72:[34, 38] Operation: 53-15=38 Moving to Node #0,2,4 Current State: 72:[34, 38], Operations: ['98-45=53', '53-15=38'] Exploring Operation: 34+38=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_5
sum_heuristic
[ 6, 18, 29, 24 ]
22
[ "18*29=522", "6+522=528", "528/24=22" ]
Current State: 22:[6, 18, 29, 24], Operations: [] Exploring Operation: 18*29=522, Resulting Numbers: [6, 24, 522] Generated Node #2: [6, 24, 522] from Operation: 18*29=522 Current State: 22:[6, 24, 522], Operations: ['18*29=522'] Exploring Operation: 6+522=528, Resulting Numbers: [24, 528] Generated Node #3: [24, 528] from Operation: 6+522=528 Current State: 22:[24, 528], Operations: ['18*29=522', '6+522=528'] Exploring Operation: 528/24=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[6, 18, 29, 24], Operations: [] Exploring Operation: 18-6=12, Resulting Numbers: [29, 24, 12] Generated Node #0,0: 22:[29, 24, 12] Operation: 18-6=12 Exploring Operation: 6+18=24, Resulting Numbers: [29, 24, 24] Generated Node #0,1: 22:[29, 24, 24] Operation: 6+18=24 Exploring Operation: 29-18=11, Resulting Numbers: [6, 24, 11] Generated Node #0,2: 22:[6, 24, 11] Operation: 29-18=11 Exploring Operation: 29-6=23, Resulting Numbers: [18, 24, 23] Generated Node #0,3: 22:[18, 24, 23] Operation: 29-6=23 Exploring Operation: 18/6=3, Resulting Numbers: [29, 24, 3] Generated Node #0,4: 22:[29, 24, 3] Operation: 18/6=3 Moving to Node #0,2 Current State: 22:[6, 24, 11], Operations: ['29-18=11'] Exploring Operation: 24-11=13, Resulting Numbers: [6, 13] Generated Node #0,2,0: 22:[6, 13] Operation: 24-11=13 Exploring Operation: 24-6=18, Resulting Numbers: [11, 18] Generated Node #0,2,1: 22:[11, 18] Operation: 24-6=18 Exploring Operation: 24/6=4, Resulting Numbers: [11, 4] Generated Node #0,2,2: 22:[11, 4] Operation: 24/6=4 Exploring Operation: 6+11=17, Resulting Numbers: [24, 17] Generated Node #0,2,3: 22:[24, 17] Operation: 6+11=17 Exploring Operation: 11-6=5, Resulting Numbers: [24, 5] Generated Node #0,2,4: 22:[24, 5] Operation: 11-6=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[11, 4], Operations: ['29-18=11', '24/6=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[11, 18], Operations: ['29-18=11', '24-6=18'] Exploring Operation: 11*18=198, Resulting Numbers: [198] 198,22 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 22:[24, 5], Operations: ['29-18=11', '11-6=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[6, 13], Operations: ['29-18=11', '24-11=13'] Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,22 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 22:[24, 17], Operations: ['29-18=11', '6+11=17'] Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 24*17=408, Resulting Numbers: [408] 408,22 unequal: No Solution Exploring Operation: 24+17=41, Resulting Numbers: [41] 41,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 22:[18, 24, 23], Operations: ['29-6=23'] Exploring Operation: 24-18=6, Resulting Numbers: [23, 6] Generated Node #0,3,0: 22:[23, 6] Operation: 24-18=6 Exploring Operation: 18+24=42, Resulting Numbers: [23, 42] Generated Node #0,3,1: 22:[23, 42] Operation: 18+24=42 Exploring Operation: 24-23=1, Resulting Numbers: [18, 1] Generated Node #0,3,2: 22:[18, 1] Operation: 24-23=1 Exploring Operation: 18+23=41, Resulting Numbers: [24, 41] Generated Node #0,3,3: 22:[24, 41] Operation: 18+23=41 Exploring Operation: 23-18=5, Resulting Numbers: [24, 5] Generated Node #0,3,4: 22:[24, 5] Operation: 23-18=5 Moving to Node #0,0 Current State: 22:[29, 24, 12], Operations: ['18-6=12'] Exploring Operation: 29-24=5, Resulting Numbers: [12, 5] Generated Node #0,0,0: 22:[12, 5] Operation: 29-24=5 Exploring Operation: 24-12=12, Resulting Numbers: [29, 12] Generated Node #0,0,1: 22:[29, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [29, 2] Generated Node #0,0,2: 22:[29, 2] Operation: 24/12=2 Exploring Operation: 29-12=17, Resulting Numbers: [24, 17] Generated Node #0,0,3: 22:[24, 17] Operation: 29-12=17 Exploring Operation: 29+12=41, Resulting Numbers: [24, 41] Generated Node #0,0,4: 22:[24, 41] Operation: 29+12=41 Moving to Node #0,4 Current State: 22:[29, 24, 3], Operations: ['18/6=3'] Exploring Operation: 29-24=5, Resulting Numbers: [3, 5] Generated Node #0,4,0: 22:[3, 5] Operation: 29-24=5 Exploring Operation: 29-3=26, Resulting Numbers: [24, 26] Generated Node #0,4,1: 22:[24, 26] Operation: 29-3=26 Exploring Operation: 29+3=32, Resulting Numbers: [24, 32] Generated Node #0,4,2: 22:[24, 32] Operation: 29+3=32 Exploring Operation: 24-3=21, Resulting Numbers: [29, 21] Generated Node #0,4,3: 22:[29, 21] Operation: 24-3=21 Exploring Operation: 24/3=8, Resulting Numbers: [29, 8] Generated Node #0,4,4: 22:[29, 8] Operation: 24/3=8 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 22:[3, 5], Operations: ['18/6=3', '29-24=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 22:[24, 26], Operations: ['18/6=3', '29-3=26'] Exploring Operation: 24*26=624, Resulting Numbers: [624] 624,22 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 22:[29, 21], Operations: ['18/6=3', '24-3=21'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,22 unequal: No Solution Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,22 unequal: No Solution Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 22:[29, 8], Operations: ['18/6=3', '24/3=8'] Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,22 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 22:[24, 32], Operations: ['18/6=3', '29+3=32'] Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,22 unequal: No Solution Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,22 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,22 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: 22:[29, 24, 24], Operations: ['6+18=24'] Exploring Operation: 29-24=5, Resulting Numbers: [24, 5] Generated Node #0,1,0: 22:[24, 5] Operation: 29-24=5 Exploring Operation: 29-24=5, Resulting Numbers: [24, 5] Generated Node #0,1,1: 22:[24, 5] Operation: 29-24=5 Exploring Operation: 24-24=0, Resulting Numbers: [29, 0] Generated Node #0,1,2: 22:[29, 0] Operation: 24-24=0 Exploring Operation: 24/24=1, Resulting Numbers: [29, 1] Generated Node #0,1,3: 22:[29, 1] Operation: 24/24=1 Exploring Operation: 29+24=53, Resulting Numbers: [24, 53] Generated Node #0,1,4: 22:[24, 53] Operation: 29+24=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[24, 5], Operations: ['6+18=24', '29-24=5'] Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[24, 5], Operations: ['6+18=24', '29-24=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 22:[29, 1], Operations: ['6+18=24', '24/24=1'] Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,22 unequal: No Solution Exploring Operation: 29-1=28, Resulting Numbers: [28] 28,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 22:[29, 0], Operations: ['6+18=24', '24-24=0'] Exploring Operation: 29-0=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 29*0=0, Resulting Numbers: [0] 0,22 unequal: No Solution Exploring Operation: 29+0=29, Resulting Numbers: [29] 29,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 22:[24, 53], Operations: ['6+18=24', '29+24=53'] Exploring Operation: 53-24=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 24*53=1272, Resulting Numbers: [1272] 1272,22 unequal: No Solution Exploring Operation: 24+53=77, Resulting Numbers: [77] 77,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 22:[12, 5], Operations: ['18-6=12', '29-24=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,22 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[23, 6], Operations: ['29-6=23', '24-18=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,22 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,22 unequal: No Solution Moving to Node #0,3,4 Current State: 22:[24, 5], Operations: ['29-6=23', '23-18=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[18, 1], Operations: ['29-6=23', '24-23=1'] Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[29, 2], Operations: ['18-6=12', '24/12=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,22 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,22 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[24, 17], Operations: ['18-6=12', '29-12=17'] Exploring Operation: 24+17=41, Resulting Numbers: [41] 41,22 unequal: No Solution Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 24*17=408, Resulting Numbers: [408] 408,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[29, 12], Operations: ['18-6=12', '24-12=12'] Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,22 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,22 unequal: No Solution Moving to Node #0,0,4 Current State: 22:[24, 41], Operations: ['18-6=12', '29+12=41'] Exploring Operation: 24+41=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 24*41=984, Resulting Numbers: [984] 984,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[24, 41], Operations: ['29-6=23', '18+23=41'] Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 24*41=984, Resulting Numbers: [984] 984,22 unequal: No Solution Exploring Operation: 24+41=65, Resulting Numbers: [65] 65,22 unequal: No Solution Moving to Node #0,3,1 Current State: 22:[23, 42], Operations: ['29-6=23', '18+24=42'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,22 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 38, 28, 33, 82 ]
98
[ "33*82=2706", "38+2706=2744", "2744/28=98" ]
Current State: 98:[38, 28, 33, 82], Operations: [] Exploring Operation: 33*82=2706, Resulting Numbers: [38, 28, 2706] Generated Node #2: [38, 28, 2706] from Operation: 33*82=2706 Current State: 98:[38, 28, 2706], Operations: ['33*82=2706'] Exploring Operation: 38+2706=2744, Resulting Numbers: [28, 2744] Generated Node #3: [28, 2744] from Operation: 38+2706=2744 Current State: 98:[28, 2744], Operations: ['33*82=2706', '38+2706=2744'] Exploring Operation: 2744/28=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[38, 28, 33, 82], Operations: [] Exploring Operation: 82-33=49, Resulting Numbers: [38, 28, 49] Generated Node #0,0: 98:[38, 28, 49] Operation: 82-33=49 Exploring Operation: 33-28=5, Resulting Numbers: [38, 82, 5] Generated Node #0,1: 98:[38, 82, 5] Operation: 33-28=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[38, 28, 49], Operations: ['82-33=49'] Exploring Operation: 38-28=10, Resulting Numbers: [49, 10] Generated Node #0,0,0: 98:[49, 10] Operation: 38-28=10 Exploring Operation: 38+28=66, Resulting Numbers: [49, 66] Generated Node #0,0,1: 98:[49, 66] Operation: 38+28=66 Moving to Node #0,0,0 Current State: 98:[49, 10], Operations: ['82-33=49', '38-28=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,98 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[49, 66], Operations: ['82-33=49', '38+28=66'] Exploring Operation: 49+66=115, Resulting Numbers: [115] 115,98 unequal: No Solution Exploring Operation: 66-49=17, Resulting Numbers: [17] 17,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[38, 82, 5], Operations: ['33-28=5'] Exploring Operation: 38+5=43, Resulting Numbers: [82, 43] Generated Node #0,1,0: 98:[82, 43] Operation: 38+5=43 Exploring Operation: 82-38=44, Resulting Numbers: [5, 44] Generated Node #0,1,1: 98:[5, 44] Operation: 82-38=44 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[5, 44], Operations: ['33-28=5', '82-38=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,98 unequal: No Solution No 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: 98:[82, 43], Operations: ['33-28=5', '38+5=43'] Exploring Operation: 82-43=39, Resulting Numbers: [39] 39,98 unequal: No Solution Exploring Operation: 82+43=125, Resulting Numbers: [125] 125,98 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
[ 48, 37, 86, 72 ]
92
[ "86*72=6192", "6192/48=129", "129-37=92" ]
Current State: 92:[48, 37, 86, 72], Operations: [] Exploring Operation: 86*72=6192, Resulting Numbers: [48, 37, 6192] Generated Node #2: [48, 37, 6192] from Operation: 86*72=6192 Current State: 92:[48, 37, 6192], Operations: ['86*72=6192'] Exploring Operation: 6192/48=129, Resulting Numbers: [37, 129] Generated Node #3: [37, 129] from Operation: 6192/48=129 Current State: 92:[37, 129], Operations: ['86*72=6192', '6192/48=129'] Exploring Operation: 129-37=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[48, 37, 86, 72], Operations: [] Exploring Operation: 86-72=14, Resulting Numbers: [48, 37, 14] Generated Node #0,0: 92:[48, 37, 14] Operation: 86-72=14 Exploring Operation: 72-48=24, Resulting Numbers: [37, 86, 24] Generated Node #0,1: 92:[37, 86, 24] Operation: 72-48=24 Exploring Operation: 72-37=35, Resulting Numbers: [48, 86, 35] Generated Node #0,2: 92:[48, 86, 35] Operation: 72-37=35 Exploring Operation: 86-37=49, Resulting Numbers: [48, 72, 49] Generated Node #0,3: 92:[48, 72, 49] Operation: 86-37=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[37, 86, 24], Operations: ['72-48=24'] Exploring Operation: 86-24=62, Resulting Numbers: [37, 62] Generated Node #0,1,0: 92:[37, 62] Operation: 86-24=62 Exploring Operation: 86-37=49, Resulting Numbers: [24, 49] Generated Node #0,1,1: 92:[24, 49] Operation: 86-37=49 Exploring Operation: 37+24=61, Resulting Numbers: [86, 61] Generated Node #0,1,2: 92:[86, 61] Operation: 37+24=61 Exploring Operation: 37-24=13, Resulting Numbers: [86, 13] Generated Node #0,1,3: 92:[86, 13] Operation: 37-24=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 92:[24, 49], Operations: ['72-48=24', '86-37=49'] Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 24*49=1176, Resulting Numbers: [1176] 1176,92 unequal: No Solution Exploring Operation: 24+49=73, Resulting Numbers: [73] 73,92 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:[86, 13], Operations: ['72-48=24', '37-24=13'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,92 unequal: No Solution Exploring Operation: 86*13=1118, Resulting Numbers: [1118] 1118,92 unequal: No Solution Exploring Operation: 86+13=99, Resulting Numbers: [99] 99,92 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:[86, 61], Operations: ['72-48=24', '37+24=61'] Exploring Operation: 86*61=5246, Resulting Numbers: [5246] 5246,92 unequal: No Solution Exploring Operation: 86-61=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 86+61=147, Resulting Numbers: [147] 147,92 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 #0,1,0 Current State: 92:[37, 62], Operations: ['72-48=24', '86-24=62'] Exploring Operation: 37*62=2294, Resulting Numbers: [2294] 2294,92 unequal: No Solution Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 37+62=99, Resulting Numbers: [99] 99,92 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:[48, 86, 35], Operations: ['72-37=35'] Exploring Operation: 48-35=13, Resulting Numbers: [86, 13] Generated Node #0,2,0: 92:[86, 13] Operation: 48-35=13 Exploring Operation: 48+35=83, Resulting Numbers: [86, 83] Generated Node #0,2,1: 92:[86, 83] Operation: 48+35=83 Exploring Operation: 86-48=38, Resulting Numbers: [35, 38] Generated Node #0,2,2: 92:[35, 38] Operation: 86-48=38 Exploring Operation: 86-35=51, Resulting Numbers: [48, 51] Generated Node #0,2,3: 92:[48, 51] Operation: 86-35=51 Moving to Node #0,2,3 Current State: 92:[48, 51], Operations: ['72-37=35', '86-35=51'] Exploring Operation: 48+51=99, Resulting Numbers: [99] 99,92 unequal: No Solution Exploring Operation: 48*51=2448, Resulting Numbers: [2448] 2448,92 unequal: No Solution Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,92 unequal: No Solution Moving to Node #0,2,1 Current State: 92:[86, 83], Operations: ['72-37=35', '48+35=83'] Exploring Operation: 86*83=7138, Resulting Numbers: [7138] 7138,92 unequal: No Solution Exploring Operation: 86-83=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 86+83=169, Resulting Numbers: [169] 169,92 unequal: No Solution Moving to Node #0,2,0 Current State: 92:[86, 13], Operations: ['72-37=35', '48-35=13'] Exploring Operation: 86*13=1118, Resulting Numbers: [1118] 1118,92 unequal: No Solution Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,92 unequal: No Solution Exploring Operation: 86+13=99, Resulting Numbers: [99] 99,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[35, 38], Operations: ['72-37=35', '86-48=38'] Exploring Operation: 35+38=73, Resulting Numbers: [73] 73,92 unequal: No Solution Exploring Operation: 35*38=1330, Resulting Numbers: [1330] 1330,92 unequal: No Solution Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[48, 37, 14], Operations: ['86-72=14'] Exploring Operation: 48-37=11, Resulting Numbers: [14, 11] Generated Node #0,0,0: 92:[14, 11] Operation: 48-37=11 Exploring Operation: 48+37=85, Resulting Numbers: [14, 85] Generated Node #0,0,1: 92:[14, 85] Operation: 48+37=85 Exploring Operation: 37+14=51, Resulting Numbers: [48, 51] Generated Node #0,0,2: 92:[48, 51] Operation: 37+14=51 Exploring Operation: 37-14=23, Resulting Numbers: [48, 23] Generated Node #0,0,3: 92:[48, 23] Operation: 37-14=23 Moving to Node #0,0,3 Current State: 92:[48, 23], Operations: ['86-72=14', '37-14=23'] Exploring Operation: 48*23=1104, Resulting Numbers: [1104] 1104,92 unequal: No Solution Exploring Operation: 48+23=71, Resulting Numbers: [71] 71,92 unequal: No Solution Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[48, 51], Operations: ['86-72=14', '37+14=51'] Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 48+51=99, Resulting Numbers: [99] 99,92 unequal: No Solution Exploring Operation: 48*51=2448, Resulting Numbers: [2448] 2448,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[14, 85], Operations: ['86-72=14', '48+37=85'] Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,92 unequal: No Solution Exploring Operation: 14+85=99, Resulting Numbers: [99] 99,92 unequal: No Solution Exploring Operation: 14*85=1190, Resulting Numbers: [1190] 1190,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[14, 11], Operations: ['86-72=14', '48-37=11'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 14*11=154, Resulting Numbers: [154] 154,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 92:[48, 72, 49], Operations: ['86-37=49'] Exploring Operation: 72-49=23, Resulting Numbers: [48, 23] Generated Node #0,3,0: 92:[48, 23] Operation: 72-49=23 Exploring Operation: 72-48=24, Resulting Numbers: [49, 24] Generated Node #0,3,1: 92:[49, 24] Operation: 72-48=24 Exploring Operation: 48+49=97, Resulting Numbers: [72, 97] Generated Node #0,3,2: 92:[72, 97] Operation: 48+49=97 Exploring Operation: 49-48=1, Resulting Numbers: [72, 1] Generated Node #0,3,3: 92:[72, 1] Operation: 49-48=1 Moving to Node #0,3,0 Current State: 92:[48, 23], Operations: ['86-37=49', '72-49=23'] Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 48+23=71, Resulting Numbers: [71] 71,92 unequal: No Solution Exploring Operation: 48*23=1104, Resulting Numbers: [1104] 1104,92 unequal: No Solution Moving to Node #0,3,1 Current State: 92:[49, 24], Operations: ['86-37=49', '72-48=24'] Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,92 unequal: No Solution Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,92 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,92 unequal: No Solution Moving to Node #0,3,3 Current State: 92:[72, 1], Operations: ['86-37=49', '49-48=1'] Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,92 unequal: No Solution Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,92 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,92 unequal: No Solution Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,92 unequal: No Solution Moving to Node #0,3,2 Current State: 92:[72, 97], Operations: ['86-37=49', '48+49=97'] Exploring Operation: 97-72=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 72*97=6984, Resulting Numbers: [6984] 6984,92 unequal: No Solution Exploring Operation: 72+97=169, Resulting Numbers: [169] 169,92 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
