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
[ 55, 47, 15, 61 ]
43
[ "61-55=6", "15*6=90", "90-47=43" ]
Current State: 43:[55, 47, 15, 61], Operations: [] Exploring Operation: 61-55=6, Resulting Numbers: [47, 15, 6] Generated Node #2: [47, 15, 6] from Operation: 61-55=6 Current State: 43:[47, 15, 6], Operations: ['61-55=6'] Exploring Operation: 15*6=90, Resulting Numbers: [47, 90] Generated Node #3: [47, 90] from Operation: 15*6=90 Current State: 43:[47, 90], Operations: ['61-55=6', '15*6=90'] Exploring Operation: 90-47=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[55, 47, 15, 61], Operations: [] Exploring Operation: 55-15=40, Resulting Numbers: [47, 61, 40] Generated Node #0,0: 43:[47, 61, 40] Operation: 55-15=40 Exploring Operation: 47+15=62, Resulting Numbers: [55, 61, 62] Generated Node #0,1: 43:[55, 61, 62] Operation: 47+15=62 Exploring Operation: 47-15=32, Resulting Numbers: [55, 61, 32] Generated Node #0,2: 43:[55, 61, 32] Operation: 47-15=32 Exploring Operation: 61-15=46, Resulting Numbers: [55, 47, 46] Generated Node #0,3: 43:[55, 47, 46] Operation: 61-15=46 Exploring Operation: 55+15=70, Resulting Numbers: [47, 61, 70] Generated Node #0,4: 43:[47, 61, 70] Operation: 55+15=70 Moving to Node #0,3 Current State: 43:[55, 47, 46], Operations: ['61-15=46'] Exploring Operation: 55-47=8, Resulting Numbers: [46, 8] Generated Node #0,3,0: 43:[46, 8] Operation: 55-47=8 Exploring Operation: 47-46=1, Resulting Numbers: [55, 1] Generated Node #0,3,1: 43:[55, 1] Operation: 47-46=1 Exploring Operation: 55-46=9, Resulting Numbers: [47, 9] Generated Node #0,3,2: 43:[47, 9] Operation: 55-46=9 Exploring Operation: 55+47=102, Resulting Numbers: [46, 102] Generated Node #0,3,3: 43:[46, 102] Operation: 55+47=102 Exploring Operation: 55+46=101, Resulting Numbers: [47, 101] Generated Node #0,3,4: 43:[47, 101] Operation: 55+46=101 Moving to Node #0,0 Current State: 43:[47, 61, 40], Operations: ['55-15=40'] Exploring Operation: 61+40=101, Resulting Numbers: [47, 101] Generated Node #0,0,0: 43:[47, 101] Operation: 61+40=101 Exploring Operation: 47+40=87, Resulting Numbers: [61, 87] Generated Node #0,0,1: 43:[61, 87] Operation: 47+40=87 Exploring Operation: 61-40=21, Resulting Numbers: [47, 21] Generated Node #0,0,2: 43:[47, 21] Operation: 61-40=21 Exploring Operation: 47-40=7, Resulting Numbers: [61, 7] Generated Node #0,0,3: 43:[61, 7] Operation: 47-40=7 Exploring Operation: 61-47=14, Resulting Numbers: [40, 14] Generated Node #0,0,4: 43:[40, 14] Operation: 61-47=14 Moving to Node #0,2 Current State: 43:[55, 61, 32], Operations: ['47-15=32'] Exploring Operation: 61-55=6, Resulting Numbers: [32, 6] Generated Node #0,2,0: 43:[32, 6] Operation: 61-55=6 Exploring Operation: 55-32=23, Resulting Numbers: [61, 23] Generated Node #0,2,1: 43:[61, 23] Operation: 55-32=23 Exploring Operation: 55+32=87, Resulting Numbers: [61, 87] Generated Node #0,2,2: 43:[61, 87] Operation: 55+32=87 Exploring Operation: 61-32=29, Resulting Numbers: [55, 29] Generated Node #0,2,3: 43:[55, 29] Operation: 61-32=29 Exploring Operation: 61+32=93, Resulting Numbers: [55, 93] Generated Node #0,2,4: 43:[55, 93] Operation: 61+32=93 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 43:[55, 29], Operations: ['47-15=32', '61-32=29'] Exploring Operation: 55*29=1595, Resulting Numbers: [1595] 1595,43 unequal: No Solution Exploring Operation: 55+29=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 43:[61, 23], Operations: ['47-15=32', '55-32=23'] Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 61+23=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 61*23=1403, Resulting Numbers: [1403] 1403,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 43:[32, 6], Operations: ['47-15=32', '61-55=6'] Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,43 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,43 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 43:[61, 87], Operations: ['47-15=32', '55+32=87'] Exploring Operation: 61*87=5307, Resulting Numbers: [5307] 5307,43 unequal: No Solution Exploring Operation: 87-61=26, Resulting Numbers: [26] 26,43 unequal: No Solution Exploring Operation: 61+87=148, Resulting Numbers: [148] 148,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 43:[55, 93], Operations: ['47-15=32', '61+32=93'] Exploring Operation: 55+93=148, Resulting Numbers: [148] 148,43 unequal: No Solution Exploring Operation: 55*93=5115, Resulting Numbers: [5115] 5115,43 unequal: No Solution Exploring Operation: 93-55=38, Resulting Numbers: [38] 38,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 43:[55, 61, 62], Operations: ['47+15=62'] Exploring Operation: 61-55=6, Resulting Numbers: [62, 6] Generated Node #0,1,0: 43:[62, 6] Operation: 61-55=6 Exploring Operation: 55+61=116, Resulting Numbers: [62, 116] Generated Node #0,1,1: 43:[62, 116] Operation: 55+61=116 Exploring Operation: 62-55=7, Resulting Numbers: [61, 7] Generated Node #0,1,2: 43:[61, 7] Operation: 62-55=7 Exploring Operation: 55+62=117, Resulting Numbers: [61, 117] Generated Node #0,1,3: 43:[61, 117] Operation: 55+62=117 Exploring Operation: 62-61=1, Resulting Numbers: [55, 1] Generated Node #0,1,4: 43:[55, 1] Operation: 62-61=1 Moving to Node #0,4 Current State: 43:[47, 61, 70], Operations: ['55+15=70'] Exploring Operation: 47+61=108, Resulting Numbers: [70, 108] Generated Node #0,4,0: 43:[70, 108] Operation: 47+61=108 Exploring Operation: 70-47=23, Resulting Numbers: [61, 23] Generated Node #0,4,1: 43:[61, 23] Operation: 70-47=23 Exploring Operation: 47+70=117, Resulting Numbers: [61, 117] Generated Node #0,4,2: 43:[61, 117] Operation: 47+70=117 Exploring Operation: 61-47=14, Resulting Numbers: [70, 14] Generated Node #0,4,3: 43:[70, 14] Operation: 61-47=14 Exploring Operation: 70-61=9, Resulting Numbers: [47, 9] Generated Node #0,4,4: 43:[47, 9] Operation: 70-61=9 Moving to Node #0,0,2 Current State: 43:[47, 21], Operations: ['55-15=40', '61-40=21'] Exploring Operation: 47*21=987, Resulting Numbers: [987] 987,43 unequal: No Solution Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,43 unequal: No Solution Exploring Operation: 47+21=68, Resulting Numbers: [68] 68,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[40, 14], Operations: ['55-15=40', '61-47=14'] Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,43 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,43 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,43 unequal: No Solution Moving to Node #0,3,0 Current State: 43:[46, 8], Operations: ['61-15=46', '55-47=8'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,43 unequal: No Solution Moving to Node #0,3,2 Current State: 43:[47, 9], Operations: ['61-15=46', '55-46=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 47*9=423, Resulting Numbers: [423] 423,43 unequal: No Solution Moving to Node #0,4,1 Current State: 43:[61, 23], Operations: ['55+15=70', '70-47=23'] Exploring Operation: 61*23=1403, Resulting Numbers: [1403] 1403,43 unequal: No Solution Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 61+23=84, Resulting Numbers: [84] 84,43 unequal: No Solution Moving to Node #0,4,4 Current State: 43:[47, 9], Operations: ['55+15=70', '70-61=9'] Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 47*9=423, Resulting Numbers: [423] 423,43 unequal: No Solution Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,43 unequal: No Solution Moving to Node #0,3,1 Current State: 43:[55, 1], Operations: ['61-15=46', '47-46=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,43 unequal: No Solution Moving to Node #0,1,4 Current State: 43:[55, 1], Operations: ['47+15=62', '62-61=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[61, 7], Operations: ['47+15=62', '62-55=7'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 61*7=427, Resulting Numbers: [427] 427,43 unequal: No Solution Exploring Operation: 61+7=68, Resulting Numbers: [68] 68,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[61, 7], Operations: ['55-15=40', '47-40=7'] Exploring Operation: 61*7=427, Resulting Numbers: [427] 427,43 unequal: No Solution Exploring Operation: 61+7=68, Resulting Numbers: [68] 68,43 unequal: No Solution Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[62, 6], Operations: ['47+15=62', '61-55=6'] Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,43 unequal: No Solution Exploring Operation: 62*6=372, Resulting Numbers: [372] 372,43 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,43 unequal: No Solution Moving to Node #0,4,3 Current State: 43:[70, 14], Operations: ['55+15=70', '61-47=14'] Exploring Operation: 70-14=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 70*14=980, Resulting Numbers: [980] 980,43 unequal: No Solution Exploring Operation: 70/14=5, Resulting Numbers: [5] 5,43 unequal: No Solution Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[47, 101], Operations: ['55-15=40', '61+40=101'] Exploring Operation: 47*101=4747, Resulting Numbers: [4747] 4747,43 unequal: No Solution Exploring Operation: 47+101=148, Resulting Numbers: [148] 148,43 unequal: No Solution Exploring Operation: 101-47=54, Resulting Numbers: [54] 54,43 unequal: No Solution Moving to Node #0,3,4 Current State: 43:[47, 101], Operations: ['61-15=46', '55+46=101'] Exploring Operation: 101-47=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 47+101=148, Resulting Numbers: [148] 148,43 unequal: No Solution Exploring Operation: 47*101=4747, Resulting Numbers: [4747] 4747,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[61, 87], Operations: ['55-15=40', '47+40=87'] Exploring Operation: 61*87=5307, Resulting Numbers: [5307] 5307,43 unequal: No Solution Exploring Operation: 61+87=148, Resulting Numbers: [148] 148,43 unequal: No Solution Exploring Operation: 87-61=26, Resulting Numbers: [26] 26,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[46, 102], Operations: ['61-15=46', '55+47=102'] Exploring Operation: 46*102=4692, Resulting Numbers: [4692] 4692,43 unequal: No Solution Exploring Operation: 46+102=148, Resulting Numbers: [148] 148,43 unequal: No Solution Exploring Operation: 102-46=56, Resulting Numbers: [56] 56,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[61, 117], Operations: ['47+15=62', '55+62=117'] Exploring Operation: 61*117=7137, Resulting Numbers: [7137] 7137,43 unequal: No Solution Exploring Operation: 117-61=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 61+117=178, Resulting Numbers: [178] 178,43 unequal: No Solution Moving to Node #0,4,2 Current State: 43:[61, 117], Operations: ['55+15=70', '47+70=117'] Exploring Operation: 61*117=7137, Resulting Numbers: [7137] 7137,43 unequal: No Solution Exploring Operation: 61+117=178, Resulting Numbers: [178] 178,43 unequal: No Solution Exploring Operation: 117-61=56, Resulting Numbers: [56] 56,43 unequal: No Solution Moving to Node #0,4,0 Current State: 43:[70, 108], Operations: ['55+15=70', '47+61=108'] Exploring Operation: 70*108=7560, Resulting Numbers: [7560] 7560,43 unequal: No Solution Exploring Operation: 70+108=178, Resulting Numbers: [178] 178,43 unequal: No Solution Exploring Operation: 108-70=38, Resulting Numbers: [38] 38,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[62, 116], Operations: ['47+15=62', '55+61=116'] Exploring Operation: 116-62=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 62*116=7192, Resulting Numbers: [7192] 7192,43 unequal: No Solution Exploring Operation: 62+116=178, Resulting Numbers: [178] 178,43 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 9, 2, 28, 71 ]
92
[ "9-2=7", "28+71=99", "99-7=92" ]
Current State: 92:[9, 2, 28, 71], Operations: [] Exploring Operation: 9-2=7, Resulting Numbers: [28, 71, 7] Generated Node #2: [28, 71, 7] from Operation: 9-2=7 Current State: 92:[28, 71, 7], Operations: ['9-2=7'] Exploring Operation: 28+71=99, Resulting Numbers: [7, 99] Generated Node #3: [7, 99] from Operation: 28+71=99 Current State: 92:[7, 99], Operations: ['9-2=7', '28+71=99'] Exploring Operation: 99-7=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[9, 2, 28, 71], Operations: [] Exploring Operation: 9+71=80, Resulting Numbers: [2, 28, 80] Generated Node #0,0: 92:[2, 28, 80] Operation: 9+71=80 Exploring Operation: 71-9=62, Resulting Numbers: [2, 28, 62] Generated Node #0,1: 92:[2, 28, 62] Operation: 71-9=62 Exploring Operation: 71-28=43, Resulting Numbers: [9, 2, 43] Generated Node #0,2: 92:[9, 2, 43] Operation: 71-28=43 Exploring Operation: 28+71=99, Resulting Numbers: [9, 2, 99] Generated Node #0,3: 92:[9, 2, 99] Operation: 28+71=99 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[9, 2, 43], Operations: ['71-28=43'] Exploring Operation: 9*2=18, Resulting Numbers: [43, 18] Generated Node #0,2,0: 92:[43, 18] Operation: 9*2=18 Exploring Operation: 9-2=7, Resulting Numbers: [43, 7] Generated Node #0,2,1: 92:[43, 7] Operation: 9-2=7 Exploring Operation: 9+43=52, Resulting Numbers: [2, 52] Generated Node #0,2,2: 92:[2, 52] Operation: 9+43=52 Exploring Operation: 2+43=45, Resulting Numbers: [9, 45] Generated Node #0,2,3: 92:[9, 45] Operation: 2+43=45 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 92:[43, 7], Operations: ['71-28=43', '9-2=7'] Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,92 unequal: No Solution Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,92 unequal: No Solution Exploring Operation: 43*7=301, Resulting Numbers: [301] 301,92 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 #0,2,2 Current State: 92:[2, 52], Operations: ['71-28=43', '9+43=52'] Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,92 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,92 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,92 unequal: No Solution Exploring Operation: 2*52=104, Resulting Numbers: [104] 104,92 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 #0,2,3 Current State: 92:[9, 45], Operations: ['71-28=43', '2+43=45'] Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,92 unequal: No Solution Exploring Operation: 9*45=405, Resulting Numbers: [405] 405,92 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,92 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,92 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 #0,2,0 Current State: 92:[43, 18], Operations: ['71-28=43', '9*2=18'] Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,92 unequal: No Solution Exploring Operation: 43*18=774, Resulting Numbers: [774] 774,92 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 #0,3 Current State: 92:[9, 2, 99], Operations: ['28+71=99'] Exploring Operation: 99-9=90, Resulting Numbers: [2, 90] Generated Node #0,3,0: 92:[2, 90] Operation: 99-9=90 Exploring Operation: 9-2=7, Resulting Numbers: [99, 7] Generated Node #0,3,1: 92:[99, 7] Operation: 9-2=7 Exploring Operation: 99/9=11, Resulting Numbers: [2, 11] Generated Node #0,3,2: 92:[2, 11] Operation: 99/9=11 Exploring Operation: 99-2=97, Resulting Numbers: [9, 97] Generated Node #0,3,3: 92:[9, 97] Operation: 99-2=97 Moving to Node #0,3,0 Current State: 92:[2, 90], Operations: ['28+71=99', '99-9=90'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,92 unequal: No Solution Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[9, 2, 28, 71], Operations: [] Exploring Operation: 28+71=99, Resulting Numbers: [9, 2, 99] Generated Node #0,3: 92:[9, 2, 99] Operation: 28+71=99 Moving to Node #0,3 Current State: 92:[9, 2, 99], Operations: ['28+71=99'] Exploring Operation: 99-9=90, Resulting Numbers: [2, 90] Generated Node #0,3,0: 92:[2, 90] Operation: 99-9=90 Moving to Node #0,3,0 Current State: 92:[2, 90], Operations: ['28+71=99', '99-9=90'] Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 3, 59, 42, 93 ]
70
[ "93/3=31", "59+42=101", "101-31=70" ]
Current State: 70:[3, 59, 42, 93], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [59, 42, 31] Generated Node #2: [59, 42, 31] from Operation: 93/3=31 Current State: 70:[59, 42, 31], Operations: ['93/3=31'] Exploring Operation: 59+42=101, Resulting Numbers: [31, 101] Generated Node #3: [31, 101] from Operation: 59+42=101 Current State: 70:[31, 101], Operations: ['93/3=31', '59+42=101'] Exploring Operation: 101-31=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[3, 59, 42, 93], Operations: [] Exploring Operation: 93-59=34, Resulting Numbers: [3, 42, 34] Generated Node #0,0: 70:[3, 42, 34] Operation: 93-59=34 Exploring Operation: 93/3=31, Resulting Numbers: [59, 42, 31] Generated Node #0,1: 70:[59, 42, 31] Operation: 93/3=31 Moving to Node #0,0 Current State: 70:[3, 42, 34], Operations: ['93-59=34'] Exploring Operation: 42/3=14, Resulting Numbers: [34, 14] Generated Node #0,0,0: 70:[34, 14] Operation: 42/3=14 Exploring Operation: 42-34=8, Resulting Numbers: [3, 8] Generated Node #0,0,1: 70:[3, 8] Operation: 42-34=8 Moving to Node #0,1 Current State: 70:[59, 42, 31], Operations: ['93/3=31'] Exploring Operation: 59-42=17, Resulting Numbers: [31, 17] Generated Node #0,1,0: 70:[31, 17] Operation: 59-42=17 Exploring Operation: 42-31=11, Resulting Numbers: [59, 11] Generated Node #0,1,1: 70:[59, 11] Operation: 42-31=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 70:[31, 17], Operations: ['93/3=31', '59-42=17'] Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 31+17=48, Resulting Numbers: [48] 48,70 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 #0,1,1 Current State: 70:[59, 11], Operations: ['93/3=31', '42-31=11'] Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,70 unequal: No Solution Exploring Operation: 59+11=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[3, 59, 42, 93], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [59, 42, 31] Generated Node #0,1: 70:[59, 42, 31] Operation: 93/3=31 Moving to Node #0,1 Current State: 70:[59, 42, 31], Operations: ['93/3=31'] Exploring Operation: 42-31=11, Resulting Numbers: [59, 11] Generated Node #0,1,1: 70:[59, 11] Operation: 42-31=11 Moving to Node #0,1,1 Current State: 70:[59, 11], Operations: ['93/3=31', '42-31=11'] Exploring Operation: 59+11=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
sum_heuristic
[ 33, 30, 36, 58 ]
29
[ "33*58=1914", "30+36=66", "1914/66=29" ]
Current State: 29:[33, 30, 36, 58], Operations: [] Exploring Operation: 33*58=1914, Resulting Numbers: [30, 36, 1914] Generated Node #2: [30, 36, 1914] from Operation: 33*58=1914 Current State: 29:[30, 36, 1914], Operations: ['33*58=1914'] Exploring Operation: 30+36=66, Resulting Numbers: [1914, 66] Generated Node #3: [1914, 66] from Operation: 30+36=66 Current State: 29:[1914, 66], Operations: ['33*58=1914', '30+36=66'] Exploring Operation: 1914/66=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[33, 30, 36, 58], Operations: [] Exploring Operation: 58-30=28, Resulting Numbers: [33, 36, 28] Generated Node #0,0: 29:[33, 36, 28] Operation: 58-30=28 Exploring Operation: 58-33=25, Resulting Numbers: [30, 36, 25] Generated Node #0,1: 29:[30, 36, 25] Operation: 58-33=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[33, 36, 28], Operations: ['58-30=28'] Exploring Operation: 36-33=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 29:[28, 3] Operation: 36-33=3 Exploring Operation: 36-28=8, Resulting Numbers: [33, 8] Generated Node #0,0,1: 29:[33, 8] Operation: 36-28=8 Moving to Node #0,0,1 Current State: 29:[33, 8], Operations: ['58-30=28', '36-28=8'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,29 unequal: No Solution Exploring Operation: 33+8=41, Resulting Numbers: [41] 41,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[28, 3], Operations: ['58-30=28', '36-33=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,29 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[30, 36, 25], Operations: ['58-33=25'] Exploring Operation: 36-30=6, Resulting Numbers: [25, 6] Generated Node #0,1,0: 29:[25, 6] Operation: 36-30=6 Exploring Operation: 36-25=11, Resulting Numbers: [30, 11] Generated Node #0,1,1: 29:[30, 11] Operation: 36-25=11 Moving to Node #0,1,1 Current State: 29:[30, 11], Operations: ['58-33=25', '36-25=11'] Exploring Operation: 30+11=41, Resulting Numbers: [41] 41,29 unequal: No Solution Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[25, 6], Operations: ['58-33=25', '36-30=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,29 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,29 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
[ 46, 87, 44, 13 ]
61
[ "46-44=2", "13*2=26", "87-26=61" ]
Current State: 61:[46, 87, 44, 13], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [87, 13, 2] Generated Node #2: [87, 13, 2] from Operation: 46-44=2 Current State: 61:[87, 13, 2], Operations: ['46-44=2'] Exploring Operation: 13*2=26, Resulting Numbers: [87, 26] Generated Node #3: [87, 26] from Operation: 13*2=26 Current State: 61:[87, 26], Operations: ['46-44=2', '13*2=26'] Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[46, 87, 44, 13], Operations: [] Exploring Operation: 44+13=57, Resulting Numbers: [46, 87, 57] Generated Node #0,0: 61:[46, 87, 57] Operation: 44+13=57 Exploring Operation: 46+13=59, Resulting Numbers: [87, 44, 59] Generated Node #0,1: 61:[87, 44, 59] Operation: 46+13=59 Exploring Operation: 46-13=33, Resulting Numbers: [87, 44, 33] Generated Node #0,2: 61:[87, 44, 33] Operation: 46-13=33 Exploring Operation: 87-13=74, Resulting Numbers: [46, 44, 74] Generated Node #0,3: 61:[46, 44, 74] Operation: 87-13=74 Exploring Operation: 87+13=100, Resulting Numbers: [46, 44, 100] Generated Node #0,4: 61:[46, 44, 100] Operation: 87+13=100 Moving to Node #0,0 Current State: 61:[46, 87, 57], Operations: ['44+13=57'] Exploring Operation: 46+87=133, Resulting Numbers: [57, 133] Generated Node #0,0,0: 61:[57, 133] Operation: 46+87=133 Exploring Operation: 57-46=11, Resulting Numbers: [87, 11] Generated Node #0,0,1: 61:[87, 11] Operation: 57-46=11 Exploring Operation: 87-57=30, Resulting Numbers: [46, 30] Generated Node #0,0,2: 61:[46, 30] Operation: 87-57=30 Exploring Operation: 87-46=41, Resulting Numbers: [57, 41] Generated Node #0,0,3: 61:[57, 41] Operation: 87-46=41 Exploring Operation: 46+57=103, Resulting Numbers: [87, 103] Generated Node #0,0,4: 61:[87, 103] Operation: 46+57=103 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[57, 41], Operations: ['44+13=57', '87-46=41'] Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 57+41=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 57*41=2337, Resulting Numbers: [2337] 2337,61 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:[46, 30], Operations: ['44+13=57', '87-57=30'] Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,61 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,61 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 #0,0,4 Current State: 61:[87, 103], Operations: ['44+13=57', '46+57=103'] Exploring Operation: 87*103=8961, Resulting Numbers: [8961] 8961,61 unequal: No Solution Exploring Operation: 103-87=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 87+103=190, Resulting Numbers: [190] 190,61 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:[57, 133], Operations: ['44+13=57', '46+87=133'] Exploring Operation: 57*133=7581, Resulting Numbers: [7581] 7581,61 unequal: No Solution Exploring Operation: 57+133=190, Resulting Numbers: [190] 190,61 unequal: No Solution Exploring Operation: 133-57=76, Resulting Numbers: [76] 76,61 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 #0,0,1 Current State: 61:[87, 11], Operations: ['44+13=57', '57-46=11'] Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 87+11=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 87*11=957, Resulting Numbers: [957] 957,61 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: 61:[46, 44, 74], Operations: ['87-13=74'] Exploring Operation: 74-44=30, Resulting Numbers: [46, 30] Generated Node #0,3,0: 61:[46, 30] Operation: 74-44=30 Exploring Operation: 46+44=90, Resulting Numbers: [74, 90] Generated Node #0,3,1: 61:[74, 90] Operation: 46+44=90 Exploring Operation: 74-46=28, Resulting Numbers: [44, 28] Generated Node #0,3,2: 61:[44, 28] Operation: 74-46=28 Exploring Operation: 44+74=118, Resulting Numbers: [46, 118] Generated Node #0,3,3: 61:[46, 118] Operation: 44+74=118 Exploring Operation: 46-44=2, Resulting Numbers: [74, 2] Generated Node #0,3,4: 61:[74, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 61:[74, 90], Operations: ['87-13=74', '46+44=90'] Exploring Operation: 74*90=6660, Resulting Numbers: [6660] 6660,61 unequal: No Solution Exploring Operation: 74+90=164, Resulting Numbers: [164] 164,61 unequal: No Solution Exploring Operation: 90-74=16, Resulting Numbers: [16] 16,61 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 #0,3,0 Current State: 61:[46, 30], Operations: ['87-13=74', '74-44=30'] Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,61 unequal: No Solution Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,61 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 #0,3,2 Current State: 61:[44, 28], Operations: ['87-13=74', '74-46=28'] Exploring Operation: 44*28=1232, Resulting Numbers: [1232] 1232,61 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,61 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 #0,3,3 Current State: 61:[46, 118], Operations: ['87-13=74', '44+74=118'] Exploring Operation: 118-46=72, Resulting Numbers: [72] 72,61 unequal: No Solution Exploring Operation: 46+118=164, Resulting Numbers: [164] 164,61 unequal: No Solution Exploring Operation: 46*118=5428, Resulting Numbers: [5428] 5428,61 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 #0,3,4 Current State: 61:[74, 2], Operations: ['87-13=74', '46-44=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,61 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,61 unequal: No Solution Exploring Operation: 