[ 69, 35, 42, 9 ]
67
[ "69-35=34", "42-9=33", "34+33=67" ]
Current State: 67:[69, 35, 42, 9], Operations: [] Exploring Operation: 69-35=34, Resulting Numbers: [42, 9, 34] Generated Node #2: [42, 9, 34] from Operation: 69-35=34 Current State: 67:[42, 9, 34], Operations: ['69-35=34'] Exploring Operation: 42-9=33, Resulting Numbers: [34, 33] Generated Node #3: [34, 33] from Operation: 42-9=33 Current State: 67:[34, 33], Operations: ['69-35=34', '42-9=33'] Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[69, 35, 42, 9], Operations: [] Exploring Operation: 69-9=60, Resulting Numbers: [35, 42, 60] Generated Node #0,0: 67:[35, 42, 60] Operation: 69-9=60 Exploring Operation: 69+9=78, Resulting Numbers: [35, 42, 78] Generated Node #0,1: 67:[35, 42, 78] Operation: 69+9=78 Exploring Operation: 35+9=44, Resulting Numbers: [69, 42, 44] Generated Node #0,2: 67:[69, 42, 44] Operation: 35+9=44 Exploring Operation: 42+9=51, Resulting Numbers: [69, 35, 51] Generated Node #0,3: 67:[69, 35, 51] Operation: 42+9=51 Moving to Node #0,2 Current State: 67:[69, 42, 44], Operations: ['35+9=44'] Exploring Operation: 69-42=27, Resulting Numbers: [44, 27] Generated Node #0,2,0: 67:[44, 27] Operation: 69-42=27 Exploring Operation: 69-44=25, Resulting Numbers: [42, 25] Generated Node #0,2,1: 67:[42, 25] Operation: 69-44=25 Exploring Operation: 42+44=86, Resulting Numbers: [69, 86] Generated Node #0,2,2: 67:[69, 86] Operation: 42+44=86 Exploring Operation: 69+42=111, Resulting Numbers: [44, 111] Generated Node #0,2,3: 67:[44, 111] Operation: 69+42=111 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[69, 86], Operations: ['35+9=44', '42+44=86'] Exploring Operation: 86-69=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 69+86=155, Resulting Numbers: [155] 155,67 unequal: No Solution Exploring Operation: 69*86=5934, Resulting Numbers: [5934] 5934,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[44, 27], Operations: ['35+9=44', '69-42=27'] Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,67 unequal: No Solution Exploring Operation: 44*27=1188, Resulting Numbers: [1188] 1188,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[42, 25], Operations: ['35+9=44', '69-44=25'] Exploring Operation: 42*25=1050, Resulting Numbers: [1050] 1050,67 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 42+25=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[69, 35, 42, 9], Operations: [] Exploring Operation: 35+9=44, Resulting Numbers: [69, 42, 44] Generated Node #0,2: 67:[69, 42, 44] Operation: 35+9=44 Moving to Node #0,2 Current State: 67:[69, 42, 44], Operations: ['35+9=44'] Exploring Operation: 69-44=25, Resulting Numbers: [42, 25] Generated Node #0,2,1: 67:[42, 25] Operation: 69-44=25 Moving to Node #0,2,1 Current State: 67:[42, 25], Operations: ['35+9=44', '69-44=25'] Exploring Operation: 42+25=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 8, 75, 12, 38 ]
57
[ "8+75=83", "38-12=26", "83-26=57" ]
Current State: 57:[8, 75, 12, 38], Operations: [] Exploring Operation: 8+75=83, Resulting Numbers: [12, 38, 83] Generated Node #2: [12, 38, 83] from Operation: 8+75=83 Current State: 57:[12, 38, 83], Operations: ['8+75=83'] Exploring Operation: 38-12=26, Resulting Numbers: [83, 26] Generated Node #3: [83, 26] from Operation: 38-12=26 Current State: 57:[83, 26], Operations: ['8+75=83', '38-12=26'] Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[8, 75, 12, 38], Operations: [] Exploring Operation: 75-38=37, Resulting Numbers: [8, 12, 37] Generated Node #0,0: 57:[8, 12, 37] Operation: 75-38=37 Exploring Operation: 75-12=63, Resulting Numbers: [8, 38, 63] Generated Node #0,1: 57:[8, 38, 63] Operation: 75-12=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[8, 12, 37], Operations: ['75-38=37'] Exploring Operation: 12+37=49, Resulting Numbers: [8, 49] Generated Node #0,0,0: 57:[8, 49] Operation: 12+37=49 Exploring Operation: 37-12=25, Resulting Numbers: [8, 25] Generated Node #0,0,1: 57:[8, 25] Operation: 37-12=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[8, 25], Operations: ['75-38=37', '37-12=25'] Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[8, 49], Operations: ['75-38=37', '12+37=49'] Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[8, 75, 12, 38], Operations: [] Exploring Operation: 75-38=37, Resulting Numbers: [8, 12, 37] Generated Node #0,0: 57:[8, 12, 37] Operation: 75-38=37 Moving to Node #0,0 Current State: 57:[8, 12, 37], Operations: ['75-38=37'] Exploring Operation: 12+37=49, Resulting Numbers: [8, 49] Generated Node #0,0,0: 57:[8, 49] Operation: 12+37=49 Moving to Node #0,0,0 Current State: 57:[8, 49], Operations: ['75-38=37', '12+37=49'] Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 63, 70, 56, 84 ]
82
[ "63-56=7", "84/7=12", "70+12=82" ]
Current State: 82:[63, 70, 56, 84], Operations: [] Exploring Operation: 63-56=7, Resulting Numbers: [70, 84, 7] Generated Node #2: [70, 84, 7] from Operation: 63-56=7 Current State: 82:[70, 84, 7], Operations: ['63-56=7'] Exploring Operation: 84/7=12, Resulting Numbers: [70, 12] Generated Node #3: [70, 12] from Operation: 84/7=12 Current State: 82:[70, 12], Operations: ['63-56=7', '84/7=12'] Exploring Operation: 70+12=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[63, 70, 56, 84], Operations: [] Exploring Operation: 70-56=14, Resulting Numbers: [63, 84, 14] Generated Node #0,0: 82:[63, 84, 14] Operation: 70-56=14 Exploring Operation: 70-63=7, Resulting Numbers: [56, 84, 7] Generated Node #0,1: 82:[56, 84, 7] Operation: 70-63=7 Exploring Operation: 63-56=7, Resulting Numbers: [70, 84, 7] Generated Node #0,2: 82:[70, 84, 7] Operation: 63-56=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[70, 84, 7], Operations: ['63-56=7'] Exploring Operation: 70+7=77, Resulting Numbers: [84, 77] Generated Node #0,2,0: 82:[84, 77] Operation: 70+7=77 Exploring Operation: 70/7=10, Resulting Numbers: [84, 10] Generated Node #0,2,1: 82:[84, 10] Operation: 70/7=10 Exploring Operation: 84-70=14, Resulting Numbers: [7, 14] Generated Node #0,2,2: 82:[7, 14] Operation: 84-70=14 Moving to Node #0,2,0 Current State: 82:[84, 77], Operations: ['63-56=7', '70+7=77'] Exploring Operation: 84*77=6468, Resulting Numbers: [6468] 6468,82 unequal: No Solution Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 84+77=161, Resulting Numbers: [161] 161,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[84, 10], Operations: ['63-56=7', '70/7=10'] Exploring Operation: 84-10=74, Resulting Numbers: [74] 74,82 unequal: No Solution Exploring Operation: 84*10=840, Resulting Numbers: [840] 840,82 unequal: No Solution Exploring Operation: 84+10=94, Resulting Numbers: [94] 94,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[7, 14], Operations: ['63-56=7', '84-70=14'] Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,82 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[56, 84, 7], Operations: ['70-63=7'] Exploring Operation: 56/7=8, Resulting Numbers: [84, 8] Generated Node #0,1,0: 82:[84, 8] Operation: 56/7=8 Exploring Operation: 84-56=28, Resulting Numbers: [7, 28] Generated Node #0,1,1: 82:[7, 28] Operation: 84-56=28 Exploring Operation: 56-7=49, Resulting Numbers: [84, 49] Generated Node #0,1,2: 82:[84, 49] Operation: 56-7=49 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[84, 8], Operations: ['70-63=7', '56/7=8'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,82 unequal: No Solution Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 84*8=672, Resulting Numbers: [672] 672,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[84, 49], Operations: ['70-63=7', '56-7=49'] Exploring Operation: 84+49=133, Resulting Numbers: [133] 133,82 unequal: No Solution Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,82 unequal: No Solution Exploring Operation: 84*49=4116, Resulting Numbers: [4116] 4116,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[7, 28], Operations: ['70-63=7', '84-56=28'] Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 7+28=35, Resulting Numbers: [35] 35,82 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[63, 84, 14], Operations: ['70-56=14'] Exploring Operation: 63-14=49, Resulting Numbers: [84, 49] Generated Node #0,0,0: 82:[84, 49] Operation: 63-14=49 Exploring Operation: 84/14=6, Resulting Numbers: [63, 6] Generated Node #0,0,1: 82:[63, 6] Operation: 84/14=6 Exploring Operation: 63+14=77, Resulting Numbers: [84, 77] Generated Node #0,0,2: 82:[84, 77] Operation: 63+14=77 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[84, 77], Operations: ['70-56=14', '63+14=77'] Exploring Operation: 84+77=161, Resulting Numbers: [161] 161,82 unequal: No Solution Exploring Operation: 84*77=6468, Resulting Numbers: [6468] 6468,82 unequal: No Solution Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[84, 49], Operations: ['70-56=14', '63-14=49'] Exploring Operation: 84+49=133, Resulting Numbers: [133] 133,82 unequal: No Solution Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,82 unequal: No Solution Exploring Operation: 84*49=4116, Resulting Numbers: [4116] 4116,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[63, 6], Operations: ['70-56=14', '84/14=6'] Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,82 unequal: No Solution Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,82 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 11, 24, 98, 57 ]
95
[ "57-24=33", "33/11=3", "98-3=95" ]
Current State: 95:[11, 24, 98, 57], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [11, 98, 33] Generated Node #2: [11, 98, 33] from Operation: 57-24=33 Current State: 95:[11, 98, 33], Operations: ['57-24=33'] Exploring Operation: 33/11=3, Resulting Numbers: [98, 3] Generated Node #3: [98, 3] from Operation: 33/11=3 Current State: 95:[98, 3], Operations: ['57-24=33', '33/11=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[11, 24, 98, 57], Operations: [] Exploring Operation: 24+57=81, Resulting Numbers: [11, 98, 81] Generated Node #0,0: 95:[11, 98, 81] Operation: 24+57=81 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[11, 98, 81], Operations: ['24+57=81'] Exploring Operation: 11+81=92, Resulting Numbers: [98, 92] Generated Node #0,0,0: 95:[98, 92] Operation: 11+81=92 Moving to Node #0,0,0 Current State: 95:[98, 92], Operations: ['24+57=81', '11+81=92'] Exploring Operation: 98-92=6, Resulting Numbers: [6] 6,95 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
[ 85, 32, 22, 98 ]
23
[ "85-32=53", "98-22=76", "76-53=23" ]
Current State: 23:[85, 32, 22, 98], Operations: [] Exploring Operation: 85-32=53, Resulting Numbers: [22, 98, 53] Generated Node #2: [22, 98, 53] from Operation: 85-32=53 Current State: 23:[22, 98, 53], Operations: ['85-32=53'] Exploring Operation: 98-22=76, Resulting Numbers: [53, 76] Generated Node #3: [53, 76] from Operation: 98-22=76 Current State: 23:[53, 76], Operations: ['85-32=53', '98-22=76'] Exploring Operation: 76-53=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[85, 32, 22, 98], Operations: [] Exploring Operation: 98-85=13, Resulting Numbers: [32, 22, 13] Generated Node #0,0: 23:[32, 22, 13] Operation: 98-85=13 Moving to Node #0,0 Current State: 23:[32, 22, 13], Operations: ['98-85=13'] Exploring Operation: 32-13=19, Resulting Numbers: [22, 19] Generated Node #0,0,0: 23:[22, 19] Operation: 32-13=19 Moving to Node #0,0,0 Current State: 23:[22, 19], Operations: ['98-85=13', '32-13=19'] Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,23 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 80, 30, 34, 89 ]
73
[ "80-30=50", "34+89=123", "123-50=73" ]
Current State: 73:[80, 30, 34, 89], Operations: [] Exploring Operation: 80-30=50, Resulting Numbers: [34, 89, 50] Generated Node #2: [34, 89, 50] from Operation: 80-30=50 Current State: 73:[34, 89, 50], Operations: ['80-30=50'] Exploring Operation: 34+89=123, Resulting Numbers: [50, 123] Generated Node #3: [50, 123] from Operation: 34+89=123 Current State: 73:[50, 123], Operations: ['80-30=50', '34+89=123'] Exploring Operation: 123-50=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[80, 30, 34, 89], Operations: [] Exploring Operation: 80-30=50, Resulting Numbers: [34, 89, 50] Generated Node #0,0: 73:[34, 89, 50] Operation: 80-30=50 Exploring Operation: 89-34=55, Resulting Numbers: [80, 30, 55] Generated Node #0,1: 73:[80, 30, 55] Operation: 89-34=55 Exploring Operation: 89-30=59, Resulting Numbers: [80, 34, 59] Generated Node #0,2: 73:[80, 34, 59] Operation: 89-30=59 Exploring Operation: 30+34=64, Resulting Numbers: [80, 89, 64] Generated Node #0,3: 73:[80, 89, 64] Operation: 30+34=64 Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[80, 89, 64], Operations: ['30+34=64'] Exploring Operation: 80+64=144, Resulting Numbers: [89, 144] Generated Node #0,3,0: 73:[89, 144] Operation: 80+64=144 Exploring Operation: 89-80=9, Resulting Numbers: [64, 9] Generated Node #0,3,1: 73:[64, 9] Operation: 89-80=9 Exploring Operation: 89-64=25, Resulting Numbers: [80, 25] Generated Node #0,3,2: 73:[80, 25] Operation: 89-64=25 Exploring Operation: 80-64=16, Resulting Numbers: [89, 16] Generated Node #0,3,3: 73:[89, 16] Operation: 80-64=16 Moving to Node #0,3,2 Current State: 73:[80, 25], Operations: ['30+34=64', '89-64=25'] Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,73 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,73 unequal: No Solution Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,73 unequal: No Solution Moving to Node #0,3,3 Current State: 73:[89, 16], Operations: ['30+34=64', '80-64=16'] Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,73 unequal: No Solution Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[80, 30, 34, 89], Operations: [] Exploring Operation: 30+34=64, Resulting Numbers: [80, 89, 64] Generated Node #0,3: 73:[80, 89, 64] Operation: 30+34=64 Moving to Node #0,3 Current State: 73:[80, 89, 64], Operations: ['30+34=64'] Exploring Operation: 80-64=16, Resulting Numbers: [89, 16] Generated Node #0,3,3: 73:[89, 16] Operation: 80-64=16 Moving to Node #0,3,3 Current State: 73:[89, 16], Operations: ['30+34=64', '80-64=16'] Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 10, 53, 21, 39 ]
59
[ "21+39=60", "60/10=6", "53+6=59" ]
Current State: 59:[10, 53, 21, 39], Operations: [] Exploring Operation: 21+39=60, Resulting Numbers: [10, 53, 60] Generated Node #2: [10, 53, 60] from Operation: 21+39=60 Current State: 59:[10, 53, 60], Operations: ['21+39=60'] Exploring Operation: 60/10=6, Resulting Numbers: [53, 6] Generated Node #3: [53, 6] from Operation: 60/10=6 Current State: 59:[53, 6], Operations: ['21+39=60', '60/10=6'] Exploring Operation: 53+6=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[10, 53, 21, 39], Operations: [] Exploring Operation: 10+21=31, Resulting Numbers: [53, 39, 31] Generated Node #0,0: 59:[53, 39, 31] Operation: 10+21=31 Exploring Operation: 10+53=63, Resulting Numbers: [21, 39, 63] Generated Node #0,1: 59:[21, 39, 63] Operation: 10+53=63 Exploring Operation: 10+39=49, Resulting Numbers: [53, 21, 49] Generated Node #0,2: 59:[53, 21, 49] Operation: 10+39=49 Exploring Operation: 21+39=60, Resulting Numbers: [10, 53, 60] Generated Node #0,3: 59:[10, 53, 60] Operation: 21+39=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[53, 39, 31], Operations: ['10+21=31'] Exploring Operation: 53-31=22, Resulting Numbers: [39, 22] Generated Node #0,0,0: 59:[39, 22] Operation: 53-31=22 Exploring Operation: 39-31=8, Resulting Numbers: [53, 8] Generated Node #0,0,1: 59:[53, 8] Operation: 39-31=8 Exploring Operation: 39+31=70, Resulting Numbers: [53, 70] Generated Node #0,0,2: 59:[53, 70] Operation: 39+31=70 Exploring Operation: 53+31=84, Resulting Numbers: [39, 84] Generated Node #0,0,3: 59:[39, 84] Operation: 53+31=84 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 59:[53, 70], Operations: ['10+21=31', '39+31=70'] Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 53*70=3710, Resulting Numbers: [3710] 3710,59 unequal: No Solution Exploring Operation: 53+70=123, Resulting Numbers: [123] 123,59 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:[39, 84], Operations: ['10+21=31', '53+31=84'] Exploring Operation: 39*84=3276, Resulting Numbers: [3276] 3276,59 unequal: No Solution Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 39+84=123, Resulting Numbers: [123] 123,59 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 #0,0,0 Current State: 59:[39, 22], Operations: ['10+21=31', '53-31=22'] Exploring Operation: 39*22=858, Resulting Numbers: [858] 858,59 unequal: No Solution Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,59 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:[53, 8], Operations: ['10+21=31', '39-31=8'] Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,59 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,59 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 #0,2 Current State: 59:[53, 21, 49], Operations: ['10+39=49'] Exploring Operation: 49-21=28, Resulting Numbers: [53, 28] Generated Node #0,2,0: 59:[53, 28] Operation: 49-21=28 Exploring Operation: 21+49=70, Resulting Numbers: [53, 70] Generated Node #0,2,1: 59:[53, 70] Operation: 21+49=70 Exploring Operation: 53-21=32, Resulting Numbers: [49, 32] Generated Node #0,2,2: 59:[49, 32] Operation: 53-21=32 Exploring Operation: 53+21=74, Resulting Numbers: [49, 74] Generated Node #0,2,3: 59:[49, 74] Operation: 53+21=74 Moving to Node #0,2,1 Current State: 59:[53, 70], Operations: ['10+39=49', '21+49=70'] Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 53+70=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 53*70=3710, Resulting Numbers: [3710] 3710,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[49, 74], Operations: ['10+39=49', '53+21=74'] Exploring Operation: 49*74=3626, Resulting Numbers: [3626] 3626,59 unequal: No Solution Exploring Operation: 49+74=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[49, 32], Operations: ['10+39=49', '53-21=32'] Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,59 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[53, 28], Operations: ['10+39=49', '49-21=28'] Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,59 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,59 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 #0,3 Current State: 59:[10, 53, 60], Operations: ['21+39=60'] Exploring Operation: 60-10=50, Resulting Numbers: [53, 50] Generated Node #0,3,0: 59:[53, 50] Operation: 60-10=50 Exploring Operation: 10+60=70, Resulting Numbers: [53, 70] Generated Node #0,3,1: 59:[53, 70] Operation: 10+60=70 Exploring Operation: 10+53=63, Resulting Numbers: [60, 63] Generated Node #0,3,2: 59:[60, 63] Operation: 10+53=63 Exploring Operation: 53-10=43, Resulting Numbers: [60, 43] Generated Node #0,3,3: 59:[60, 43] Operation: 53-10=43 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 59:[60, 63], Operations: ['21+39=60', '10+53=63'] Exploring Operation: 60*63=3780, Resulting Numbers: [3780] 3780,59 unequal: No Solution Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 60+63=123, Resulting Numbers: [123] 123,59 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 #0,3,0 Current State: 59:[53, 50], Operations: ['21+39=60', '60-10=50'] Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,59 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,59 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 #0,3,1 Current State: 59:[53, 70], Operations: ['21+39=60', '10+60=70'] Exploring Operation: 53+70=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 53*70=3710, Resulting Numbers: [3710] 3710,59 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 #0,3,3 Current State: 59:[60, 43], Operations: ['21+39=60', '53-10=43'] Exploring Operation: 60*43=2580, Resulting Numbers: [2580] 2580,59 unequal: No Solution Exploring Operation: 60-43=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 60+43=103, Resulting Numbers: [103] 103,59 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:[21, 39, 63], Operations: ['10+53=63'] Exploring Operation: 21+39=60, Resulting Numbers: [63, 60] Generated Node #0,1,0: 59:[63, 60] Operation: 21+39=60 Exploring Operation: 63-21=42, Resulting Numbers: [39, 42] Generated Node #0,1,1: 59:[39, 42] Operation: 63-21=42 Exploring Operation: 21+63=84, Resulting Numbers: [39, 84] Generated Node #0,1,2: 59:[39, 84] Operation: 21+63=84 Exploring Operation: 39-21=18, Resulting Numbers: [63, 18] Generated Node #0,1,3: 59:[63, 18] Operation: 39-21=18 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[63, 60], Operations: ['10+53=63', '21+39=60'] Exploring Operation: 63+60=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 63*60=3780, Resulting Numbers: [3780] 3780,59 unequal: No Solution Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,59 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 #0,1,1 Current State: 59:[39, 42], Operations: ['10+53=63', '63-21=42'] Exploring Operation: 39*42=1638, Resulting Numbers: [1638] 1638,59 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 39+42=81, Resulting Numbers: [81] 81,59 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 #0,1,2 Current State: 59:[39, 84], Operations: ['10+53=63', '21+63=84'] Exploring Operation: 39+84=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 39*84=3276, Resulting Numbers: [3276] 3276,59 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 #0,1,3 Current State: 59:[63, 18], Operations: ['10+53=63', '39-21=18'] Exploring Operation: 63*18=1134, Resulting Numbers: [1134] 1134,59 unequal: No Solution Exploring Operation: 63+18=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,59 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_4
mult_heuristic
[ 81, 21, 35, 63 ]
62
[ "81*21=1701", "1701/63=27", "35+27=62" ]
Current State: 62:[81, 21, 35, 63], Operations: [] Exploring Operation: 81*21=1701, Resulting Numbers: [35, 63, 1701] Generated Node #2: [35, 63, 1701] from Operation: 81*21=1701 Current State: 62:[35, 63, 1701], Operations: ['81*21=1701'] Exploring Operation: 1701/63=27, Resulting Numbers: [35, 27] Generated Node #3: [35, 27] from Operation: 1701/63=27 Current State: 62:[35, 27], Operations: ['81*21=1701', '1701/63=27'] Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[81, 21, 35, 63], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [81, 35, 3] Generated Node #0,0: 62:[81, 35, 3] Operation: 63/21=3 Exploring Operation: 81-21=60, Resulting Numbers: [35, 63, 60] Generated Node #0,1: 62:[35, 63, 60] Operation: 81-21=60 Exploring Operation: 81-35=46, Resulting Numbers: [21, 63, 46] Generated Node #0,2: 62:[21, 63, 46] Operation: 81-35=46 Moving to Node #0,1 Current State: 62:[35, 63, 60], Operations: ['81-21=60'] Exploring Operation: 63-35=28, Resulting Numbers: [60, 28] Generated Node #0,1,0: 62:[60, 28] Operation: 63-35=28 Exploring Operation: 60-35=25, Resulting Numbers: [63, 25] Generated Node #0,1,1: 62:[63, 25] Operation: 60-35=25 Exploring Operation: 63-60=3, Resulting Numbers: [35, 3] Generated Node #0,1,2: 62:[35, 3] Operation: 63-60=3 Moving to Node #0,0 Current State: 62:[81, 35, 3], Operations: ['63/21=3'] Exploring Operation: 81-3=78, Resulting Numbers: [35, 78] Generated Node #0,0,0: 62:[35, 78] Operation: 81-3=78 Exploring Operation: 81-35=46, Resulting Numbers: [3, 46] Generated Node #0,0,1: 62:[3, 46] Operation: 81-35=46 Exploring Operation: 81/3=27, Resulting Numbers: [35, 27] Generated Node #0,0,2: 62:[35, 27] Operation: 81/3=27 Moving to Node #0,2 Current State: 62:[21, 63, 46], Operations: ['81-35=46'] Exploring Operation: 21+46=67, Resulting Numbers: [63, 67] Generated Node #0,2,0: 62:[63, 67] Operation: 21+46=67 Exploring Operation: 46-21=25, Resulting Numbers: [63, 25] Generated Node #0,2,1: 62:[63, 25] Operation: 46-21=25 Exploring Operation: 63/21=3, Resulting Numbers: [46, 3] Generated Node #0,2,2: 62:[46, 3] Operation: 63/21=3 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 62:[63, 67], Operations: ['81-35=46', '21+46=67'] Exploring Operation: 63+67=130, Resulting Numbers: [130] 130,62 unequal: No Solution Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 63*67=4221, Resulting Numbers: [4221] 4221,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 62:[63, 25], Operations: ['81-35=46', '46-21=25'] Exploring Operation: 63*25=1575, Resulting Numbers: [1575] 1575,62 unequal: No Solution Exploring Operation: 63+25=88, Resulting Numbers: [88] 88,62 unequal: No Solution Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 62:[46, 3], Operations: ['81-35=46', '63/21=3'] Exploring Operation: 46*3=138, Resulting Numbers: [138] 138,62 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,62 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: 62:[60, 28], Operations: ['81-21=60', '63-35=28'] Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 60*28=1680, Resulting Numbers: [1680] 1680,62 unequal: No Solution Exploring Operation: 60+28=88, Resulting Numbers: [88] 88,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[35, 3], Operations: ['81-21=60', '63-60=3'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,62 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[63, 25], Operations: ['81-21=60', '60-35=25'] Exploring Operation: 63+25=88, Resulting Numbers: [88] 88,62 unequal: No Solution Exploring Operation: 63*25=1575, Resulting Numbers: [1575] 1575,62 unequal: No Solution Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[35, 27], Operations: ['63/21=3', '81/3=27'] Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[81, 21, 35, 63], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [81, 35, 3] Generated Node #0,0: 62:[81, 35, 3] Operation: 63/21=3 Moving to Node #0,0 Current State: 62:[81, 35, 3], Operations: ['63/21=3'] Exploring Operation: 81/3=27, Resulting Numbers: [35, 27] Generated Node #0,0,2: 62:[35, 27] Operation: 81/3=27 Moving to Node #0,0,2 Current State: 62:[35, 27], Operations: ['63/21=3', '81/3=27'] Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.969618
hs_3
sum_heuristic
[ 42, 94, 35, 18 ]
79
[ "35*18=630", "630/42=15", "94-15=79" ]
Current State: 79:[42, 94, 35, 18], Operations: [] Exploring Operation: 35*18=630, Resulting Numbers: [42, 94, 630] Generated Node #2: [42, 94, 630] from Operation: 35*18=630 Current State: 79:[42, 94, 630], Operations: ['35*18=630'] Exploring Operation: 630/42=15, Resulting Numbers: [94, 15] Generated Node #3: [94, 15] from Operation: 630/42=15 Current State: 79:[94, 15], Operations: ['35*18=630', '630/42=15'] Exploring Operation: 94-15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[42, 94, 35, 18], Operations: [] Exploring Operation: 35+18=53, Resulting Numbers: [42, 94, 53] Generated Node #0,0: 79:[42, 94, 53] Operation: 35+18=53 Exploring Operation: 42+35=77, Resulting Numbers: [94, 18, 77] Generated Node #0,1: 79:[94, 18, 77] Operation: 42+35=77 Exploring Operation: 42+18=60, Resulting Numbers: [94, 35, 60] Generated Node #0,2: 79:[94, 35, 60] Operation: 42+18=60 Moving to Node #0,0 Current State: 79:[42, 94, 53], Operations: ['35+18=53'] Exploring Operation: 94-42=52, Resulting Numbers: [53, 52] Generated Node #0,0,0: 79:[53, 52] Operation: 94-42=52 Exploring Operation: 94-53=41, Resulting Numbers: [42, 41] Generated Node #0,0,1: 79:[42, 41] Operation: 94-53=41 Exploring Operation: 42+53=95, Resulting Numbers: [94, 95] Generated Node #0,0,2: 79:[94, 95] Operation: 42+53=95 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[94, 95], Operations: ['35+18=53', '42+53=95'] Exploring Operation: 94*95=8930, Resulting Numbers: [8930] 8930,79 unequal: No Solution Exploring Operation: 95-94=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 94+95=189, Resulting Numbers: [189] 189,79 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 #0,0,0 Current State: 79:[53, 52], Operations: ['35+18=53', '94-42=52'] Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 53*52=2756, Resulting Numbers: [2756] 2756,79 unequal: No Solution Exploring Operation: 53+52=105, Resulting Numbers: [105] 105,79 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 #0,0,1 Current State: 79:[42, 41], Operations: ['35+18=53', '94-53=41'] Exploring Operation: 42*41=1722, Resulting Numbers: [1722] 1722,79 unequal: No Solution Exploring Operation: 42+41=83, Resulting Numbers: [83] 83,79 unequal: No Solution Exploring Operation: 42-41=1, Resulting Numbers: [1] 1,79 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: 79:[94, 18, 77], Operations: ['42+35=77'] Exploring Operation: 94+18=112, Resulting Numbers: [77, 112] Generated Node #0,1,0: 79:[77, 112] Operation: 94+18=112 Exploring Operation: 94-18=76, Resulting Numbers: [77, 76] Generated Node #0,1,1: 79:[77, 76] Operation: 94-18=76 Exploring Operation: 18+77=95, Resulting Numbers: [94, 95] Generated Node #0,1,2: 79:[94, 95] Operation: 18+77=95 Moving to Node #0,2 Current State: 79:[94, 35, 60], Operations: ['42+18=60'] Exploring Operation: 94+35=129, Resulting Numbers: [60, 129] Generated Node #0,2,0: 79:[60, 129] Operation: 94+35=129 Exploring Operation: 35+60=95, Resulting Numbers: [94, 95] Generated Node #0,2,1: 79:[94, 95] Operation: 35+60=95 Exploring Operation: 94-35=59, Resulting Numbers: [60, 59] Generated Node #0,2,2: 79:[60, 59] Operation: 94-35=59 Moving to Node #0,1,1 Current State: 79:[77, 76], Operations: ['42+35=77', '94-18=76'] Exploring Operation: 77-76=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 77*76=5852, Resulting Numbers: [5852] 5852,79 unequal: No Solution Exploring Operation: 77+76=153, Resulting Numbers: [153] 153,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[94, 95], Operations: ['42+35=77', '18+77=95'] Exploring Operation: 95-94=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 94+95=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 94*95=8930, Resulting Numbers: [8930] 8930,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[94, 95], Operations: ['42+18=60', '35+60=95'] Exploring Operation: 94*95=8930, Resulting Numbers: [8930] 8930,79 unequal: No Solution Exploring Operation: 95-94=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 94+95=189, Resulting Numbers: [189] 189,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[77, 112], Operations: ['42+35=77', '94+18=112'] Exploring Operation: 112-77=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 77*112=8624, Resulting Numbers: [8624] 8624,79 unequal: No Solution Exploring Operation: 77+112=189, Resulting Numbers: [189] 189,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[60, 59], Operations: ['42+18=60', '94-35=59'] Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 60*59=3540, Resulting Numbers: [3540] 3540,79 unequal: No Solution Exploring Operation: 60+59=119, Resulting Numbers: [119] 119,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[60, 129], Operations: ['42+18=60', '94+35=129'] Exploring Operation: 60*129=7740, Resulting Numbers: [7740] 7740,79 unequal: No Solution Exploring Operation: 129-60=69, Resulting Numbers: [69] 69,79 unequal: No Solution Exploring Operation: 60+129=189, Resulting Numbers: [189] 189,79 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 75, 99, 29, 48 ]
58
[ "99-75=24", "29*48=1392", "1392/24=58" ]
Current State: 58:[75, 99, 29, 48], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [29, 48, 24] Generated Node #2: [29, 48, 24] from Operation: 99-75=24 Current State: 58:[29, 48, 24], Operations: ['99-75=24'] Exploring Operation: 29*48=1392, Resulting Numbers: [24, 1392] Generated Node #3: [24, 1392] from Operation: 29*48=1392 Current State: 58:[24, 1392], Operations: ['99-75=24', '29*48=1392'] Exploring Operation: 1392/24=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[75, 99, 29, 48], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [29, 48, 24] Generated Node #0,0: 58:[29, 48, 24] Operation: 99-75=24 Exploring Operation: 75-48=27, Resulting Numbers: [99, 29, 27] Generated Node #0,1: 58:[99, 29, 27] Operation: 75-48=27 Exploring Operation: 99-48=51, Resulting Numbers: [75, 29, 51] Generated Node #0,2: 58:[75, 29, 51] Operation: 99-48=51 Exploring Operation: 99-29=70, Resulting Numbers: [75, 48, 70] Generated Node #0,3: 58:[75, 48, 70] Operation: 99-29=70 Moving to Node #0,0 Current State: 58:[29, 48, 24], Operations: ['99-75=24'] Exploring Operation: 48+24=72, Resulting Numbers: [29, 72] Generated Node #0,0,0: 58:[29, 72] Operation: 48+24=72 Exploring Operation: 29-24=5, Resulting Numbers: [48, 5] Generated Node #0,0,1: 58:[48, 5] Operation: 29-24=5 Exploring Operation: 48-24=24, Resulting Numbers: [29, 24] Generated Node #0,0,2: 58:[29, 24] Operation: 48-24=24 Exploring Operation: 48/24=2, Resulting Numbers: [29, 2] Generated Node #0,0,3: 58:[29, 2] Operation: 48/24=2 Moving to Node #0,2 Current State: 58:[75, 29, 51], Operations: ['99-48=51'] Exploring Operation: 29+51=80, Resulting Numbers: [75, 80] Generated Node #0,2,0: 58:[75, 80] Operation: 29+51=80 Exploring Operation: 51-29=22, Resulting Numbers: [75, 22] Generated Node #0,2,1: 58:[75, 22] Operation: 51-29=22 Exploring Operation: 75-29=46, Resulting Numbers: [51, 46] Generated Node #0,2,2: 58:[51, 46] Operation: 75-29=46 Exploring Operation: 75-51=24, Resulting Numbers: [29, 24] Generated Node #0,2,3: 58:[29, 24] Operation: 75-51=24 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 58:[29, 24], Operations: ['99-48=51', '75-51=24'] Exploring Operation: 29*24=696, Resulting Numbers: [696] 696,58 unequal: No Solution Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,58 unequal: No Solution Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 58:[51, 46], Operations: ['99-48=51', '75-29=46'] Exploring Operation: 51*46=2346, Resulting Numbers: [2346] 2346,58 unequal: No Solution Exploring Operation: 51+46=97, Resulting Numbers: [97] 97,58 unequal: No Solution Exploring Operation: 51-46=5, Resulting Numbers: [5] 5,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 58:[75, 22], Operations: ['99-48=51', '51-29=22'] Exploring Operation: 75+22=97, Resulting Numbers: [97] 97,58 unequal: No Solution Exploring Operation: 75-22=53, Resulting Numbers: [53] 53,58 unequal: No Solution Exploring Operation: 75*22=1650, Resulting Numbers: [1650] 1650,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 58:[75, 80], Operations: ['99-48=51', '29+51=80'] Exploring Operation: 75+80=155, Resulting Numbers: [155] 155,58 unequal: No Solution Exploring Operation: 80-75=5, Resulting Numbers: [5] 5,58 unequal: No Solution Exploring Operation: 75*80=6000, Resulting Numbers: [6000] 6000,58 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: 58:[75, 48, 70], Operations: ['99-29=70'] Exploring Operation: 75-48=27, Resulting Numbers: [70, 27] Generated Node #0,3,0: 58:[70, 27] Operation: 75-48=27 Exploring Operation: 75+48=123, Resulting Numbers: [70, 123] Generated Node #0,3,1: 58:[70, 123] Operation: 75+48=123 Exploring Operation: 70-48=22, Resulting Numbers: [75, 22] Generated Node #0,3,2: 58:[75, 22] Operation: 70-48=22 Exploring Operation: 75-70=5, Resulting Numbers: [48, 5] Generated Node #0,3,3: 58:[48, 5] Operation: 75-70=5 Moving to Node #0,1 Current State: 58:[99, 29, 27], Operations: ['75-48=27'] Exploring Operation: 29+27=56, Resulting Numbers: [99, 56] Generated Node #0,1,0: 58:[99, 56] Operation: 29+27=56 Exploring Operation: 29-27=2, Resulting Numbers: [99, 2] Generated Node #0,1,1: 58:[99, 2] Operation: 29-27=2 Exploring Operation: 99-29=70, Resulting Numbers: [27, 70] Generated Node #0,1,2: 58:[27, 70] Operation: 99-29=70 Exploring Operation: 99-27=72, Resulting Numbers: [29, 72] Generated Node #0,1,3: 58:[29, 72] Operation: 99-27=72 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 58:[27, 70], Operations: ['75-48=27', '99-29=70'] Exploring Operation: 70-27=43, Resulting Numbers: [43] 43,58 unequal: No Solution Exploring Operation: 27+70=97, Resulting Numbers: [97] 97,58 unequal: No Solution Exploring Operation: 27*70=1890, Resulting Numbers: [1890] 1890,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 58:[29, 72], Operations: ['75-48=27', '99-27=72'] Exploring Operation: 29*72=2088, Resulting Numbers: [2088] 2088,58 unequal: No Solution Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,58 unequal: No Solution Exploring Operation: 29+72=101, Resulting Numbers: [101] 101,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[99, 2], Operations: ['75-48=27', '29-27=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,58 unequal: No Solution Exploring Operation: 99*2=198, Resulting Numbers: [198] 198,58 unequal: No Solution Exploring Operation: 99+2=101, Resulting Numbers: [101] 101,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 58:[99, 56], Operations: ['75-48=27', '29+27=56'] Exploring Operation: 99*56=5544, Resulting Numbers: [5544] 5544,58 unequal: No Solution Exploring Operation: 99-56=43, Resulting Numbers: [43] 43,58 unequal: No Solution Exploring Operation: 99+56=155, Resulting Numbers: [155] 155,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 58:[29, 2], Operations: ['99-75=24', '48/24=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[75, 99, 29, 48], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [29, 48, 24] Generated Node #0,0: 58:[29, 48, 24] Operation: 99-75=24 Moving to Node #0,0 Current State: 58:[29, 48, 24], Operations: ['99-75=24'] Exploring Operation: 48/24=2, Resulting Numbers: [29, 2] Generated Node #0,0,3: 58:[29, 2] Operation: 48/24=2 Moving to Node #0,0,3 Current State: 58:[29, 2], Operations: ['99-75=24', '48/24=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.955729
hs_4
mult_heuristic
[ 34, 77, 68, 6 ]
73
[ "68/34=2", "77-6=71", "2+71=73" ]