74*2=148, Resulting Numbers: [148] 148,61 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:[87, 44, 59], Operations: ['46+13=59'] Exploring Operation: 87-59=28, Resulting Numbers: [44, 28] Generated Node #0,1,0: 61:[44, 28] Operation: 87-59=28 Exploring Operation: 44+59=103, Resulting Numbers: [87, 103] Generated Node #0,1,1: 61:[87, 103] Operation: 44+59=103 Exploring Operation: 59-44=15, Resulting Numbers: [87, 15] Generated Node #0,1,2: 61:[87, 15] Operation: 59-44=15 Exploring Operation: 87+44=131, Resulting Numbers: [59, 131] Generated Node #0,1,3: 61:[59, 131] Operation: 87+44=131 Exploring Operation: 87-44=43, Resulting Numbers: [59, 43] Generated Node #0,1,4: 61:[59, 43] Operation: 87-44=43 Moving to Node #0,2 Current State: 61:[87, 44, 33], Operations: ['46-13=33'] Exploring Operation: 87-33=54, Resulting Numbers: [44, 54] Generated Node #0,2,0: 61:[44, 54] Operation: 87-33=54 Exploring Operation: 87-44=43, Resulting Numbers: [33, 43] Generated Node #0,2,1: 61:[33, 43] Operation: 87-44=43 Exploring Operation: 44+33=77, Resulting Numbers: [87, 77] Generated Node #0,2,2: 61:[87, 77] Operation: 44+33=77 Exploring Operation: 87+33=120, Resulting Numbers: [44, 120] Generated Node #0,2,3: 61:[44, 120] Operation: 87+33=120 Exploring Operation: 44-33=11, Resulting Numbers: [87, 11] Generated Node #0,2,4: 61:[87, 11] Operation: 44-33=11 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[44, 54], Operations: ['46-13=33', '87-33=54'] Exploring Operation: 44*54=2376, Resulting Numbers: [2376] 2376,61 unequal: No Solution Exploring Operation: 44+54=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,61 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 #0,2,2 Current State: 61:[87, 77], Operations: ['46-13=33', '44+33=77'] Exploring Operation: 87*77=6699, Resulting Numbers: [6699] 6699,61 unequal: No Solution Exploring Operation: 87-77=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 87+77=164, Resulting Numbers: [164] 164,61 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 #0,2,1 Current State: 61:[33, 43], Operations: ['46-13=33', '87-44=43'] Exploring Operation: 33+43=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 33*43=1419, Resulting Numbers: [1419] 1419,61 unequal: No Solution Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,61 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 #0,2,3 Current State: 61:[44, 120], Operations: ['46-13=33', '87+33=120'] Exploring Operation: 120-44=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 44+120=164, Resulting Numbers: [164] 164,61 unequal: No Solution Exploring Operation: 44*120=5280, Resulting Numbers: [5280] 5280,61 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 #0,2,4 Current State: 61:[87, 11], Operations: ['46-13=33', '44-33=11'] Exploring Operation: 87*11=957, Resulting Numbers: [957] 957,61 unequal: No Solution Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 87+11=98, Resulting Numbers: [98] 98,61 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: 61:[46, 44, 100], Operations: ['87+13=100'] Exploring Operation: 100-44=56, Resulting Numbers: [46, 56] Generated Node #0,4,0: 61:[46, 56] Operation: 100-44=56 Exploring Operation: 44+100=144, Resulting Numbers: [46, 144] Generated Node #0,4,1: 61:[46, 144] Operation: 44+100=144 Exploring Operation: 46+44=90, Resulting Numbers: [100, 90] Generated Node #0,4,2: 61:[100, 90] Operation: 46+44=90 Exploring Operation: 46-44=2, Resulting Numbers: [100, 2] Generated Node #0,4,3: 61:[100, 2] Operation: 46-44=2 Exploring Operation: 100-46=54, Resulting Numbers: [44, 54] Generated Node #0,4,4: 61:[44, 54] Operation: 100-46=54 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 61:[46, 56], Operations: ['87+13=100', '100-44=56'] Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 46*56=2576, Resulting Numbers: [2576] 2576,61 unequal: No Solution Exploring Operation: 46+56=102, Resulting Numbers: [102] 102,61 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 #0,4,4 Current State: 61:[44, 54], Operations: ['87+13=100', '100-46=54'] Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 44*54=2376, Resulting Numbers: [2376] 2376,61 unequal: No Solution Exploring Operation: 44+54=98, Resulting Numbers: [98] 98,61 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 #0,4,2 Current State: 61:[100, 90], Operations: ['87+13=100', '46+44=90'] Exploring Operation: 100+90=190, Resulting Numbers: [190] 190,61 unequal: No Solution Exploring Operation: 100-90=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 100*90=9000, Resulting Numbers: [9000] 9000,61 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 #0,4,1 Current State: 61:[46, 144], Operations: ['87+13=100', '44+100=144'] Exploring Operation: 46+144=190, Resulting Numbers: [190] 190,61 unequal: No Solution Exploring Operation: 144-46=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 46*144=6624, Resulting Numbers: [6624] 6624,61 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 #0,4,3 Current State: 61:[100, 2], Operations: ['87+13=100', '46-44=2'] Exploring Operation: 100/2=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 100*2=200, Resulting Numbers: [200] 200,61 unequal: No Solution Exploring Operation: 100+2=102, Resulting Numbers: [102] 102,61 unequal: No Solution Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,61 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: 61:[59, 43], Operations: ['46+13=59', '87-44=43'] Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 59*43=2537, Resulting Numbers: [2537] 2537,61 unequal: No Solution Exploring Operation: 59+43=102, Resulting Numbers: [102] 102,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[44, 28], Operations: ['46+13=59', '87-59=28'] Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 44*28=1232, Resulting Numbers: [1232] 1232,61 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[87, 103], Operations: ['46+13=59', '44+59=103'] Exploring Operation: 103-87=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 87+103=190, Resulting Numbers: [190] 190,61 unequal: No Solution Exploring Operation: 87*103=8961, Resulting Numbers: [8961] 8961,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[87, 15], Operations: ['46+13=59', '59-44=15'] Exploring Operation: 87*15=1305, Resulting Numbers: [1305] 1305,61 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,61 unequal: No Solution Exploring Operation: 87+15=102, Resulting Numbers: [102] 102,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[59, 131], Operations: ['46+13=59', '87+44=131'] Exploring Operation: 59+131=190, Resulting Numbers: [190] 190,61 unequal: No Solution Exploring Operation: 59*131=7729, Resulting Numbers: [7729] 7729,61 unequal: No Solution Exploring Operation: 131-59=72, Resulting Numbers: [72] 72,61 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 45, 54, 90, 31 ]
58
[ "45*54=2430", "2430/90=27", "31+27=58" ]
Current State: 58:[45, 54, 90, 31], Operations: [] Exploring Operation: 45*54=2430, Resulting Numbers: [90, 31, 2430] Generated Node #2: [90, 31, 2430] from Operation: 45*54=2430 Current State: 58:[90, 31, 2430], Operations: ['45*54=2430'] Exploring Operation: 2430/90=27, Resulting Numbers: [31, 27] Generated Node #3: [31, 27] from Operation: 2430/90=27 Current State: 58:[31, 27], Operations: ['45*54=2430', '2430/90=27'] Exploring Operation: 31+27=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[45, 54, 90, 31], Operations: [] Exploring Operation: 90/45=2, Resulting Numbers: [54, 31, 2] Generated Node #0,0: 58:[54, 31, 2] Operation: 90/45=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[54, 31, 2], Operations: ['90/45=2'] Exploring Operation: 54+2=56, Resulting Numbers: [31, 56] Generated Node #0,0,0: 58:[31, 56] Operation: 54+2=56 Moving to Node #0,0,0 Current State: 58:[31, 56], Operations: ['90/45=2', '54+2=56'] Exploring Operation: 56-31=25, Resulting Numbers: [25] 25,58 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
[ 11, 80, 30, 35 ]
100
[ "35-11=24", "80*30=2400", "2400/24=100" ]
Current State: 100:[11, 80, 30, 35], Operations: [] Exploring Operation: 35-11=24, Resulting Numbers: [80, 30, 24] Generated Node #2: [80, 30, 24] from Operation: 35-11=24 Current State: 100:[80, 30, 24], Operations: ['35-11=24'] Exploring Operation: 80*30=2400, Resulting Numbers: [24, 2400] Generated Node #3: [24, 2400] from Operation: 80*30=2400 Current State: 100:[24, 2400], Operations: ['35-11=24', '80*30=2400'] Exploring Operation: 2400/24=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[11, 80, 30, 35], Operations: [] Exploring Operation: 80-30=50, Resulting Numbers: [11, 35, 50] Generated Node #0,0: 100:[11, 35, 50] Operation: 80-30=50 Moving to Node #0,0 Current State: 100:[11, 35, 50], Operations: ['80-30=50'] Exploring Operation: 35-11=24, Resulting Numbers: [50, 24] Generated Node #0,0,0: 100:[50, 24] Operation: 35-11=24 Moving to Node #0,0,0 Current State: 100:[50, 24], Operations: ['80-30=50', '35-11=24'] Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,100 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 32, 8, 75, 99 ]
28
[ "32/8=4", "99-75=24", "4+24=28" ]
Current State: 28:[32, 8, 75, 99], Operations: [] Exploring Operation: 32/8=4, Resulting Numbers: [75, 99, 4] Generated Node #2: [75, 99, 4] from Operation: 32/8=4 Current State: 28:[75, 99, 4], Operations: ['32/8=4'] Exploring Operation: 99-75=24, Resulting Numbers: [4, 24] Generated Node #3: [4, 24] from Operation: 99-75=24 Current State: 28:[4, 24], Operations: ['32/8=4', '99-75=24'] Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[32, 8, 75, 99], Operations: [] Exploring Operation: 75-8=67, Resulting Numbers: [32, 99, 67] Generated Node #0,0: 28:[32, 99, 67] Operation: 75-8=67 Exploring Operation: 99-32=67, Resulting Numbers: [8, 75, 67] Generated Node #0,1: 28:[8, 75, 67] Operation: 99-32=67 Exploring Operation: 99-8=91, Resulting Numbers: [32, 75, 91] Generated Node #0,2: 28:[32, 75, 91] Operation: 99-8=91 Exploring Operation: 75-32=43, Resulting Numbers: [8, 99, 43] Generated Node #0,3: 28:[8, 99, 43] Operation: 75-32=43 Exploring Operation: 99-75=24, Resulting Numbers: [32, 8, 24] Generated Node #0,4: 28:[32, 8, 24] Operation: 99-75=24 Start Sub Search at level 1: Moving to Node #0,4 Current State: 28:[32, 8, 24], Operations: ['99-75=24'] Exploring Operation: 32/8=4, Resulting Numbers: [24, 4] Generated Node #0,4,0: 28:[24, 4] Operation: 32/8=4 Exploring Operation: 32-24=8, Resulting Numbers: [8, 8] Generated Node #0,4,1: 28:[8, 8] Operation: 32-24=8 Exploring Operation: 32-8=24, Resulting Numbers: [24, 24] Generated Node #0,4,2: 28:[24, 24] Operation: 32-8=24 Exploring Operation: 24-8=16, Resulting Numbers: [32, 16] Generated Node #0,4,3: 28:[32, 16] Operation: 24-8=16 Exploring Operation: 24/8=3, Resulting Numbers: [32, 3] Generated Node #0,4,4: 28:[32, 3] Operation: 24/8=3 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 28:[8, 8], Operations: ['99-75=24', '32-24=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,28 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,28 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 #0,4,0 Current State: 28:[24, 4], Operations: ['99-75=24', '32/8=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,28 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,28 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[32, 8, 75, 99], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [32, 8, 24] Generated Node #0,4: 28:[32, 8, 24] Operation: 99-75=24 Moving to Node #0,4 Current State: 28:[32, 8, 24], Operations: ['99-75=24'] Exploring Operation: 32/8=4, Resulting Numbers: [24, 4] Generated Node #0,4,0: 28:[24, 4] Operation: 32/8=4 Moving to Node #0,4,0 Current State: 28:[24, 4], Operations: ['99-75=24', '32/8=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 48, 18, 77, 94 ]
33
[ "48*77=3696", "18+94=112", "3696/112=33" ]
Current State: 33:[48, 18, 77, 94], Operations: [] Exploring Operation: 48*77=3696, Resulting Numbers: [18, 94, 3696] Generated Node #2: [18, 94, 3696] from Operation: 48*77=3696 Current State: 33:[18, 94, 3696], Operations: ['48*77=3696'] Exploring Operation: 18+94=112, Resulting Numbers: [3696, 112] Generated Node #3: [3696, 112] from Operation: 18+94=112 Current State: 33:[3696, 112], Operations: ['48*77=3696', '18+94=112'] Exploring Operation: 3696/112=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[48, 18, 77, 94], Operations: [] Exploring Operation: 77-48=29, Resulting Numbers: [18, 94, 29] Generated Node #0,0: 33:[18, 94, 29] Operation: 77-48=29 Exploring Operation: 94-48=46, Resulting Numbers: [18, 77, 46] Generated Node #0,1: 33:[18, 77, 46] Operation: 94-48=46 Exploring Operation: 77-18=59, Resulting Numbers: [48, 94, 59] Generated Node #0,2: 33:[48, 94, 59] Operation: 77-18=59 Exploring Operation: 94-77=17, Resulting Numbers: [48, 18, 17] Generated Node #0,3: 33:[48, 18, 17] Operation: 94-77=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 33:[48, 18, 17], Operations: ['94-77=17'] Exploring Operation: 48-18=30, Resulting Numbers: [17, 30] Generated Node #0,3,0: 33:[17, 30] Operation: 48-18=30 Exploring Operation: 18-17=1, Resulting Numbers: [48, 1] Generated Node #0,3,1: 33:[48, 1] Operation: 18-17=1 Exploring Operation: 18+17=35, Resulting Numbers: [48, 35] Generated Node #0,3,2: 33:[48, 35] Operation: 18+17=35 Exploring Operation: 48-17=31, Resulting Numbers: [18, 31] Generated Node #0,3,3: 33:[18, 31] Operation: 48-17=31 Moving to Node #0,3,0 Current State: 33:[17, 30], Operations: ['94-77=17', '48-18=30'] Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,33 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,33 unequal: No Solution Moving to Node #0,3,3 Current State: 33:[18, 31], Operations: ['94-77=17', '48-17=31'] Exploring Operation: 18+31=49, Resulting Numbers: [49] 49,33 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 18*31=558, Resulting Numbers: [558] 558,33 unequal: No Solution Moving to Node #0,3,2 Current State: 33:[48, 35], Operations: ['94-77=17', '18+17=35'] Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 48+35=83, Resulting Numbers: [83] 83,33 unequal: No Solution Exploring Operation: 48*35=1680, Resulting Numbers: [1680] 1680,33 unequal: No Solution Moving to Node #0,3,1 Current State: 33:[48, 1], Operations: ['94-77=17', '18-17=1'] Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,33 unequal: No Solution Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,33 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,33 unequal: No Solution Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[18, 77, 46], Operations: ['94-48=46'] Exploring Operation: 77-18=59, Resulting Numbers: [46, 59] Generated Node #0,1,0: 33:[46, 59] Operation: 77-18=59 Exploring Operation: 46-18=28, Resulting Numbers: [77, 28] Generated Node #0,1,1: 33:[77, 28] Operation: 46-18=28 Exploring Operation: 18+77=95, Resulting Numbers: [46, 95] Generated Node #0,1,2: 33:[46, 95] Operation: 18+77=95 Exploring Operation: 77-46=31, Resulting Numbers: [18, 31] Generated Node #0,1,3: 33:[18, 31] Operation: 77-46=31 Moving to Node #0,1,3 Current State: 33:[18, 31], Operations: ['94-48=46', '77-46=31'] Exploring Operation: 18+31=49, Resulting Numbers: [49] 49,33 unequal: No Solution Exploring Operation: 18*31=558, Resulting Numbers: [558] 558,33 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[46, 59], Operations: ['94-48=46', '77-18=59'] Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 46+59=105, Resulting Numbers: [105] 105,33 unequal: No Solution Exploring Operation: 46*59=2714, Resulting Numbers: [2714] 2714,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[77, 28], Operations: ['94-48=46', '46-18=28'] Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,33 unequal: No Solution Exploring Operation: 77*28=2156, Resulting Numbers: [2156] 2156,33 unequal: No Solution Exploring Operation: 77+28=105, Resulting Numbers: [105] 105,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[46, 95], Operations: ['94-48=46', '18+77=95'] Exploring Operation: 46+95=141, Resulting Numbers: [141] 141,33 unequal: No Solution Exploring Operation: 95-46=49, Resulting Numbers: [49] 49,33 unequal: No Solution Exploring Operation: 46*95=4370, Resulting Numbers: [4370] 4370,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[18, 94, 29], Operations: ['77-48=29'] Exploring Operation: 29-18=11, Resulting Numbers: [94, 11] Generated Node #0,0,0: 33:[94, 11] Operation: 29-18=11 Exploring Operation: 94-18=76, Resulting Numbers: [29, 76] Generated Node #0,0,1: 33:[29, 76] Operation: 94-18=76 Exploring Operation: 94-29=65, Resulting Numbers: [18, 65] Generated Node #0,0,2: 33:[18, 65] Operation: 94-29=65 Exploring Operation: 18+29=47, Resulting Numbers: [94, 47] Generated Node #0,0,3: 33:[94, 47] Operation: 18+29=47 Moving to Node #0,0,2 Current State: 33:[18, 65], Operations: ['77-48=29', '94-29=65'] Exploring Operation: 18+65=83, Resulting Numbers: [83] 83,33 unequal: No Solution Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,33 unequal: No Solution Exploring Operation: 18*65=1170, Resulting Numbers: [1170] 1170,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[29, 76], Operations: ['77-48=29', '94-18=76'] Exploring Operation: 76-29=47, Resulting Numbers: [47] 47,33 unequal: No Solution Exploring Operation: 29*76=2204, Resulting Numbers: [2204] 2204,33 unequal: No Solution Exploring Operation: 29+76=105, Resulting Numbers: [105] 105,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[94, 11], Operations: ['77-48=29', '29-18=11'] Exploring Operation: 94+11=105, Resulting Numbers: [105] 105,33 unequal: No Solution Exploring Operation: 94*11=1034, Resulting Numbers: [1034] 1034,33 unequal: No Solution Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,33 unequal: No Solution Moving to Node #0,0,3 Current State: 33:[94, 47], Operations: ['77-48=29', '18+29=47'] Exploring Operation: 94+47=141, Resulting Numbers: [141] 141,33 unequal: No Solution Exploring Operation: 94/47=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 94*47=4418, Resulting Numbers: [4418] 4418,33 unequal: No Solution Exploring Operation: 94-47=47, Resulting Numbers: [47] 47,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[48, 94, 59], Operations: ['77-18=59'] Exploring Operation: 59-48=11, Resulting Numbers: [94, 11] Generated Node #0,2,0: 33:[94, 11] Operation: 59-48=11 Exploring Operation: 94-59=35, Resulting Numbers: [48, 35] Generated Node #0,2,1: 33:[48, 35] Operation: 94-59=35 Exploring Operation: 94-48=46, Resulting Numbers: [59, 46] Generated Node #0,2,2: 33:[59, 46] Operation: 94-48=46 Exploring Operation: 48+94=142, Resulting Numbers: [59, 142] Generated Node #0,2,3: 33:[59, 142] Operation: 48+94=142 Moving to Node #0,2,1 Current State: 33:[48, 35], Operations: ['77-18=59', '94-59=35'] Exploring Operation: 48+35=83, Resulting Numbers: [83] 83,33 unequal: No Solution Exploring Operation: 48*35=1680, Resulting Numbers: [1680] 1680,33 unequal: No Solution Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,33 unequal: No Solution Moving to Node #0,2,2 Current State: 33:[59, 46], Operations: ['77-18=59', '94-48=46'] Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,33 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,33 unequal: No Solution Moving to Node #0,2,0 Current State: 33:[94, 11], Operations: ['77-18=59', '59-48=11'] Exploring Operation: 94*11=1034, Resulting Numbers: [1034] 1034,33 unequal: No Solution Exploring Operation: 94+11=105, Resulting Numbers: [105] 105,33 unequal: No Solution Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,33 unequal: No Solution Moving to Node #0,2,3 Current State: 33:[59, 142], Operations: ['77-18=59', '48+94=142'] Exploring Operation: 59+142=201, Resulting Numbers: [201] 201,33 unequal: No Solution Exploring Operation: 59*142=8378, Resulting Numbers: [8378] 8378,33 unequal: No Solution Exploring Operation: 142-59=83, Resulting Numbers: [83] 83,33 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
[ 7, 14, 39, 54 ]
17
[ "14/7=2", "54-39=15", "2+15=17" ]
Current State: 17:[7, 14, 39, 54], Operations: [] Exploring Operation: 14/7=2, Resulting Numbers: [39, 54, 2] Generated Node #2: [39, 54, 2] from Operation: 14/7=2 Current State: 17:[39, 54, 2], Operations: ['14/7=2'] Exploring Operation: 54-39=15, Resulting Numbers: [2, 15] Generated Node #3: [2, 15] from Operation: 54-39=15 Current State: 17:[2, 15], Operations: ['14/7=2', '54-39=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[7, 14, 39, 54], Operations: [] Exploring Operation: 54-39=15, Resulting Numbers: [7, 14, 15] Generated Node #0,0: 17:[7, 14, 15] Operation: 54-39=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[7, 14, 15], Operations: ['54-39=15'] Exploring Operation: 7+14=21, Resulting Numbers: [15, 21] Generated Node #0,0,0: 17:[15, 21] Operation: 7+14=21 Moving to Node #0,0,0 Current State: 17:[15, 21], Operations: ['54-39=15', '7+14=21'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,17 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
[ 21, 29, 31, 7 ]
35
[ "31-29=2", "21*2=42", "42-7=35" ]
Current State: 35:[21, 29, 31, 7], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [21, 7, 2] Generated Node #2: [21, 7, 2] from Operation: 31-29=2 Current State: 35:[21, 7, 2], Operations: ['31-29=2'] Exploring Operation: 21*2=42, Resulting Numbers: [7, 42] Generated Node #3: [7, 42] from Operation: 21*2=42 Current State: 35:[7, 42], Operations: ['31-29=2', '21*2=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[21, 29, 31, 7], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [31, 7, 8] Generated Node #0,0: 35:[31, 7, 8] Operation: 29-21=8 Exploring Operation: 31-21=10, Resulting Numbers: [29, 7, 10] Generated Node #0,1: 35:[29, 7, 10] Operation: 31-21=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[31, 7, 8], Operations: ['29-21=8'] Exploring Operation: 31+8=39, Resulting Numbers: [7, 39] Generated Node #0,0,0: 35:[7, 39] Operation: 31+8=39 Exploring Operation: 31+7=38, Resulting Numbers: [8, 38] Generated Node #0,0,1: 35:[8, 38] Operation: 31+7=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[7, 39], Operations: ['29-21=8', '31+8=39'] Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,35 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 #0,0,1 Current State: 35:[8, 38], Operations: ['29-21=8', '31+7=38'] Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 38-8=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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[29, 7, 10], Operations: ['31-21=10'] Exploring Operation: 29+7=36, Resulting Numbers: [10, 36] Generated Node #0,1,0: 35:[10, 36] Operation: 29+7=36 Exploring Operation: 29+10=39, Resulting Numbers: [7, 39] Generated Node #0,1,1: 35:[7, 39] Operation: 29+10=39 Moving to Node #0,1,0 Current State: 35:[10, 36], Operations: ['31-21=10', '29+7=36'] Exploring Operation: 10+36=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[7, 39], Operations: ['31-21=10', '29+10=39'] Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,35 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 44, 6, 50, 44 ]
43
[ "44+6=50", "50/50=1", "44-1=43" ]
Current State: 43:[44, 6, 50, 44], Operations: [] Exploring Operation: 44+6=50, Resulting Numbers: [50, 50] Generated Node #2: [50, 50] from Operation: 44+6=50 Current State: 43:[50, 50], Operations: ['44+6=50'] Exploring Operation: 50/50=1, Resulting Numbers: [1] 1,43 equal: Goal Reached Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[44, 6, 50, 44], Operations: [] Exploring Operation: 44-6=38, Resulting Numbers: [44, 50, 38] Generated Node #0,0: 43:[44, 50, 38] Operation: 44-6=38 Exploring Operation: 44+6=50, Resulting Numbers: [50, 44, 50] Generated Node #0,1: 43:[50, 44, 50] Operation: 44+6=50 Exploring Operation: 50-6=44, Resulting Numbers: [44, 44, 44] Generated Node #0,2: 43:[44, 44, 44] Operation: 50-6=44 Exploring Operation: 44-6=38, Resulting Numbers: [50, 44, 38] Generated Node #0,3: 43:[50, 44, 38] Operation: 44-6=38 Moving to Node #0,2 Current State: 43:[44, 44, 44], Operations: ['50-6=44'] Exploring Operation: 44/44=1, Resulting Numbers: [44, 1] Generated Node #0,2,0: 43:[44, 1] Operation: 44/44=1 Exploring Operation: 44/44=1, Resulting Numbers: [44, 1] Generated Node #0,2,1: 43:[44, 1] Operation: 44/44=1 Exploring Operation: 44/44=1, Resulting Numbers: [44, 1] Generated Node #0,2,2: 43:[44, 1] Operation: 44/44=1 Exploring Operation: 44-44=0, Resulting Numbers: [44, 0] Generated Node #0,2,3: 43:[44, 0] Operation: 44-44=0 Moving to Node #0,3 Current State: 43:[50, 44, 38], Operations: ['44-6=38'] Exploring Operation: 44-38=6, Resulting Numbers: [50, 6] Generated Node #0,3,0: 43:[50, 6] Operation: 44-38=6 Exploring Operation: 50-38=12, Resulting Numbers: [44, 12] Generated Node #0,3,1: 43:[44, 12] Operation: 50-38=12 Exploring Operation: 50-44=6, Resulting Numbers: [38, 6] Generated Node #0,3,2: 43:[38, 6] Operation: 50-44=6 Exploring Operation: 50+38=88, Resulting Numbers: [44, 88] Generated Node #0,3,3: 43:[44, 88] Operation: 50+38=88 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 43:[44, 12], Operations: ['44-6=38', '50-38=12'] Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,43 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 43:[38, 6], Operations: ['44-6=38', '50-44=6'] Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,43 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 43:[50, 6], Operations: ['44-6=38', '44-38=6'] Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,43 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 43:[44, 88], Operations: ['44-6=38', '50+38=88'] Exploring Operation: 88/44=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 44*88=3872, Resulting Numbers: [3872] 3872,43 unequal: No Solution Exploring Operation: 88-44=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 44+88=132, Resulting Numbers: [132] 132,43 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: 43:[44, 50, 38], Operations: ['44-6=38'] Exploring Operation: 50-38=12, Resulting Numbers: [44, 12] Generated Node #0,0,0: 43:[44, 12] Operation: 50-38=12 Exploring Operation: 44+38=82, Resulting Numbers: [50, 82] Generated Node #0,0,1: 43:[50, 82] Operation: 44+38=82 Exploring Operation: 50-44=6, Resulting Numbers: [38, 6] Generated Node #0,0,2: 43:[38, 6] Operation: 50-44=6 Exploring Operation: 44-38=6, Resulting Numbers: [50, 6] Generated Node #0,0,3: 43:[50, 6] Operation: 44-38=6 Moving to Node #0,1 Current State: 43:[50, 44, 50], Operations: ['44+6=50'] Exploring Operation: 50/50=1, Resulting Numbers: [44, 1] Generated Node #0,1,0: 43:[44, 1] Operation: 50/50=1 Exploring Operation: 50-44=6, Resulting Numbers: [50, 6] Generated Node #0,1,1: 43:[50, 6] Operation: 50-44=6 Exploring Operation: 50-50=0, Resulting Numbers: [44, 0] Generated Node #0,1,2: 43:[44, 0] Operation: 50-50=0 Exploring Operation: 50-44=6, Resulting Numbers: [50, 6] Generated Node #0,1,3: 43:[50, 6] Operation: 50-44=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[44, 1], Operations: ['44+6=50', '50/50=1'] Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[44, 6, 50, 44], Operations: [] Exploring Operation: 44+6=50, Resulting Numbers: [50, 44, 50] Generated Node #0,1: 43:[50, 44, 50] Operation: 44+6=50 Moving to Node #0,1 Current State: 43:[50, 44, 50], Operations: ['44+6=50'] Exploring Operation: 50/50=1, Resulting Numbers: [44, 1] Generated Node #0,1,0: 43:[44, 1] Operation: 50/50=1 Moving to Node #0,1,0 Current State: 43:[44, 1], Operations: ['44+6=50', '50/50=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