Current State: 73:[34, 77, 68, 6], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [77, 6, 2] Generated Node #2: [77, 6, 2] from Operation: 68/34=2 Current State: 73:[77, 6, 2], Operations: ['68/34=2'] Exploring Operation: 77-6=71, Resulting Numbers: [2, 71] Generated Node #3: [2, 71] from Operation: 77-6=71 Current State: 73:[2, 71], Operations: ['68/34=2', '77-6=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[34, 77, 68, 6], Operations: [] Exploring Operation: 34+6=40, Resulting Numbers: [77, 68, 40] Generated Node #0,0: 73:[77, 68, 40] Operation: 34+6=40 Moving to Node #0,0 Current State: 73:[77, 68, 40], Operations: ['34+6=40'] Exploring Operation: 68+40=108, Resulting Numbers: [77, 108] Generated Node #0,0,0: 73:[77, 108] Operation: 68+40=108 Moving to Node #0,0,0 Current State: 73:[77, 108], Operations: ['34+6=40', '68+40=108'] Exploring Operation: 108-77=31, Resulting Numbers: [31] 31,73 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 31, 11, 55, 3 ]
69
[ "31+11=42", "42/3=14", "55+14=69" ]
Current State: 69:[31, 11, 55, 3], Operations: [] Exploring Operation: 31+11=42, Resulting Numbers: [55, 3, 42] Generated Node #2: [55, 3, 42] from Operation: 31+11=42 Current State: 69:[55, 3, 42], Operations: ['31+11=42'] Exploring Operation: 42/3=14, Resulting Numbers: [55, 14] Generated Node #3: [55, 14] from Operation: 42/3=14 Current State: 69:[55, 14], Operations: ['31+11=42', '42/3=14'] Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[31, 11, 55, 3], Operations: [] Exploring Operation: 55/11=5, Resulting Numbers: [31, 3, 5] Generated Node #0,0: 69:[31, 3, 5] Operation: 55/11=5 Exploring Operation: 55-31=24, Resulting Numbers: [11, 3, 24] Generated Node #0,1: 69:[11, 3, 24] Operation: 55-31=24 Moving to Node #0,1 Current State: 69:[11, 3, 24], Operations: ['55-31=24'] Exploring Operation: 11+3=14, Resulting Numbers: [24, 14] Generated Node #0,1,0: 69:[24, 14] Operation: 11+3=14 Exploring Operation: 11-3=8, Resulting Numbers: [24, 8] Generated Node #0,1,1: 69:[24, 8] Operation: 11-3=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[24, 8], Operations: ['55-31=24', '11-3=8'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[24, 14], Operations: ['55-31=24', '11+3=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,69 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: 69:[31, 3, 5], Operations: ['55/11=5'] Exploring Operation: 31-3=28, Resulting Numbers: [5, 28] Generated Node #0,0,0: 69:[5, 28] Operation: 31-3=28 Exploring Operation: 31-5=26, Resulting Numbers: [3, 26] Generated Node #0,0,1: 69:[3, 26] Operation: 31-5=26 Moving to Node #0,0,1 Current State: 69:[3, 26], Operations: ['55/11=5', '31-5=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[5, 28], Operations: ['55/11=5', '31-3=28'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,69 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 42, 9, 69, 2 ]
24
[ "42*2=84", "69-9=60", "84-60=24" ]
Current State: 24:[42, 9, 69, 2], Operations: [] Exploring Operation: 42*2=84, Resulting Numbers: [9, 69, 84] Generated Node #2: [9, 69, 84] from Operation: 42*2=84 Current State: 24:[9, 69, 84], Operations: ['42*2=84'] Exploring Operation: 69-9=60, Resulting Numbers: [84, 60] Generated Node #3: [84, 60] from Operation: 69-9=60 Current State: 24:[84, 60], Operations: ['42*2=84', '69-9=60'] Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[42, 9, 69, 2], Operations: [] Exploring Operation: 42-2=40, Resulting Numbers: [9, 69, 40] Generated Node #0,0: 24:[9, 69, 40] Operation: 42-2=40 Exploring Operation: 69-9=60, Resulting Numbers: [42, 2, 60] Generated Node #0,1: 24:[42, 2, 60] Operation: 69-9=60 Exploring Operation: 42-9=33, Resulting Numbers: [69, 2, 33] Generated Node #0,2: 24:[69, 2, 33] Operation: 42-9=33 Exploring Operation: 69-42=27, Resulting Numbers: [9, 2, 27] Generated Node #0,3: 24:[9, 2, 27] Operation: 69-42=27 Exploring Operation: 42/2=21, Resulting Numbers: [9, 69, 21] Generated Node #0,4: 24:[9, 69, 21] Operation: 42/2=21 Moving to Node #0,3 Current State: 24:[9, 2, 27], Operations: ['69-42=27'] Exploring Operation: 27/9=3, Resulting Numbers: [2, 3] Generated Node #0,3,0: 24:[2, 3] Operation: 27/9=3 Exploring Operation: 27-9=18, Resulting Numbers: [2, 18] Generated Node #0,3,1: 24:[2, 18] Operation: 27-9=18 Exploring Operation: 9+2=11, Resulting Numbers: [27, 11] Generated Node #0,3,2: 24:[27, 11] Operation: 9+2=11 Exploring Operation: 27-2=25, Resulting Numbers: [9, 25] Generated Node #0,3,3: 24:[9, 25] Operation: 27-2=25 Exploring Operation: 9-2=7, Resulting Numbers: [27, 7] Generated Node #0,3,4: 24:[27, 7] Operation: 9-2=7 Moving to Node #0,4 Current State: 24:[9, 69, 21], Operations: ['42/2=21'] Exploring Operation: 69-21=48, Resulting Numbers: [9, 48] Generated Node #0,4,0: 24:[9, 48] Operation: 69-21=48 Exploring Operation: 9+69=78, Resulting Numbers: [21, 78] Generated Node #0,4,1: 24:[21, 78] Operation: 9+69=78 Exploring Operation: 69-9=60, Resulting Numbers: [21, 60] Generated Node #0,4,2: 24:[21, 60] Operation: 69-9=60 Exploring Operation: 9+21=30, Resulting Numbers: [69, 30] Generated Node #0,4,3: 24:[69, 30] Operation: 9+21=30 Exploring Operation: 21-9=12, Resulting Numbers: [69, 12] Generated Node #0,4,4: 24:[69, 12] Operation: 21-9=12 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 24:[9, 48], Operations: ['42/2=21', '69-21=48'] Exploring Operation: 9+48=57, Resulting Numbers: [57] 57,24 unequal: No Solution Exploring Operation: 9*48=432, Resulting Numbers: [432] 432,24 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 24:[21, 60], Operations: ['42/2=21', '69-9=60'] Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 21+60=81, Resulting Numbers: [81] 81,24 unequal: No Solution Exploring Operation: 21*60=1260, Resulting Numbers: [1260] 1260,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 24:[69, 12], Operations: ['42/2=21', '21-9=12'] Exploring Operation: 69*12=828, Resulting Numbers: [828] 828,24 unequal: No Solution Exploring Operation: 69+12=81, Resulting Numbers: [81] 81,24 unequal: No Solution Exploring Operation: 69-12=57, Resulting Numbers: [57] 57,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 24:[69, 30], Operations: ['42/2=21', '9+21=30'] Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 69*30=2070, Resulting Numbers: [2070] 2070,24 unequal: No Solution Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 24:[21, 78], Operations: ['42/2=21', '9+69=78'] Exploring Operation: 21*78=1638, Resulting Numbers: [1638] 1638,24 unequal: No Solution Exploring Operation: 78-21=57, Resulting Numbers: [57] 57,24 unequal: No Solution Exploring Operation: 21+78=99, Resulting Numbers: [99] 99,24 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: 24:[42, 2, 60], Operations: ['69-9=60'] Exploring Operation: 60-42=18, Resulting Numbers: [2, 18] Generated Node #0,1,0: 24:[2, 18] Operation: 60-42=18 Exploring Operation: 42-2=40, Resulting Numbers: [60, 40] Generated Node #0,1,1: 24:[60, 40] Operation: 42-2=40 Exploring Operation: 60-2=58, Resulting Numbers: [42, 58] Generated Node #0,1,2: 24:[42, 58] Operation: 60-2=58 Exploring Operation: 42/2=21, Resulting Numbers: [60, 21] Generated Node #0,1,3: 24:[60, 21] Operation: 42/2=21 Exploring Operation: 60/2=30, Resulting Numbers: [42, 30] Generated Node #0,1,4: 24:[42, 30] Operation: 60/2=30 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[2, 18], Operations: ['69-9=60', '60-42=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 24:[42, 30], Operations: ['69-9=60', '60/2=30'] Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 42+30=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 42*30=1260, Resulting Numbers: [1260] 1260,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 24:[60, 21], Operations: ['69-9=60', '42/2=21'] Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,24 unequal: No Solution Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,24 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[60, 40], Operations: ['69-9=60', '42-2=40'] Exploring Operation: 60+40=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 60-40=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 60*40=2400, Resulting Numbers: [2400] 2400,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[42, 58], Operations: ['69-9=60', '60-2=58'] Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 42*58=2436, Resulting Numbers: [2436] 2436,24 unequal: No Solution Exploring Operation: 42+58=100, Resulting Numbers: [100] 100,24 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: 24:[69, 2, 33], Operations: ['42-9=33'] Exploring Operation: 69-2=67, Resulting Numbers: [33, 67] Generated Node #0,2,0: 24:[33, 67] Operation: 69-2=67 Exploring Operation: 2+33=35, Resulting Numbers: [69, 35] Generated Node #0,2,1: 24:[69, 35] Operation: 2+33=35 Exploring Operation: 33-2=31, Resulting Numbers: [69, 31] Generated Node #0,2,2: 24:[69, 31] Operation: 33-2=31 Exploring Operation: 69-33=36, Resulting Numbers: [2, 36] Generated Node #0,2,3: 24:[2, 36] Operation: 69-33=36 Exploring Operation: 69+2=71, Resulting Numbers: [33, 71] Generated Node #0,2,4: 24:[33, 71] Operation: 69+2=71 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 24:[2, 36], Operations: ['42-9=33', '69-33=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 24:[33, 67], Operations: ['42-9=33', '69-2=67'] Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 33*67=2211, Resulting Numbers: [2211] 2211,24 unequal: No Solution Exploring Operation: 33+67=100, Resulting Numbers: [100] 100,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 24:[69, 31], Operations: ['42-9=33', '33-2=31'] Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,24 unequal: No Solution Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 24:[69, 35], Operations: ['42-9=33', '2+33=35'] Exploring Operation: 69+35=104, Resulting Numbers: [104] 104,24 unequal: No Solution Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 69*35=2415, Resulting Numbers: [2415] 2415,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 24:[33, 71], Operations: ['42-9=33', '69+2=71'] Exploring Operation: 33*71=2343, Resulting Numbers: [2343] 2343,24 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,24 unequal: No Solution Exploring Operation: 33+71=104, Resulting Numbers: [104] 104,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 24:[9, 69, 40], Operations: ['42-2=40'] Exploring Operation: 9+69=78, Resulting Numbers: [40, 78] Generated Node #0,0,0: 24:[40, 78] Operation: 9+69=78 Exploring Operation: 69-9=60, Resulting Numbers: [40, 60] Generated Node #0,0,1: 24:[40, 60] Operation: 69-9=60 Exploring Operation: 9+40=49, Resulting Numbers: [69, 49] Generated Node #0,0,2: 24:[69, 49] Operation: 9+40=49 Exploring Operation: 40-9=31, Resulting Numbers: [69, 31] Generated Node #0,0,3: 24:[69, 31] Operation: 40-9=31 Exploring Operation: 69-40=29, Resulting Numbers: [9, 29] Generated Node #0,0,4: 24:[9, 29] Operation: 69-40=29 Moving to Node #0,3,0 Current State: 24:[2, 3], Operations: ['69-42=27', '27/9=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[9, 25], Operations: ['69-42=27', '27-2=25'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 9*25=225, Resulting Numbers: [225] 225,24 unequal: No Solution Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[27, 11], Operations: ['69-42=27', '9+2=11'] Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,24 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,24 unequal: No Solution Moving to Node #0,3,4 Current State: 24:[27, 7], Operations: ['69-42=27', '9-2=7'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,24 unequal: No Solution Moving to Node #0,0,4 Current State: 24:[9, 29], Operations: ['42-2=40', '69-40=29'] Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,24 unequal: No Solution Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[2, 18], Operations: ['69-42=27', '27-9=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[40, 60], Operations: ['42-2=40', '69-9=60'] Exploring Operation: 40*60=2400, Resulting Numbers: [2400] 2400,24 unequal: No Solution Exploring Operation: 60-40=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 40+60=100, Resulting Numbers: [100] 100,24 unequal: No Solution Moving to Node #0,0,3 Current State: 24:[69, 31], Operations: ['42-2=40', '40-9=31'] Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,24 unequal: No Solution Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[40, 78], Operations: ['42-2=40', '9+69=78'] Exploring Operation: 40+78=118, Resulting Numbers: [118] 118,24 unequal: No Solution Exploring Operation: 78-40=38, Resulting Numbers: [38] 38,24 unequal: No Solution Exploring Operation: 40*78=3120, Resulting Numbers: [3120] 3120,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[69, 49], Operations: ['42-2=40', '9+40=49'] Exploring Operation: 69+49=118, Resulting Numbers: [118] 118,24 unequal: No Solution Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 69*49=3381, Resulting Numbers: [3381] 3381,24 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 19, 18, 77, 72 ]
100
[ "19+77=96", "72/18=4", "96+4=100" ]
Current State: 100:[19, 18, 77, 72], Operations: [] Exploring Operation: 19+77=96, Resulting Numbers: [18, 72, 96] Generated Node #2: [18, 72, 96] from Operation: 19+77=96 Current State: 100:[18, 72, 96], Operations: ['19+77=96'] Exploring Operation: 72/18=4, Resulting Numbers: [96, 4] Generated Node #3: [96, 4] from Operation: 72/18=4 Current State: 100:[96, 4], Operations: ['19+77=96', '72/18=4'] Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[19, 18, 77, 72], Operations: [] Exploring Operation: 19+77=96, Resulting Numbers: [18, 72, 96] Generated Node #0,0: 100:[18, 72, 96] Operation: 19+77=96 Exploring Operation: 72/18=4, Resulting Numbers: [19, 77, 4] Generated Node #0,1: 100:[19, 77, 4] Operation: 72/18=4 Exploring Operation: 77-72=5, Resulting Numbers: [19, 18, 5] Generated Node #0,2: 100:[19, 18, 5] Operation: 77-72=5 Exploring Operation: 72-19=53, Resulting Numbers: [18, 77, 53] Generated Node #0,3: 100:[18, 77, 53] Operation: 72-19=53 Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[19, 18, 5], Operations: ['77-72=5'] Exploring Operation: 18+5=23, Resulting Numbers: [19, 23] Generated Node #0,2,0: 100:[19, 23] Operation: 18+5=23 Exploring Operation: 18-5=13, Resulting Numbers: [19, 13] Generated Node #0,2,1: 100:[19, 13] Operation: 18-5=13 Exploring Operation: 19-18=1, Resulting Numbers: [5, 1] Generated Node #0,2,2: 100:[5, 1] Operation: 19-18=1 Exploring Operation: 19+5=24, Resulting Numbers: [18, 24] Generated Node #0,2,3: 100:[18, 24] Operation: 19+5=24 Moving to Node #0,2,2 Current State: 100:[5, 1], Operations: ['77-72=5', '19-18=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,100 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,100 unequal: No Solution Moving to Node #0,2,3 Current State: 100:[18, 24], Operations: ['77-72=5', '19+5=24'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,100 unequal: No Solution Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,100 unequal: No Solution Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,100 unequal: No Solution Moving to Node #0,2,0 Current State: 100:[19, 23], Operations: ['77-72=5', '18+5=23'] Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 19*23=437, Resulting Numbers: [437] 437,100 unequal: No Solution Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[19, 13], Operations: ['77-72=5', '18-5=13'] Exploring Operation: 19*13=247, Resulting Numbers: [247] 247,100 unequal: No Solution Exploring Operation: 19+13=32, Resulting Numbers: [32] 32,100 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[19, 77, 4], Operations: ['72/18=4'] Exploring Operation: 77-4=73, Resulting Numbers: [19, 73] Generated Node #0,1,0: 100:[19, 73] Operation: 77-4=73 Exploring Operation: 77+4=81, Resulting Numbers: [19, 81] Generated Node #0,1,1: 100:[19, 81] Operation: 77+4=81 Exploring Operation: 77-19=58, Resulting Numbers: [4, 58] Generated Node #0,1,2: 100:[4, 58] Operation: 77-19=58 Exploring Operation: 19+77=96, Resulting Numbers: [4, 96] Generated Node #0,1,3: 100:[4, 96] Operation: 19+77=96 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 100:[4, 96], Operations: ['72/18=4', '19+77=96'] Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 4*96=384, Resulting Numbers: [384] 384,100 unequal: No Solution Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 4+96=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[19, 18, 77, 72], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [19, 77, 4] Generated Node #0,1: 100:[19, 77, 4] Operation: 72/18=4 Moving to Node #0,1 Current State: 100:[19, 77, 4], Operations: ['72/18=4'] Exploring Operation: 19+77=96, Resulting Numbers: [4, 96] Generated Node #0,1,3: 100:[4, 96] Operation: 19+77=96 Moving to Node #0,1,3 Current State: 100:[4, 96], Operations: ['72/18=4', '19+77=96'] Exploring Operation: 4+96=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 74, 8, 68, 6 ]
42
[ "74-68=6", "8*6=48", "48-6=42" ]
Current State: 42:[74, 8, 68, 6], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [8, 6, 6] Generated Node #2: [8, 6, 6] from Operation: 74-68=6 Current State: 42:[8, 6, 6], Operations: ['74-68=6'] Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,42 equal: Goal Reached Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[74, 8, 68, 6], Operations: [] Exploring Operation: 68-8=60, Resulting Numbers: [74, 6, 60] Generated Node #0,0: 42:[74, 6, 60] Operation: 68-8=60 Exploring Operation: 74-68=6, Resulting Numbers: [8, 6, 6] Generated Node #0,1: 42:[8, 6, 6] Operation: 74-68=6 Exploring Operation: 74-8=66, Resulting Numbers: [68, 6, 66] Generated Node #0,2: 42:[68, 6, 66] Operation: 74-8=66 Moving to Node #0,1 Current State: 42:[8, 6, 6], Operations: ['74-68=6'] Exploring Operation: 8-6=2, Resulting Numbers: [6, 2] Generated Node #0,1,0: 42:[6, 2] Operation: 8-6=2 Exploring Operation: 8+6=14, Resulting Numbers: [6, 14] Generated Node #0,1,1: 42:[6, 14] Operation: 8+6=14 Exploring Operation: 8+6=14, Resulting Numbers: [6, 14] Generated Node #0,1,2: 42:[6, 14] Operation: 8+6=14 Moving to Node #0,0 Current State: 42:[74, 6, 60], Operations: ['68-8=60'] Exploring Operation: 74-6=68, Resulting Numbers: [60, 68] Generated Node #0,0,0: 42:[60, 68] Operation: 74-6=68 Exploring Operation: 74-60=14, Resulting Numbers: [6, 14] Generated Node #0,0,1: 42:[6, 14] Operation: 74-60=14 Exploring Operation: 60/6=10, Resulting Numbers: [74, 10] Generated Node #0,0,2: 42:[74, 10] Operation: 60/6=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[6, 14], Operations: ['68-8=60', '74-60=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,42 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,42 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:[74, 10], Operations: ['68-8=60', '60/6=10'] Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,42 unequal: No Solution Exploring Operation: 74*10=740, Resulting Numbers: [740] 740,42 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:[60, 68], Operations: ['68-8=60', '74-6=68'] Exploring Operation: 60*68=4080, Resulting Numbers: [4080] 4080,42 unequal: No Solution Exploring Operation: 68-60=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 60+68=128, Resulting Numbers: [128] 128,42 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:[68, 6, 66], Operations: ['74-8=66'] Exploring Operation: 66/6=11, Resulting Numbers: [68, 11] Generated Node #0,2,0: 42:[68, 11] Operation: 66/6=11 Exploring Operation: 68-66=2, Resulting Numbers: [6, 2] Generated Node #0,2,1: 42:[6, 2] Operation: 68-66=2 Exploring Operation: 68-6=62, Resulting Numbers: [66, 62] Generated Node #0,2,2: 42:[66, 62] Operation: 68-6=62 Moving to Node #0,1,0 Current State: 42:[6, 2], Operations: ['74-68=6', '8-6=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,42 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[6, 14], Operations: ['74-68=6', '8+6=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[6, 14], Operations: ['74-68=6', '8+6=14'] Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[6, 2], Operations: ['74-8=66', '68-66=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,42 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[68, 11], Operations: ['74-8=66', '66/6=11'] Exploring Operation: 68*11=748, Resulting Numbers: [748] 748,42 unequal: No Solution Exploring Operation: 68-11=57, Resulting Numbers: [57] 57,42 unequal: No Solution Exploring Operation: 68+11=79, Resulting Numbers: [79] 79,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[66, 62], Operations: ['74-8=66', '68-6=62'] Exploring Operation: 66-62=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 66*62=4092, Resulting Numbers: [4092] 4092,42 unequal: No Solution Exploring Operation: 66+62=128, Resulting Numbers: [128] 128,42 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 23, 45, 48, 41 ]
67
[ "45-23=22", "48+41=89", "89-22=67" ]
Current State: 67:[23, 45, 48, 41], Operations: [] Exploring Operation: 45-23=22, Resulting Numbers: [48, 41, 22] Generated Node #2: [48, 41, 22] from Operation: 45-23=22 Current State: 67:[48, 41, 22], Operations: ['45-23=22'] Exploring Operation: 48+41=89, Resulting Numbers: [22, 89] Generated Node #3: [22, 89] from Operation: 48+41=89 Current State: 67:[22, 89], Operations: ['45-23=22', '48+41=89'] Exploring Operation: 89-22=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[23, 45, 48, 41], Operations: [] Exploring Operation: 23+45=68, Resulting Numbers: [48, 41, 68] Generated Node #0,0: 67:[48, 41, 68] Operation: 23+45=68 Exploring Operation: 23+41=64, Resulting Numbers: [45, 48, 64] Generated Node #0,1: 67:[45, 48, 64] Operation: 23+41=64 Exploring Operation: 45+41=86, Resulting Numbers: [23, 48, 86] Generated Node #0,2: 67:[23, 48, 86] Operation: 45+41=86 Exploring Operation: 23+48=71, Resulting Numbers: [45, 41, 71] Generated Node #0,3: 67:[45, 41, 71] Operation: 23+48=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[45, 48, 64], Operations: ['23+41=64'] Exploring Operation: 45+64=109, Resulting Numbers: [48, 109] Generated Node #0,1,0: 67:[48, 109] Operation: 45+64=109 Exploring Operation: 45+48=93, Resulting Numbers: [64, 93] Generated Node #0,1,1: 67:[64, 93] Operation: 45+48=93 Exploring Operation: 64-45=19, Resulting Numbers: [48, 19] Generated Node #0,1,2: 67:[48, 19] Operation: 64-45=19 Exploring Operation: 48-45=3, Resulting Numbers: [64, 3] Generated Node #0,1,3: 67:[64, 3] Operation: 48-45=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 67:[64, 93], Operations: ['23+41=64', '45+48=93'] Exploring Operation: 64*93=5952, Resulting Numbers: [5952] 5952,67 unequal: No Solution Exploring Operation: 64+93=157, Resulting Numbers: [157] 157,67 unequal: No Solution Exploring Operation: 93-64=29, Resulting Numbers: [29] 29,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 67:[48, 109], Operations: ['23+41=64', '45+64=109'] Exploring Operation: 48*109=5232, Resulting Numbers: [5232] 5232,67 unequal: No Solution Exploring Operation: 109-48=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 48+109=157, Resulting Numbers: [157] 157,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 67:[48, 19], Operations: ['23+41=64', '64-45=19'] Exploring Operation: 48*19=912, Resulting Numbers: [912] 912,67 unequal: No Solution Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 48+19=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[23, 45, 48, 41], Operations: [] Exploring Operation: 23+41=64, Resulting Numbers: [45, 48, 64] Generated Node #0,1: 67:[45, 48, 64] Operation: 23+41=64 Moving to Node #0,1 Current State: 67:[45, 48, 64], Operations: ['23+41=64'] Exploring Operation: 64-45=19, Resulting Numbers: [48, 19] Generated Node #0,1,2: 67:[48, 19] Operation: 64-45=19 Moving to Node #0,1,2 Current State: 67:[48, 19], Operations: ['23+41=64', '64-45=19'] Exploring Operation: 48+19=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 56, 84, 50, 4 ]
48
[ "56/4=14", "84-50=34", "14+34=48" ]
Current State: 48:[56, 84, 50, 4], Operations: [] Exploring Operation: 56/4=14, Resulting Numbers: [84, 50, 14] Generated Node #2: [84, 50, 14] from Operation: 56/4=14 Current State: 48:[84, 50, 14], Operations: ['56/4=14'] Exploring Operation: 84-50=34, Resulting Numbers: [14, 34] Generated Node #3: [14, 34] from Operation: 84-50=34 Current State: 48:[14, 34], Operations: ['56/4=14', '84-50=34'] Exploring Operation: 14+34=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[56, 84, 50, 4], Operations: [] Exploring Operation: 84-56=28, Resulting Numbers: [50, 4, 28] Generated Node #0,0: 48:[50, 4, 28] Operation: 84-56=28 Moving to Node #0,0 Current State: 48:[50, 4, 28], Operations: ['84-56=28'] Exploring Operation: 50-28=22, Resulting Numbers: [4, 22] Generated Node #0,0,0: 48:[4, 22] Operation: 50-28=22 Moving to Node #0,0,0 Current State: 48:[4, 22], Operations: ['84-56=28', '50-28=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,48 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 87, 8, 40, 11 ]
33
[ "11-8=3", "40*3=120", "120-87=33" ]
Current State: 33:[87, 8, 40, 11], Operations: [] Exploring Operation: 11-8=3, Resulting Numbers: [87, 40, 3] Generated Node #2: [87, 40, 3] from Operation: 11-8=3 Current State: 33:[87, 40, 3], Operations: ['11-8=3'] Exploring Operation: 40*3=120, Resulting Numbers: [87, 120] Generated Node #3: [87, 120] from Operation: 40*3=120 Current State: 33:[87, 120], Operations: ['11-8=3', '40*3=120'] Exploring Operation: 120-87=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[87, 8, 40, 11], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [8, 11, 47] Generated Node #0,0: 33:[8, 11, 47] Operation: 87-40=47 Moving to Node #0,0 Current State: 33:[8, 11, 47], Operations: ['87-40=47'] Exploring Operation: 47-8=39, Resulting Numbers: [11, 39] Generated Node #0,0,0: 33:[11, 39] Operation: 47-8=39 Moving to Node #0,0,0 Current State: 33:[11, 39], Operations: ['87-40=47', '47-8=39'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,33 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 6, 21, 13, 91 ]
51
[ "6+21=27", "91-13=78", "78-27=51" ]
Current State: 51:[6, 21, 13, 91], Operations: [] Exploring Operation: 6+21=27, Resulting Numbers: [13, 91, 27] Generated Node #2: [13, 91, 27] from Operation: 6+21=27 Current State: 51:[13, 91, 27], Operations: ['6+21=27'] Exploring Operation: 91-13=78, Resulting Numbers: [27, 78] Generated Node #3: [27, 78] from Operation: 91-13=78 Current State: 51:[27, 78], Operations: ['6+21=27', '91-13=78'] Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[6, 21, 13, 91], Operations: [] Exploring Operation: 91/13=7, Resulting Numbers: [6, 21, 7] Generated Node #0,0: 51:[6, 21, 7] Operation: 91/13=7 Exploring Operation: 91-21=70, Resulting Numbers: [6, 13, 70] Generated Node #0,1: 51:[6, 13, 70] Operation: 91-21=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[6, 21, 7], Operations: ['91/13=7'] Exploring Operation: 21/7=3, Resulting Numbers: [6, 3] Generated Node #0,0,0: 51:[6, 3] Operation: 21/7=3 Exploring Operation: 21-6=15, Resulting Numbers: [7, 15] Generated Node #0,0,1: 51:[7, 15] Operation: 21-6=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[6, 3], Operations: ['91/13=7', '21/7=3'] Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,51 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,51 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 #0,0,1 Current State: 51:[7, 15], Operations: ['91/13=7', '21-6=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,51 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: 51:[6, 13, 70], Operations: ['91-21=70'] Exploring Operation: 70-6=64, Resulting Numbers: [13, 64] Generated Node #0,1,0: 51:[13, 64] Operation: 70-6=64 Exploring Operation: 70-13=57, Resulting Numbers: [6, 57] Generated Node #0,1,1: 51:[6, 57] Operation: 70-13=57 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[6, 57], Operations: ['91-21=70', '70-13=57'] Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,51 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[6, 21, 13, 91], Operations: [] Exploring Operation: 91-21=70, Resulting Numbers: [6, 13, 70] Generated Node #0,1: 51:[6, 13, 70] Operation: 91-21=70 Moving to Node #0,1 Current State: 51:[6, 13, 70], Operations: ['91-21=70'] Exploring Operation: 70-13=57, Resulting Numbers: [6, 57] Generated Node #0,1,1: 51:[6, 57] Operation: 70-13=57 Moving to Node #0,1,1 Current State: 51:[6, 57], Operations: ['91-21=70', '70-13=57'] Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 61, 7, 81, 60 ]
58
[ "81-60=21", "21/7=3", "61-3=58" ]
Current State: 58:[61, 7, 81, 60], Operations: [] Exploring Operation: 81-60=21, Resulting Numbers: [61, 7, 21] Generated Node #2: [61, 7, 21] from Operation: 81-60=21 Current State: 58:[61, 7, 21], Operations: ['81-60=21'] Exploring Operation: 21/7=3, Resulting Numbers: [61, 3] Generated Node #3: [61, 3] from Operation: 21/7=3 Current State: 58:[61, 3], Operations: ['81-60=21', '21/7=3'] Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[61, 7, 81, 60], Operations: [] Exploring Operation: 81-61=20, Resulting Numbers: [7, 60, 20] Generated Node #0,0: 58:[7, 60, 20] Operation: 81-61=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[7, 60, 20], Operations: ['81-61=20'] Exploring Operation: 7+20=27, Resulting Numbers: [60, 27] Generated Node #0,0,0: 58:[60, 27] Operation: 7+20=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[60, 27], Operations: ['81-61=20', '7+20=27'] Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 81, 23, 53, 3 ]
71
[ "53-23=30", "30/3=10", "81-10=71" ]
Current State: 71:[81, 23, 53, 3], Operations: [] Exploring Operation: 53-23=30, Resulting Numbers: [81, 3, 30] Generated Node #2: [81, 3, 30] from Operation: 53-23=30 Current State: 71:[81, 3, 30], Operations: ['53-23=30'] Exploring Operation: 30/3=10, Resulting Numbers: [81, 10] Generated Node #3: [81, 10] from Operation: 30/3=10 Current State: 71:[81, 10], Operations: ['53-23=30', '30/3=10'] Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[81, 23, 53, 3], Operations: [] Exploring Operation: 53+3=56, Resulting Numbers: [81, 23, 56] Generated Node #0,0: 71:[81, 23, 56] Operation: 53+3=56 Exploring Operation: 81+3=84, Resulting Numbers: [23, 53, 84] Generated Node #0,1: 71:[23, 53, 84] Operation: 81+3=84 Exploring Operation: 23*3=69, Resulting Numbers: [81, 53, 69] Generated Node #0,2: 71:[81, 53, 69] Operation: 23*3=69 Exploring Operation: 81-3=78, Resulting Numbers: [23, 53, 78] Generated Node #0,3: 71:[23, 53, 78] Operation: 81-3=78 Exploring Operation: 23+3=26, Resulting Numbers: [81, 53, 26] Generated Node #0,4: 71:[81, 53, 26] Operation: 23+3=26 Moving to Node #0,2 Current State: 71:[81, 53, 69], Operations: ['23*3=69'] Exploring Operation: 53+69=122, Resulting Numbers: [81, 122] Generated Node #0,2,0: 71:[81, 122] Operation: 53+69=122 Exploring Operation: 69-53=16, Resulting Numbers: [81, 16] Generated Node #0,2,1: 71:[81, 16] Operation: 69-53=16 Exploring Operation: 81-69=12, Resulting Numbers: [53, 12] Generated Node #0,2,2: 71:[53, 12] Operation: 81-69=12 Exploring Operation: 81-53=28, Resulting Numbers: [69, 28] Generated Node #0,2,3: 71:[69, 28] Operation: 81-53=28 Exploring Operation: 81+53=134, Resulting Numbers: [69, 134] Generated Node #0,2,4: 71:[69, 134] Operation: 81+53=134 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 71:[69, 28], Operations: ['23*3=69', '81-53=28'] Exploring Operation: 69*28=1932, Resulting Numbers: [1932] 1932,71 unequal: No Solution Exploring Operation: 69+28=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[81, 122], Operations: ['23*3=69', '53+69=122'] Exploring Operation: 81+122=203, Resulting Numbers: [203] 203,71 unequal: No Solution Exploring Operation: 122-81=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 81*122=9882, Resulting Numbers: [9882] 9882,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[81, 16], Operations: ['23*3=69', '69-53=16'] Exploring Operation: 81+16=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,71 unequal: No Solution Exploring Operation: 81*16=1296, Resulting Numbers: [1296] 1296,71 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 #0,2,4 Current State: 71:[69, 134], Operations: ['23*3=69', '81+53=134'] Exploring Operation: 69*134=9246, Resulting Numbers: [9246] 9246,71 unequal: No Solution Exploring Operation: 69+134=203, Resulting Numbers: [203] 203,71 unequal: No Solution Exploring Operation: 134-69=65, Resulting Numbers: [65] 65,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[53, 12], Operations: ['23*3=69', '81-69=12'] Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 53*12=636, Resulting Numbers: [636] 636,71 unequal: No Solution Exploring Operation: 53+12=65, Resulting Numbers: [65] 65,71 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: 71:[23, 53, 78], Operations: ['81-3=78'] Exploring Operation: 23+78=101, Resulting Numbers: [53, 101] Generated Node #0,3,0: 71:[53, 101] Operation: 23+78=101 Exploring Operation: 78-53=25, Resulting Numbers: [23, 25] Generated Node #0,3,1: 71:[23, 25] Operation: 78-53=25 Exploring Operation: 23+53=76, Resulting Numbers: [78, 76] Generated Node #0,3,2: 71:[78, 76] Operation: 23+53=76 Exploring Operation: 53-23=30, Resulting Numbers: [78, 30] Generated Node #0,3,3: 71:[78, 30] Operation: 53-23=30 Exploring Operation: 78-23=55, Resulting Numbers: [53, 55] Generated Node #0,3,4: 71:[53, 55] Operation: 78-23=55 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 71:[78, 76], Operations: ['81-3=78', '23+53=76'] Exploring Operation: 78*76=5928, Resulting Numbers: [5928] 5928,71 unequal: No Solution Exploring Operation: 78+76=154, Resulting Numbers: [154] 154,71 unequal: No Solution Exploring Operation: 78-76=2, Resulting Numbers: [2] 2,71 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 #0,3,4 Current State: 71:[53, 55], Operations: ['81-3=78', '78-23=55'] Exploring Operation: 53*55=2915, Resulting Numbers: [2915] 2915,71 unequal: No Solution Exploring Operation: 55-53=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 53+55=108, Resulting Numbers: [108] 108,71 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 #0,3,0 Current State: 71:[53, 101], Operations: ['81-3=78', '23+78=101'] Exploring Operation: 53+101=154, Resulting Numbers: [154] 154,71 unequal: No Solution Exploring Operation: 53*101=5353, Resulting Numbers: [5353] 5353,71 unequal: No Solution Exploring Operation: 101-53=48, Resulting Numbers: [48] 48,71 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 #0,3,3 Current State: 71:[78, 30], Operations: ['81-3=78', '53-23=30'] Exploring Operation: 78*30=2340, Resulting Numbers: [2340] 2340,71 unequal: No Solution Exploring Operation: 78+30=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,71 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 #0,3,1 Current State: 71:[23, 25], Operations: ['81-3=78', '78-53=25'] Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,71 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,71 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 71:[81, 23, 56], Operations: ['53+3=56'] Exploring Operation: 56-23=33, Resulting Numbers: [81, 33] Generated Node #0,0,0: 71:[81, 33] Operation: 56-23=33 Exploring Operation: 23+56=79, Resulting Numbers: [81, 79] Generated Node #0,0,1: 71:[81, 79] Operation: 23+56=79 Exploring Operation: 81-23=58, Resulting Numbers: [56, 58] Generated Node #0,0,2: 71:[56, 58] Operation: 81-23=58 Exploring Operation: 81-56=25, Resulting Numbers: [23, 25] Generated Node #0,0,3: 71:[23, 25] Operation: 81-56=25 Exploring Operation: 81+23=104, Resulting Numbers: [56, 104] Generated Node #0,0,4: 71:[56, 104] Operation: 81+23=104 Moving to Node #0,4 Current State: 71:[81, 53, 26], Operations: ['23+3=26'] Exploring Operation: 81+26=107, Resulting Numbers: [53, 107] Generated Node #0,4,0: 71:[53, 107] Operation: 81+26=107 Exploring Operation: 81-53=28, Resulting Numbers: [26, 28] Generated Node #0,4,1: 71:[26, 28] Operation: 81-53=28 Exploring Operation: 53+26=79, Resulting Numbers: [81, 79] Generated Node #0,4,2: 71:[81, 79] Operation: 53+26=79 Exploring Operation: 53-26=27, Resulting Numbers: [81, 27] Generated Node #0,4,3: 71:[81, 27] Operation: 53-26=27 Exploring Operation: 81-26=55, Resulting Numbers: [53, 55] Generated Node #0,4,4: 71:[53, 55] Operation: 81-26=55 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 71:[81, 79], Operations: ['23+3=26', '53+26=79'] Exploring Operation: 81-79=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 81*79=6399, Resulting Numbers: [6399] 6399,71 unequal: No Solution Exploring Operation: 81+79=160, Resulting Numbers: [160] 160,71 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 #0,4,4 Current State: 71:[53, 55], Operations: ['23+3=26', '81-26=55'] Exploring Operation: 53*55=2915, Resulting Numbers: [2915] 2915,71 unequal: No Solution Exploring Operation: 53+55=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 55-53=2, Resulting Numbers: [2] 2,71 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 #0,4,0 Current State: 71:[53, 107], Operations: ['23+3=26', '81+26=107'] Exploring Operation: 107-53=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 53+107=160, Resulting Numbers: [160] 160,71 unequal: No Solution Exploring Operation: 53*107=5671, Resulting Numbers: [5671] 5671,71 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 #0,4,3 Current State: 71:[81, 27], Operations: ['23+3=26', '53-26=27'] Exploring Operation: 81+27=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 81/27=3, Resulting Numbers: [3] 3,71 unequal: No Solution Exploring Operation: 81-27=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 81*27=2187, Resulting Numbers: [2187] 2187,71 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 #0,4,1 Current State: 71:[26, 28], Operations: ['23+3=26', '81-53=28'] Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,71 unequal: No Solution Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,71 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: 71:[23, 53, 84], Operations: ['81+3=84'] Exploring Operation: 23+53=76, Resulting Numbers: [84, 76] Generated Node #0,1,0: 71:[84, 76] Operation: 23+53=76 Exploring Operation: 23+84=107, Resulting Numbers: [53, 107] Generated Node #0,1,1: 71:[53, 107] Operation: 23+84=107 Exploring Operation: 53-23=30, Resulting Numbers: [84, 30] Generated Node #0,1,2: 71:[84, 30] Operation: 53-23=30 Exploring Operation: 84-23=61, Resulting Numbers: [53, 61] Generated Node #0,1,3: 71:[53, 61] Operation: 84-23=61 Exploring Operation: 84-53=31, Resulting Numbers: [23, 31] Generated Node #0,1,4: 71:[23, 31] Operation: 84-53=31 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[84, 76], Operations: ['81+3=84', '23+53=76'] Exploring Operation: 84+76=160, Resulting Numbers: [160] 160,71 unequal: No Solution Exploring Operation: 84*76=6384, Resulting Numbers: [6384] 6384,71 unequal: No Solution Exploring Operation: 84-76=8, Resulting Numbers: [8] 8,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 71:[53, 61], Operations: ['81+3=84', '84-23=61'] Exploring Operation: 53+61=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 53*61=3233, Resulting Numbers: [3233] 3233,71 unequal: No Solution Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[53, 107], Operations: ['81+3=84', '23+84=107'] Exploring Operation: 53*107=5671, Resulting Numbers: [5671] 5671,71 unequal: No Solution Exploring Operation: 107-53=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 53+107=160, Resulting Numbers: [160] 160,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 71:[84, 30], Operations: ['81+3=84', '53-23=30'] Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 84*30=2520, Resulting Numbers: [2520] 2520,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 71:[23, 31], Operations: ['81+3=84', '84-53=31'] Exploring Operation: 23*31=713, Resulting Numbers: [713] 713,71 unequal: No Solution Exploring Operation: 23+31=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,71 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: 71:[81, 79], Operations: ['53+3=56', '23+56=79'] Exploring Operation: 81+79=160, Resulting Numbers: [160] 160,71 unequal: No Solution Exploring Operation: 81*79=6399, Resulting Numbers: [6399] 6399,71 unequal: No Solution Exploring Operation: 81-79=2, Resulting Numbers: [2] 2,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[56, 58], Operations: ['53+3=56', '81-23=58'] Exploring Operation: 56*58=3248, Resulting Numbers: [3248] 3248,71 unequal: No Solution Exploring Operation: 56+58=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 58-56=2, Resulting Numbers: [2] 2,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[81, 33], Operations: ['53+3=56', '56-23=33'] Exploring Operation: 81*33=2673, Resulting Numbers: [2673] 2673,71 unequal: No Solution Exploring Operation: 81+33=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 81-33=48, Resulting Numbers: [48] 48,71 unequal: No Solution Moving to Node #0,0,4 Current State: 71:[56, 104], Operations: ['53+3=56', '81+23=104'] Exploring Operation: 56+104=160, Resulting Numbers: [160] 160,71 unequal: No Solution Exploring Operation: 104-56=48, Resulting Numbers: [48] 48,71 unequal: No Solution Exploring Operation: 56*104=5824, Resulting Numbers: [5824] 5824,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[23, 25], Operations: ['53+3=56', '81-56=25'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,71 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,71 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 90, 54, 23, 2 ]