mult_heuristic
[ 24, 77, 22, 44 ]
40
[ "24*77=1848", "1848/22=84", "84-44=40" ]
Current State: 40:[24, 77, 22, 44], Operations: [] Exploring Operation: 24*77=1848, Resulting Numbers: [22, 44, 1848] Generated Node #2: [22, 44, 1848] from Operation: 24*77=1848 Current State: 40:[22, 44, 1848], Operations: ['24*77=1848'] Exploring Operation: 1848/22=84, Resulting Numbers: [44, 84] Generated Node #3: [44, 84] from Operation: 1848/22=84 Current State: 40:[44, 84], Operations: ['24*77=1848', '1848/22=84'] Exploring Operation: 84-44=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[24, 77, 22, 44], Operations: [] Exploring Operation: 77-22=55, Resulting Numbers: [24, 44, 55] Generated Node #0,0: 40:[24, 44, 55] Operation: 77-22=55 Exploring Operation: 77-44=33, Resulting Numbers: [24, 22, 33] Generated Node #0,1: 40:[24, 22, 33] Operation: 77-44=33 Exploring Operation: 77-24=53, Resulting Numbers: [22, 44, 53] Generated Node #0,2: 40:[22, 44, 53] Operation: 77-24=53 Exploring Operation: 44-24=20, Resulting Numbers: [77, 22, 20] Generated Node #0,3: 40:[77, 22, 20] Operation: 44-24=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[24, 22, 33], Operations: ['77-44=33'] Exploring Operation: 33-22=11, Resulting Numbers: [24, 11] Generated Node #0,1,0: 40:[24, 11] Operation: 33-22=11 Exploring Operation: 33-24=9, Resulting Numbers: [22, 9] Generated Node #0,1,1: 40:[22, 9] Operation: 33-24=9 Exploring Operation: 24+22=46, Resulting Numbers: [33, 46] Generated Node #0,1,2: 40:[33, 46] Operation: 24+22=46 Exploring Operation: 24-22=2, Resulting Numbers: [33, 2] Generated Node #0,1,3: 40:[33, 2] Operation: 24-22=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 40:[22, 9], Operations: ['77-44=33', '33-24=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,40 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,40 unequal: No Solution No 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: 40:[24, 11], Operations: ['77-44=33', '33-22=11'] Exploring Operation: 24+11=35, Resulting Numbers: [35] 35,40 unequal: No Solution Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 24*11=264, Resulting Numbers: [264] 264,40 unequal: No Solution No 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: 40:[33, 2], Operations: ['77-44=33', '24-22=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,40 unequal: No Solution Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,40 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,40 unequal: No Solution No 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: 40:[33, 46], Operations: ['77-44=33', '24+22=46'] Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 33+46=79, Resulting Numbers: [79] 79,40 unequal: No Solution Exploring Operation: 33*46=1518, Resulting Numbers: [1518] 1518,40 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: 40:[22, 44, 53], Operations: ['77-24=53'] Exploring Operation: 44/22=2, Resulting Numbers: [53, 2] Generated Node #0,2,0: 40:[53, 2] Operation: 44/22=2 Exploring Operation: 44-22=22, Resulting Numbers: [53, 22] Generated Node #0,2,1: 40:[53, 22] Operation: 44-22=22 Exploring Operation: 53-22=31, Resulting Numbers: [44, 31] Generated Node #0,2,2: 40:[44, 31] Operation: 53-22=31 Exploring Operation: 53-44=9, Resulting Numbers: [22, 9] Generated Node #0,2,3: 40:[22, 9] Operation: 53-44=9 Moving to Node #0,2,3 Current State: 40:[22, 9], Operations: ['77-24=53', '53-44=9'] Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,40 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,40 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[44, 31], Operations: ['77-24=53', '53-22=31'] Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 44+31=75, Resulting Numbers: [75] 75,40 unequal: No Solution Exploring Operation: 44*31=1364, Resulting Numbers: [1364] 1364,40 unequal: No Solution Moving to Node #0,2,0 Current State: 40:[53, 2], Operations: ['77-24=53', '44/22=2'] Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,40 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,40 unequal: No Solution Exploring Operation: 53*2=106, Resulting Numbers: [106] 106,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[53, 22], Operations: ['77-24=53', '44-22=22'] Exploring Operation: 53+22=75, Resulting Numbers: [75] 75,40 unequal: No Solution Exploring Operation: 53-22=31, Resulting Numbers: [31] 31,40 unequal: No Solution Exploring Operation: 53*22=1166, Resulting Numbers: [1166] 1166,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[24, 44, 55], Operations: ['77-22=55'] Exploring Operation: 44-24=20, Resulting Numbers: [55, 20] Generated Node #0,0,0: 40:[55, 20] Operation: 44-24=20 Exploring Operation: 55-44=11, Resulting Numbers: [24, 11] Generated Node #0,0,1: 40:[24, 11] Operation: 55-44=11 Exploring Operation: 24+44=68, Resulting Numbers: [55, 68] Generated Node #0,0,2: 40:[55, 68] Operation: 24+44=68 Exploring Operation: 55-24=31, Resulting Numbers: [44, 31] Generated Node #0,0,3: 40:[44, 31] Operation: 55-24=31 Moving to Node #0,0,1 Current State: 40:[24, 11], Operations: ['77-22=55', '55-44=11'] Exploring Operation: 24*11=264, Resulting Numbers: [264] 264,40 unequal: No Solution Exploring Operation: 24+11=35, Resulting Numbers: [35] 35,40 unequal: No Solution Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,40 unequal: No Solution Moving to Node #0,0,3 Current State: 40:[44, 31], Operations: ['77-22=55', '55-24=31'] Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 44+31=75, Resulting Numbers: [75] 75,40 unequal: No Solution Exploring Operation: 44*31=1364, Resulting Numbers: [1364] 1364,40 unequal: No Solution Moving to Node #0,0,0 Current State: 40:[55, 20], Operations: ['77-22=55', '44-24=20'] Exploring Operation: 55+20=75, Resulting Numbers: [75] 75,40 unequal: No Solution Exploring Operation: 55*20=1100, Resulting Numbers: [1100] 1100,40 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[55, 68], Operations: ['77-22=55', '24+44=68'] Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 55+68=123, Resulting Numbers: [123] 123,40 unequal: No Solution Exploring Operation: 55*68=3740, Resulting Numbers: [3740] 3740,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[77, 22, 20], Operations: ['44-24=20'] Exploring Operation: 77-20=57, Resulting Numbers: [22, 57] Generated Node #0,3,0: 40:[22, 57] Operation: 77-20=57 Exploring Operation: 22-20=2, Resulting Numbers: [77, 2] Generated Node #0,3,1: 40:[77, 2] Operation: 22-20=2 Exploring Operation: 22+20=42, Resulting Numbers: [77, 42] Generated Node #0,3,2: 40:[77, 42] Operation: 22+20=42 Exploring Operation: 77-22=55, Resulting Numbers: [20, 55] Generated Node #0,3,3: 40:[20, 55] Operation: 77-22=55 Moving to Node #0,3,3 Current State: 40:[20, 55], Operations: ['44-24=20', '77-22=55'] Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,40 unequal: No Solution Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,40 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,40 unequal: No Solution Moving to Node #0,3,0 Current State: 40:[22, 57], Operations: ['44-24=20', '77-20=57'] Exploring Operation: 22*57=1254, Resulting Numbers: [1254] 1254,40 unequal: No Solution Exploring Operation: 57-22=35, Resulting Numbers: [35] 35,40 unequal: No Solution Exploring Operation: 22+57=79, Resulting Numbers: [79] 79,40 unequal: No Solution Moving to Node #0,3,1 Current State: 40:[77, 2], Operations: ['44-24=20', '22-20=2'] Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,40 unequal: No Solution Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,40 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,40 unequal: No Solution Moving to Node #0,3,2 Current State: 40:[77, 42], Operations: ['44-24=20', '22+20=42'] Exploring Operation: 77-42=35, Resulting Numbers: [35] 35,40 unequal: No Solution Exploring Operation: 77*42=3234, Resulting Numbers: [3234] 3234,40 unequal: No Solution Exploring Operation: 77+42=119, Resulting Numbers: [119] 119,40 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
[ 4, 17, 97, 41 ]
21
[ "97-17=80", "80/4=20", "41-20=21" ]
Current State: 21:[4, 17, 97, 41], Operations: [] Exploring Operation: 97-17=80, Resulting Numbers: [4, 41, 80] Generated Node #2: [4, 41, 80] from Operation: 97-17=80 Current State: 21:[4, 41, 80], Operations: ['97-17=80'] Exploring Operation: 80/4=20, Resulting Numbers: [41, 20] Generated Node #3: [41, 20] from Operation: 80/4=20 Current State: 21:[41, 20], Operations: ['97-17=80', '80/4=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[4, 17, 97, 41], Operations: [] Exploring Operation: 41-17=24, Resulting Numbers: [4, 97, 24] Generated Node #0,0: 21:[4, 97, 24] Operation: 41-17=24 Exploring Operation: 97-41=56, Resulting Numbers: [4, 17, 56] Generated Node #0,1: 21:[4, 17, 56] Operation: 97-41=56 Exploring Operation: 97-17=80, Resulting Numbers: [4, 41, 80] Generated Node #0,2: 21:[4, 41, 80] Operation: 97-17=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[4, 17, 56], Operations: ['97-41=56'] Exploring Operation: 56-17=39, Resulting Numbers: [4, 39] Generated Node #0,1,0: 21:[4, 39] Operation: 56-17=39 Exploring Operation: 4+17=21, Resulting Numbers: [56, 21] Generated Node #0,1,1: 21:[56, 21] Operation: 4+17=21 Exploring Operation: 56/4=14, Resulting Numbers: [17, 14] Generated Node #0,1,2: 21:[17, 14] Operation: 56/4=14 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 21:[17, 14], Operations: ['97-41=56', '56/4=14'] Exploring Operation: 17*14=238, Resulting Numbers: [238] 238,21 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,21 unequal: No Solution No 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: 21:[4, 39], Operations: ['97-41=56', '56-17=39'] Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,21 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,21 unequal: No Solution No 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: 21:[56, 21], Operations: ['97-41=56', '4+17=21'] Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 56+21=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 56*21=1176, Resulting Numbers: [1176] 1176,21 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: 21:[4, 97, 24], Operations: ['41-17=24'] Exploring Operation: 24-4=20, Resulting Numbers: [97, 20] Generated Node #0,0,0: 21:[97, 20] Operation: 24-4=20 Exploring Operation: 97-24=73, Resulting Numbers: [4, 73] Generated Node #0,0,1: 21:[4, 73] Operation: 97-24=73 Exploring Operation: 97-4=93, Resulting Numbers: [24, 93] Generated Node #0,0,2: 21:[24, 93] Operation: 97-4=93 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 21:[4, 73], Operations: ['41-17=24', '97-24=73'] Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,21 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,21 unequal: No Solution No 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: 21:[24, 93], Operations: ['41-17=24', '97-4=93'] Exploring Operation: 24+93=117, Resulting Numbers: [117] 117,21 unequal: No Solution Exploring Operation: 93-24=69, Resulting Numbers: [69] 69,21 unequal: No Solution Exploring Operation: 24*93=2232, Resulting Numbers: [2232] 2232,21 unequal: No Solution No 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: 21:[97, 20], Operations: ['41-17=24', '24-4=20'] Exploring Operation: 97+20=117, Resulting Numbers: [117] 117,21 unequal: No Solution Exploring Operation: 97*20=1940, Resulting Numbers: [1940] 1940,21 unequal: No Solution Exploring Operation: 97-20=77, Resulting Numbers: [77] 77,21 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: 21:[4, 41, 80], Operations: ['97-17=80'] Exploring Operation: 80/4=20, Resulting Numbers: [41, 20] Generated Node #0,2,0: 21:[41, 20] Operation: 80/4=20 Exploring Operation: 41-4=37, Resulting Numbers: [80, 37] Generated Node #0,2,1: 21:[80, 37] Operation: 41-4=37 Exploring Operation: 80-41=39, Resulting Numbers: [4, 39] Generated Node #0,2,2: 21:[4, 39] Operation: 80-41=39 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 21:[4, 39], Operations: ['97-17=80', '80-41=39'] Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,21 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,21 unequal: No Solution No 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: 21:[41, 20], Operations: ['97-17=80', '80/4=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[4, 17, 97, 41], Operations: [] Exploring Operation: 97-17=80, Resulting Numbers: [4, 41, 80] Generated Node #0,2: 21:[4, 41, 80] Operation: 97-17=80 Moving to Node #0,2 Current State: 21:[4, 41, 80], Operations: ['97-17=80'] Exploring Operation: 80/4=20, Resulting Numbers: [41, 20] Generated Node #0,2,0: 21:[41, 20] Operation: 80/4=20 Moving to Node #0,2,0 Current State: 21:[41, 20], Operations: ['97-17=80', '80/4=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_3
sum_heuristic
[ 16, 15, 78, 3 ]
83
[ "16*78=1248", "1248-3=1245", "1245/15=83" ]
Current State: 83:[16, 15, 78, 3], Operations: [] Exploring Operation: 16*78=1248, Resulting Numbers: [15, 3, 1248] Generated Node #2: [15, 3, 1248] from Operation: 16*78=1248 Current State: 83:[15, 3, 1248], Operations: ['16*78=1248'] Exploring Operation: 1248-3=1245, Resulting Numbers: [15, 1245] Generated Node #3: [15, 1245] from Operation: 1248-3=1245 Current State: 83:[15, 1245], Operations: ['16*78=1248', '1248-3=1245'] Exploring Operation: 1245/15=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[16, 15, 78, 3], Operations: [] Exploring Operation: 16*3=48, Resulting Numbers: [15, 78, 48] Generated Node #0,0: 83:[15, 78, 48] Operation: 16*3=48 Exploring Operation: 15*3=45, Resulting Numbers: [16, 78, 45] Generated Node #0,1: 83:[16, 78, 45] Operation: 15*3=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[15, 78, 48], Operations: ['16*3=48'] Exploring Operation: 15+48=63, Resulting Numbers: [78, 63] Generated Node #0,0,0: 83:[78, 63] Operation: 15+48=63 Exploring Operation: 15+78=93, Resulting Numbers: [48, 93] Generated Node #0,0,1: 83:[48, 93] Operation: 15+78=93 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[78, 63], Operations: ['16*3=48', '15+48=63'] Exploring Operation: 78-63=15, Resulting Numbers: [15] 15,83 unequal: No Solution Exploring Operation: 78+63=141, Resulting Numbers: [141] 141,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[48, 93], Operations: ['16*3=48', '15+78=93'] Exploring Operation: 48+93=141, Resulting Numbers: [141] 141,83 unequal: No Solution Exploring Operation: 93-48=45, Resulting Numbers: [45] 45,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[16, 78, 45], Operations: ['15*3=45'] Exploring Operation: 16+78=94, Resulting Numbers: [45, 94] Generated Node #0,1,0: 83:[45, 94] Operation: 16+78=94 Exploring Operation: 16+45=61, Resulting Numbers: [78, 61] Generated Node #0,1,1: 83:[78, 61] Operation: 16+45=61 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[78, 61], Operations: ['15*3=45', '16+45=61'] Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,83 unequal: No Solution Exploring Operation: 78+61=139, Resulting Numbers: [139] 139,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[45, 94], Operations: ['15*3=45', '16+78=94'] Exploring Operation: 45+94=139, Resulting Numbers: [139] 139,83 unequal: No Solution Exploring Operation: 94-45=49, Resulting Numbers: [49] 49,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 79, 36, 12, 12 ]
88
[ "79+12=91", "36/12=3", "91-3=88" ]
Current State: 88:[79, 36, 12, 12], Operations: [] Exploring Operation: 79+12=91, Resulting Numbers: [36, 91] Generated Node #2: [36, 91] from Operation: 79+12=91 Current State: 88:[36, 91], Operations: ['79+12=91'] Exploring Operation: 36/12=3, Resulting Numbers: [91, 3] Generated Node #3: [91, 3] from Operation: 36/12=3 Current State: 88:[91, 3], Operations: ['79+12=91', '36/12=3'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[79, 36, 12, 12], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [79, 12, 3] Generated Node #0,0: 88:[79, 12, 3] Operation: 36/12=3 Exploring Operation: 79-36=43, Resulting Numbers: [12, 12, 43] Generated Node #0,1: 88:[12, 12, 43] Operation: 79-36=43 Moving to Node #0,1 Current State: 88:[12, 12, 43], Operations: ['79-36=43'] Exploring Operation: 12/12=1, Resulting Numbers: [43, 1] Generated Node #0,1,0: 88:[43, 1] Operation: 12/12=1 Exploring Operation: 12+12=24, Resulting Numbers: [43, 24] Generated Node #0,1,1: 88:[43, 24] Operation: 12+12=24 Moving to Node #0,0 Current State: 88:[79, 12, 3], Operations: ['36/12=3'] Exploring Operation: 79+12=91, Resulting Numbers: [3, 91] Generated Node #0,0,0: 88:[3, 91] Operation: 79+12=91 Exploring Operation: 79+3=82, Resulting Numbers: [12, 82] Generated Node #0,0,1: 88:[12, 82] Operation: 79+3=82 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[3, 91], Operations: ['36/12=3', '79+12=91'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[79, 36, 12, 12], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [79, 12, 3] Generated Node #0,0: 88:[79, 12, 3] Operation: 36/12=3 Moving to Node #0,0 Current State: 88:[79, 12, 3], Operations: ['36/12=3'] Exploring Operation: 79+12=91, Resulting Numbers: [3, 91] Generated Node #0,0,0: 88:[3, 91] Operation: 79+12=91 Moving to Node #0,0,0 Current State: 88:[3, 91], Operations: ['36/12=3', '79+12=91'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 40, 32, 18, 16 ]
60
[ "40+18=58", "32/16=2", "58+2=60" ]
Current State: 60:[40, 32, 18, 16], Operations: [] Exploring Operation: 40+18=58, Resulting Numbers: [32, 16, 58] Generated Node #2: [32, 16, 58] from Operation: 40+18=58 Current State: 60:[32, 16, 58], Operations: ['40+18=58'] Exploring Operation: 32/16=2, Resulting Numbers: [58, 2] Generated Node #3: [58, 2] from Operation: 32/16=2 Current State: 60:[58, 2], Operations: ['40+18=58', '32/16=2'] Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[40, 32, 18, 16], Operations: [] Exploring Operation: 40-18=22, Resulting Numbers: [32, 16, 22] Generated Node #0,0: 60:[32, 16, 22] Operation: 40-18=22 Exploring Operation: 40+18=58, Resulting Numbers: [32, 16, 58] Generated Node #0,1: 60:[32, 16, 58] Operation: 40+18=58 Exploring Operation: 40-32=8, Resulting Numbers: [18, 16, 8] Generated Node #0,2: 60:[18, 16, 8] Operation: 40-32=8 Exploring Operation: 40+16=56, Resulting Numbers: [32, 18, 56] Generated Node #0,3: 60:[32, 18, 56] Operation: 40+16=56 Moving to Node #0,0 Current State: 60:[32, 16, 22], Operations: ['40-18=22'] Exploring Operation: 32-22=10, Resulting Numbers: [16, 10] Generated Node #0,0,0: 60:[16, 10] Operation: 32-22=10 Exploring Operation: 32-16=16, Resulting Numbers: [22, 16] Generated Node #0,0,1: 60:[22, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [22, 2] Generated Node #0,0,2: 60:[22, 2] Operation: 32/16=2 Exploring Operation: 22-16=6, Resulting Numbers: [32, 6] Generated Node #0,0,3: 60:[32, 6] Operation: 22-16=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[16, 10], Operations: ['40-18=22', '32-22=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,60 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[22, 2], Operations: ['40-18=22', '32/16=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,60 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,60 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 60:[32, 6], Operations: ['40-18=22', '22-16=6'] Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,60 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[22, 16], Operations: ['40-18=22', '32-16=16'] Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,60 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,60 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,60 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: 60:[18, 16, 8], Operations: ['40-32=8'] Exploring Operation: 16-8=8, Resulting Numbers: [18, 8] Generated Node #0,2,0: 60:[18, 8] Operation: 16-8=8 Exploring Operation: 18-8=10, Resulting Numbers: [16, 10] Generated Node #0,2,1: 60:[16, 10] Operation: 18-8=10 Exploring Operation: 18-16=2, Resulting Numbers: [8, 2] Generated Node #0,2,2: 60:[8, 2] Operation: 18-16=2 Exploring Operation: 16/8=2, Resulting Numbers: [18, 2] Generated Node #0,2,3: 60:[18, 2] Operation: 16/8=2 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[16, 10], Operations: ['40-32=8', '18-8=10'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 60:[8, 2], Operations: ['40-32=8', '18-16=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 60:[18, 2], Operations: ['40-32=8', '16/8=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,60 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,60 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[18, 8], Operations: ['40-32=8', '16-8=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,60 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,60 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: 60:[32, 16, 58], Operations: ['40+18=58'] Exploring Operation: 58-32=26, Resulting Numbers: [16, 26] Generated Node #0,1,0: 60:[16, 26] Operation: 58-32=26 Exploring Operation: 32+16=48, Resulting Numbers: [58, 48] Generated Node #0,1,1: 60:[58, 48] Operation: 32+16=48 Exploring Operation: 32/16=2, Resulting Numbers: [58, 2] Generated Node #0,1,2: 60:[58, 2] Operation: 32/16=2 Exploring Operation: 32-16=16, Resulting Numbers: [58, 16] Generated Node #0,1,3: 60:[58, 16] Operation: 32-16=16 Moving to Node #0,3 Current State: 60:[32, 18, 56], Operations: ['40+16=56'] Exploring Operation: 32+18=50, Resulting Numbers: [56, 50] Generated Node #0,3,0: 60:[56, 50] Operation: 32+18=50 Exploring Operation: 32-18=14, Resulting Numbers: [56, 14] Generated Node #0,3,1: 60:[56, 14] Operation: 32-18=14 Exploring Operation: 56-32=24, Resulting Numbers: [18, 24] Generated Node #0,3,2: 60:[18, 24] Operation: 56-32=24 Exploring Operation: 56-18=38, Resulting Numbers: [32, 38] Generated Node #0,3,3: 60:[32, 38] Operation: 56-18=38 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 60:[56, 14], Operations: ['40+16=56', '32-18=14'] Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,60 unequal: No Solution Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,60 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,60 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 60:[18, 24], Operations: ['40+16=56', '56-32=24'] Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,60 unequal: No Solution Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,60 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 60:[32, 38], Operations: ['40+16=56', '56-18=38'] Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,60 unequal: No Solution Exploring Operation: 32*38=1216, Resulting Numbers: [1216] 1216,60 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 60:[56, 50], Operations: ['40+16=56', '32+18=50'] Exploring Operation: 56+50=106, Resulting Numbers: [106] 106,60 unequal: No Solution Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 56*50=2800, Resulting Numbers: [2800] 2800,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 60:[58, 2], Operations: ['40+18=58', '32/16=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,60 unequal: No Solution Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[40, 32, 18, 16], Operations: [] Exploring Operation: 40+18=58, Resulting Numbers: [32, 16, 58] Generated Node #0,1: 60:[32, 16, 58] Operation: 40+18=58 Moving to Node #0,1 Current State: 60:[32, 16, 58], Operations: ['40+18=58'] Exploring Operation: 32/16=2, Resulting Numbers: [58, 2] Generated Node #0,1,2: 60:[58, 2] Operation: 32/16=2 Moving to Node #0,1,2 Current State: 60:[58, 2], Operations: ['40+18=58', '32/16=2'] Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.942708
hs_4
sum_heuristic
[ 93, 22, 64, 83 ]
56
[ "93+83=176", "176/22=8", "64-8=56" ]