26
[ "90-54=36", "36-23=13", "2*13=26" ]
Current State: 26:[90, 54, 23, 2], Operations: [] Exploring Operation: 90-54=36, Resulting Numbers: [23, 2, 36] Generated Node #2: [23, 2, 36] from Operation: 90-54=36 Current State: 26:[23, 2, 36], Operations: ['90-54=36'] Exploring Operation: 36-23=13, Resulting Numbers: [2, 13] Generated Node #3: [2, 13] from Operation: 36-23=13 Current State: 26:[2, 13], Operations: ['90-54=36', '36-23=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[90, 54, 23, 2], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [54, 23, 45] Generated Node #0,0: 26:[54, 23, 45] Operation: 90/2=45 Exploring Operation: 54-23=31, Resulting Numbers: [90, 2, 31] Generated Node #0,1: 26:[90, 2, 31] Operation: 54-23=31 Exploring Operation: 90-54=36, Resulting Numbers: [23, 2, 36] Generated Node #0,2: 26:[23, 2, 36] Operation: 90-54=36 Exploring Operation: 54/2=27, Resulting Numbers: [90, 23, 27] Generated Node #0,3: 26:[90, 23, 27] Operation: 54/2=27 Exploring Operation: 90-23=67, Resulting Numbers: [54, 2, 67] Generated Node #0,4: 26:[54, 2, 67] Operation: 90-23=67 Moving to Node #0,2 Current State: 26:[23, 2, 36], Operations: ['90-54=36'] Exploring Operation: 36-2=34, Resulting Numbers: [23, 34] Generated Node #0,2,0: 26:[23, 34] Operation: 36-2=34 Exploring Operation: 23-2=21, Resulting Numbers: [36, 21] Generated Node #0,2,1: 26:[36, 21] Operation: 23-2=21 Exploring Operation: 36/2=18, Resulting Numbers: [23, 18] Generated Node #0,2,2: 26:[23, 18] Operation: 36/2=18 Exploring Operation: 36-23=13, Resulting Numbers: [2, 13] Generated Node #0,2,3: 26:[2, 13] Operation: 36-23=13 Exploring Operation: 23+2=25, Resulting Numbers: [36, 25] Generated Node #0,2,4: 26:[36, 25] Operation: 23+2=25 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 26:[2, 13], Operations: ['90-54=36', '36-23=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[90, 54, 23, 2], Operations: [] Exploring Operation: 90-54=36, Resulting Numbers: [23, 2, 36] Generated Node #0,2: 26:[23, 2, 36] Operation: 90-54=36 Moving to Node #0,2 Current State: 26:[23, 2, 36], Operations: ['90-54=36'] Exploring Operation: 36-23=13, Resulting Numbers: [2, 13] Generated Node #0,2,3: 26:[2, 13] Operation: 36-23=13 Moving to Node #0,2,3 Current State: 26:[2, 13], Operations: ['90-54=36', '36-23=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 66, 37, 55, 31 ]
79
[ "66+37=103", "55-31=24", "103-24=79" ]
Current State: 79:[66, 37, 55, 31], Operations: [] Exploring Operation: 66+37=103, Resulting Numbers: [55, 31, 103] Generated Node #2: [55, 31, 103] from Operation: 66+37=103 Current State: 79:[55, 31, 103], Operations: ['66+37=103'] Exploring Operation: 55-31=24, Resulting Numbers: [103, 24] Generated Node #3: [103, 24] from Operation: 55-31=24 Current State: 79:[103, 24], Operations: ['66+37=103', '55-31=24'] Exploring Operation: 103-24=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[66, 37, 55, 31], Operations: [] Exploring Operation: 66+31=97, Resulting Numbers: [37, 55, 97] Generated Node #0,0: 79:[37, 55, 97] Operation: 66+31=97 Exploring Operation: 37+31=68, Resulting Numbers: [66, 55, 68] Generated Node #0,1: 79:[66, 55, 68] Operation: 37+31=68 Exploring Operation: 55+31=86, Resulting Numbers: [66, 37, 86] Generated Node #0,2: 79:[66, 37, 86] Operation: 55+31=86 Exploring Operation: 37+55=92, Resulting Numbers: [66, 31, 92] Generated Node #0,3: 79:[66, 31, 92] Operation: 37+55=92 Moving to Node #0,1 Current State: 79:[66, 55, 68], Operations: ['37+31=68'] Exploring Operation: 66-55=11, Resulting Numbers: [68, 11] Generated Node #0,1,0: 79:[68, 11] Operation: 66-55=11 Exploring Operation: 55+68=123, Resulting Numbers: [66, 123] Generated Node #0,1,1: 79:[66, 123] Operation: 55+68=123 Exploring Operation: 66+68=134, Resulting Numbers: [55, 134] Generated Node #0,1,2: 79:[55, 134] Operation: 66+68=134 Exploring Operation: 66+55=121, Resulting Numbers: [68, 121] Generated Node #0,1,3: 79:[68, 121] Operation: 66+55=121 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[68, 121], Operations: ['37+31=68', '66+55=121'] Exploring Operation: 68+121=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 68*121=8228, Resulting Numbers: [8228] 8228,79 unequal: No Solution Exploring Operation: 121-68=53, Resulting Numbers: [53] 53,79 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 #0,1,1 Current State: 79:[66, 123], Operations: ['37+31=68', '55+68=123'] Exploring Operation: 66*123=8118, Resulting Numbers: [8118] 8118,79 unequal: No Solution Exploring Operation: 66+123=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 123-66=57, Resulting Numbers: [57] 57,79 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 #0,1,0 Current State: 79:[68, 11], Operations: ['37+31=68', '66-55=11'] Exploring Operation: 68+11=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[66, 37, 55, 31], Operations: [] Exploring Operation: 37+31=68, Resulting Numbers: [66, 55, 68] Generated Node #0,1: 79:[66, 55, 68] Operation: 37+31=68 Moving to Node #0,1 Current State: 79:[66, 55, 68], Operations: ['37+31=68'] Exploring Operation: 66-55=11, Resulting Numbers: [68, 11] Generated Node #0,1,0: 79:[68, 11] Operation: 66-55=11 Moving to Node #0,1,0 Current State: 79:[68, 11], Operations: ['37+31=68', '66-55=11'] Exploring Operation: 68+11=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 1, 2, 56, 50 ]
82
[ "1+56=57", "50/2=25", "57+25=82" ]
Current State: 82:[1, 2, 56, 50], Operations: [] Exploring Operation: 1+56=57, Resulting Numbers: [2, 50, 57] Generated Node #2: [2, 50, 57] from Operation: 1+56=57 Current State: 82:[2, 50, 57], Operations: ['1+56=57'] Exploring Operation: 50/2=25, Resulting Numbers: [57, 25] Generated Node #3: [57, 25] from Operation: 50/2=25 Current State: 82:[57, 25], Operations: ['1+56=57', '50/2=25'] Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[1, 2, 56, 50], Operations: [] Exploring Operation: 56-2=54, Resulting Numbers: [1, 50, 54] Generated Node #0,0: 82:[1, 50, 54] Operation: 56-2=54 Exploring Operation: 56-50=6, Resulting Numbers: [1, 2, 6] Generated Node #0,1: 82:[1, 2, 6] Operation: 56-50=6 Exploring Operation: 56-1=55, Resulting Numbers: [2, 50, 55] Generated Node #0,2: 82:[2, 50, 55] Operation: 56-1=55 Exploring Operation: 50-1=49, Resulting Numbers: [2, 56, 49] Generated Node #0,3: 82:[2, 56, 49] Operation: 50-1=49 Exploring Operation: 56/2=28, Resulting Numbers: [1, 50, 28] Generated Node #0,4: 82:[1, 50, 28] Operation: 56/2=28 Moving to Node #0,1 Current State: 82:[1, 2, 6], Operations: ['56-50=6'] Exploring Operation: 6-1=5, Resulting Numbers: [2, 5] Generated Node #0,1,0: 82:[2, 5] Operation: 6-1=5 Exploring Operation: 2/1=2, Resulting Numbers: [6, 2] Generated Node #0,1,1: 82:[6, 2] Operation: 2/1=2 Exploring Operation: 1*2=2, Resulting Numbers: [6, 2] Generated Node #0,1,2: 82:[6, 2] Operation: 1*2=2 Exploring Operation: 6-2=4, Resulting Numbers: [1, 4] Generated Node #0,1,3: 82:[1, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [1, 3] Generated Node #0,1,4: 82:[1, 3] Operation: 6/2=3 Moving to Node #0,2 Current State: 82:[2, 50, 55], Operations: ['56-1=55'] Exploring Operation: 2+50=52, Resulting Numbers: [55, 52] Generated Node #0,2,0: 82:[55, 52] Operation: 2+50=52 Exploring Operation: 55-2=53, Resulting Numbers: [50, 53] Generated Node #0,2,1: 82:[50, 53] Operation: 55-2=53 Exploring Operation: 50+55=105, Resulting Numbers: [2, 105] Generated Node #0,2,2: 82:[2, 105] Operation: 50+55=105 Exploring Operation: 55-50=5, Resulting Numbers: [2, 5] Generated Node #0,2,3: 82:[2, 5] Operation: 55-50=5 Exploring Operation: 50-2=48, Resulting Numbers: [55, 48] Generated Node #0,2,4: 82:[55, 48] Operation: 50-2=48 Moving to Node #0,4 Current State: 82:[1, 50, 28], Operations: ['56/2=28'] Exploring Operation: 50-1=49, Resulting Numbers: [28, 49] Generated Node #0,4,0: 82:[28, 49] Operation: 50-1=49 Exploring Operation: 1+28=29, Resulting Numbers: [50, 29] Generated Node #0,4,1: 82:[50, 29] Operation: 1+28=29 Exploring Operation: 50+28=78, Resulting Numbers: [1, 78] Generated Node #0,4,2: 82:[1, 78] Operation: 50+28=78 Exploring Operation: 50-28=22, Resulting Numbers: [1, 22] Generated Node #0,4,3: 82:[1, 22] Operation: 50-28=22 Exploring Operation: 1*50=50, Resulting Numbers: [28, 50] Generated Node #0,4,4: 82:[28, 50] Operation: 1*50=50 Moving to Node #0,0 Current State: 82:[1, 50, 54], Operations: ['56-2=54'] Exploring Operation: 1*50=50, Resulting Numbers: [54, 50] Generated Node #0,0,0: 82:[54, 50] Operation: 1*50=50 Exploring Operation: 54-1=53, Resulting Numbers: [50, 53] Generated Node #0,0,1: 82:[50, 53] Operation: 54-1=53 Exploring Operation: 50-1=49, Resulting Numbers: [54, 49] Generated Node #0,0,2: 82:[54, 49] Operation: 50-1=49 Exploring Operation: 50/1=50, Resulting Numbers: [54, 50] Generated Node #0,0,3: 82:[54, 50] Operation: 50/1=50 Exploring Operation: 54-50=4, Resulting Numbers: [1, 4] Generated Node #0,0,4: 82:[1, 4] Operation: 54-50=4 Moving to Node #0,3 Current State: 82:[2, 56, 49], Operations: ['50-1=49'] Exploring Operation: 56+49=105, Resulting Numbers: [2, 105] Generated Node #0,3,0: 82:[2, 105] Operation: 56+49=105 Exploring Operation: 49-2=47, Resulting Numbers: [56, 47] Generated Node #0,3,1: 82:[56, 47] Operation: 49-2=47 Exploring Operation: 56-2=54, Resulting Numbers: [49, 54] Generated Node #0,3,2: 82:[49, 54] Operation: 56-2=54 Exploring Operation: 56/2=28, Resulting Numbers: [49, 28] Generated Node #0,3,3: 82:[49, 28] Operation: 56/2=28 Exploring Operation: 56-49=7, Resulting Numbers: [2, 7] Generated Node #0,3,4: 82:[2, 7] Operation: 56-49=7 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 82:[2, 7], Operations: ['50-1=49', '56-49=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,82 unequal: No Solution No 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: 82:[56, 47], Operations: ['50-1=49', '49-2=47'] Exploring Operation: 56*47=2632, Resulting Numbers: [2632] 2632,82 unequal: No Solution Exploring Operation: 56+47=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,82 unequal: No Solution No 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: 82:[49, 54], Operations: ['50-1=49', '56-2=54'] Exploring Operation: 49*54=2646, Resulting Numbers: [2646] 2646,82 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 49+54=103, Resulting Numbers: [103] 103,82 unequal: No Solution No 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: 82:[49, 28], Operations: ['50-1=49', '56/2=28'] Exploring Operation: 49*28=1372, Resulting Numbers: [1372] 1372,82 unequal: No Solution Exploring Operation: 49+28=77, Resulting Numbers: [77] 77,82 unequal: No Solution Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,82 unequal: No Solution No 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: 82:[2, 105], Operations: ['50-1=49', '56+49=105'] Exploring Operation: 105-2=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 2+105=107, Resulting Numbers: [107] 107,82 unequal: No Solution Exploring Operation: 2*105=210, Resulting Numbers: [210] 210,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 82:[1, 3], Operations: ['56-50=6', '6/2=3'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[1, 4], Operations: ['56-50=6', '6-2=4'] Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,82 unequal: No Solution Moving to Node #0,2,3 Current State: 82:[2, 5], Operations: ['56-1=55', '55-50=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,82 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[2, 5], Operations: ['56-50=6', '6-1=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,82 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,82 unequal: No Solution Moving to Node #0,0,4 Current State: 82:[1, 4], Operations: ['56-2=54', '54-50=4'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[6, 2], Operations: ['56-50=6', '1*2=2'] Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,82 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[6, 2], Operations: ['56-50=6', '2/1=2'] Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,82 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,82 unequal: No Solution Moving to Node #0,4,2 Current State: 82:[1, 78], Operations: ['56/2=28', '50+28=78'] Exploring Operation: 1*78=78, Resulting Numbers: [78] 78,82 unequal: No Solution Exploring Operation: 78/1=78, Resulting Numbers: [78] 78,82 unequal: No Solution Exploring Operation: 1+78=79, Resulting Numbers: [79] 79,82 unequal: No Solution Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,82 unequal: No Solution Moving to Node #0,4,3 Current State: 82:[1, 22], Operations: ['56/2=28', '50-28=22'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,82 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,82 unequal: No Solution Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,82 unequal: No Solution Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[50, 53], Operations: ['56-1=55', '55-2=53'] Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,82 unequal: No Solution Moving to Node #0,4,0 Current State: 82:[28, 49], Operations: ['56/2=28', '50-1=49'] Exploring Operation: 28*49=1372, Resulting Numbers: [1372] 1372,82 unequal: No Solution Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,82 unequal: No Solution Exploring Operation: 28+49=77, Resulting Numbers: [77] 77,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[54, 49], Operations: ['56-2=54', '50-1=49'] Exploring Operation: 54+49=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 54*49=2646, Resulting Numbers: [2646] 2646,82 unequal: No Solution Moving to Node #0,2,4 Current State: 82:[55, 48], Operations: ['56-1=55', '50-2=48'] Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,82 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,82 unequal: No Solution Moving to Node #0,4,1 Current State: 82:[50, 29], Operations: ['56/2=28', '1+28=29'] Exploring Operation: 50*29=1450, Resulting Numbers: [1450] 1450,82 unequal: No Solution Exploring Operation: 50+29=79, Resulting Numbers: [79] 79,82 unequal: No Solution Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[50, 53], Operations: ['56-2=54', '54-1=53'] Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,82 unequal: No Solution Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[54, 50], Operations: ['56-2=54', '1*50=50'] Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 54+50=104, Resulting Numbers: [104] 104,82 unequal: No Solution Exploring Operation: 54*50=2700, Resulting Numbers: [2700] 2700,82 unequal: No Solution Moving to Node #0,0,3 Current State: 82:[54, 50], Operations: ['56-2=54', '50/1=50'] Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 54+50=104, Resulting Numbers: [104] 104,82 unequal: No Solution Exploring Operation: 54*50=2700, Resulting Numbers: [2700] 2700,82 unequal: No Solution Moving to Node #0,4,4 Current State: 82:[28, 50], Operations: ['56/2=28', '1*50=50'] Exploring Operation: 28*50=1400, Resulting Numbers: [1400] 1400,82 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,82 unequal: No Solution Exploring Operation: 28+50=78, Resulting Numbers: [78] 78,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[2, 105], Operations: ['56-1=55', '50+55=105'] Exploring Operation: 105-2=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 2*105=210, Resulting Numbers: [210] 210,82 unequal: No Solution Exploring Operation: 2+105=107, Resulting Numbers: [107] 107,82 unequal: No Solution Moving to Node #0,2,0 Current State: 82:[55, 52], Operations: ['56-1=55', '2+50=52'] Exploring Operation: 55*52=2860, Resulting Numbers: [2860] 2860,82 unequal: No Solution Exploring Operation: 55-52=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 55+52=107, Resulting Numbers: [107] 107,82 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 75, 48, 23, 72 ]
18
[ "75-48=27", "27-23=4", "72/4=18" ]