Current State: 56:[93, 22, 64, 83], Operations: [] Exploring Operation: 93+83=176, Resulting Numbers: [22, 64, 176] Generated Node #2: [22, 64, 176] from Operation: 93+83=176 Current State: 56:[22, 64, 176], Operations: ['93+83=176'] Exploring Operation: 176/22=8, Resulting Numbers: [64, 8] Generated Node #3: [64, 8] from Operation: 176/22=8 Current State: 56:[64, 8], Operations: ['93+83=176', '176/22=8'] Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[93, 22, 64, 83], Operations: [] Exploring Operation: 93-22=71, Resulting Numbers: [64, 83, 71] Generated Node #0,0: 56:[64, 83, 71] Operation: 93-22=71 Exploring Operation: 93-64=29, Resulting Numbers: [22, 83, 29] Generated Node #0,1: 56:[22, 83, 29] Operation: 93-64=29 Exploring Operation: 83-64=19, Resulting Numbers: [93, 22, 19] Generated Node #0,2: 56:[93, 22, 19] Operation: 83-64=19 Exploring Operation: 93-83=10, Resulting Numbers: [22, 64, 10] Generated Node #0,3: 56:[22, 64, 10] Operation: 93-83=10 Moving to Node #0,3 Current State: 56:[22, 64, 10], Operations: ['93-83=10'] Exploring Operation: 22+10=32, Resulting Numbers: [64, 32] Generated Node #0,3,0: 56:[64, 32] Operation: 22+10=32 Exploring Operation: 64-10=54, Resulting Numbers: [22, 54] Generated Node #0,3,1: 56:[22, 54] Operation: 64-10=54 Exploring Operation: 64-22=42, Resulting Numbers: [10, 42] Generated Node #0,3,2: 56:[10, 42] Operation: 64-22=42 Exploring Operation: 22-10=12, Resulting Numbers: [64, 12] Generated Node #0,3,3: 56:[64, 12] Operation: 22-10=12 Moving to Node #0,1 Current State: 56:[22, 83, 29], Operations: ['93-64=29'] Exploring Operation: 83-22=61, Resulting Numbers: [29, 61] Generated Node #0,1,0: 56:[29, 61] Operation: 83-22=61 Exploring Operation: 83-29=54, Resulting Numbers: [22, 54] Generated Node #0,1,1: 56:[22, 54] Operation: 83-29=54 Exploring Operation: 29-22=7, Resulting Numbers: [83, 7] Generated Node #0,1,2: 56:[83, 7] Operation: 29-22=7 Exploring Operation: 22+29=51, Resulting Numbers: [83, 51] Generated Node #0,1,3: 56:[83, 51] Operation: 22+29=51 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[29, 61], Operations: ['93-64=29', '83-22=61'] Exploring Operation: 29*61=1769, Resulting Numbers: [1769] 1769,56 unequal: No Solution Exploring Operation: 29+61=90, Resulting Numbers: [90] 90,56 unequal: No Solution Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[22, 54], Operations: ['93-64=29', '83-29=54'] Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 22*54=1188, Resulting Numbers: [1188] 1188,56 unequal: No Solution Exploring Operation: 22+54=76, Resulting Numbers: [76] 76,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 56:[83, 7], Operations: ['93-64=29', '29-22=7'] Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,56 unequal: No Solution Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,56 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 56:[83, 51], Operations: ['93-64=29', '22+29=51'] Exploring Operation: 83+51=134, Resulting Numbers: [134] 134,56 unequal: No Solution Exploring Operation: 83*51=4233, Resulting Numbers: [4233] 4233,56 unequal: No Solution Exploring Operation: 83-51=32, Resulting Numbers: [32] 32,56 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: 56:[93, 22, 19], Operations: ['83-64=19'] Exploring Operation: 22+19=41, Resulting Numbers: [93, 41] Generated Node #0,2,0: 56:[93, 41] Operation: 22+19=41 Exploring Operation: 93-19=74, Resulting Numbers: [22, 74] Generated Node #0,2,1: 56:[22, 74] Operation: 93-19=74 Exploring Operation: 22-19=3, Resulting Numbers: [93, 3] Generated Node #0,2,2: 56:[93, 3] Operation: 22-19=3 Exploring Operation: 93-22=71, Resulting Numbers: [19, 71] Generated Node #0,2,3: 56:[19, 71] Operation: 93-22=71 Moving to Node #0,0 Current State: 56:[64, 83, 71], Operations: ['93-22=71'] Exploring Operation: 64+83=147, Resulting Numbers: [71, 147] Generated Node #0,0,0: 56:[71, 147] Operation: 64+83=147 Exploring Operation: 83-64=19, Resulting Numbers: [71, 19] Generated Node #0,0,1: 56:[71, 19] Operation: 83-64=19 Exploring Operation: 83-71=12, Resulting Numbers: [64, 12] Generated Node #0,0,2: 56:[64, 12] Operation: 83-71=12 Exploring Operation: 71-64=7, Resulting Numbers: [83, 7] Generated Node #0,0,3: 56:[83, 7] Operation: 71-64=7 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 56:[64, 12], Operations: ['93-22=71', '83-71=12'] Exploring Operation: 64+12=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 64*12=768, Resulting Numbers: [768] 768,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[71, 19], Operations: ['93-22=71', '83-64=19'] Exploring Operation: 71-19=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 71+19=90, Resulting Numbers: [90] 90,56 unequal: No Solution Exploring Operation: 71*19=1349, Resulting Numbers: [1349] 1349,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 56:[83, 7], Operations: ['93-22=71', '71-64=7'] Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,56 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[71, 147], Operations: ['93-22=71', '64+83=147'] Exploring Operation: 147-71=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 71+147=218, Resulting Numbers: [218] 218,56 unequal: No Solution Exploring Operation: 71*147=10437, Resulting Numbers: [10437] 10437,56 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: 56:[22, 54], Operations: ['93-83=10', '64-10=54'] Exploring Operation: 22*54=1188, Resulting Numbers: [1188] 1188,56 unequal: No Solution Exploring Operation: 22+54=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[64, 12], Operations: ['93-83=10', '22-10=12'] Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 64+12=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 64*12=768, Resulting Numbers: [768] 768,56 unequal: No Solution Moving to Node #0,3,0 Current State: 56:[64, 32], Operations: ['93-83=10', '22+10=32'] Exploring Operation: 64+32=96, Resulting Numbers: [96] 96,56 unequal: No Solution Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 64*32=2048, Resulting Numbers: [2048] 2048,56 unequal: No Solution Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[10, 42], Operations: ['93-83=10', '64-22=42'] Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,56 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,56 unequal: No Solution Moving to Node #0,2,3 Current State: 56:[19, 71], Operations: ['83-64=19', '93-22=71'] Exploring Operation: 19+71=90, Resulting Numbers: [90] 90,56 unequal: No Solution Exploring Operation: 71-19=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 19*71=1349, Resulting Numbers: [1349] 1349,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[22, 74], Operations: ['83-64=19', '93-19=74'] Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,56 unequal: No Solution Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,56 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[93, 3], Operations: ['83-64=19', '22-19=3'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,56 unequal: No Solution Exploring Operation: 93*3=279, Resulting Numbers: [279] 279,56 unequal: No Solution Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,56 unequal: No Solution Moving to Node #0,2,0 Current State: 56:[93, 41], Operations: ['83-64=19', '22+19=41'] Exploring Operation: 93-41=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 93+41=134, Resulting Numbers: [134] 134,56 unequal: No Solution Exploring Operation: 93*41=3813, Resulting Numbers: [3813] 3813,56 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 53, 21, 2, 16 ]
11
[ "53+2=55", "21-16=5", "55/5=11" ]
Current State: 11:[53, 21, 2, 16], Operations: [] Exploring Operation: 53+2=55, Resulting Numbers: [21, 16, 55] Generated Node #2: [21, 16, 55] from Operation: 53+2=55 Current State: 11:[21, 16, 55], Operations: ['53+2=55'] Exploring Operation: 21-16=5, Resulting Numbers: [55, 5] Generated Node #3: [55, 5] from Operation: 21-16=5 Current State: 11:[55, 5], Operations: ['53+2=55', '21-16=5'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[53, 21, 2, 16], Operations: [] Exploring Operation: 21-2=19, Resulting Numbers: [53, 16, 19] Generated Node #0,0: 11:[53, 16, 19] Operation: 21-2=19 Exploring Operation: 53-2=51, Resulting Numbers: [21, 16, 51] Generated Node #0,1: 11:[21, 16, 51] Operation: 53-2=51 Exploring Operation: 53-21=32, Resulting Numbers: [2, 16, 32] Generated Node #0,2: 11:[2, 16, 32] Operation: 53-21=32 Exploring Operation: 53-16=37, Resulting Numbers: [21, 2, 37] Generated Node #0,3: 11:[21, 2, 37] Operation: 53-16=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 11:[2, 16, 32], Operations: ['53-21=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16, 16] Generated Node #0,2,0: 11:[16, 16] Operation: 32/2=16 Exploring Operation: 32-16=16, Resulting Numbers: [2, 16] Generated Node #0,2,1: 11:[2, 16] Operation: 32-16=16 Exploring Operation: 16-2=14, Resulting Numbers: [32, 14] Generated Node #0,2,2: 11:[32, 14] Operation: 16-2=14 Exploring Operation: 32/16=2, Resulting Numbers: [2, 2] Generated Node #0,2,3: 11:[2, 2] Operation: 32/16=2 Moving to Node #0,2,0 Current State: 11:[16, 16], Operations: ['53-21=32', '32/2=16'] Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,11 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,11 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[2, 16], Operations: ['53-21=32', '32-16=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,11 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,11 unequal: No Solution Moving to Node #0,2,3 Current State: 11:[2, 2], Operations: ['53-21=32', '32/16=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,11 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,11 unequal: No Solution Moving to Node #0,2,2 Current State: 11:[32, 14], Operations: ['53-21=32', '16-2=14'] Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,11 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 11:[21, 2, 37], Operations: ['53-16=37'] Exploring Operation: 37-21=16, Resulting Numbers: [2, 16] Generated Node #0,3,0: 11:[2, 16] Operation: 37-21=16 Exploring Operation: 37-2=35, Resulting Numbers: [21, 35] Generated Node #0,3,1: 11:[21, 35] Operation: 37-2=35 Exploring Operation: 21+2=23, Resulting Numbers: [37, 23] Generated Node #0,3,2: 11:[37, 23] Operation: 21+2=23 Exploring Operation: 21-2=19, Resulting Numbers: [37, 19] Generated Node #0,3,3: 11:[37, 19] Operation: 21-2=19 Moving to Node #0,3,0 Current State: 11:[2, 16], Operations: ['53-16=37', '37-21=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,11 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[37, 19], Operations: ['53-16=37', '21-2=19'] Exploring Operation: 37+19=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 37*19=703, Resulting Numbers: [703] 703,11 unequal: No Solution Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[21, 35], Operations: ['53-16=37', '37-2=35'] Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,11 unequal: No Solution Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[37, 23], Operations: ['53-16=37', '21+2=23'] Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,11 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[53, 16, 19], Operations: ['21-2=19'] Exploring Operation: 53-19=34, Resulting Numbers: [16, 34] Generated Node #0,0,0: 11:[16, 34] Operation: 53-19=34 Exploring Operation: 53+16=69, Resulting Numbers: [19, 69] Generated Node #0,0,1: 11:[19, 69] Operation: 53+16=69 Exploring Operation: 19-16=3, Resulting Numbers: [53, 3] Generated Node #0,0,2: 11:[53, 3] Operation: 19-16=3 Exploring Operation: 53-16=37, Resulting Numbers: [19, 37] Generated Node #0,0,3: 11:[19, 37] Operation: 53-16=37 Moving to Node #0,0,0 Current State: 11:[16, 34], Operations: ['21-2=19', '53-19=34'] Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,11 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[19, 37], Operations: ['21-2=19', '53-16=37'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[53, 3], Operations: ['21-2=19', '19-16=3'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 53*3=159, Resulting Numbers: [159] 159,11 unequal: No Solution Exploring Operation: 53+3=56, Resulting Numbers: [56] 56,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[19, 69], Operations: ['21-2=19', '53+16=69'] Exploring Operation: 19*69=1311, Resulting Numbers: [1311] 1311,11 unequal: No Solution Exploring Operation: 19+69=88, Resulting Numbers: [88] 88,11 unequal: No Solution Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[21, 16, 51], Operations: ['53-2=51'] Exploring Operation: 21+16=37, Resulting Numbers: [51, 37] Generated Node #0,1,0: 11:[51, 37] Operation: 21+16=37 Exploring Operation: 21-16=5, Resulting Numbers: [51, 5] Generated Node #0,1,1: 11:[51, 5] Operation: 21-16=5 Exploring Operation: 51-16=35, Resulting Numbers: [21, 35] Generated Node #0,1,2: 11:[21, 35] Operation: 51-16=35 Exploring Operation: 51-21=30, Resulting Numbers: [16, 30] Generated Node #0,1,3: 11:[16, 30] Operation: 51-21=30 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 11:[16, 30], Operations: ['53-2=51', '51-21=30'] Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,11 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 11:[21, 35], Operations: ['53-2=51', '51-16=35'] Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,11 unequal: No Solution Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 11:[51, 5], Operations: ['53-2=51', '21-16=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[51, 37], Operations: ['53-2=51', '21+16=37'] Exploring Operation: 51*37=1887, Resulting Numbers: [1887] 1887,11 unequal: No Solution Exploring Operation: 51+37=88, Resulting Numbers: [88] 88,11 unequal: No Solution Exploring Operation: 51-37=14, Resulting Numbers: [14] 14,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 28, 35, 50, 90 ]
70
[ "35+90=125", "28*125=3500", "3500/50=70" ]
Current State: 70:[28, 35, 50, 90], Operations: [] Exploring Operation: 35+90=125, Resulting Numbers: [28, 50, 125] Generated Node #2: [28, 50, 125] from Operation: 35+90=125 Current State: 70:[28, 50, 125], Operations: ['35+90=125'] Exploring Operation: 28*125=3500, Resulting Numbers: [50, 3500] Generated Node #3: [50, 3500] from Operation: 28*125=3500 Current State: 70:[50, 3500], Operations: ['35+90=125', '28*125=3500'] Exploring Operation: 3500/50=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[28, 35, 50, 90], Operations: [] Exploring Operation: 28+50=78, Resulting Numbers: [35, 90, 78] Generated Node #0,0: 70:[35, 90, 78] Operation: 28+50=78 Exploring Operation: 90-50=40, Resulting Numbers: [28, 35, 40] Generated Node #0,1: 70:[28, 35, 40] Operation: 90-50=40 Exploring Operation: 90-28=62, Resulting Numbers: [35, 50, 62] Generated Node #0,2: 70:[35, 50, 62] Operation: 90-28=62 Exploring Operation: 50-28=22, Resulting Numbers: [35, 90, 22] Generated Node #0,3: 70:[35, 90, 22] Operation: 50-28=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[28, 35, 40], Operations: ['90-50=40'] Exploring Operation: 40-35=5, Resulting Numbers: [28, 5] Generated Node #0,1,0: 70:[28, 5] Operation: 40-35=5 Exploring Operation: 35-28=7, Resulting Numbers: [40, 7] Generated Node #0,1,1: 70:[40, 7] Operation: 35-28=7 Exploring Operation: 40-28=12, Resulting Numbers: [35, 12] Generated Node #0,1,2: 70:[35, 12] Operation: 40-28=12 Exploring Operation: 28+40=68, Resulting Numbers: [35, 68] Generated Node #0,1,3: 70:[35, 68] Operation: 28+40=68 Moving to Node #0,1,2 Current State: 70:[35, 12], Operations: ['90-50=40', '40-28=12'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,70 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,70 unequal: No Solution Moving to Node #0,1,3 Current State: 70:[35, 68], Operations: ['90-50=40', '28+40=68'] Exploring Operation: 35+68=103, Resulting Numbers: [103] 103,70 unequal: No Solution Exploring Operation: 35*68=2380, Resulting Numbers: [2380] 2380,70 unequal: No Solution Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[40, 7], Operations: ['90-50=40', '35-28=7'] Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,70 unequal: No Solution Exploring Operation: 40*7=280, Resulting Numbers: [280] 280,70 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[28, 5], Operations: ['90-50=40', '40-35=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,70 unequal: No Solution Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,70 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 #0,2 Current State: 70:[35, 50, 62], Operations: ['90-28=62'] Exploring Operation: 35+50=85, Resulting Numbers: [62, 85] Generated Node #0,2,0: 70:[62, 85] Operation: 35+50=85 Exploring Operation: 62-50=12, Resulting Numbers: [35, 12] Generated Node #0,2,1: 70:[35, 12] Operation: 62-50=12 Exploring Operation: 62-35=27, Resulting Numbers: [50, 27] Generated Node #0,2,2: 70:[50, 27] Operation: 62-35=27 Exploring Operation: 50-35=15, Resulting Numbers: [62, 15] Generated Node #0,2,3: 70:[62, 15] Operation: 50-35=15 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 70:[35, 12], Operations: ['90-28=62', '62-50=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,70 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 70:[62, 15], Operations: ['90-28=62', '50-35=15'] Exploring Operation: 62*15=930, Resulting Numbers: [930] 930,70 unequal: No Solution Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,70 unequal: No Solution Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[62, 85], Operations: ['90-28=62', '35+50=85'] Exploring Operation: 62+85=147, Resulting Numbers: [147] 147,70 unequal: No Solution Exploring Operation: 62*85=5270, Resulting Numbers: [5270] 5270,70 unequal: No Solution Exploring Operation: 85-62=23, Resulting Numbers: [23] 23,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 70:[50, 27], Operations: ['90-28=62', '62-35=27'] Exploring Operation: 50-27=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 50+27=77, Resulting Numbers: [77] 77,70 unequal: No Solution Exploring Operation: 50*27=1350, Resulting Numbers: [1350] 1350,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[35, 90, 78], Operations: ['28+50=78'] Exploring Operation: 35+90=125, Resulting Numbers: [78, 125] Generated Node #0,0,0: 70:[78, 125] Operation: 35+90=125 Exploring Operation: 90-35=55, Resulting Numbers: [78, 55] Generated Node #0,0,1: 70:[78, 55] Operation: 90-35=55 Exploring Operation: 90-78=12, Resulting Numbers: [35, 12] Generated Node #0,0,2: 70:[35, 12] Operation: 90-78=12 Exploring Operation: 78-35=43, Resulting Numbers: [90, 43] Generated Node #0,0,3: 70:[90, 43] Operation: 78-35=43 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 70:[35, 12], Operations: ['28+50=78', '90-78=12'] Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,70 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 70:[78, 55], Operations: ['28+50=78', '90-35=55'] Exploring Operation: 78*55=4290, Resulting Numbers: [4290] 4290,70 unequal: No Solution Exploring Operation: 78+55=133, Resulting Numbers: [133] 133,70 unequal: No Solution Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 70:[90, 43], Operations: ['28+50=78', '78-35=43'] Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,70 unequal: No Solution Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,70 unequal: No Solution Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[78, 125], Operations: ['28+50=78', '35+90=125'] Exploring Operation: 78*125=9750, Resulting Numbers: [9750] 9750,70 unequal: No Solution Exploring Operation: 125-78=47, Resulting Numbers: [47] 47,70 unequal: No Solution Exploring Operation: 78+125=203, Resulting Numbers: [203] 203,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[35, 90, 22], Operations: ['50-28=22'] Exploring Operation: 90-22=68, Resulting Numbers: [35, 68] Generated Node #0,3,0: 70:[35, 68] Operation: 90-22=68 Exploring Operation: 35-22=13, Resulting Numbers: [90, 13] Generated Node #0,3,1: 70:[90, 13] Operation: 35-22=13 Exploring Operation: 35+22=57, Resulting Numbers: [90, 57] Generated Node #0,3,2: 70:[90, 57] Operation: 35+22=57 Exploring Operation: 90-35=55, Resulting Numbers: [22, 55] Generated Node #0,3,3: 70:[22, 55] Operation: 90-35=55 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 70:[35, 68], Operations: ['50-28=22', '90-22=68'] Exploring Operation: 35*68=2380, Resulting Numbers: [2380] 2380,70 unequal: No Solution Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,70 unequal: No Solution Exploring Operation: 35+68=103, Resulting Numbers: [103] 103,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 70:[90, 13], Operations: ['50-28=22', '35-22=13'] Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,70 unequal: No Solution Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,70 unequal: No Solution Exploring Operation: 90*13=1170, Resulting Numbers: [1170] 1170,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 70:[22, 55], Operations: ['50-28=22', '90-35=55'] Exploring Operation: 22+55=77, Resulting Numbers: [77] 77,70 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,70 unequal: No Solution Exploring Operation: 22*55=1210, Resulting Numbers: [1210] 1210,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 70:[90, 57], Operations: ['50-28=22', '35+22=57'] Exploring Operation: 90*57=5130, Resulting Numbers: [5130] 5130,70 unequal: No Solution Exploring Operation: 90+57=147, Resulting Numbers: [147] 147,70 unequal: No Solution Exploring Operation: 90-57=33, Resulting Numbers: [33] 33,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 47, 27, 63, 50 ]
61
[ "47+27=74", "63-50=13", "74-13=61" ]
Current State: 61:[47, 27, 63, 50], Operations: [] Exploring Operation: 47+27=74, Resulting Numbers: [63, 50, 74] Generated Node #2: [63, 50, 74] from Operation: 47+27=74 Current State: 61:[63, 50, 74], Operations: ['47+27=74'] Exploring Operation: 63-50=13, Resulting Numbers: [74, 13] Generated Node #3: [74, 13] from Operation: 63-50=13 Current State: 61:[74, 13], Operations: ['47+27=74', '63-50=13'] Exploring Operation: 74-13=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[47, 27, 63, 50], Operations: [] Exploring Operation: 47+27=74, Resulting Numbers: [63, 50, 74] Generated Node #0,0: 61:[63, 50, 74] Operation: 47+27=74 Exploring Operation: 63-27=36, Resulting Numbers: [47, 50, 36] Generated Node #0,1: 61:[47, 50, 36] Operation: 63-27=36 Exploring Operation: 27+63=90, Resulting Numbers: [47, 50, 90] Generated Node #0,2: 61:[47, 50, 90] Operation: 27+63=90 Exploring Operation: 47-27=20, Resulting Numbers: [63, 50, 20] Generated Node #0,3: 61:[63, 50, 20] Operation: 47-27=20 Exploring Operation: 27+50=77, Resulting Numbers: [47, 63, 77] Generated Node #0,4: 61:[47, 63, 77] Operation: 27+50=77 Moving to Node #0,0 Current State: 61:[63, 50, 74], Operations: ['47+27=74'] Exploring Operation: 50+74=124, Resulting Numbers: [63, 124] Generated Node #0,0,0: 61:[63, 124] Operation: 50+74=124 Exploring Operation: 74-50=24, Resulting Numbers: [63, 24] Generated Node #0,0,1: 61:[63, 24] Operation: 74-50=24 Exploring Operation: 63-50=13, Resulting Numbers: [74, 13] Generated Node #0,0,2: 61:[74, 13] Operation: 63-50=13 Exploring Operation: 63+50=113, Resulting Numbers: [74, 113] Generated Node #0,0,3: 61:[74, 113] Operation: 63+50=113 Exploring Operation: 74-63=11, Resulting Numbers: [50, 11] Generated Node #0,0,4: 61:[50, 11] Operation: 74-63=11 Moving to Node #0,4 Current State: 61:[47, 63, 77], Operations: ['27+50=77'] Exploring Operation: 47+77=124, Resulting Numbers: [63, 124] Generated Node #0,4,0: 61:[63, 124] Operation: 47+77=124 Exploring Operation: 77-63=14, Resulting Numbers: [47, 14] Generated Node #0,4,1: 61:[47, 14] Operation: 77-63=14 Exploring Operation: 63-47=16, Resulting Numbers: [77, 16] Generated Node #0,4,2: 61:[77, 16] Operation: 63-47=16 Exploring Operation: 77-47=30, Resulting Numbers: [63, 30] Generated Node #0,4,3: 61:[63, 30] Operation: 77-47=30 Exploring Operation: 47+63=110, Resulting Numbers: [77, 110] Generated Node #0,4,4: 61:[77, 110] Operation: 47+63=110 Moving to Node #0,1 Current State: 61:[47, 50, 36], Operations: ['63-27=36'] Exploring Operation: 50+36=86, Resulting Numbers: [47, 86] Generated Node #0,1,0: 61:[47, 86] Operation: 50+36=86 Exploring Operation: 47-36=11, Resulting Numbers: [50, 11] Generated Node #0,1,1: 61:[50, 11] Operation: 47-36=11 Exploring Operation: 47+50=97, Resulting Numbers: [36, 97] Generated Node #0,1,2: 61:[36, 97] Operation: 47+50=97 Exploring Operation: 50-36=14, Resulting Numbers: [47, 14] Generated Node #0,1,3: 61:[47, 14] Operation: 50-36=14 Exploring Operation: 47+36=83, Resulting Numbers: [50, 83] Generated Node #0,1,4: 61:[50, 83] Operation: 47+36=83 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 61:[50, 83], Operations: ['63-27=36', '47+36=83'] Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,61 unequal: No Solution Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,61 unequal: No Solution Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,61 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 #0,1,0 Current State: 61:[47, 86], Operations: ['63-27=36', '50+36=86'] Exploring Operation: 47+86=133, Resulting Numbers: [133] 133,61 unequal: No Solution Exploring Operation: 86-47=39, Resulting Numbers: [39] 39,61 unequal: No Solution Exploring Operation: 47*86=4042, Resulting Numbers: [4042] 4042,61 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:[50, 11], Operations: ['63-27=36', '47-36=11'] Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[47, 27, 63, 50], Operations: [] Exploring Operation: 63-27=36, Resulting Numbers: [47, 50, 36] Generated Node #0,1: 61:[47, 50, 36] Operation: 63-27=36 Moving to Node #0,1 Current State: 61:[47, 50, 36], Operations: ['63-27=36'] Exploring Operation: 47-36=11, Resulting Numbers: [50, 11] Generated Node #0,1,1: 61:[50, 11] Operation: 47-36=11 Moving to Node #0,1,1 Current State: 61:[50, 11], Operations: ['63-27=36', '47-36=11'] Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_5
mult_heuristic
[ 61, 58, 16, 71 ]
52
[ "61-58=3", "71-16=55", "55-3=52" ]
Current State: 52:[61, 58, 16, 71], Operations: [] Exploring Operation: 61-58=3, Resulting Numbers: [16, 71, 3] Generated Node #2: [16, 71, 3] from Operation: 61-58=3 Current State: 52:[16, 71, 3], Operations: ['61-58=3'] Exploring Operation: 71-16=55, Resulting Numbers: [3, 55] Generated Node #3: [3, 55] from Operation: 71-16=55 Current State: 52:[3, 55], Operations: ['61-58=3', '71-16=55'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[61, 58, 16, 71], Operations: [] Exploring Operation: 71-61=10, Resulting Numbers: [58, 16, 10] Generated Node #0,0: 52:[58, 16, 10] Operation: 71-61=10 Exploring Operation: 71-58=13, Resulting Numbers: [61, 16, 13] Generated Node #0,1: 52:[61, 16, 13] Operation: 71-58=13 Exploring Operation: 71-16=55, Resulting Numbers: [61, 58, 55] Generated Node #0,2: 52:[61, 58, 55] Operation: 71-16=55 Exploring Operation: 61-58=3, Resulting Numbers: [16, 71, 3] Generated Node #0,3: 52:[16, 71, 3] Operation: 61-58=3 Moving to Node #0,0 Current State: 52:[58, 16, 10], Operations: ['71-61=10'] Exploring Operation: 58-16=42, Resulting Numbers: [10, 42] Generated Node #0,0,0: 52:[10, 42] Operation: 58-16=42 Exploring Operation: 16+10=26, Resulting Numbers: [58, 26] Generated Node #0,0,1: 52:[58, 26] Operation: 16+10=26 Exploring Operation: 16-10=6, Resulting Numbers: [58, 6] Generated Node #0,0,2: 52:[58, 6] Operation: 16-10=6 Exploring Operation: 58-10=48, Resulting Numbers: [16, 48] Generated Node #0,0,3: 52:[16, 48] Operation: 58-10=48 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[58, 26], Operations: ['71-61=10', '16+10=26'] Exploring Operation: 58-26=32, Resulting Numbers: [32] 32,52 unequal: No Solution Exploring Operation: 58*26=1508, Resulting Numbers: [1508] 1508,52 unequal: No Solution Exploring Operation: 58+26=84, Resulting Numbers: [84] 84,52 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 #0,0,3 Current State: 52:[16, 48], Operations: ['71-61=10', '58-10=48'] Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,52 unequal: No Solution Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 16*48=768, Resulting Numbers: [768] 768,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 52:[58, 6], Operations: ['71-61=10', '16-10=6'] Exploring Operation: 58*6=348, Resulting Numbers: [348] 348,52 unequal: No Solution Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[61, 58, 16, 71], Operations: [] Exploring Operation: 71-61=10, Resulting Numbers: [58, 16, 10] Generated Node #0,0: 52:[58, 16, 10] Operation: 71-61=10 Moving to Node #0,0 Current State: 52:[58, 16, 10], Operations: ['71-61=10'] Exploring Operation: 16-10=6, Resulting Numbers: [58, 6] Generated Node #0,0,2: 52:[58, 6] Operation: 16-10=6 Moving to Node #0,0,2 Current State: 52:[58, 6], Operations: ['71-61=10', '16-10=6'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 23, 49, 75, 62 ]
46
[ "49+75=124", "23*124=2852", "2852/62=46" ]
Current State: 46:[23, 49, 75, 62], Operations: [] Exploring Operation: 49+75=124, Resulting Numbers: [23, 62, 124] Generated Node #2: [23, 62, 124] from Operation: 49+75=124 Current State: 46:[23, 62, 124], Operations: ['49+75=124'] Exploring Operation: 23*124=2852, Resulting Numbers: [62, 2852] Generated Node #3: [62, 2852] from Operation: 23*124=2852 Current State: 46:[62, 2852], Operations: ['49+75=124', '23*124=2852'] Exploring Operation: 2852/62=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[23, 49, 75, 62], Operations: [] Exploring Operation: 75-62=13, Resulting Numbers: [23, 49, 13] Generated Node #0,0: 46:[23, 49, 13] Operation: 75-62=13 Exploring Operation: 75-49=26, Resulting Numbers: [23, 62, 26] Generated Node #0,1: 46:[23, 62, 26] Operation: 75-49=26 Exploring Operation: 75-23=52, Resulting Numbers: [49, 62, 52] Generated Node #0,2: 46:[49, 62, 52] Operation: 75-23=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[23, 49, 13], Operations: ['75-62=13'] Exploring Operation: 49-23=26, Resulting Numbers: [13, 26] Generated Node #0,0,0: 46:[13, 26] Operation: 49-23=26 Exploring Operation: 49-13=36, Resulting Numbers: [23, 36] Generated Node #0,0,1: 46:[23, 36] Operation: 49-13=36 Exploring Operation: 23-13=10, Resulting Numbers: [49, 10] Generated Node #0,0,2: 46:[49, 10] Operation: 23-13=10 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 46:[23, 36], Operations: ['75-62=13', '49-13=36'] Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 46:[49, 10], Operations: ['75-62=13', '23-13=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,46 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[13, 26], Operations: ['75-62=13', '49-23=26'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[23, 62, 26], Operations: ['75-49=26'] Exploring Operation: 62-23=39, Resulting Numbers: [26, 39] Generated Node #0,1,0: 46:[26, 39] Operation: 62-23=39 Exploring Operation: 62-26=36, Resulting Numbers: [23, 36] Generated Node #0,1,1: 46:[23, 36] Operation: 62-26=36 Exploring Operation: 26-23=3, Resulting Numbers: [62, 3] Generated Node #0,1,2: 46:[62, 3] Operation: 26-23=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[26, 39], Operations: ['75-49=26', '62-23=39'] Exploring Operation: 26*39=1014, Resulting Numbers: [1014] 1014,46 unequal: No Solution Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 26+39=65, Resulting Numbers: [65] 65,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[23, 36], Operations: ['75-49=26', '62-26=36'] Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,46 unequal: No Solution Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[62, 3], Operations: ['75-49=26', '26-23=3'] Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[49, 62, 52], Operations: ['75-23=52'] Exploring Operation: 62-49=13, Resulting Numbers: [52, 13] Generated Node #0,2,0: 46:[52, 13] Operation: 62-49=13 Exploring Operation: 52-49=3, Resulting Numbers: [62, 3] Generated Node #0,2,1: 46:[62, 3] Operation: 52-49=3 Exploring Operation: 62-52=10, Resulting Numbers: [49, 10] Generated Node #0,2,2: 46:[49, 10] Operation: 62-52=10 Moving to Node #0,2,2 Current State: 46:[49, 10], Operations: ['75-23=52', '62-52=10'] Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,46 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[52, 13], Operations: ['75-23=52', '62-49=13'] Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 52+13=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[62, 3], Operations: ['75-23=52', '52-49=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,46 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
[ 74, 20, 50, 4 ]
48
[ "74+20=94", "50-4=46", "94-46=48" ]
Current State: 48:[74, 20, 50, 4], Operations: [] Exploring Operation: 74+20=94, Resulting Numbers: [50, 4, 94] Generated Node #2: [50, 4, 94] from Operation: 74+20=94 Current State: 48:[50, 4, 94], Operations: ['74+20=94'] Exploring Operation: 50-4=46, Resulting Numbers: [94, 46] Generated Node #3: [94, 46] from Operation: 50-4=46 Current State: 48:[94, 46], Operations: ['74+20=94', '50-4=46'] Exploring Operation: 94-46=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[74, 20, 50, 4], Operations: [] Exploring Operation: 74-4=70, Resulting Numbers: [20, 50, 70] Generated Node #0,0: 48:[20, 50, 70] Operation: 74-4=70 Exploring Operation: 74-20=54, Resulting Numbers: [50, 4, 54] Generated Node #0,1: 48:[50, 4, 54] Operation: 74-20=54 Exploring Operation: 74-50=24, Resulting Numbers: [20, 4, 24] Generated Node #0,2: 48:[20, 4, 24] Operation: 74-50=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[20, 4, 24], Operations: ['74-50=24'] Exploring Operation: 24-20=4, Resulting Numbers: [4, 4] Generated Node #0,2,0: 48:[4, 4] Operation: 24-20=4 Exploring Operation: 20-4=16, Resulting Numbers: [24, 16] Generated Node #0,2,1: 48:[24, 16] Operation: 20-4=16 Exploring Operation: 20+4=24, Resulting Numbers: [24, 24] Generated Node #0,2,2: 48:[24, 24] Operation: 20+4=24 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 48:[4, 4], Operations: ['74-50=24', '24-20=4'] Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,48 unequal: No Solution No 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: 48:[24, 16], Operations: ['74-50=24', '20-4=16'] Exploring Operation: 24*16=384, Resulting Numbers: [384] 384,48 unequal: No Solution Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 24+16=40, Resulting Numbers: [40] 40,48 unequal: No Solution No 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: 48:[24, 24], Operations: ['74-50=24', '20+4=24'] Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[74, 20, 50, 4], Operations: [] Exploring Operation: 74-50=24, Resulting Numbers: [20, 4, 24] Generated Node #0,2: 48:[20, 4, 24] Operation: 74-50=24 Moving to Node #0,2 Current State: 48:[20, 4, 24], Operations: ['74-50=24'] Exploring Operation: 20+4=24, Resulting Numbers: [24, 24] Generated Node #0,2,2: 48:[24, 24] Operation: 20+4=24 Moving to Node #0,2,2 Current State: 48:[24, 24], Operations: ['74-50=24', '20+4=24'] Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 3, 1, 19, 6 ]
98
[ "6-1=5", "19*5=95", "3+95=98" ]
Current State: 98:[3, 1, 19, 6], Operations: [] Exploring Operation: 6-1=5, Resulting Numbers: [3, 19, 5] Generated Node #2: [3, 19, 5] from Operation: 6-1=5 Current State: 98:[3, 19, 5], Operations: ['6-1=5'] Exploring Operation: 19*5=95, Resulting Numbers: [3, 95] Generated Node #3: [3, 95] from Operation: 19*5=95 Current State: 98:[3, 95], Operations: ['6-1=5', '19*5=95'] Exploring Operation: 3+95=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[3, 1, 19, 6], Operations: [] Exploring Operation: 19-6=13, Resulting Numbers: [3, 1, 13] Generated Node #0,0: 98:[3, 1, 13] Operation: 19-6=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[3, 1, 13], Operations: ['19-6=13'] Exploring Operation: 3-1=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 98:[13, 2] Operation: 3-1=2 Moving to Node #0,0,0 Current State: 98:[13, 2], Operations: ['19-6=13', '3-1=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 81, 10, 89, 7 ]
100
[ "81+89=170", "10*7=70", "170-70=100" ]
Current State: 100:[81, 10, 89, 7], Operations: [] Exploring Operation: 81+89=170, Resulting Numbers: [10, 7, 170] Generated Node #2: [10, 7, 170] from Operation: 81+89=170 Current State: 100:[10, 7, 170], Operations: ['81+89=170'] Exploring Operation: 10*7=70, Resulting Numbers: [170, 70] Generated Node #3: [170, 70] from Operation: 10*7=70 Current State: 100:[170, 70], Operations: ['81+89=170', '10*7=70'] Exploring Operation: 170-70=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[81, 10, 89, 7], Operations: [] Exploring Operation: 89-81=8, Resulting Numbers: [10, 7, 8] Generated Node #0,0: 100:[10, 7, 8] Operation: 89-81=8 Exploring Operation: 10+89=99, Resulting Numbers: [81, 7, 99] Generated Node #0,1: 100:[81, 7, 99] Operation: 10+89=99 Exploring Operation: 81+10=91, Resulting Numbers: [89, 7, 91] Generated Node #0,2: 100:[89, 7, 91] Operation: 81+10=91 Exploring Operation: 81+7=88, Resulting Numbers: [10, 89, 88] Generated Node #0,3: 100:[10, 89, 88] Operation: 81+7=88 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[10, 7, 8], Operations: ['89-81=8'] Exploring Operation: 10+8=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 100:[7, 18] Operation: 10+8=18 Exploring Operation: 10-8=2, Resulting Numbers: [7, 2] Generated Node #0,0,1: 100:[7, 2] Operation: 10-8=2 Exploring Operation: 8-7=1, Resulting Numbers: [10, 1] Generated Node #0,0,2: 100:[10, 1] Operation: 8-7=1 Exploring Operation: 10-7=3, Resulting Numbers: [8, 3] Generated Node #0,0,3: 100:[8, 3] Operation: 10-7=3 Moving to Node #0,0,2 Current State: 100:[10, 1], Operations: ['89-81=8', '8-7=1'] Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[7, 2], Operations: ['89-81=8', '10-8=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,100 unequal: No Solution Moving to Node #0,0,3 Current State: 100:[8, 3], Operations: ['89-81=8', '10-7=3'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[7, 18], Operations: ['89-81=8', '10+8=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,100 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,100 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:[81, 7, 99], Operations: ['10+89=99'] Exploring Operation: 81-7=74, Resulting Numbers: [99, 74] Generated Node #0,1,0: 100:[99, 74] Operation: 81-7=74 Exploring Operation: 99-81=18, Resulting Numbers: [7, 18] Generated Node #0,1,1: 100:[7, 18] Operation: 99-81=18 Exploring Operation: 7+99=106, Resulting Numbers: [81, 106] Generated Node #0,1,2: 100:[81, 106] Operation: 7+99=106 Exploring Operation: 81+7=88, Resulting Numbers: [99, 88] Generated Node #0,1,3: 100:[99, 88] Operation: 81+7=88 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[7, 18], Operations: ['10+89=99', '99-81=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,100 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,100 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 #0,1,3 Current State: 100:[99, 88], Operations: ['10+89=99', '81+7=88'] Exploring Operation: 99-88=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 99+88=187, Resulting Numbers: [187] 187,100 unequal: No Solution Exploring Operation: 99*88=8712, Resulting Numbers: [8712] 8712,100 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 #0,1,0 Current State: 100:[99, 74], Operations: ['10+89=99', '81-7=74'] Exploring Operation: 99-74=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 99*74=7326, Resulting Numbers: [7326] 7326,100 unequal: No Solution Exploring Operation: 99+74=173, Resulting Numbers: [173] 173,100 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 #0,1,2 Current State: 100:[81, 106], Operations: ['10+89=99', '7+99=106'] Exploring Operation: 81+106=187, Resulting Numbers: [187] 187,100 unequal: No Solution Exploring Operation: 81*106=8586, Resulting Numbers: [8586] 8586,100 unequal: No Solution Exploring Operation: 106-81=25, Resulting Numbers: [25] 25,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[89, 7, 91], Operations: ['81+10=91'] Exploring Operation: 91/7=13, Resulting Numbers: [89, 13] Generated Node #0,2,0: 100:[89, 13] Operation: 91/7=13 Exploring Operation: 7+91=98, Resulting Numbers: [89, 98] Generated Node #0,2,1: 100:[89, 98] Operation: 7+91=98 Exploring Operation: 89+7=96, Resulting Numbers: [91, 96] Generated Node #0,2,2: 100:[91, 96] Operation: 89+7=96 Exploring Operation: 91-89=2, Resulting Numbers: [7, 2] Generated Node #0,2,3: 100:[7, 2] Operation: 91-89=2 Moving to Node #0,2,3 Current State: 100:[7, 2], Operations: ['81+10=91', '91-89=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,100 unequal: No Solution Moving to Node #0,2,2 Current State: 100:[91, 96], Operations: ['81+10=91', '89+7=96'] Exploring Operation: 91+96=187, Resulting Numbers: [187] 187,100 unequal: No Solution Exploring Operation: 96-91=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 91*96=8736, Resulting Numbers: [8736] 8736,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[89, 98], Operations: ['81+10=91', '7+91=98'] Exploring Operation: 98-89=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 89+98=187, Resulting Numbers: [187] 187,100 unequal: No Solution Exploring Operation: 89*98=8722, Resulting Numbers: [8722] 8722,100 unequal: No Solution Moving to Node #0,2,0 Current State: 100:[89, 13], Operations: ['81+10=91', '91/7=13'] Exploring Operation: 89-13=76, Resulting Numbers: [76] 76,100 unequal: No Solution Exploring Operation: 89+13=102, Resulting Numbers: [102] 102,100 unequal: No Solution Exploring Operation: 89*13=1157, Resulting Numbers: [1157] 1157,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[10, 89, 88], Operations: ['81+7=88'] Exploring Operation: 89-10=79, Resulting Numbers: [88, 79] Generated Node #0,3,0: 100:[88, 79] Operation: 89-10=79 Exploring Operation: 89-88=1, Resulting Numbers: [10, 1] Generated Node #0,3,1: 100:[10, 1] Operation: 89-88=1 Exploring Operation: 10+88=98, Resulting Numbers: [89, 98] Generated Node #0,3,2: 100:[89, 98] Operation: 10+88=98 Exploring Operation: 10+89=99, Resulting Numbers: [88, 99] Generated Node #0,3,3: 100:[88, 99] Operation: 10+89=99 Moving to Node #0,3,1 Current State: 100:[10, 1], Operations: ['81+7=88', '89-88=1'] Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,100 unequal: No Solution Moving to Node #0,3,3 Current State: 100:[88, 99], Operations: ['81+7=88', '10+89=99'] Exploring Operation: 99-88=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 88+99=187, Resulting Numbers: [187] 187,100 unequal: No Solution Exploring Operation: 88*99=8712, Resulting Numbers: [8712] 8712,100 unequal: No Solution Moving to Node #0,3,2 Current State: 100:[89, 98], Operations: ['81+7=88', '10+88=98'] Exploring Operation: 98-89=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 89+98=187, Resulting Numbers: [187] 187,100 unequal: No Solution Exploring Operation: 89*98=8722, Resulting Numbers: [8722] 8722,100 unequal: No Solution Moving to Node #0,3,0 Current State: 100:[88, 79], Operations: ['81+7=88', '89-10=79'] Exploring Operation: 88-79=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 88+79=167, Resulting Numbers: [167] 167,100 unequal: No Solution Exploring Operation: 88*79=6952, Resulting Numbers: [6952] 6952,100 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
[ 9, 90, 7, 52 ]
69
[ "90/9=10", "7+52=59", "10+59=69" ]
Current State: 69:[9, 90, 7, 52], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [7, 52, 10] Generated Node #2: [7, 52, 10] from Operation: 90/9=10 Current State: 69:[7, 52, 10], Operations: ['90/9=10'] Exploring Operation: 7+52=59, Resulting Numbers: [10, 59] Generated Node #3: [10, 59] from Operation: 7+52=59 Current State: 69:[10, 59], Operations: ['90/9=10', '7+52=59'] Exploring Operation: 10+59=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[9, 90, 7, 52], Operations: [] Exploring Operation: 90-9=81, Resulting Numbers: [7, 52, 81] Generated Node #0,0: 69:[7, 52, 81] Operation: 90-9=81 Exploring Operation: 90-52=38, Resulting Numbers: [9, 7, 38] Generated Node #0,1: 69:[9, 7, 38] Operation: 90-52=38 Exploring Operation: 9+52=61, Resulting Numbers: [90, 7, 61] Generated Node #0,2: 69:[90, 7, 61] Operation: 9+52=61 Exploring Operation: 90/9=10, Resulting Numbers: [7, 52, 10] Generated Node #0,3: 69:[7, 52, 10] Operation: 90/9=10 Moving to Node #0,1 Current State: 69:[9, 7, 38], Operations: ['90-52=38'] Exploring Operation: 9-7=2, Resulting Numbers: [38, 2] Generated Node #0,1,0: 69:[38, 2] Operation: 9-7=2 Exploring Operation: 38-7=31, Resulting Numbers: [9, 31] Generated Node #0,1,1: 69:[9, 31] Operation: 38-7=31 Exploring Operation: 9*7=63, Resulting Numbers: [38, 63] Generated Node #0,1,2: 69:[38, 63] Operation: 9*7=63 Exploring Operation: 38-9=29, Resulting Numbers: [7, 29] Generated Node #0,1,3: 69:[7, 29] Operation: 38-9=29 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[7, 29], Operations: ['90-52=38', '38-9=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,69 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 #0,1,1 Current State: 69:[9, 31], Operations: ['90-52=38', '38-7=31'] Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 9*31=279, Resulting Numbers: [279] 279,69 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,69 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:[38, 2], Operations: ['90-52=38', '9-7=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,69 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,69 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 #0,1,2 Current State: 69:[38, 63], Operations: ['90-52=38', '9*7=63'] Exploring Operation: 38+63=101, Resulting Numbers: [101] 101,69 unequal: No Solution Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 38*63=2394, Resulting Numbers: [2394] 2394,69 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: 69:[7, 52, 10], Operations: ['90/9=10'] Exploring Operation: 10-7=3, Resulting Numbers: [52, 3] Generated Node #0,3,0: 69:[52, 3] Operation: 10-7=3 Exploring Operation: 7*10=70, Resulting Numbers: [52, 70] Generated Node #0,3,1: 69:[52, 70] Operation: 7*10=70 Exploring Operation: 52+10=62, Resulting Numbers: [7, 62] Generated Node #0,3,2: 69:[7, 62] Operation: 52+10=62 Exploring Operation: 7+52=59, Resulting Numbers: [10, 59] Generated Node #0,3,3: 69:[10, 59] Operation: 7+52=59 Moving to Node #0,2 Current State: 69:[90, 7, 61], Operations: ['9+52=61'] Exploring Operation: 7+61=68, Resulting Numbers: [90, 68] Generated Node #0,2,0: 69:[90, 68] Operation: 7+61=68 Exploring Operation: 90+7=97, Resulting Numbers: [61, 97] Generated Node #0,2,1: 69:[61, 97] Operation: 90+7=97 Exploring Operation: 90-61=29, Resulting Numbers: [7, 29] Generated Node #0,2,2: 69:[7, 29] Operation: 90-61=29 Exploring Operation: 90-7=83, Resulting Numbers: [61, 83] Generated Node #0,2,3: 69:[61, 83] Operation: 90-7=83 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[7, 29], Operations: ['9+52=61', '90-61=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,69 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,69 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 #0,2,0 Current State: 69:[90, 68], Operations: ['9+52=61', '7+61=68'] Exploring Operation: 90+68=158, Resulting Numbers: [158] 158,69 unequal: No Solution Exploring Operation: 90*68=6120, Resulting Numbers: [6120] 6120,69 unequal: No Solution Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,69 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 #0,2,3 Current State: 69:[61, 83], Operations: ['9+52=61', '90-7=83'] Exploring Operation: 83-61=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 61*83=5063, Resulting Numbers: [5063] 5063,69 unequal: No Solution Exploring Operation: 61+83=144, Resulting Numbers: [144] 144,69 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 #0,2,1 Current State: 69:[61, 97], Operations: ['9+52=61', '90+7=97'] Exploring Operation: 61*97=5917, Resulting Numbers: [5917] 5917,69 unequal: No Solution Exploring Operation: 97-61=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 61+97=158, Resulting Numbers: [158] 158,69 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:[7, 52, 81], Operations: ['90-9=81'] Exploring Operation: 52-7=45, Resulting Numbers: [81, 45] Generated Node #0,0,0: 69:[81, 45] Operation: 52-7=45 Exploring Operation: 81-52=29, Resulting Numbers: [7, 29] Generated Node #0,0,1: 69:[7, 29] Operation: 81-52=29 Exploring Operation: 81-7=74, Resulting Numbers: [52, 74] Generated Node #0,0,2: 69:[52, 74] Operation: 81-7=74 Exploring Operation: 7+52=59, Resulting Numbers: [81, 59] Generated Node #0,0,3: 69:[81, 59] Operation: 7+52=59 Moving to Node #0,0,1 Current State: 69:[7, 29], Operations: ['90-9=81', '81-52=29'] Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,69 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[7, 62], Operations: ['90/9=10', '52+10=62'] Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[9, 90, 7, 52], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [7, 52, 10] Generated Node #0,3: 69:[7, 52, 10] Operation: 90/9=10 Moving to Node #0,3 Current State: 69:[7, 52, 10], Operations: ['90/9=10'] Exploring Operation: 52+10=62, Resulting Numbers: [7, 62] Generated Node #0,3,2: 69:[7, 62] Operation: 52+10=62 Moving to Node #0,3,2 Current State: 69:[7, 62], Operations: ['90/9=10', '52+10=62'] Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.953993
hs_4
sum_heuristic
[ 34, 5, 41, 32 ]
51
[ "34-32=2", "5*2=10", "41+10=51" ]
Current State: 51:[34, 5, 41, 32], Operations: [] Exploring Operation: 34-32=2, Resulting Numbers: [5, 41, 2] Generated Node #2: [5, 41, 2] from Operation: 34-32=2 Current State: 51:[5, 41, 2], Operations: ['34-32=2'] Exploring Operation: 5*2=10, Resulting Numbers: [41, 10] Generated Node #3: [41, 10] from Operation: 5*2=10 Current State: 51:[41, 10], Operations: ['34-32=2', '5*2=10'] Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[34, 5, 41, 32], Operations: [] Exploring Operation: 34-32=2, Resulting Numbers: [5, 41, 2] Generated Node #0,0: 51:[5, 41, 2] Operation: 34-32=2 Exploring Operation: 41-34=7, Resulting Numbers: [5, 32, 7] Generated Node #0,1: 51:[5, 32, 7] Operation: 41-34=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[5, 41, 2], Operations: ['34-32=2'] Exploring Operation: 5-2=3, Resulting Numbers: [41, 3] Generated Node #0,0,0: 51:[41, 3] Operation: 5-2=3 Exploring Operation: 5+41=46, Resulting Numbers: [2, 46] Generated Node #0,0,1: 51:[2, 46] Operation: 5+41=46 Moving to Node #0,0,1 Current State: 51:[2, 46], Operations: ['34-32=2', '5+41=46'] Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,51 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[41, 3], Operations: ['34-32=2', '5-2=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,51 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 Current State: 51:[5, 32, 7], Operations: ['41-34=7'] Exploring Operation: 32-5=27, Resulting Numbers: [7, 27] Generated Node #0,1,0: 51:[7, 27] Operation: 32-5=27 Exploring Operation: 32-7=25, Resulting Numbers: [5, 25] Generated Node #0,1,1: 51:[5, 25] Operation: 32-7=25 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[5, 25], Operations: ['41-34=7', '32-7=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,51 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:[7, 27], Operations: ['41-34=7', '32-5=27'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,51 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 No solution found.