Current State: 18:[75, 48, 23, 72], Operations: [] Exploring Operation: 75-48=27, Resulting Numbers: [23, 72, 27] Generated Node #2: [23, 72, 27] from Operation: 75-48=27 Current State: 18:[23, 72, 27], Operations: ['75-48=27'] Exploring Operation: 27-23=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 27-23=4 Current State: 18:[72, 4], Operations: ['75-48=27', '27-23=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[75, 48, 23, 72], Operations: [] Exploring Operation: 75-23=52, Resulting Numbers: [48, 72, 52] Generated Node #0,0: 18:[48, 72, 52] Operation: 75-23=52 Exploring Operation: 75-72=3, Resulting Numbers: [48, 23, 3] Generated Node #0,1: 18:[48, 23, 3] Operation: 75-72=3 Exploring Operation: 72-48=24, Resulting Numbers: [75, 23, 24] Generated Node #0,2: 18:[75, 23, 24] Operation: 72-48=24 Exploring Operation: 48-23=25, Resulting Numbers: [75, 72, 25] Generated Node #0,3: 18:[75, 72, 25] Operation: 48-23=25 Exploring Operation: 75-48=27, Resulting Numbers: [23, 72, 27] Generated Node #0,4: 18:[23, 72, 27] Operation: 75-48=27 Moving to Node #0,1 Current State: 18:[48, 23, 3], Operations: ['75-72=3'] Exploring Operation: 48+3=51, Resulting Numbers: [23, 51] Generated Node #0,1,0: 18:[23, 51] Operation: 48+3=51 Exploring Operation: 48/3=16, Resulting Numbers: [23, 16] Generated Node #0,1,1: 18:[23, 16] Operation: 48/3=16 Exploring Operation: 48-23=25, Resulting Numbers: [3, 25] Generated Node #0,1,2: 18:[3, 25] Operation: 48-23=25 Exploring Operation: 23-3=20, Resulting Numbers: [48, 20] Generated Node #0,1,3: 18:[48, 20] Operation: 23-3=20 Exploring Operation: 48-3=45, Resulting Numbers: [23, 45] Generated Node #0,1,4: 18:[23, 45] Operation: 48-3=45 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[23, 16], Operations: ['75-72=3', '48/3=16'] Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 23*16=368, Resulting Numbers: [368] 368,18 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,18 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:[3, 25], Operations: ['75-72=3', '48-23=25'] Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,18 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,18 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 #0,1,3 Current State: 18:[48, 20], Operations: ['75-72=3', '23-3=20'] Exploring Operation: 48*20=960, Resulting Numbers: [960] 960,18 unequal: No Solution Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 48+20=68, Resulting Numbers: [68] 68,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[23, 45], Operations: ['75-72=3', '48-3=45'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 23*45=1035, Resulting Numbers: [1035] 1035,18 unequal: No Solution Exploring Operation: 23+45=68, Resulting Numbers: [68] 68,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[23, 51], Operations: ['75-72=3', '48+3=51'] Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,18 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,18 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: 18:[23, 72, 27], Operations: ['75-48=27'] Exploring Operation: 72-23=49, Resulting Numbers: [27, 49] Generated Node #0,4,0: 18:[27, 49] Operation: 72-23=49 Exploring Operation: 27-23=4, Resulting Numbers: [72, 4] Generated Node #0,4,1: 18:[72, 4] Operation: 27-23=4 Exploring Operation: 23+27=50, Resulting Numbers: [72, 50] Generated Node #0,4,2: 18:[72, 50] Operation: 23+27=50 Exploring Operation: 23+72=95, Resulting Numbers: [27, 95] Generated Node #0,4,3: 18:[27, 95] Operation: 23+72=95 Exploring Operation: 72-27=45, Resulting Numbers: [23, 45] Generated Node #0,4,4: 18:[23, 45] Operation: 72-27=45 Moving to Node #0,2 Current State: 18:[75, 23, 24], Operations: ['72-48=24'] Exploring Operation: 75-24=51, Resulting Numbers: [23, 51] Generated Node #0,2,0: 18:[23, 51] Operation: 75-24=51 Exploring Operation: 75+24=99, Resulting Numbers: [23, 99] Generated Node #0,2,1: 18:[23, 99] Operation: 75+24=99 Exploring Operation: 75+23=98, Resulting Numbers: [24, 98] Generated Node #0,2,2: 18:[24, 98] Operation: 75+23=98 Exploring Operation: 75-23=52, Resulting Numbers: [24, 52] Generated Node #0,2,3: 18:[24, 52] Operation: 75-23=52 Exploring Operation: 24-23=1, Resulting Numbers: [75, 1] Generated Node #0,2,4: 18:[75, 1] Operation: 24-23=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[23, 51], Operations: ['72-48=24', '75-24=51'] Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,18 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[24, 52], Operations: ['72-48=24', '75-23=52'] Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 24*52=1248, Resulting Numbers: [1248] 1248,18 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 #0,2,4 Current State: 18:[75, 1], Operations: ['72-48=24', '24-23=1'] Exploring Operation: 75+1=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,18 unequal: No Solution Exploring Operation: 75*1=75, Resulting Numbers: [75] 75,18 unequal: No Solution Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[23, 99], Operations: ['72-48=24', '75+24=99'] Exploring Operation: 23*99=2277, Resulting Numbers: [2277] 2277,18 unequal: No Solution Exploring Operation: 23+99=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,18 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:[24, 98], Operations: ['72-48=24', '75+23=98'] Exploring Operation: 24*98=2352, Resulting Numbers: [2352] 2352,18 unequal: No Solution Exploring Operation: 98-24=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 24+98=122, Resulting Numbers: [122] 122,18 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: 18:[48, 72, 52], Operations: ['75-23=52'] Exploring Operation: 72-48=24, Resulting Numbers: [52, 24] Generated Node #0,0,0: 18:[52, 24] Operation: 72-48=24 Exploring Operation: 48+52=100, Resulting Numbers: [72, 100] Generated Node #0,0,1: 18:[72, 100] Operation: 48+52=100 Exploring Operation: 52-48=4, Resulting Numbers: [72, 4] Generated Node #0,0,2: 18:[72, 4] Operation: 52-48=4 Exploring Operation: 72-52=20, Resulting Numbers: [48, 20] Generated Node #0,0,3: 18:[48, 20] Operation: 72-52=20 Exploring Operation: 48+72=120, Resulting Numbers: [52, 120] Generated Node #0,0,4: 18:[52, 120] Operation: 48+72=120 Moving to Node #0,3 Current State: 18:[75, 72, 25], Operations: ['48-23=25'] Exploring Operation: 75/25=3, Resulting Numbers: [72, 3] Generated Node #0,3,0: 18:[72, 3] Operation: 75/25=3 Exploring Operation: 75-25=50, Resulting Numbers: [72, 50] Generated Node #0,3,1: 18:[72, 50] Operation: 75-25=50 Exploring Operation: 75+72=147, Resulting Numbers: [25, 147] Generated Node #0,3,2: 18:[25, 147] Operation: 75+72=147 Exploring Operation: 72-25=47, Resulting Numbers: [75, 47] Generated Node #0,3,3: 18:[75, 47] Operation: 72-25=47 Exploring Operation: 75-72=3, Resulting Numbers: [25, 3] Generated Node #0,3,4: 18:[25, 3] Operation: 75-72=3 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 18:[25, 3], Operations: ['48-23=25', '75-72=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,18 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[72, 3], Operations: ['48-23=25', '75/25=3'] Exploring Operation: 72*3=216, Resulting Numbers: [216] 216,18 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,18 unequal: No Solution Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[72, 50], Operations: ['48-23=25', '75-25=50'] Exploring Operation: 72*50=3600, Resulting Numbers: [3600] 3600,18 unequal: No Solution Exploring Operation: 72-50=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 72+50=122, Resulting Numbers: [122] 122,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 18:[75, 47], Operations: ['48-23=25', '72-25=47'] Exploring Operation: 75*47=3525, Resulting Numbers: [3525] 3525,18 unequal: No Solution Exploring Operation: 75+47=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 75-47=28, Resulting Numbers: [28] 28,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[25, 147], Operations: ['48-23=25', '75+72=147'] Exploring Operation: 25*147=3675, Resulting Numbers: [3675] 3675,18 unequal: No Solution Exploring Operation: 147-25=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 25+147=172, Resulting Numbers: [172] 172,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,4 Current State: 18:[23, 45], Operations: ['75-48=27', '72-27=45'] Exploring Operation: 23*45=1035, Resulting Numbers: [1035] 1035,18 unequal: No Solution Exploring Operation: 23+45=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[48, 20], Operations: ['75-23=52', '72-52=20'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 48*20=960, Resulting Numbers: [960] 960,18 unequal: No Solution Exploring Operation: 48+20=68, Resulting Numbers: [68] 68,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[52, 24], Operations: ['75-23=52', '72-48=24'] Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 52*24=1248, Resulting Numbers: [1248] 1248,18 unequal: No Solution Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[27, 49], Operations: ['75-48=27', '72-23=49'] Exploring Operation: 27*49=1323, Resulting Numbers: [1323] 1323,18 unequal: No Solution Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,18 unequal: No Solution Moving to Node #0,4,1 Current State: 18:[72, 4], Operations: ['75-48=27', '27-23=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[75, 48, 23, 72], Operations: [] Exploring Operation: 75-48=27, Resulting Numbers: [23, 72, 27] Generated Node #0,4: 18:[23, 72, 27] Operation: 75-48=27 Moving to Node #0,4 Current State: 18:[23, 72, 27], Operations: ['75-48=27'] Exploring Operation: 27-23=4, Resulting Numbers: [72, 4] Generated Node #0,4,1: 18:[72, 4] Operation: 27-23=4 Moving to Node #0,4,1 Current State: 18:[72, 4], Operations: ['75-48=27', '27-23=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.917535
hs_5
sum_heuristic
[ 38, 16, 39, 31 ]
73
[ "38-31=7", "16*7=112", "112-39=73" ]
Current State: 73:[38, 16, 39, 31], Operations: [] Exploring Operation: 38-31=7, Resulting Numbers: [16, 39, 7] Generated Node #2: [16, 39, 7] from Operation: 38-31=7 Current State: 73:[16, 39, 7], Operations: ['38-31=7'] Exploring Operation: 16*7=112, Resulting Numbers: [39, 112] Generated Node #3: [39, 112] from Operation: 16*7=112 Current State: 73:[39, 112], Operations: ['38-31=7', '16*7=112'] Exploring Operation: 112-39=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[38, 16, 39, 31], Operations: [] Exploring Operation: 38+16=54, Resulting Numbers: [39, 31, 54] Generated Node #0,0: 73:[39, 31, 54] Operation: 38+16=54 Exploring Operation: 38+31=69, Resulting Numbers: [16, 39, 69] Generated Node #0,1: 73:[16, 39, 69] Operation: 38+31=69 Moving to Node #0,0 Current State: 73:[39, 31, 54], Operations: ['38+16=54'] Exploring Operation: 39+31=70, Resulting Numbers: [54, 70] Generated Node #0,0,0: 73:[54, 70] Operation: 39+31=70 Exploring Operation: 31+54=85, Resulting Numbers: [39, 85] Generated Node #0,0,1: 73:[39, 85] Operation: 31+54=85 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[54, 70], Operations: ['38+16=54', '39+31=70'] Exploring Operation: 70-54=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 54+70=124, Resulting Numbers: [124] 124,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[39, 85], Operations: ['38+16=54', '31+54=85'] Exploring Operation: 39+85=124, Resulting Numbers: [124] 124,73 unequal: No Solution Exploring Operation: 85-39=46, Resulting Numbers: [46] 46,73 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: 73:[16, 39, 69], Operations: ['38+31=69'] Exploring Operation: 16+39=55, Resulting Numbers: [69, 55] Generated Node #0,1,0: 73:[69, 55] Operation: 16+39=55 Exploring Operation: 16+69=85, Resulting Numbers: [39, 85] Generated Node #0,1,1: 73:[39, 85] Operation: 16+69=85 Moving to Node #0,1,0 Current State: 73:[69, 55], Operations: ['38+31=69', '16+39=55'] Exploring Operation: 69-55=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 69+55=124, Resulting Numbers: [124] 124,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[39, 85], Operations: ['38+31=69', '16+69=85'] Exploring Operation: 85-39=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 39+85=124, Resulting Numbers: [124] 124,73 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 8, 78, 59, 64 ]
91
[ "8+78=86", "64-59=5", "86+5=91" ]
Current State: 91:[8, 78, 59, 64], Operations: [] Exploring Operation: 8+78=86, Resulting Numbers: [59, 64, 86] Generated Node #2: [59, 64, 86] from Operation: 8+78=86 Current State: 91:[59, 64, 86], Operations: ['8+78=86'] Exploring Operation: 64-59=5, Resulting Numbers: [86, 5] Generated Node #3: [86, 5] from Operation: 64-59=5 Current State: 91:[86, 5], Operations: ['8+78=86', '64-59=5'] Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[8, 78, 59, 64], Operations: [] Exploring Operation: 78-59=19, Resulting Numbers: [8, 64, 19] Generated Node #0,0: 91:[8, 64, 19] Operation: 78-59=19 Exploring Operation: 64/8=8, Resulting Numbers: [78, 59, 8] Generated Node #0,1: 91:[78, 59, 8] Operation: 64/8=8 Exploring Operation: 64-59=5, Resulting Numbers: [8, 78, 5] Generated Node #0,2: 91:[8, 78, 5] Operation: 64-59=5 Exploring Operation: 78-64=14, Resulting Numbers: [8, 59, 14] Generated Node #0,3: 91:[8, 59, 14] Operation: 78-64=14 Moving to Node #0,2 Current State: 91:[8, 78, 5], Operations: ['64-59=5'] Exploring Operation: 78+5=83, Resulting Numbers: [8, 83] Generated Node #0,2,0: 91:[8, 83] Operation: 78+5=83 Exploring Operation: 8+78=86, Resulting Numbers: [5, 86] Generated Node #0,2,1: 91:[5, 86] Operation: 8+78=86 Exploring Operation: 8+5=13, Resulting Numbers: [78, 13] Generated Node #0,2,2: 91:[78, 13] Operation: 8+5=13 Exploring Operation: 8-5=3, Resulting Numbers: [78, 3] Generated Node #0,2,3: 91:[78, 3] Operation: 8-5=3 Moving to Node #0,3 Current State: 91:[8, 59, 14], Operations: ['78-64=14'] Exploring Operation: 8+59=67, Resulting Numbers: [14, 67] Generated Node #0,3,0: 91:[14, 67] Operation: 8+59=67 Exploring Operation: 59-14=45, Resulting Numbers: [8, 45] Generated Node #0,3,1: 91:[8, 45] Operation: 59-14=45 Exploring Operation: 14-8=6, Resulting Numbers: [59, 6] Generated Node #0,3,2: 91:[59, 6] Operation: 14-8=6 Exploring Operation: 59+14=73, Resulting Numbers: [8, 73] Generated Node #0,3,3: 91:[8, 73] Operation: 59+14=73 Moving to Node #0,0 Current State: 91:[8, 64, 19], Operations: ['78-59=19'] Exploring Operation: 64/8=8, Resulting Numbers: [19, 8] Generated Node #0,0,0: 91:[19, 8] Operation: 64/8=8 Exploring Operation: 8+64=72, Resulting Numbers: [19, 72] Generated Node #0,0,1: 91:[19, 72] Operation: 8+64=72 Exploring Operation: 64+19=83, Resulting Numbers: [8, 83] Generated Node #0,0,2: 91:[8, 83] Operation: 64+19=83 Exploring Operation: 19-8=11, Resulting Numbers: [64, 11] Generated Node #0,0,3: 91:[64, 11] Operation: 19-8=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[19, 8], Operations: ['78-59=19', '64/8=8'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 91:[8, 83], Operations: ['78-59=19', '64+19=83'] Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,91 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[8, 78, 59, 64], Operations: [] Exploring Operation: 78-59=19, Resulting Numbers: [8, 64, 19] Generated Node #0,0: 91:[8, 64, 19] Operation: 78-59=19 Moving to Node #0,0 Current State: 91:[8, 64, 19], Operations: ['78-59=19'] Exploring Operation: 64+19=83, Resulting Numbers: [8, 83] Generated Node #0,0,2: 91:[8, 83] Operation: 64+19=83 Moving to Node #0,0,2 Current State: 91:[8, 83], Operations: ['78-59=19', '64+19=83'] Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_4
mult_heuristic
[ 16, 81, 85, 35 ]
99
[ "85-81=4", "16*4=64", "35+64=99" ]
Current State: 99:[16, 81, 85, 35], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [16, 35, 4] Generated Node #2: [16, 35, 4] from Operation: 85-81=4 Current State: 99:[16, 35, 4], Operations: ['85-81=4'] Exploring Operation: 16*4=64, Resulting Numbers: [35, 64] Generated Node #3: [35, 64] from Operation: 16*4=64 Current State: 99:[35, 64], Operations: ['85-81=4', '16*4=64'] Exploring Operation: 35+64=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[16, 81, 85, 35], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [16, 35, 4] Generated Node #0,0: 99:[16, 35, 4] Operation: 85-81=4 Moving to Node #0,0 Current State: 99:[16, 35, 4], Operations: ['85-81=4'] Exploring Operation: 16-4=12, Resulting Numbers: [35, 12] Generated Node #0,0,0: 99:[35, 12] Operation: 16-4=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[35, 12], Operations: ['85-81=4', '16-4=12'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 74, 19, 40, 74 ]
59
[ "74+19=93", "74-40=34", "93-34=59" ]
Current State: 59:[74, 19, 40, 74], Operations: [] Exploring Operation: 74+19=93, Resulting Numbers: [40, 93] Generated Node #2: [40, 93] from Operation: 74+19=93 Current State: 59:[40, 93], Operations: ['74+19=93'] Exploring Operation: 74-40=34, Resulting Numbers: [93, 34] Generated Node #3: [93, 34] from Operation: 74-40=34 Current State: 59:[93, 34], Operations: ['74+19=93', '74-40=34'] Exploring Operation: 93-34=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[74, 19, 40, 74], Operations: [] Exploring Operation: 19+40=59, Resulting Numbers: [74, 74, 59] Generated Node #0,0: 59:[74, 74, 59] Operation: 19+40=59 Moving to Node #0,0 Current State: 59:[74, 74, 59], Operations: ['19+40=59'] Exploring Operation: 74/74=1, Resulting Numbers: [59, 1] Generated Node #0,0,0: 59:[59, 1] Operation: 74/74=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[59, 1], Operations: ['19+40=59', '74/74=1'] Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[74, 19, 40, 74], Operations: [] Exploring Operation: 19+40=59, Resulting Numbers: [74, 74, 59] Generated Node #0,0: 59:[74, 74, 59] Operation: 19+40=59 Moving to Node #0,0 Current State: 59:[74, 74, 59], Operations: ['19+40=59'] Exploring Operation: 74/74=1, Resulting Numbers: [59, 1] Generated Node #0,0,0: 59:[59, 1] Operation: 74/74=1 Moving to Node #0,0,0 Current State: 59:[59, 1], Operations: ['19+40=59', '74/74=1'] Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 2, 48, 22, 92 ]
59
[ "48-22=26", "92+26=118", "118/2=59" ]