0
hs_2
mult_heuristic
[ 47, 80, 19, 11 ]
63
[ "80-47=33", "19+11=30", "33+30=63" ]
Current State: 63:[47, 80, 19, 11], Operations: [] Exploring Operation: 80-47=33, Resulting Numbers: [19, 11, 33] Generated Node #2: [19, 11, 33] from Operation: 80-47=33 Current State: 63:[19, 11, 33], Operations: ['80-47=33'] Exploring Operation: 19+11=30, Resulting Numbers: [33, 30] Generated Node #3: [33, 30] from Operation: 19+11=30 Current State: 63:[33, 30], Operations: ['80-47=33', '19+11=30'] Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[47, 80, 19, 11], Operations: [] Exploring Operation: 80-19=61, Resulting Numbers: [47, 11, 61] Generated Node #0,0: 63:[47, 11, 61] Operation: 80-19=61 Exploring Operation: 47+19=66, Resulting Numbers: [80, 11, 66] Generated Node #0,1: 63:[80, 11, 66] Operation: 47+19=66 Exploring Operation: 80-47=33, Resulting Numbers: [19, 11, 33] Generated Node #0,2: 63:[19, 11, 33] Operation: 80-47=33 Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[19, 11, 33], Operations: ['80-47=33'] Exploring Operation: 33-11=22, Resulting Numbers: [19, 22] Generated Node #0,2,0: 63:[19, 22] Operation: 33-11=22 Exploring Operation: 33/11=3, Resulting Numbers: [19, 3] Generated Node #0,2,1: 63:[19, 3] Operation: 33/11=3 Exploring Operation: 33-19=14, Resulting Numbers: [11, 14] Generated Node #0,2,2: 63:[11, 14] Operation: 33-19=14 Moving to Node #0,2,1 Current State: 63:[19, 3], Operations: ['80-47=33', '33/11=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[19, 22], Operations: ['80-47=33', '33-11=22'] Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[11, 14], Operations: ['80-47=33', '33-19=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[47, 11, 61], Operations: ['80-19=61'] Exploring Operation: 47-11=36, Resulting Numbers: [61, 36] Generated Node #0,0,0: 63:[61, 36] Operation: 47-11=36 Exploring Operation: 61-47=14, Resulting Numbers: [11, 14] Generated Node #0,0,1: 63:[11, 14] Operation: 61-47=14 Exploring Operation: 47+11=58, Resulting Numbers: [61, 58] Generated Node #0,0,2: 63:[61, 58] Operation: 47+11=58 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[11, 14], Operations: ['80-19=61', '61-47=14'] Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,63 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 63:[61, 58], Operations: ['80-19=61', '47+11=58'] Exploring Operation: 61*58=3538, Resulting Numbers: [3538] 3538,63 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 61+58=119, Resulting Numbers: [119] 119,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[61, 36], Operations: ['80-19=61', '47-11=36'] Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 61+36=97, Resulting Numbers: [97] 97,63 unequal: No Solution Exploring Operation: 61*36=2196, Resulting Numbers: [2196] 2196,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[80, 11, 66], Operations: ['47+19=66'] Exploring Operation: 80-11=69, Resulting Numbers: [66, 69] Generated Node #0,1,0: 63:[66, 69] Operation: 80-11=69 Exploring Operation: 66/11=6, Resulting Numbers: [80, 6] Generated Node #0,1,1: 63:[80, 6] Operation: 66/11=6 Exploring Operation: 80-66=14, Resulting Numbers: [11, 14] Generated Node #0,1,2: 63:[11, 14] Operation: 80-66=14 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 63:[11, 14], Operations: ['47+19=66', '80-66=14'] Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,63 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[66, 69], Operations: ['47+19=66', '80-11=69'] Exploring Operation: 69-66=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 66*69=4554, Resulting Numbers: [4554] 4554,63 unequal: No Solution Exploring Operation: 66+69=135, Resulting Numbers: [135] 135,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[80, 6], Operations: ['47+19=66', '66/11=6'] Exploring Operation: 80+6=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 80*6=480, Resulting Numbers: [480] 480,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 49, 2, 38, 53 ]
31
[ "49-38=11", "2*11=22", "53-22=31" ]
Current State: 31:[49, 2, 38, 53], Operations: [] Exploring Operation: 49-38=11, Resulting Numbers: [2, 53, 11] Generated Node #2: [2, 53, 11] from Operation: 49-38=11 Current State: 31:[2, 53, 11], Operations: ['49-38=11'] Exploring Operation: 2*11=22, Resulting Numbers: [53, 22] Generated Node #3: [53, 22] from Operation: 2*11=22 Current State: 31:[53, 22], Operations: ['49-38=11', '2*11=22'] Exploring Operation: 53-22=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[49, 2, 38, 53], Operations: [] Exploring Operation: 38-2=36, Resulting Numbers: [49, 53, 36] Generated Node #0,0: 31:[49, 53, 36] Operation: 38-2=36 Exploring Operation: 49-2=47, Resulting Numbers: [38, 53, 47] Generated Node #0,1: 31:[38, 53, 47] Operation: 49-2=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[49, 53, 36], Operations: ['38-2=36'] Exploring Operation: 53-36=17, Resulting Numbers: [49, 17] Generated Node #0,0,0: 31:[49, 17] Operation: 53-36=17 Exploring Operation: 53-49=4, Resulting Numbers: [36, 4] Generated Node #0,0,1: 31:[36, 4] Operation: 53-49=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[49, 17], Operations: ['38-2=36', '53-36=17'] Exploring Operation: 49+17=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 31:[36, 4], Operations: ['38-2=36', '53-49=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[38, 53, 47], Operations: ['49-2=47'] Exploring Operation: 53-38=15, Resulting Numbers: [47, 15] Generated Node #0,1,0: 31:[47, 15] Operation: 53-38=15 Exploring Operation: 53-47=6, Resulting Numbers: [38, 6] Generated Node #0,1,1: 31:[38, 6] Operation: 53-47=6 Moving to Node #0,1,0 Current State: 31:[47, 15], Operations: ['49-2=47', '53-38=15'] Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 47+15=62, Resulting Numbers: [62] 62,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[38, 6], Operations: ['49-2=47', '53-47=6'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 84, 77, 26, 31 ]
35
[ "84-77=7", "31-26=5", "7*5=35" ]
Current State: 35:[84, 77, 26, 31], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [26, 31, 7] Generated Node #2: [26, 31, 7] from Operation: 84-77=7 Current State: 35:[26, 31, 7], Operations: ['84-77=7'] Exploring Operation: 31-26=5, Resulting Numbers: [7, 5] Generated Node #3: [7, 5] from Operation: 31-26=5 Current State: 35:[7, 5], Operations: ['84-77=7', '31-26=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[84, 77, 26, 31], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [26, 31, 7] Generated Node #0,0: 35:[26, 31, 7] Operation: 84-77=7 Exploring Operation: 84-26=58, Resulting Numbers: [77, 31, 58] Generated Node #0,1: 35:[77, 31, 58] Operation: 84-26=58 Exploring Operation: 84-31=53, Resulting Numbers: [77, 26, 53] Generated Node #0,2: 35:[77, 26, 53] Operation: 84-31=53 Exploring Operation: 77-26=51, Resulting Numbers: [84, 31, 51] Generated Node #0,3: 35:[84, 31, 51] Operation: 77-26=51 Exploring Operation: 77-31=46, Resulting Numbers: [84, 26, 46] Generated Node #0,4: 35:[84, 26, 46] Operation: 77-31=46 Moving to Node #0,0 Current State: 35:[26, 31, 7], Operations: ['84-77=7'] Exploring Operation: 31-26=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 31-26=5 Exploring Operation: 31-7=24, Resulting Numbers: [26, 24] Generated Node #0,0,1: 35:[26, 24] Operation: 31-7=24 Exploring Operation: 26+7=33, Resulting Numbers: [31, 33] Generated Node #0,0,2: 35:[31, 33] Operation: 26+7=33 Exploring Operation: 26-7=19, Resulting Numbers: [31, 19] Generated Node #0,0,3: 35:[31, 19] Operation: 26-7=19 Exploring Operation: 31+7=38, Resulting Numbers: [26, 38] Generated Node #0,0,4: 35:[26, 38] Operation: 31+7=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['84-77=7', '31-26=5'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[84, 77, 26, 31], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [26, 31, 7] Generated Node #0,0: 35:[26, 31, 7] Operation: 84-77=7 Moving to Node #0,0 Current State: 35:[26, 31, 7], Operations: ['84-77=7'] Exploring Operation: 31-26=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 31-26=5 Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['84-77=7', '31-26=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 28, 68, 1, 7 ]
65
[ "28/7=4", "68+1=69", "69-4=65" ]
Current State: 65:[28, 68, 1, 7], Operations: [] Exploring Operation: 28/7=4, Resulting Numbers: [68, 1, 4] Generated Node #2: [68, 1, 4] from Operation: 28/7=4 Current State: 65:[68, 1, 4], Operations: ['28/7=4'] Exploring Operation: 68+1=69, Resulting Numbers: [4, 69] Generated Node #3: [4, 69] from Operation: 68+1=69 Current State: 65:[4, 69], Operations: ['28/7=4', '68+1=69'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[28, 68, 1, 7], Operations: [] Exploring Operation: 28-7=21, Resulting Numbers: [68, 1, 21] Generated Node #0,0: 65:[68, 1, 21] Operation: 28-7=21 Exploring Operation: 28/7=4, Resulting Numbers: [68, 1, 4] Generated Node #0,1: 65:[68, 1, 4] Operation: 28/7=4 Exploring Operation: 7-1=6, Resulting Numbers: [28, 68, 6] Generated Node #0,2: 65:[28, 68, 6] Operation: 7-1=6 Exploring Operation: 68-1=67, Resulting Numbers: [28, 7, 67] Generated Node #0,3: 65:[28, 7, 67] Operation: 68-1=67 Exploring Operation: 28-1=27, Resulting Numbers: [68, 7, 27] Generated Node #0,4: 65:[68, 7, 27] Operation: 28-1=27 Moving to Node #0,1 Current State: 65:[68, 1, 4], Operations: ['28/7=4'] Exploring Operation: 68-1=67, Resulting Numbers: [4, 67] Generated Node #0,1,0: 65:[4, 67] Operation: 68-1=67 Exploring Operation: 68/1=68, Resulting Numbers: [4, 68] Generated Node #0,1,1: 65:[4, 68] Operation: 68/1=68 Exploring Operation: 1+4=5, Resulting Numbers: [68, 5] Generated Node #0,1,2: 65:[68, 5] Operation: 1+4=5 Exploring Operation: 68*1=68, Resulting Numbers: [4, 68] Generated Node #0,1,3: 65:[4, 68] Operation: 68*1=68 Exploring Operation: 1*4=4, Resulting Numbers: [68, 4] Generated Node #0,1,4: 65:[68, 4] Operation: 1*4=4 Moving to Node #0,0 Current State: 65:[68, 1, 21], Operations: ['28-7=21'] Exploring Operation: 21-1=20, Resulting Numbers: [68, 20] Generated Node #0,0,0: 65:[68, 20] Operation: 21-1=20 Exploring Operation: 68*1=68, Resulting Numbers: [21, 68] Generated Node #0,0,1: 65:[21, 68] Operation: 68*1=68 Exploring Operation: 1*21=21, Resulting Numbers: [68, 21] Generated Node #0,0,2: 65:[68, 21] Operation: 1*21=21 Exploring Operation: 68-1=67, Resulting Numbers: [21, 67] Generated Node #0,0,3: 65:[21, 67] Operation: 68-1=67 Exploring Operation: 68/1=68, Resulting Numbers: [21, 68] Generated Node #0,0,4: 65:[21, 68] Operation: 68/1=68 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[68, 20], Operations: ['28-7=21', '21-1=20'] Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,65 unequal: No Solution Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,65 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 #0,0,3 Current State: 65:[21, 67], Operations: ['28-7=21', '68-1=67'] Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 21*67=1407, Resulting Numbers: [1407] 1407,65 unequal: No Solution Exploring Operation: 21+67=88, Resulting Numbers: [88] 88,65 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 #0,0,1 Current State: 65:[21, 68], Operations: ['28-7=21', '68*1=68'] Exploring Operation: 68-21=47, Resulting Numbers: [47] 47,65 unequal: No Solution Exploring Operation: 21*68=1428, Resulting Numbers: [1428] 1428,65 unequal: No Solution Exploring Operation: 21+68=89, Resulting Numbers: [89] 89,65 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 #0,0,2 Current State: 65:[68, 21], Operations: ['28-7=21', '1*21=21'] Exploring Operation: 68*21=1428, Resulting Numbers: [1428] 1428,65 unequal: No Solution Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,65 unequal: No Solution Exploring Operation: 68-21=47, Resulting Numbers: [47] 47,65 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 #0,0,4 Current State: 65:[21, 68], Operations: ['28-7=21', '68/1=68'] Exploring Operation: 21+68=89, Resulting Numbers: [89] 89,65 unequal: No Solution Exploring Operation: 21*68=1428, Resulting Numbers: [1428] 1428,65 unequal: No Solution Exploring Operation: 68-21=47, Resulting Numbers: [47] 47,65 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: 65:[28, 68, 6], Operations: ['7-1=6'] Exploring Operation: 68-28=40, Resulting Numbers: [6, 40] Generated Node #0,2,0: 65:[6, 40] Operation: 68-28=40 Exploring Operation: 28+6=34, Resulting Numbers: [68, 34] Generated Node #0,2,1: 65:[68, 34] Operation: 28+6=34 Exploring Operation: 68+6=74, Resulting Numbers: [28, 74] Generated Node #0,2,2: 65:[28, 74] Operation: 68+6=74 Exploring Operation: 68-6=62, Resulting Numbers: [28, 62] Generated Node #0,2,3: 65:[28, 62] Operation: 68-6=62 Exploring Operation: 28-6=22, Resulting Numbers: [68, 22] Generated Node #0,2,4: 65:[68, 22] Operation: 28-6=22 Moving to Node #0,3 Current State: 65:[28, 7, 67], Operations: ['68-1=67'] Exploring Operation: 67-7=60, Resulting Numbers: [28, 60] Generated Node #0,3,0: 65:[28, 60] Operation: 67-7=60 Exploring Operation: 28/7=4, Resulting Numbers: [67, 4] Generated Node #0,3,1: 65:[67, 4] Operation: 28/7=4 Exploring Operation: 28-7=21, Resulting Numbers: [67, 21] Generated Node #0,3,2: 65:[67, 21] Operation: 28-7=21 Exploring Operation: 28+7=35, Resulting Numbers: [67, 35] Generated Node #0,3,3: 65:[67, 35] Operation: 28+7=35 Exploring Operation: 7+67=74, Resulting Numbers: [28, 74] Generated Node #0,3,4: 65:[28, 74] Operation: 7+67=74 Moving to Node #0,4 Current State: 65:[68, 7, 27], Operations: ['28-1=27'] Exploring Operation: 68+7=75, Resulting Numbers: [27, 75] Generated Node #0,4,0: 65:[27, 75] Operation: 68+7=75 Exploring Operation: 27-7=20, Resulting Numbers: [68, 20] Generated Node #0,4,1: 65:[68, 20] Operation: 27-7=20 Exploring Operation: 68-7=61, Resulting Numbers: [27, 61] Generated Node #0,4,2: 65:[27, 61] Operation: 68-7=61 Exploring Operation: 68-27=41, Resulting Numbers: [7, 41] Generated Node #0,4,3: 65:[7, 41] Operation: 68-27=41 Exploring Operation: 7+27=34, Resulting Numbers: [68, 34] Generated Node #0,4,4: 65:[68, 34] Operation: 7+27=34 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 65:[68, 20], Operations: ['28-1=27', '27-7=20'] Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,65 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,65 unequal: No Solution Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,65 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 #0,4,2 Current State: 65:[27, 61], Operations: ['28-1=27', '68-7=61'] Exploring Operation: 61-27=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 27*61=1647, Resulting Numbers: [1647] 1647,65 unequal: No Solution Exploring Operation: 27+61=88, Resulting Numbers: [88] 88,65 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 #0,4,0 Current State: 65:[27, 75], Operations: ['28-1=27', '68+7=75'] Exploring Operation: 27+75=102, Resulting Numbers: [102] 102,65 unequal: No Solution Exploring Operation: 27*75=2025, Resulting Numbers: [2025] 2025,65 unequal: No Solution Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,65 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 #0,4,4 Current State: 65:[68, 34], Operations: ['28-1=27', '7+27=34'] Exploring Operation: 68+34=102, Resulting Numbers: [102] 102,65 unequal: No Solution Exploring Operation: 68*34=2312, Resulting Numbers: [2312] 2312,65 unequal: No Solution Exploring Operation: 68/34=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 68-34=34, Resulting Numbers: [34] 34,65 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 #0,4,3 Current State: 65:[7, 41], Operations: ['28-1=27', '68-27=41'] Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,65 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 7*41=287, Resulting Numbers: [287] 287,65 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: 65:[4, 67], Operations: ['28/7=4', '68-1=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,65 unequal: No Solution Exploring Operation: 4*67=268, Resulting Numbers: [268] 268,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[68, 5], Operations: ['28/7=4', '1+4=5'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 68*5=340, Resulting Numbers: [340] 340,65 unequal: No Solution Exploring Operation: 68+5=73, Resulting Numbers: [73] 73,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[67, 4], Operations: ['68-1=67', '28/7=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,65 unequal: No Solution Exploring Operation: 67*4=268, Resulting Numbers: [268] 268,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[4, 68], Operations: ['28/7=4', '68/1=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,65 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,65 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,65 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,65 unequal: No Solution Moving to Node #0,1,4 Current State: 65:[68, 4], Operations: ['28/7=4', '1*4=4'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,65 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,65 unequal: No Solution Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,65 unequal: No Solution Exploring Operation: 68*4=272, Resulting Numbers: [272] 272,65 unequal: No Solution Moving to Node #0,1,3 Current State: 65:[4, 68], Operations: ['28/7=4', '68*1=68'] Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,65 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,65 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,65 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[67, 21], Operations: ['68-1=67', '28-7=21'] Exploring Operation: 67*21=1407, Resulting Numbers: [1407] 1407,65 unequal: No Solution Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 67+21=88, Resulting Numbers: [88] 88,65 unequal: No Solution Moving to Node #0,2,4 Current State: 65:[68, 22], Operations: ['7-1=6', '28-6=22'] Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 68*22=1496, Resulting Numbers: [1496] 1496,65 unequal: No Solution Exploring Operation: 68+22=90, Resulting Numbers: [90] 90,65 unequal: No Solution Moving to Node #0,2,3 Current State: 65:[28, 62], Operations: ['7-1=6', '68-6=62'] Exploring Operation: 28+62=90, Resulting Numbers: [90] 90,65 unequal: No Solution Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 28*62=1736, Resulting Numbers: [1736] 1736,65 unequal: No Solution Moving to Node #0,3,0 Current State: 65:[28, 60], Operations: ['68-1=67', '67-7=60'] Exploring Operation: 28+60=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 28*60=1680, Resulting Numbers: [1680] 1680,65 unequal: No Solution Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,65 unequal: No Solution Moving to Node #0,3,3 Current State: 65:[67, 35], Operations: ['68-1=67', '28+7=35'] Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,65 unequal: No Solution Exploring Operation: 67*35=2345, Resulting Numbers: [2345] 2345,65 unequal: No Solution Exploring Operation: 67+35=102, Resulting Numbers: [102] 102,65 unequal: No Solution Moving to Node #0,3,4 Current State: 65:[28, 74], Operations: ['68-1=67', '7+67=74'] Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 28*74=2072, Resulting Numbers: [2072] 2072,65 unequal: No Solution Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[28, 74], Operations: ['7-1=6', '68+6=74'] Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,65 unequal: No Solution Exploring Operation: 28*74=2072, Resulting Numbers: [2072] 2072,65 unequal: No Solution Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[68, 34], Operations: ['7-1=6', '28+6=34'] Exploring Operation: 68+34=102, Resulting Numbers: [102] 102,65 unequal: No Solution Exploring Operation: 68-34=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 68*34=2312, Resulting Numbers: [2312] 2312,65 unequal: No Solution Exploring Operation: 68/34=2, Resulting Numbers: [2] 2,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[6, 40], Operations: ['7-1=6', '68-28=40'] Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,65 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,65 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 33, 26, 29, 48 ]
49
[ "29-26=3", "48/3=16", "33+16=49" ]
Current State: 49:[33, 26, 29, 48], Operations: [] Exploring Operation: 29-26=3, Resulting Numbers: [33, 48, 3] Generated Node #2: [33, 48, 3] from Operation: 29-26=3 Current State: 49:[33, 48, 3], Operations: ['29-26=3'] Exploring Operation: 48/3=16, Resulting Numbers: [33, 16] Generated Node #3: [33, 16] from Operation: 48/3=16 Current State: 49:[33, 16], Operations: ['29-26=3', '48/3=16'] Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[33, 26, 29, 48], Operations: [] Exploring Operation: 33-26=7, Resulting Numbers: [29, 48, 7] Generated Node #0,0: 49:[29, 48, 7] Operation: 33-26=7 Exploring Operation: 26+29=55, Resulting Numbers: [33, 48, 55] Generated Node #0,1: 49:[33, 48, 55] Operation: 26+29=55 Exploring Operation: 33-29=4, Resulting Numbers: [26, 48, 4] Generated Node #0,2: 49:[26, 48, 4] Operation: 33-29=4 Exploring Operation: 29-26=3, Resulting Numbers: [33, 48, 3] Generated Node #0,3: 49:[33, 48, 3] Operation: 29-26=3 Exploring Operation: 33+26=59, Resulting Numbers: [29, 48, 59] Generated Node #0,4: 49:[29, 48, 59] Operation: 33+26=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[29, 48, 7], Operations: ['33-26=7'] Exploring Operation: 48-29=19, Resulting Numbers: [7, 19] Generated Node #0,0,0: 49:[7, 19] Operation: 48-29=19 Exploring Operation: 29+7=36, Resulting Numbers: [48, 36] Generated Node #0,0,1: 49:[48, 36] Operation: 29+7=36 Exploring Operation: 48+7=55, Resulting Numbers: [29, 55] Generated Node #0,0,2: 49:[29, 55] Operation: 48+7=55 Exploring Operation: 29+48=77, Resulting Numbers: [7, 77] Generated Node #0,0,3: 49:[7, 77] Operation: 29+48=77 Exploring Operation: 29-7=22, Resulting Numbers: [48, 22] Generated Node #0,0,4: 49:[48, 22] Operation: 29-7=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[7, 19], Operations: ['33-26=7', '48-29=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[48, 36], Operations: ['33-26=7', '29+7=36'] Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 49:[48, 22], Operations: ['33-26=7', '29-7=22'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,49 unequal: No Solution Exploring Operation: 48*22=1056, Resulting Numbers: [1056] 1056,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[29, 55], Operations: ['33-26=7', '48+7=55'] Exploring Operation: 29*55=1595, Resulting Numbers: [1595] 1595,49 unequal: No Solution Exploring Operation: 29+55=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 49:[7, 77], Operations: ['33-26=7', '29+48=77'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 7+77=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 7*77=539, Resulting Numbers: [539] 539,49 unequal: No Solution Exploring Operation: 77-7=70, Resulting Numbers: [70] 70,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[33, 48, 3], Operations: ['29-26=3'] Exploring Operation: 33/3=11, Resulting Numbers: [48, 11] Generated Node #0,3,0: 49:[48, 11] Operation: 33/3=11 Exploring Operation: 33+3=36, Resulting Numbers: [48, 36] Generated Node #0,3,1: 49:[48, 36] Operation: 33+3=36 Exploring Operation: 33-3=30, Resulting Numbers: [48, 30] Generated Node #0,3,2: 49:[48, 30] Operation: 33-3=30 Exploring Operation: 48-33=15, Resulting Numbers: [3, 15] Generated Node #0,3,3: 49:[3, 15] Operation: 48-33=15 Exploring Operation: 48+3=51, Resulting Numbers: [33, 51] Generated Node #0,3,4: 49:[33, 51] Operation: 48+3=51 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 49:[48, 11], Operations: ['29-26=3', '33/3=11'] Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,49 unequal: No Solution Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 48*11=528, Resulting Numbers: [528] 528,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 49:[3, 15], Operations: ['29-26=3', '48-33=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,49 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 49:[48, 36], Operations: ['29-26=3', '33+3=36'] Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 49:[33, 51], Operations: ['29-26=3', '48+3=51'] Exploring Operation: 33+51=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 33*51=1683, Resulting Numbers: [1683] 1683,49 unequal: No Solution Exploring Operation: 51-33=18, Resulting Numbers: [18] 18,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 49:[48, 30], Operations: ['29-26=3', '33-3=30'] Exploring Operation: 48*30=1440, Resulting Numbers: [1440] 1440,49 unequal: No Solution Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,49 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[33, 48, 55], Operations: ['26+29=55'] Exploring Operation: 33+48=81, Resulting Numbers: [55, 81] Generated Node #0,1,0: 49:[55, 81] Operation: 33+48=81 Exploring Operation: 55-48=7, Resulting Numbers: [33, 7] Generated Node #0,1,1: 49:[33, 7] Operation: 55-48=7 Exploring Operation: 48-33=15, Resulting Numbers: [55, 15] Generated Node #0,1,2: 49:[55, 15] Operation: 48-33=15 Exploring Operation: 55-33=22, Resulting Numbers: [48, 22] Generated Node #0,1,3: 49:[48, 22] Operation: 55-33=22 Exploring Operation: 33+55=88, Resulting Numbers: [48, 88] Generated Node #0,1,4: 49:[48, 88] Operation: 33+55=88 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 49:[55, 15], Operations: ['26+29=55', '48-33=15'] Exploring Operation: 55+15=70, Resulting Numbers: [70] 70,49 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,49 unequal: No Solution Exploring Operation: 55*15=825, Resulting Numbers: [825] 825,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[33, 7], Operations: ['26+29=55', '55-48=7'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,49 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 49:[48, 22], Operations: ['26+29=55', '55-33=22'] Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,49 unequal: No Solution Exploring Operation: 48*22=1056, Resulting Numbers: [1056] 1056,49 unequal: No Solution Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[55, 81], Operations: ['26+29=55', '33+48=81'] Exploring Operation: 81-55=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 55*81=4455, Resulting Numbers: [4455] 4455,49 unequal: No Solution Exploring Operation: 55+81=136, Resulting Numbers: [136] 136,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 49:[48, 88], Operations: ['26+29=55', '33+55=88'] Exploring Operation: 48+88=136, Resulting Numbers: [136] 136,49 unequal: No Solution Exploring Operation: 48*88=4224, Resulting Numbers: [4224] 4224,49 unequal: No Solution Exploring Operation: 88-48=40, Resulting Numbers: [40] 40,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[26, 48, 4], Operations: ['33-29=4'] Exploring Operation: 26-4=22, Resulting Numbers: [48, 22] Generated Node #0,2,0: 49:[48, 22] Operation: 26-4=22 Exploring Operation: 26+4=30, Resulting Numbers: [48, 30] Generated Node #0,2,1: 49:[48, 30] Operation: 26+4=30 Exploring Operation: 48-26=22, Resulting Numbers: [4, 22] Generated Node #0,2,2: 49:[4, 22] Operation: 48-26=22 Exploring Operation: 48+4=52, Resulting Numbers: [26, 52] Generated Node #0,2,3: 49:[26, 52] Operation: 48+4=52 Exploring Operation: 48-4=44, Resulting Numbers: [26, 44] Generated Node #0,2,4: 49:[26, 44] Operation: 48-4=44 Moving to Node #0,2,0 Current State: 49:[48, 22], Operations: ['33-29=4', '26-4=22'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 48*22=1056, Resulting Numbers: [1056] 1056,49 unequal: No Solution Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[4, 22], Operations: ['33-29=4', '48-26=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[48, 30], Operations: ['33-29=4', '26+4=30'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 48*30=1440, Resulting Numbers: [1440] 1440,49 unequal: No Solution Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,49 unequal: No Solution Moving to Node #0,2,3 Current State: 49:[26, 52], Operations: ['33-29=4', '48+4=52'] Exploring Operation: 52/26=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 26+52=78, Resulting Numbers: [78] 78,49 unequal: No Solution Exploring Operation: 52-26=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 26*52=1352, Resulting Numbers: [1352] 1352,49 unequal: No Solution Moving to Node #0,2,4 Current State: 49:[26, 44], Operations: ['33-29=4', '48-4=44'] Exploring Operation: 26+44=70, Resulting Numbers: [70] 70,49 unequal: No Solution Exploring Operation: 26*44=1144, Resulting Numbers: [1144] 1144,49 unequal: No Solution Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[29, 48, 59], Operations: ['33+26=59'] Exploring Operation: 59-29=30, Resulting Numbers: [48, 30] Generated Node #0,4,0: 49:[48, 30] Operation: 59-29=30 Exploring Operation: 59-48=11, Resulting Numbers: [29, 11] Generated Node #0,4,1: 49:[29, 11] Operation: 59-48=11 Exploring Operation: 29+48=77, Resulting Numbers: [59, 77] Generated Node #0,4,2: 49:[59, 77] Operation: 29+48=77 Exploring Operation: 29+59=88, Resulting Numbers: [48, 88] Generated Node #0,4,3: 49:[48, 88] Operation: 29+59=88 Exploring Operation: 48-29=19, Resulting Numbers: [59, 19] Generated Node #0,4,4: 49:[59, 19] Operation: 48-29=19 Moving to Node #0,4,0 Current State: 49:[48, 30], Operations: ['33+26=59', '59-29=30'] Exploring Operation: 48*30=1440, Resulting Numbers: [1440] 1440,49 unequal: No Solution Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,49 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,49 unequal: No Solution Moving to Node #0,4,4 Current State: 49:[59, 19], Operations: ['33+26=59', '48-29=19'] Exploring Operation: 59+19=78, Resulting Numbers: [78] 78,49 unequal: No Solution Exploring Operation: 59-19=40, Resulting Numbers: [40] 40,49 unequal: No Solution Exploring Operation: 59*19=1121, Resulting Numbers: [1121] 1121,49 unequal: No Solution Moving to Node #0,4,1 Current State: 49:[29, 11], Operations: ['33+26=59', '59-48=11'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 29+11=40, Resulting Numbers: [40] 40,49 unequal: No Solution Exploring Operation: 29*11=319, Resulting Numbers: [319] 319,49 unequal: No Solution Moving to Node #0,4,2 Current State: 49:[59, 77], Operations: ['33+26=59', '29+48=77'] Exploring Operation: 59*77=4543, Resulting Numbers: [4543] 4543,49 unequal: No Solution Exploring Operation: 77-59=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 59+77=136, Resulting Numbers: [136] 136,49 unequal: No Solution Moving to Node #0,4,3 Current State: 49:[48, 88], Operations: ['33+26=59', '29+59=88'] Exploring Operation: 48+88=136, Resulting Numbers: [136] 136,49 unequal: No Solution Exploring Operation: 88-48=40, Resulting Numbers: [40] 40,49 unequal: No Solution Exploring Operation: 48*88=4224, Resulting Numbers: [4224] 4224,49 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
[ 24, 61, 62, 56 ]
91
[ "24+61=85", "62-56=6", "85+6=91" ]
Current State: 91:[24, 61, 62, 56], Operations: [] Exploring Operation: 24+61=85, Resulting Numbers: [62, 56, 85] Generated Node #2: [62, 56, 85] from Operation: 24+61=85 Current State: 91:[62, 56, 85], Operations: ['24+61=85'] Exploring Operation: 62-56=6, Resulting Numbers: [85, 6] Generated Node #3: [85, 6] from Operation: 62-56=6 Current State: 91:[85, 6], Operations: ['24+61=85', '62-56=6'] Exploring Operation: 85+6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[24, 61, 62, 56], Operations: [] Exploring Operation: 62+56=118, Resulting Numbers: [24, 61, 118] Generated Node #0,0: 91:[24, 61, 118] Operation: 62+56=118 Exploring Operation: 62-56=6, Resulting Numbers: [24, 61, 6] Generated Node #0,1: 91:[24, 61, 6] Operation: 62-56=6 Exploring Operation: 61+56=117, Resulting Numbers: [24, 62, 117] Generated Node #0,2: 91:[24, 62, 117] Operation: 61+56=117 Exploring Operation: 61-56=5, Resulting Numbers: [24, 62, 5] Generated Node #0,3: 91:[24, 62, 5] Operation: 61-56=5 Exploring Operation: 62-61=1, Resulting Numbers: [24, 56, 1] Generated Node #0,4: 91:[24, 56, 1] Operation: 62-61=1 Moving to Node #0,1 Current State: 91:[24, 61, 6], Operations: ['62-56=6'] Exploring Operation: 24/6=4, Resulting Numbers: [61, 4] Generated Node #0,1,0: 91:[61, 4] Operation: 24/6=4 Exploring Operation: 61+6=67, Resulting Numbers: [24, 67] Generated Node #0,1,1: 91:[24, 67] Operation: 61+6=67 Exploring Operation: 24+61=85, Resulting Numbers: [6, 85] Generated Node #0,1,2: 91:[6, 85] Operation: 24+61=85 Exploring Operation: 61-24=37, Resulting Numbers: [6, 37] Generated Node #0,1,3: 91:[6, 37] Operation: 61-24=37 Exploring Operation: 24-6=18, Resulting Numbers: [61, 18] Generated Node #0,1,4: 91:[61, 18] Operation: 24-6=18 Moving to Node #0,3 Current State: 91:[24, 62, 5], Operations: ['61-56=5'] Exploring Operation: 24+62=86, Resulting Numbers: [5, 86] Generated Node #0,3,0: 91:[5, 86] Operation: 24+62=86 Exploring Operation: 24-5=19, Resulting Numbers: [62, 19] Generated Node #0,3,1: 91:[62, 19] Operation: 24-5=19 Exploring Operation: 62+5=67, Resulting Numbers: [24, 67] Generated Node #0,3,2: 91:[24, 67] Operation: 62+5=67 Exploring Operation: 24+5=29, Resulting Numbers: [62, 29] Generated Node #0,3,3: 91:[62, 29] Operation: 24+5=29 Exploring Operation: 62-24=38, Resulting Numbers: [5, 38] Generated Node #0,3,4: 91:[5, 38] Operation: 62-24=38 Moving to Node #0,4 Current State: 91:[24, 56, 1], Operations: ['62-61=1'] Exploring Operation: 24-1=23, Resulting Numbers: [56, 23] Generated Node #0,4,0: 91:[56, 23] Operation: 24-1=23 Exploring Operation: 56-24=32, Resulting Numbers: [1, 32] Generated Node #0,4,1: 91:[1, 32] Operation: 56-24=32 Exploring Operation: 24+56=80, Resulting Numbers: [1, 80] Generated Node #0,4,2: 91:[1, 80] Operation: 24+56=80 Exploring Operation: 24*1=24, Resulting Numbers: [56, 24] Generated Node #0,4,3: 91:[56, 24] Operation: 24*1=24 Exploring Operation: 56+1=57, Resulting Numbers: [24, 57] Generated Node #0,4,4: 91:[24, 57] Operation: 56+1=57 Moving to Node #0,2 Current State: 91:[24, 62, 117], Operations: ['61+56=117'] Exploring Operation: 24+62=86, Resulting Numbers: [117, 86] Generated Node #0,2,0: 91:[117, 86] Operation: 24+62=86 Exploring Operation: 117-62=55, Resulting Numbers: [24, 55] Generated Node #0,2,1: 91:[24, 55] Operation: 117-62=55 Exploring Operation: 24+117=141, Resulting Numbers: [62, 141] Generated Node #0,2,2: 91:[62, 141] Operation: 24+117=141 Exploring Operation: 62-24=38, Resulting Numbers: [117, 38] Generated Node #0,2,3: 91:[117, 38] Operation: 62-24=38 Exploring Operation: 117-24=93, Resulting Numbers: [62, 93] Generated Node #0,2,4: 91:[62, 93] Operation: 117-24=93 Moving to Node #0,0 Current State: 91:[24, 61, 118], Operations: ['62+56=118'] Exploring Operation: 118-24=94, Resulting Numbers: [61, 94] Generated Node #0,0,0: 91:[61, 94] Operation: 118-24=94 Exploring Operation: 24+118=142, Resulting Numbers: [61, 142] Generated Node #0,0,1: 91:[61, 142] Operation: 24+118=142 Exploring Operation: 61-24=37, Resulting Numbers: [118, 37] Generated Node #0,0,2: 91:[118, 37] Operation: 61-24=37 Exploring Operation: 24+61=85, Resulting Numbers: [118, 85] Generated Node #0,0,3: 91:[118, 85] Operation: 24+61=85 Exploring Operation: 118-61=57, Resulting Numbers: [24, 57] Generated Node #0,0,4: 91:[24, 57] Operation: 118-61=57 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[61, 94], Operations: ['62+56=118', '118-24=94'] Exploring Operation: 61+94=155, Resulting Numbers: [155] 155,91 unequal: No Solution Exploring Operation: 61*94=5734, Resulting Numbers: [5734] 5734,91 unequal: No Solution Exploring Operation: 94-61=33, Resulting Numbers: [33] 33,91 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 #0,0,3 Current State: 91:[118, 85], Operations: ['62+56=118', '24+61=85'] Exploring Operation: 118*85=10030, Resulting Numbers: [10030] 10030,91 unequal: No Solution Exploring Operation: 118-85=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 118+85=203, Resulting Numbers: [203] 203,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 91:[24, 57], Operations: ['62+56=118', '118-61=57'] Exploring Operation: 24*57=1368, Resulting Numbers: [1368] 1368,91 unequal: No Solution Exploring Operation: 24+57=81, Resulting Numbers: [81] 81,91 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,91 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:[118, 37], Operations: ['62+56=118', '61-24=37'] Exploring Operation: 118+37=155, Resulting Numbers: [155] 155,91 unequal: No Solution Exploring Operation: 118-37=81, Resulting Numbers: [81] 81,91 unequal: No Solution Exploring Operation: 118*37=4366, Resulting Numbers: [4366] 4366,91 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 #0,0,1 Current State: 91:[61, 142], Operations: ['62+56=118', '24+118=142'] Exploring Operation: 61+142=203, Resulting Numbers: [203] 203,91 unequal: No Solution Exploring Operation: 61*142=8662, Resulting Numbers: [8662] 8662,91 unequal: No Solution Exploring Operation: 142-61=81, Resulting Numbers: [81] 81,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 91:[6, 85], Operations: ['62-56=6', '24+61=85'] Exploring Operation: 6+85=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[24, 61, 62, 56], Operations: [] Exploring Operation: 62-56=6, Resulting Numbers: [24, 61, 6] Generated Node #0,1: 91:[24, 61, 6] Operation: 62-56=6 Moving to Node #0,1 Current State: 91:[24, 61, 6], Operations: ['62-56=6'] Exploring Operation: 24+61=85, Resulting Numbers: [6, 85] Generated Node #0,1,2: 91:[6, 85] Operation: 24+61=85 Moving to Node #0,1,2 Current State: 91:[6, 85], Operations: ['62-56=6', '24+61=85'] Exploring Operation: 6+85=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
0.956597
hs_5
mult_heuristic
[ 18, 32, 8, 36 ]
12
[ "36/18=2", "32-8=24", "24/2=12" ]
Current State: 12:[18, 32, 8, 36], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [32, 8, 2] Generated Node #2: [32, 8, 2] from Operation: 36/18=2 Current State: 12:[32, 8, 2], Operations: ['36/18=2'] Exploring Operation: 32-8=24, Resulting Numbers: [2, 24] Generated Node #3: [2, 24] from Operation: 32-8=24 Current State: 12:[2, 24], Operations: ['36/18=2', '32-8=24'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[18, 32, 8, 36], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [32, 8, 2] Generated Node #0,0: 12:[32, 8, 2] Operation: 36/18=2 Exploring Operation: 36-32=4, Resulting Numbers: [18, 8, 4] Generated Node #0,1: 12:[18, 8, 4] Operation: 36-32=4 Moving to Node #0,1 Current State: 12:[18, 8, 4], Operations: ['36-32=4'] Exploring Operation: 18-8=10, Resulting Numbers: [4, 10] Generated Node #0,1,0: 12:[4, 10] Operation: 18-8=10 Exploring Operation: 18-4=14, Resulting Numbers: [8, 14] Generated Node #0,1,1: 12:[8, 14] Operation: 18-4=14 Moving to Node #0,0 Current State: 12:[32, 8, 2], Operations: ['36/18=2'] Exploring Operation: 32/2=16, Resulting Numbers: [8, 16] Generated Node #0,0,0: 12:[8, 16] Operation: 32/2=16 Exploring Operation: 32/8=4, Resulting Numbers: [2, 4] Generated Node #0,0,1: 12:[2, 4] Operation: 32/8=4 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[2, 4], Operations: ['36/18=2', '32/8=4'] Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[8, 16], Operations: ['36/18=2', '32/2=16'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 12:[4, 10], Operations: ['36-32=4', '18-8=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[8, 14], Operations: ['36-32=4', '18-4=14'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,12 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 78, 27, 20, 30 ]
18
[ "30-27=3", "20*3=60", "78-60=18" ]
Current State: 18:[78, 27, 20, 30], Operations: [] Exploring Operation: 30-27=3, Resulting Numbers: [78, 20, 3] Generated Node #2: [78, 20, 3] from Operation: 30-27=3 Current State: 18:[78, 20, 3], Operations: ['30-27=3'] Exploring Operation: 20*3=60, Resulting Numbers: [78, 60] Generated Node #3: [78, 60] from Operation: 20*3=60 Current State: 18:[78, 60], Operations: ['30-27=3', '20*3=60'] Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[78, 27, 20, 30], Operations: [] Exploring Operation: 78-30=48, Resulting Numbers: [27, 20, 48] Generated Node #0,0: 18:[27, 20, 48] Operation: 78-30=48 Exploring Operation: 78-27=51, Resulting Numbers: [20, 30, 51] Generated Node #0,1: 18:[20, 30, 51] Operation: 78-27=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[27, 20, 48], Operations: ['78-30=48'] Exploring Operation: 48-27=21, Resulting Numbers: [20, 21] Generated Node #0,0,0: 18:[20, 21] Operation: 48-27=21 Exploring Operation: 48-20=28, Resulting Numbers: [27, 28] Generated Node #0,0,1: 18:[27, 28] Operation: 48-20=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[20, 21], Operations: ['78-30=48', '48-27=21'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 18:[27, 28], Operations: ['78-30=48', '48-20=28'] Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,18 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[20, 30, 51], Operations: ['78-27=51'] Exploring Operation: 51-20=31, Resulting Numbers: [30, 31] Generated Node #0,1,0: 18:[30, 31] Operation: 51-20=31 Exploring Operation: 51-30=21, Resulting Numbers: [20, 21] Generated Node #0,1,1: 18:[20, 21] Operation: 51-30=21 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 18:[20, 21], Operations: ['78-27=51', '51-30=21'] Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 18:[30, 31], Operations: ['78-27=51', '51-20=31'] Exploring Operation: 30+31=61, Resulting Numbers: [61] 61,18 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 5, 26, 13, 9 ]
17
[ "26-5=21", "13-9=4", "21-4=17" ]
Current State: 17:[5, 26, 13, 9], Operations: [] Exploring Operation: 26-5=21, Resulting Numbers: [13, 9, 21] Generated Node #2: [13, 9, 21] from Operation: 26-5=21 Current State: 17:[13, 9, 21], Operations: ['26-5=21'] Exploring Operation: 13-9=4, Resulting Numbers: [21, 4] Generated Node #3: [21, 4] from Operation: 13-9=4 Current State: 17:[21, 4], Operations: ['26-5=21', '13-9=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[5, 26, 13, 9], Operations: [] Exploring Operation: 26-5=21, Resulting Numbers: [13, 9, 21] Generated Node #0,0: 17:[13, 9, 21] Operation: 26-5=21 Exploring Operation: 5+9=14, Resulting Numbers: [26, 13, 14] Generated Node #0,1: 17:[26, 13, 14] Operation: 5+9=14 Exploring Operation: 26-9=17, Resulting Numbers: [5, 13, 17] Generated Node #0,2: 17:[5, 13, 17] Operation: 26-9=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[13, 9, 21], Operations: ['26-5=21'] Exploring Operation: 13+9=22, Resulting Numbers: [21, 22] Generated Node #0,0,0: 17:[21, 22] Operation: 13+9=22 Exploring Operation: 21-9=12, Resulting Numbers: [13, 12] Generated Node #0,0,1: 17:[13, 12] Operation: 21-9=12 Exploring Operation: 13-9=4, Resulting Numbers: [21, 4] Generated Node #0,0,2: 17:[21, 4] Operation: 13-9=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[21, 22], Operations: ['26-5=21', '13+9=22'] Exploring Operation: 21+22=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 21*22=462, Resulting Numbers: [462] 462,17 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:[13, 12], Operations: ['26-5=21', '21-9=12'] Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,17 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 13*12=156, Resulting Numbers: [156] 156,17 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 #0,0,2 Current State: 17:[21, 4], Operations: ['26-5=21', '13-9=4'] Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,17 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[5, 26, 13, 9], Operations: [] Exploring Operation: 26-5=21, Resulting Numbers: [13, 9, 21] Generated Node #0,0: 17:[13, 9, 21] Operation: 26-5=21 Moving to Node #0,0 Current State: 17:[13, 9, 21], Operations: ['26-5=21'] Exploring Operation: 13-9=4, Resulting Numbers: [21, 4] Generated Node #0,0,2: 17:[21, 4] Operation: 13-9=4 Moving to Node #0,0,2 Current State: 17:[21, 4], Operations: ['26-5=21', '13-9=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 21, 78, 48, 51 ]
73
[ "78*48=3744", "3744-21=3723", "3723/51=73" ]
Current State: 73:[21, 78, 48, 51], Operations: [] Exploring Operation: 78*48=3744, Resulting Numbers: [21, 51, 3744] Generated Node #2: [21, 51, 3744] from Operation: 78*48=3744 Current State: 73:[21, 51, 3744], Operations: ['78*48=3744'] Exploring Operation: 3744-21=3723, Resulting Numbers: [51, 3723] Generated Node #3: [51, 3723] from Operation: 3744-21=3723 Current State: 73:[51, 3723], Operations: ['78*48=3744', '3744-21=3723'] Exploring Operation: 3723/51=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[21, 78, 48, 51], Operations: [] Exploring Operation: 21+48=69, Resulting Numbers: [78, 51, 69] Generated Node #0,0: 73:[78, 51, 69] Operation: 21+48=69 Exploring Operation: 21+51=72, Resulting Numbers: [78, 48, 72] Generated Node #0,1: 73:[78, 48, 72] Operation: 21+51=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[78, 51, 69], Operations: ['21+48=69'] Exploring Operation: 51+69=120, Resulting Numbers: [78, 120] Generated Node #0,0,0: 73:[78, 120] Operation: 51+69=120 Exploring Operation: 78-51=27, Resulting Numbers: [69, 27] Generated Node #0,0,1: 73:[69, 27] Operation: 78-51=27 Moving to Node #0,0,1 Current State: 73:[69, 27], Operations: ['21+48=69', '78-51=27'] Exploring Operation: 69+27=96, Resulting Numbers: [96] 96,73 unequal: No Solution Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[78, 120], Operations: ['21+48=69', '51+69=120'] Exploring Operation: 78+120=198, Resulting Numbers: [198] 198,73 unequal: No Solution Exploring Operation: 120-78=42, Resulting Numbers: [42] 42,73 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 #0,1 Current State: 73:[78, 48, 72], Operations: ['21+51=72'] Exploring Operation: 48+72=120, Resulting Numbers: [78, 120] Generated Node #0,1,0: 73:[78, 120] Operation: 48+72=120 Exploring Operation: 78-48=30, Resulting Numbers: [72, 30] Generated Node #0,1,1: 73:[72, 30] Operation: 78-48=30 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[72, 30], Operations: ['21+51=72', '78-48=30'] Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[78, 120], Operations: ['21+51=72', '48+72=120'] Exploring Operation: 78+120=198, Resulting Numbers: [198] 198,73 unequal: No Solution Exploring Operation: 120-78=42, Resulting Numbers: [42] 42,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 32, 66, 33, 14 ]
52
[ "33-32=1", "66-14=52", "1*52=52" ]