Current State: 59:[2, 48, 22, 92], Operations: [] Exploring Operation: 48-22=26, Resulting Numbers: [2, 92, 26] Generated Node #2: [2, 92, 26] from Operation: 48-22=26 Current State: 59:[2, 92, 26], Operations: ['48-22=26'] Exploring Operation: 92+26=118, Resulting Numbers: [2, 118] Generated Node #3: [2, 118] from Operation: 92+26=118 Current State: 59:[2, 118], Operations: ['48-22=26', '92+26=118'] Exploring Operation: 118/2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[2, 48, 22, 92], Operations: [] Exploring Operation: 2+22=24, Resulting Numbers: [48, 92, 24] Generated Node #0,0: 59:[48, 92, 24] Operation: 2+22=24 Exploring Operation: 2+48=50, Resulting Numbers: [22, 92, 50] Generated Node #0,1: 59:[22, 92, 50] Operation: 2+48=50 Exploring Operation: 92/2=46, Resulting Numbers: [48, 22, 46] Generated Node #0,2: 59:[48, 22, 46] Operation: 92/2=46 Exploring Operation: 2*22=44, Resulting Numbers: [48, 92, 44] Generated Node #0,3: 59:[48, 92, 44] Operation: 2*22=44 Moving to Node #0,3 Current State: 59:[48, 92, 44], Operations: ['2*22=44'] Exploring Operation: 92-44=48, Resulting Numbers: [48, 48] Generated Node #0,3,0: 59:[48, 48] Operation: 92-44=48 Exploring Operation: 48-44=4, Resulting Numbers: [92, 4] Generated Node #0,3,1: 59:[92, 4] Operation: 48-44=4 Exploring Operation: 92-48=44, Resulting Numbers: [44, 44] Generated Node #0,3,2: 59:[44, 44] Operation: 92-48=44 Exploring Operation: 48+44=92, Resulting Numbers: [92, 92] Generated Node #0,3,3: 59:[92, 92] Operation: 48+44=92 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[48, 48], Operations: ['2*22=44', '92-44=48'] Exploring Operation: 48-48=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 48+48=96, Resulting Numbers: [96] 96,59 unequal: No Solution Exploring Operation: 48/48=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 48*48=2304, Resulting Numbers: [2304] 2304,59 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 #0,3,2 Current State: 59:[44, 44], Operations: ['2*22=44', '92-48=44'] Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,59 unequal: No Solution Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,59 unequal: No Solution Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,59 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 #0,3,3 Current State: 59:[92, 92], Operations: ['2*22=44', '48+44=92'] Exploring Operation: 92*92=8464, Resulting Numbers: [8464] 8464,59 unequal: No Solution Exploring Operation: 92+92=184, Resulting Numbers: [184] 184,59 unequal: No Solution Exploring Operation: 92/92=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 92-92=0, Resulting Numbers: [0] 0,59 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 #0,3,1 Current State: 59:[92, 4], Operations: ['2*22=44', '48-44=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,59 unequal: No Solution Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,59 unequal: No Solution Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,59 unequal: No Solution Exploring Operation: 92*4=368, Resulting Numbers: [368] 368,59 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: 59:[48, 22, 46], Operations: ['92/2=46'] Exploring Operation: 46-22=24, Resulting Numbers: [48, 24] Generated Node #0,2,0: 59:[48, 24] Operation: 46-22=24 Exploring Operation: 22+46=68, Resulting Numbers: [48, 68] Generated Node #0,2,1: 59:[48, 68] Operation: 22+46=68 Exploring Operation: 48+22=70, Resulting Numbers: [46, 70] Generated Node #0,2,2: 59:[46, 70] Operation: 48+22=70 Exploring Operation: 48-22=26, Resulting Numbers: [46, 26] Generated Node #0,2,3: 59:[46, 26] Operation: 48-22=26 Moving to Node #0,1 Current State: 59:[22, 92, 50], Operations: ['2+48=50'] Exploring Operation: 92-22=70, Resulting Numbers: [50, 70] Generated Node #0,1,0: 59:[50, 70] Operation: 92-22=70 Exploring Operation: 22+92=114, Resulting Numbers: [50, 114] Generated Node #0,1,1: 59:[50, 114] Operation: 22+92=114 Exploring Operation: 22+50=72, Resulting Numbers: [92, 72] Generated Node #0,1,2: 59:[92, 72] Operation: 22+50=72 Exploring Operation: 92-50=42, Resulting Numbers: [22, 42] Generated Node #0,1,3: 59:[22, 42] Operation: 92-50=42 Moving to Node #0,0 Current State: 59:[48, 92, 24], Operations: ['2+22=24'] Exploring Operation: 48-24=24, Resulting Numbers: [92, 24] Generated Node #0,0,0: 59:[92, 24] Operation: 48-24=24 Exploring Operation: 48+24=72, Resulting Numbers: [92, 72] Generated Node #0,0,1: 59:[92, 72] Operation: 48+24=72 Exploring Operation: 92-24=68, Resulting Numbers: [48, 68] Generated Node #0,0,2: 59:[48, 68] Operation: 92-24=68 Exploring Operation: 92-48=44, Resulting Numbers: [24, 44] Generated Node #0,0,3: 59:[24, 44] Operation: 92-48=44 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[48, 68], Operations: ['2+22=24', '92-24=68'] Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 48+68=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 48*68=3264, Resulting Numbers: [3264] 3264,59 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 #0,0,1 Current State: 59:[92, 72], Operations: ['2+22=24', '48+24=72'] Exploring Operation: 92-72=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 92*72=6624, Resulting Numbers: [6624] 6624,59 unequal: No Solution Exploring Operation: 92+72=164, Resulting Numbers: [164] 164,59 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 #0,0,3 Current State: 59:[24, 44], Operations: ['2+22=24', '92-48=44'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,59 unequal: No Solution Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,59 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 #0,0,0 Current State: 59:[92, 24], Operations: ['2+22=24', '48-24=24'] Exploring Operation: 92+24=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,59 unequal: No Solution Exploring Operation: 92*24=2208, Resulting Numbers: [2208] 2208,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 59:[48, 68], Operations: ['92/2=46', '22+46=68'] Exploring Operation: 48*68=3264, Resulting Numbers: [3264] 3264,59 unequal: No Solution Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 48+68=116, Resulting Numbers: [116] 116,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[50, 70], Operations: ['2+48=50', '92-22=70'] Exploring Operation: 70-50=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 50+70=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 50*70=3500, Resulting Numbers: [3500] 3500,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[46, 70], Operations: ['92/2=46', '48+22=70'] Exploring Operation: 46+70=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 46*70=3220, Resulting Numbers: [3220] 3220,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[48, 24], Operations: ['92/2=46', '46-22=24'] Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,59 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[92, 72], Operations: ['2+48=50', '22+50=72'] Exploring Operation: 92+72=164, Resulting Numbers: [164] 164,59 unequal: No Solution Exploring Operation: 92*72=6624, Resulting Numbers: [6624] 6624,59 unequal: No Solution Exploring Operation: 92-72=20, Resulting Numbers: [20] 20,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[46, 26], Operations: ['92/2=46', '48-22=26'] Exploring Operation: 46*26=1196, Resulting Numbers: [1196] 1196,59 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 46+26=72, Resulting Numbers: [72] 72,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[22, 42], Operations: ['2+48=50', '92-50=42'] Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 22*42=924, Resulting Numbers: [924] 924,59 unequal: No Solution Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[50, 114], Operations: ['2+48=50', '22+92=114'] Exploring Operation: 114-50=64, Resulting Numbers: [64] 64,59 unequal: No Solution Exploring Operation: 50+114=164, Resulting Numbers: [164] 164,59 unequal: No Solution Exploring Operation: 50*114=5700, Resulting Numbers: [5700] 5700,59 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 78, 34, 73, 97 ]
68
[ "78-34=44", "97-73=24", "44+24=68" ]
Current State: 68:[78, 34, 73, 97], Operations: [] Exploring Operation: 78-34=44, Resulting Numbers: [73, 97, 44] Generated Node #2: [73, 97, 44] from Operation: 78-34=44 Current State: 68:[73, 97, 44], Operations: ['78-34=44'] Exploring Operation: 97-73=24, Resulting Numbers: [44, 24] Generated Node #3: [44, 24] from Operation: 97-73=24 Current State: 68:[44, 24], Operations: ['78-34=44', '97-73=24'] Exploring Operation: 44+24=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[78, 34, 73, 97], Operations: [] Exploring Operation: 97-78=19, Resulting Numbers: [34, 73, 19] Generated Node #0,0: 68:[34, 73, 19] Operation: 97-78=19 Exploring Operation: 97-73=24, Resulting Numbers: [78, 34, 24] Generated Node #0,1: 68:[78, 34, 24] Operation: 97-73=24 Moving to Node #0,0 Current State: 68:[34, 73, 19], Operations: ['97-78=19'] Exploring Operation: 73-34=39, Resulting Numbers: [19, 39] Generated Node #0,0,0: 68:[19, 39] Operation: 73-34=39 Exploring Operation: 34-19=15, Resulting Numbers: [73, 15] Generated Node #0,0,1: 68:[73, 15] Operation: 34-19=15 Moving to Node #0,1 Current State: 68:[78, 34, 24], Operations: ['97-73=24'] Exploring Operation: 34-24=10, Resulting Numbers: [78, 10] Generated Node #0,1,0: 68:[78, 10] Operation: 34-24=10 Exploring Operation: 78-24=54, Resulting Numbers: [34, 54] Generated Node #0,1,1: 68:[34, 54] Operation: 78-24=54 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[34, 54], Operations: ['97-73=24', '78-24=54'] Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 34+54=88, Resulting Numbers: [88] 88,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[78, 10], Operations: ['97-73=24', '34-24=10'] Exploring Operation: 78+10=88, Resulting Numbers: [88] 88,68 unequal: No Solution Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[78, 34, 73, 97], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [78, 34, 24] Generated Node #0,1: 68:[78, 34, 24] Operation: 97-73=24 Moving to Node #0,1 Current State: 68:[78, 34, 24], Operations: ['97-73=24'] Exploring Operation: 34-24=10, Resulting Numbers: [78, 10] Generated Node #0,1,0: 68:[78, 10] Operation: 34-24=10 Moving to Node #0,1,0 Current State: 68:[78, 10], Operations: ['97-73=24', '34-24=10'] Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
sum_heuristic
[ 6, 46, 74, 78 ]
70
[ "78-74=4", "6*4=24", "46+24=70" ]
Current State: 70:[6, 46, 74, 78], Operations: [] Exploring Operation: 78-74=4, Resulting Numbers: [6, 46, 4] Generated Node #2: [6, 46, 4] from Operation: 78-74=4 Current State: 70:[6, 46, 4], Operations: ['78-74=4'] Exploring Operation: 6*4=24, Resulting Numbers: [46, 24] Generated Node #3: [46, 24] from Operation: 6*4=24 Current State: 70:[46, 24], Operations: ['78-74=4', '6*4=24'] Exploring Operation: 46+24=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[6, 46, 74, 78], Operations: [] Exploring Operation: 78-74=4, Resulting Numbers: [6, 46, 4] Generated Node #0,0: 70:[6, 46, 4] Operation: 78-74=4 Exploring Operation: 78-46=32, Resulting Numbers: [6, 74, 32] Generated Node #0,1: 70:[6, 74, 32] Operation: 78-46=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[6, 74, 32], Operations: ['78-46=32'] Exploring Operation: 74-6=68, Resulting Numbers: [32, 68] Generated Node #0,1,0: 70:[32, 68] Operation: 74-6=68 Exploring Operation: 6+32=38, Resulting Numbers: [74, 38] Generated Node #0,1,1: 70:[74, 38] Operation: 6+32=38 Moving to Node #0,1,0 Current State: 70:[32, 68], Operations: ['78-46=32', '74-6=68'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,70 unequal: No Solution Exploring Operation: 32+68=100, Resulting Numbers: [100] 100,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[74, 38], Operations: ['78-46=32', '6+32=38'] Exploring Operation: 74-38=36, Resulting Numbers: [36] 36,70 unequal: No Solution Exploring Operation: 74+38=112, Resulting Numbers: [112] 112,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[6, 46, 4], Operations: ['78-74=4'] Exploring Operation: 46-4=42, Resulting Numbers: [6, 42] Generated Node #0,0,0: 70:[6, 42] Operation: 46-4=42 Exploring Operation: 46-6=40, Resulting Numbers: [4, 40] Generated Node #0,0,1: 70:[4, 40] Operation: 46-6=40 Moving to Node #0,0,1 Current State: 70:[4, 40], Operations: ['78-74=4', '46-6=40'] Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,70 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[6, 42], Operations: ['78-74=4', '46-4=42'] Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 62, 47, 54, 21 ]
48
[ "62-47=15", "54-21=33", "15+33=48" ]
Current State: 48:[62, 47, 54, 21], Operations: [] Exploring Operation: 62-47=15, Resulting Numbers: [54, 21, 15] Generated Node #2: [54, 21, 15] from Operation: 62-47=15 Current State: 48:[54, 21, 15], Operations: ['62-47=15'] Exploring Operation: 54-21=33, Resulting Numbers: [15, 33] Generated Node #3: [15, 33] from Operation: 54-21=33 Current State: 48:[15, 33], Operations: ['62-47=15', '54-21=33'] Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[62, 47, 54, 21], Operations: [] Exploring Operation: 62-47=15, Resulting Numbers: [54, 21, 15] Generated Node #0,0: 48:[54, 21, 15] Operation: 62-47=15 Exploring Operation: 62-21=41, Resulting Numbers: [47, 54, 41] Generated Node #0,1: 48:[47, 54, 41] Operation: 62-21=41 Exploring Operation: 62-54=8, Resulting Numbers: [47, 21, 8] Generated Node #0,2: 48:[47, 21, 8] Operation: 62-54=8 Moving to Node #0,2 Current State: 48:[47, 21, 8], Operations: ['62-54=8'] Exploring Operation: 21+8=29, Resulting Numbers: [47, 29] Generated Node #0,2,0: 48:[47, 29] Operation: 21+8=29 Exploring Operation: 47-21=26, Resulting Numbers: [8, 26] Generated Node #0,2,1: 48:[8, 26] Operation: 47-21=26 Exploring Operation: 21-8=13, Resulting Numbers: [47, 13] Generated Node #0,2,2: 48:[47, 13] Operation: 21-8=13 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[8, 26], Operations: ['62-54=8', '47-21=26'] Exploring Operation: 8+26=34, Resulting Numbers: [34] 34,48 unequal: No Solution Exploring Operation: 8*26=208, Resulting Numbers: [208] 208,48 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[47, 13], Operations: ['62-54=8', '21-8=13'] Exploring Operation: 47*13=611, Resulting Numbers: [611] 611,48 unequal: No Solution Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[47, 29], Operations: ['62-54=8', '21+8=29'] Exploring Operation: 47*29=1363, Resulting Numbers: [1363] 1363,48 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 47+29=76, Resulting Numbers: [76] 76,48 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: 48:[54, 21, 15], Operations: ['62-47=15'] Exploring Operation: 54-21=33, Resulting Numbers: [15, 33] Generated Node #0,0,0: 48:[15, 33] Operation: 54-21=33 Exploring Operation: 21-15=6, Resulting Numbers: [54, 6] Generated Node #0,0,1: 48:[54, 6] Operation: 21-15=6 Exploring Operation: 54-15=39, Resulting Numbers: [21, 39] Generated Node #0,0,2: 48:[21, 39] Operation: 54-15=39 Moving to Node #0,1 Current State: 48:[47, 54, 41], Operations: ['62-21=41'] Exploring Operation: 54-47=7, Resulting Numbers: [41, 7] Generated Node #0,1,0: 48:[41, 7] Operation: 54-47=7 Exploring Operation: 54-41=13, Resulting Numbers: [47, 13] Generated Node #0,1,1: 48:[47, 13] Operation: 54-41=13 Exploring Operation: 47-41=6, Resulting Numbers: [54, 6] Generated Node #0,1,2: 48:[54, 6] Operation: 47-41=6 Moving to Node #0,1,1 Current State: 48:[47, 13], Operations: ['62-21=41', '54-41=13'] Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,48 unequal: No Solution Exploring Operation: 47*13=611, Resulting Numbers: [611] 611,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[54, 6], Operations: ['62-47=15', '21-15=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,48 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[62, 47, 54, 21], Operations: [] Exploring Operation: 62-47=15, Resulting Numbers: [54, 21, 15] Generated Node #0,0: 48:[54, 21, 15] Operation: 62-47=15 Moving to Node #0,0 Current State: 48:[54, 21, 15], Operations: ['62-47=15'] Exploring Operation: 21-15=6, Resulting Numbers: [54, 6] Generated Node #0,0,1: 48:[54, 6] Operation: 21-15=6 Moving to Node #0,0,1 Current State: 48:[54, 6], Operations: ['62-47=15', '21-15=6'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.97309
hs_3
mult_heuristic
[ 6, 5, 83, 6 ]
76
[ "6-5=1", "83-6=77", "77-1=76" ]
Current State: 76:[6, 5, 83, 6], Operations: [] Exploring Operation: 6-5=1, Resulting Numbers: [83, 1] Generated Node #2: [83, 1] from Operation: 6-5=1 Current State: 76:[83, 1], Operations: ['6-5=1'] Exploring Operation: 83-6=77, Resulting Numbers: [1, 77] Generated Node #3: [1, 77] from Operation: 83-6=77 Current State: 76:[1, 77], Operations: ['6-5=1', '83-6=77'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[6, 5, 83, 6], Operations: [] Exploring Operation: 83-6=77, Resulting Numbers: [5, 6, 77] Generated Node #0,0: 76:[5, 6, 77] Operation: 83-6=77 Moving to Node #0,0 Current State: 76:[5, 6, 77], Operations: ['83-6=77'] Exploring Operation: 6-5=1, Resulting Numbers: [77, 1] Generated Node #0,0,0: 76:[77, 1] Operation: 6-5=1 Moving to Node #0,0,0 Current State: 76:[77, 1], Operations: ['83-6=77', '6-5=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[6, 5, 83, 6], Operations: [] Exploring Operation: 83-6=77, Resulting Numbers: [5, 6, 77] Generated Node #0,0: 76:[5, 6, 77] Operation: 83-6=77 Moving to Node #0,0 Current State: 76:[5, 6, 77], Operations: ['83-6=77'] Exploring Operation: 6-5=1, Resulting Numbers: [77, 1] Generated Node #0,0,0: 76:[77, 1] Operation: 6-5=1 Moving to Node #0,0,0 Current State: 76:[77, 1], Operations: ['83-6=77', '6-5=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 47, 32, 69, 9 ]
75
[ "47-32=15", "69-9=60", "15+60=75" ]
Current State: 75:[47, 32, 69, 9], Operations: [] Exploring Operation: 47-32=15, Resulting Numbers: [69, 9, 15] Generated Node #2: [69, 9, 15] from Operation: 47-32=15 Current State: 75:[69, 9, 15], Operations: ['47-32=15'] Exploring Operation: 69-9=60, Resulting Numbers: [15, 60] Generated Node #3: [15, 60] from Operation: 69-9=60 Current State: 75:[15, 60], Operations: ['47-32=15', '69-9=60'] Exploring Operation: 15+60=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[47, 32, 69, 9], Operations: [] Exploring Operation: 47+32=79, Resulting Numbers: [69, 9, 79] Generated Node #0,0: 75:[69, 9, 79] Operation: 47+32=79 Exploring Operation: 47-32=15, Resulting Numbers: [69, 9, 15] Generated Node #0,1: 75:[69, 9, 15] Operation: 47-32=15 Exploring Operation: 69-47=22, Resulting Numbers: [32, 9, 22] Generated Node #0,2: 75:[32, 9, 22] Operation: 69-47=22 Moving to Node #0,1 Current State: 75:[69, 9, 15], Operations: ['47-32=15'] Exploring Operation: 69+9=78, Resulting Numbers: [15, 78] Generated Node #0,1,0: 75:[15, 78] Operation: 69+9=78 Exploring Operation: 15-9=6, Resulting Numbers: [69, 6] Generated Node #0,1,1: 75:[69, 6] Operation: 15-9=6 Exploring Operation: 9+15=24, Resulting Numbers: [69, 24] Generated Node #0,1,2: 75:[69, 24] Operation: 9+15=24 Moving to Node #0,0 Current State: 75:[69, 9, 79], Operations: ['47+32=79'] Exploring Operation: 79-9=70, Resulting Numbers: [69, 70] Generated Node #0,0,0: 75:[69, 70] Operation: 79-9=70 Exploring Operation: 79-69=10, Resulting Numbers: [9, 10] Generated Node #0,0,1: 75:[9, 10] Operation: 79-69=10 Exploring Operation: 69+9=78, Resulting Numbers: [79, 78] Generated Node #0,0,2: 75:[79, 78] Operation: 69+9=78 Moving to Node #0,2 Current State: 75:[32, 9, 22], Operations: ['69-47=22'] Exploring Operation: 22-9=13, Resulting Numbers: [32, 13] Generated Node #0,2,0: 75:[32, 13] Operation: 22-9=13 Exploring Operation: 32-9=23, Resulting Numbers: [22, 23] Generated Node #0,2,1: 75:[22, 23] Operation: 32-9=23 Exploring Operation: 32-22=10, Resulting Numbers: [9, 10] Generated Node #0,2,2: 75:[9, 10] Operation: 32-22=10 Moving to Node #0,1,0 Current State: 75:[15, 78], Operations: ['47-32=15', '69+9=78'] Exploring Operation: 15+78=93, Resulting Numbers: [93] 93,75 unequal: No Solution Exploring Operation: 15*78=1170, Resulting Numbers: [1170] 1170,75 unequal: No Solution Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[22, 23], Operations: ['69-47=22', '32-9=23'] Exploring Operation: 22*23=506, Resulting Numbers: [506] 506,75 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[69, 24], Operations: ['47-32=15', '9+15=24'] Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,75 unequal: No Solution Exploring Operation: 69*24=1656, Resulting Numbers: [1656] 1656,75 unequal: No Solution Exploring Operation: 69+24=93, Resulting Numbers: [93] 93,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[69, 6], Operations: ['47-32=15', '15-9=6'] Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[47, 32, 69, 9], Operations: [] Exploring Operation: 47-32=15, Resulting Numbers: [69, 9, 15] Generated Node #0,1: 75:[69, 9, 15] Operation: 47-32=15 Moving to Node #0,1 Current State: 75:[69, 9, 15], Operations: ['47-32=15'] Exploring Operation: 15-9=6, Resulting Numbers: [69, 6] Generated Node #0,1,1: 75:[69, 6] Operation: 15-9=6 Moving to Node #0,1,1 Current State: 75:[69, 6], Operations: ['47-32=15', '15-9=6'] Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.977431
hs_3
mult_heuristic