Current State: 52:[32, 66, 33, 14], Operations: [] Exploring Operation: 33-32=1, Resulting Numbers: [66, 14, 1] Generated Node #2: [66, 14, 1] from Operation: 33-32=1 Current State: 52:[66, 14, 1], Operations: ['33-32=1'] Exploring Operation: 66-14=52, Resulting Numbers: [1, 52] Generated Node #3: [1, 52] from Operation: 66-14=52 Current State: 52:[1, 52], Operations: ['33-32=1', '66-14=52'] Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[32, 66, 33, 14], Operations: [] Exploring Operation: 66-14=52, Resulting Numbers: [32, 33, 52] Generated Node #0,0: 52:[32, 33, 52] Operation: 66-14=52 Exploring Operation: 66-33=33, Resulting Numbers: [32, 14, 33] Generated Node #0,1: 52:[32, 14, 33] Operation: 66-33=33 Exploring Operation: 66-32=34, Resulting Numbers: [33, 14, 34] Generated Node #0,2: 52:[33, 14, 34] Operation: 66-32=34 Exploring Operation: 66/33=2, Resulting Numbers: [32, 14, 2] Generated Node #0,3: 52:[32, 14, 2] Operation: 66/33=2 Moving to Node #0,3 Current State: 52:[32, 14, 2], Operations: ['66/33=2'] Exploring Operation: 32-14=18, Resulting Numbers: [2, 18] Generated Node #0,3,0: 52:[2, 18] Operation: 32-14=18 Exploring Operation: 32+14=46, Resulting Numbers: [2, 46] Generated Node #0,3,1: 52:[2, 46] Operation: 32+14=46 Exploring Operation: 32-2=30, Resulting Numbers: [14, 30] Generated Node #0,3,2: 52:[14, 30] Operation: 32-2=30 Exploring Operation: 32/2=16, Resulting Numbers: [14, 16] Generated Node #0,3,3: 52:[14, 16] Operation: 32/2=16 Moving to Node #0,0 Current State: 52:[32, 33, 52], Operations: ['66-14=52'] Exploring Operation: 52-33=19, Resulting Numbers: [32, 19] Generated Node #0,0,0: 52:[32, 19] Operation: 52-33=19 Exploring Operation: 33-32=1, Resulting Numbers: [52, 1] Generated Node #0,0,1: 52:[52, 1] Operation: 33-32=1 Exploring Operation: 52-32=20, Resulting Numbers: [33, 20] Generated Node #0,0,2: 52:[33, 20] Operation: 52-32=20 Exploring Operation: 32+33=65, Resulting Numbers: [52, 65] Generated Node #0,0,3: 52:[52, 65] Operation: 32+33=65 Moving to Node #0,1 Current State: 52:[32, 14, 33], Operations: ['66-33=33'] Exploring Operation: 33-32=1, Resulting Numbers: [14, 1] Generated Node #0,1,0: 52:[14, 1] Operation: 33-32=1 Exploring Operation: 14+33=47, Resulting Numbers: [32, 47] Generated Node #0,1,1: 52:[32, 47] Operation: 14+33=47 Exploring Operation: 33-14=19, Resulting Numbers: [32, 19] Generated Node #0,1,2: 52:[32, 19] Operation: 33-14=19 Exploring Operation: 32-14=18, Resulting Numbers: [33, 18] Generated Node #0,1,3: 52:[33, 18] Operation: 32-14=18 Moving to Node #0,2 Current State: 52:[33, 14, 34], Operations: ['66-32=34'] Exploring Operation: 33+14=47, Resulting Numbers: [34, 47] Generated Node #0,2,0: 52:[34, 47] Operation: 33+14=47 Exploring Operation: 14+34=48, Resulting Numbers: [33, 48] Generated Node #0,2,1: 52:[33, 48] Operation: 14+34=48 Exploring Operation: 34-33=1, Resulting Numbers: [14, 1] Generated Node #0,2,2: 52:[14, 1] Operation: 34-33=1 Exploring Operation: 34-14=20, Resulting Numbers: [33, 20] Generated Node #0,2,3: 52:[33, 20] Operation: 34-14=20 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[14, 1], Operations: ['66-32=34', '34-33=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,52 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,52 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[33, 48], Operations: ['66-32=34', '14+34=48'] Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,52 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,52 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[34, 47], Operations: ['66-32=34', '33+14=47'] Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,52 unequal: No Solution Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 34*47=1598, Resulting Numbers: [1598] 1598,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 52:[33, 20], Operations: ['66-32=34', '34-14=20'] Exploring Operation: 33*20=660, Resulting Numbers: [660] 660,52 unequal: No Solution Exploring Operation: 33+20=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,52 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: 52:[52, 1], Operations: ['66-14=52', '33-32=1'] Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[32, 66, 33, 14], Operations: [] Exploring Operation: 66-14=52, Resulting Numbers: [32, 33, 52] Generated Node #0,0: 52:[32, 33, 52] Operation: 66-14=52 Moving to Node #0,0 Current State: 52:[32, 33, 52], Operations: ['66-14=52'] Exploring Operation: 33-32=1, Resulting Numbers: [52, 1] Generated Node #0,0,1: 52:[52, 1] Operation: 33-32=1 Moving to Node #0,0,1 Current State: 52:[52, 1], Operations: ['66-14=52', '33-32=1'] Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 57, 27, 20, 7 ]
56
[ "57+27=84", "20*7=140", "140-84=56" ]
Current State: 56:[57, 27, 20, 7], Operations: [] Exploring Operation: 57+27=84, Resulting Numbers: [20, 7, 84] Generated Node #2: [20, 7, 84] from Operation: 57+27=84 Current State: 56:[20, 7, 84], Operations: ['57+27=84'] Exploring Operation: 20*7=140, Resulting Numbers: [84, 140] Generated Node #3: [84, 140] from Operation: 20*7=140 Current State: 56:[84, 140], Operations: ['57+27=84', '20*7=140'] Exploring Operation: 140-84=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[57, 27, 20, 7], Operations: [] Exploring Operation: 20+7=27, Resulting Numbers: [57, 27, 27] Generated Node #0,0: 56:[57, 27, 27] Operation: 20+7=27 Exploring Operation: 27-20=7, Resulting Numbers: [57, 7, 7] Generated Node #0,1: 56:[57, 7, 7] Operation: 27-20=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[57, 7, 7], Operations: ['27-20=7'] Exploring Operation: 7/7=1, Resulting Numbers: [57, 1] Generated Node #0,1,0: 56:[57, 1] Operation: 7/7=1 Exploring Operation: 7+7=14, Resulting Numbers: [57, 14] Generated Node #0,1,1: 56:[57, 14] Operation: 7+7=14 Moving to Node #0,1,1 Current State: 56:[57, 14], Operations: ['27-20=7', '7+7=14'] Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,56 unequal: No Solution Exploring Operation: 57+14=71, Resulting Numbers: [71] 71,56 unequal: No Solution Moving to Node #0,1,0 Current State: 56:[57, 1], Operations: ['27-20=7', '7/7=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[57, 27, 20, 7], Operations: [] Exploring Operation: 27-20=7, Resulting Numbers: [57, 7, 7] Generated Node #0,1: 56:[57, 7, 7] Operation: 27-20=7 Moving to Node #0,1 Current State: 56:[57, 7, 7], Operations: ['27-20=7'] Exploring Operation: 7/7=1, Resulting Numbers: [57, 1] Generated Node #0,1,0: 56:[57, 1] Operation: 7/7=1 Moving to Node #0,1,0 Current State: 56:[57, 1], Operations: ['27-20=7', '7/7=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 46, 42, 65, 92 ]
31
[ "46-42=4", "92-65=27", "4+27=31" ]
Current State: 31:[46, 42, 65, 92], Operations: [] Exploring Operation: 46-42=4, Resulting Numbers: [65, 92, 4] Generated Node #2: [65, 92, 4] from Operation: 46-42=4 Current State: 31:[65, 92, 4], Operations: ['46-42=4'] Exploring Operation: 92-65=27, Resulting Numbers: [4, 27] Generated Node #3: [4, 27] from Operation: 92-65=27 Current State: 31:[4, 27], Operations: ['46-42=4', '92-65=27'] Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[46, 42, 65, 92], Operations: [] Exploring Operation: 92-42=50, Resulting Numbers: [46, 65, 50] Generated Node #0,0: 31:[46, 65, 50] Operation: 92-42=50 Exploring Operation: 92-46=46, Resulting Numbers: [42, 65, 46] Generated Node #0,1: 31:[42, 65, 46] Operation: 92-46=46 Exploring Operation: 92-65=27, Resulting Numbers: [46, 42, 27] Generated Node #0,2: 31:[46, 42, 27] Operation: 92-65=27 Moving to Node #0,2 Current State: 31:[46, 42, 27], Operations: ['92-65=27'] Exploring Operation: 42-27=15, Resulting Numbers: [46, 15] Generated Node #0,2,0: 31:[46, 15] Operation: 42-27=15 Exploring Operation: 46-27=19, Resulting Numbers: [42, 19] Generated Node #0,2,1: 31:[42, 19] Operation: 46-27=19 Exploring Operation: 46-42=4, Resulting Numbers: [27, 4] Generated Node #0,2,2: 31:[27, 4] Operation: 46-42=4 Moving to Node #0,1 Current State: 31:[42, 65, 46], Operations: ['92-46=46'] Exploring Operation: 46-42=4, Resulting Numbers: [65, 4] Generated Node #0,1,0: 31:[65, 4] Operation: 46-42=4 Exploring Operation: 65-42=23, Resulting Numbers: [46, 23] Generated Node #0,1,1: 31:[46, 23] Operation: 65-42=23 Exploring Operation: 65-46=19, Resulting Numbers: [42, 19] Generated Node #0,1,2: 31:[42, 19] Operation: 65-46=19 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[46, 23], Operations: ['92-46=46', '65-42=23'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 46+23=69, Resulting Numbers: [69] 69,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[42, 19], Operations: ['92-46=46', '65-46=19'] Exploring Operation: 42-19=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 42*19=798, Resulting Numbers: [798] 798,31 unequal: No Solution Exploring Operation: 42+19=61, Resulting Numbers: [61] 61,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[65, 4], Operations: ['92-46=46', '46-42=4'] Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,31 unequal: No Solution Exploring Operation: 65*4=260, Resulting Numbers: [260] 260,31 unequal: No Solution Exploring Operation: 65+4=69, Resulting Numbers: [69] 69,31 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: 31:[46, 65, 50], Operations: ['92-42=50'] Exploring Operation: 65-46=19, Resulting Numbers: [50, 19] Generated Node #0,0,0: 31:[50, 19] Operation: 65-46=19 Exploring Operation: 50-46=4, Resulting Numbers: [65, 4] Generated Node #0,0,1: 31:[65, 4] Operation: 50-46=4 Exploring Operation: 65-50=15, Resulting Numbers: [46, 15] Generated Node #0,0,2: 31:[46, 15] Operation: 65-50=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[50, 19], Operations: ['92-42=50', '65-46=19'] Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[46, 42, 65, 92], Operations: [] Exploring Operation: 92-42=50, Resulting Numbers: [46, 65, 50] Generated Node #0,0: 31:[46, 65, 50] Operation: 92-42=50 Moving to Node #0,0 Current State: 31:[46, 65, 50], Operations: ['92-42=50'] Exploring Operation: 65-46=19, Resulting Numbers: [50, 19] Generated Node #0,0,0: 31:[50, 19] Operation: 65-46=19 Moving to Node #0,0,0 Current State: 31:[50, 19], Operations: ['92-42=50', '65-46=19'] Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
sum_heuristic
[ 44, 96, 13, 60 ]
15
[ "96-44=52", "13*60=780", "780/52=15" ]
Current State: 15:[44, 96, 13, 60], Operations: [] Exploring Operation: 96-44=52, Resulting Numbers: [13, 60, 52] Generated Node #2: [13, 60, 52] from Operation: 96-44=52 Current State: 15:[13, 60, 52], Operations: ['96-44=52'] Exploring Operation: 13*60=780, Resulting Numbers: [52, 780] Generated Node #3: [52, 780] from Operation: 13*60=780 Current State: 15:[52, 780], Operations: ['96-44=52', '13*60=780'] Exploring Operation: 780/52=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[44, 96, 13, 60], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [96, 13, 16] Generated Node #0,0: 15:[96, 13, 16] Operation: 60-44=16 Exploring Operation: 96-44=52, Resulting Numbers: [13, 60, 52] Generated Node #0,1: 15:[13, 60, 52] Operation: 96-44=52 Exploring Operation: 96-60=36, Resulting Numbers: [44, 13, 36] Generated Node #0,2: 15:[44, 13, 36] Operation: 96-60=36 Exploring Operation: 44-13=31, Resulting Numbers: [96, 60, 31] Generated Node #0,3: 15:[96, 60, 31] Operation: 44-13=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[44, 13, 36], Operations: ['96-60=36'] Exploring Operation: 44-36=8, Resulting Numbers: [13, 8] Generated Node #0,2,0: 15:[13, 8] Operation: 44-36=8 Exploring Operation: 36-13=23, Resulting Numbers: [44, 23] Generated Node #0,2,1: 15:[44, 23] Operation: 36-13=23 Exploring Operation: 44-13=31, Resulting Numbers: [36, 31] Generated Node #0,2,2: 15:[36, 31] Operation: 44-13=31 Exploring Operation: 44+13=57, Resulting Numbers: [36, 57] Generated Node #0,2,3: 15:[36, 57] Operation: 44+13=57 Moving to Node #0,2,0 Current State: 15:[13, 8], Operations: ['96-60=36', '44-36=8'] Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,15 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[36, 31], Operations: ['96-60=36', '44-13=31'] Exploring Operation: 36*31=1116, Resulting Numbers: [1116] 1116,15 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[44, 23], Operations: ['96-60=36', '36-13=23'] Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,15 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[36, 57], Operations: ['96-60=36', '44+13=57'] Exploring Operation: 57-36=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 36*57=2052, Resulting Numbers: [2052] 2052,15 unequal: No Solution Exploring Operation: 36+57=93, Resulting Numbers: [93] 93,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[96, 13, 16], Operations: ['60-44=16'] Exploring Operation: 16-13=3, Resulting Numbers: [96, 3] Generated Node #0,0,0: 15:[96, 3] Operation: 16-13=3 Exploring Operation: 96-16=80, Resulting Numbers: [13, 80] Generated Node #0,0,1: 15:[13, 80] Operation: 96-16=80 Exploring Operation: 96-13=83, Resulting Numbers: [16, 83] Generated Node #0,0,2: 15:[16, 83] Operation: 96-13=83 Exploring Operation: 96/16=6, Resulting Numbers: [13, 6] Generated Node #0,0,3: 15:[13, 6] Operation: 96/16=6 Moving to Node #0,0,3 Current State: 15:[13, 6], Operations: ['60-44=16', '96/16=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,15 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[13, 80], Operations: ['60-44=16', '96-16=80'] Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 13+80=93, Resulting Numbers: [93] 93,15 unequal: No Solution Exploring Operation: 13*80=1040, Resulting Numbers: [1040] 1040,15 unequal: No Solution Moving to Node #0,0,2 Current State: 15:[16, 83], Operations: ['60-44=16', '96-13=83'] Exploring Operation: 16*83=1328, Resulting Numbers: [1328] 1328,15 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 16+83=99, Resulting Numbers: [99] 99,15 unequal: No Solution Moving to Node #0,0,0 Current State: 15:[96, 3], Operations: ['60-44=16', '16-13=3'] Exploring Operation: 96*3=288, Resulting Numbers: [288] 288,15 unequal: No Solution Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,15 unequal: No Solution Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,15 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[13, 60, 52], Operations: ['96-44=52'] Exploring Operation: 52-13=39, Resulting Numbers: [60, 39] Generated Node #0,1,0: 15:[60, 39] Operation: 52-13=39 Exploring Operation: 60-52=8, Resulting Numbers: [13, 8] Generated Node #0,1,1: 15:[13, 8] Operation: 60-52=8 Exploring Operation: 52/13=4, Resulting Numbers: [60, 4] Generated Node #0,1,2: 15:[60, 4] Operation: 52/13=4 Exploring Operation: 60-13=47, Resulting Numbers: [52, 47] Generated Node #0,1,3: 15:[52, 47] Operation: 60-13=47 Moving to Node #0,1,1 Current State: 15:[13, 8], Operations: ['96-44=52', '60-52=8'] Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,15 unequal: No Solution Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[60, 4], Operations: ['96-44=52', '52/13=4'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[44, 96, 13, 60], Operations: [] Exploring Operation: 96-44=52, Resulting Numbers: [13, 60, 52] Generated Node #0,1: 15:[13, 60, 52] Operation: 96-44=52 Moving to Node #0,1 Current State: 15:[13, 60, 52], Operations: ['96-44=52'] Exploring Operation: 52/13=4, Resulting Numbers: [60, 4] Generated Node #0,1,2: 15:[60, 4] Operation: 52/13=4 Moving to Node #0,1,2 Current State: 15:[60, 4], Operations: ['96-44=52', '52/13=4'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 57, 23, 69, 78 ]
43
[ "57-23=34", "78-69=9", "34+9=43" ]
Current State: 43:[57, 23, 69, 78], Operations: [] Exploring Operation: 57-23=34, Resulting Numbers: [69, 78, 34] Generated Node #2: [69, 78, 34] from Operation: 57-23=34 Current State: 43:[69, 78, 34], Operations: ['57-23=34'] Exploring Operation: 78-69=9, Resulting Numbers: [34, 9] Generated Node #3: [34, 9] from Operation: 78-69=9 Current State: 43:[34, 9], Operations: ['57-23=34', '78-69=9'] Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[57, 23, 69, 78], Operations: [] Exploring Operation: 69-23=46, Resulting Numbers: [57, 78, 46] Generated Node #0,0: 43:[57, 78, 46] Operation: 69-23=46 Exploring Operation: 78-69=9, Resulting Numbers: [57, 23, 9] Generated Node #0,1: 43:[57, 23, 9] Operation: 78-69=9 Exploring Operation: 78-57=21, Resulting Numbers: [23, 69, 21] Generated Node #0,2: 43:[23, 69, 21] Operation: 78-57=21 Exploring Operation: 57-23=34, Resulting Numbers: [69, 78, 34] Generated Node #0,3: 43:[69, 78, 34] Operation: 57-23=34 Exploring Operation: 78-23=55, Resulting Numbers: [57, 69, 55] Generated Node #0,4: 43:[57, 69, 55] Operation: 78-23=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[57, 78, 46], Operations: ['69-23=46'] Exploring Operation: 78-46=32, Resulting Numbers: [57, 32] Generated Node #0,0,0: 43:[57, 32] Operation: 78-46=32 Exploring Operation: 57+78=135, Resulting Numbers: [46, 135] Generated Node #0,0,1: 43:[46, 135] Operation: 57+78=135 Exploring Operation: 57-46=11, Resulting Numbers: [78, 11] Generated Node #0,0,2: 43:[78, 11] Operation: 57-46=11 Exploring Operation: 78-57=21, Resulting Numbers: [46, 21] Generated Node #0,0,3: 43:[46, 21] Operation: 78-57=21 Exploring Operation: 57+46=103, Resulting Numbers: [78, 103] Generated Node #0,0,4: 43:[78, 103] Operation: 57+46=103 Moving to Node #0,0,0 Current State: 43:[57, 32], Operations: ['69-23=46', '78-46=32'] Exploring Operation: 57-32=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 57*32=1824, Resulting Numbers: [1824] 1824,43 unequal: No Solution Exploring Operation: 57+32=89, Resulting Numbers: [89] 89,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[46, 21], Operations: ['69-23=46', '78-57=21'] Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,43 unequal: No Solution Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[78, 11], Operations: ['69-23=46', '57-46=11'] Exploring Operation: 78*11=858, Resulting Numbers: [858] 858,43 unequal: No Solution Exploring Operation: 78+11=89, Resulting Numbers: [89] 89,43 unequal: No Solution Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[46, 135], Operations: ['69-23=46', '57+78=135'] Exploring Operation: 135-46=89, Resulting Numbers: [89] 89,43 unequal: No Solution Exploring Operation: 46*135=6210, Resulting Numbers: [6210] 6210,43 unequal: No Solution Exploring Operation: 46+135=181, Resulting Numbers: [181] 181,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[78, 103], Operations: ['69-23=46', '57+46=103'] Exploring Operation: 78+103=181, Resulting Numbers: [181] 181,43 unequal: No Solution Exploring Operation: 78*103=8034, Resulting Numbers: [8034] 8034,43 unequal: No Solution Exploring Operation: 103-78=25, Resulting Numbers: [25] 25,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 43:[57, 69, 55], Operations: ['78-23=55'] Exploring Operation: 57-55=2, Resulting Numbers: [69, 2] Generated Node #0,4,0: 43:[69, 2] Operation: 57-55=2 Exploring Operation: 69-57=12, Resulting Numbers: [55, 12] Generated Node #0,4,1: 43:[55, 12] Operation: 69-57=12 Exploring Operation: 69-55=14, Resulting Numbers: [57, 14] Generated Node #0,4,2: 43:[57, 14] Operation: 69-55=14 Exploring Operation: 57+55=112, Resulting Numbers: [69, 112] Generated Node #0,4,3: 43:[69, 112] Operation: 57+55=112 Exploring Operation: 57+69=126, Resulting Numbers: [55, 126] Generated Node #0,4,4: 43:[55, 126] Operation: 57+69=126 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 43:[55, 12], Operations: ['78-23=55', '69-57=12'] Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[57, 23, 69, 78], Operations: [] Exploring Operation: 78-23=55, Resulting Numbers: [57, 69, 55] Generated Node #0,4: 43:[57, 69, 55] Operation: 78-23=55 Moving to Node #0,4 Current State: 43:[57, 69, 55], Operations: ['78-23=55'] Exploring Operation: 69-57=12, Resulting Numbers: [55, 12] Generated Node #0,4,1: 43:[55, 12] Operation: 69-57=12 Moving to Node #0,4,1 Current State: 43:[55, 12], Operations: ['78-23=55', '69-57=12'] Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_5
sum_heuristic
[ 69, 73, 66, 60 ]
10
[ "73-69=4", "66-60=6", "4+6=10" ]
Current State: 10:[69, 73, 66, 60], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [66, 60, 4] Generated Node #2: [66, 60, 4] from Operation: 73-69=4 Current State: 10:[66, 60, 4], Operations: ['73-69=4'] Exploring Operation: 66-60=6, Resulting Numbers: [4, 6] Generated Node #3: [4, 6] from Operation: 66-60=6 Current State: 10:[4, 6], Operations: ['73-69=4', '66-60=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[69, 73, 66, 60], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [66, 60, 4] Generated Node #0,0: 10:[66, 60, 4] Operation: 73-69=4 Exploring Operation: 69-66=3, Resulting Numbers: [73, 60, 3] Generated Node #0,1: 10:[73, 60, 3] Operation: 69-66=3 Exploring Operation: 73-66=7, Resulting Numbers: [69, 60, 7] Generated Node #0,2: 10:[69, 60, 7] Operation: 73-66=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[66, 60, 4], Operations: ['73-69=4'] Exploring Operation: 60/4=15, Resulting Numbers: [66, 15] Generated Node #0,0,0: 10:[66, 15] Operation: 60/4=15 Exploring Operation: 66-60=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 10:[4, 6] Operation: 66-60=6 Exploring Operation: 66-4=62, Resulting Numbers: [60, 62] Generated Node #0,0,2: 10:[60, 62] Operation: 66-4=62 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[4, 6], Operations: ['73-69=4', '66-60=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[69, 73, 66, 60], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [66, 60, 4] Generated Node #0,0: 10:[66, 60, 4] Operation: 73-69=4 Moving to Node #0,0 Current State: 10:[66, 60, 4], Operations: ['73-69=4'] Exploring Operation: 66-60=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 10:[4, 6] Operation: 66-60=6 Moving to Node #0,0,1 Current State: 10:[4, 6], Operations: ['73-69=4', '66-60=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 63, 2, 74, 76 ]
50
[ "76-63=13", "74/2=37", "13+37=50" ]
Current State: 50:[63, 2, 74, 76], Operations: [] Exploring Operation: 76-63=13, Resulting Numbers: [2, 74, 13] Generated Node #2: [2, 74, 13] from Operation: 76-63=13 Current State: 50:[2, 74, 13], Operations: ['76-63=13'] Exploring Operation: 74/2=37, Resulting Numbers: [13, 37] Generated Node #3: [13, 37] from Operation: 74/2=37 Current State: 50:[13, 37], Operations: ['76-63=13', '74/2=37'] Exploring Operation: 13+37=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[63, 2, 74, 76], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [63, 2, 2] Generated Node #0,0: 50:[63, 2, 2] Operation: 76-74=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[63, 2, 2], Operations: ['76-74=2'] Exploring Operation: 63-2=61, Resulting Numbers: [2, 61] Generated Node #0,0,0: 50:[2, 61] Operation: 63-2=61 Moving to Node #0,0,0 Current State: 50:[2, 61], Operations: ['76-74=2', '63-2=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 66, 63, 39, 61 ]
56
[ "66-63=3", "39*3=117", "117-61=56" ]
Current State: 56:[66, 63, 39, 61], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [39, 61, 3] Generated Node #2: [39, 61, 3] from Operation: 66-63=3 Current State: 56:[39, 61, 3], Operations: ['66-63=3'] Exploring Operation: 39*3=117, Resulting Numbers: [61, 117] Generated Node #3: [61, 117] from Operation: 39*3=117 Current State: 56:[61, 117], Operations: ['66-63=3', '39*3=117'] Exploring Operation: 117-61=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[66, 63, 39, 61], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [39, 61, 3] Generated Node #0,0: 56:[39, 61, 3] Operation: 66-63=3 Exploring Operation: 63-39=24, Resulting Numbers: [66, 61, 24] Generated Node #0,1: 56:[66, 61, 24] Operation: 63-39=24 Exploring Operation: 66-39=27, Resulting Numbers: [63, 61, 27] Generated Node #0,2: 56:[63, 61, 27] Operation: 66-39=27 Exploring Operation: 63-61=2, Resulting Numbers: [66, 39, 2] Generated Node #0,3: 56:[66, 39, 2] Operation: 63-61=2 Exploring Operation: 66-61=5, Resulting Numbers: [63, 39, 5] Generated Node #0,4: 56:[63, 39, 5] Operation: 66-61=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[63, 61, 27], Operations: ['66-39=27'] Exploring Operation: 61-27=34, Resulting Numbers: [63, 34] Generated Node #0,2,0: 56:[63, 34] Operation: 61-27=34 Exploring Operation: 63-61=2, Resulting Numbers: [27, 2] Generated Node #0,2,1: 56:[27, 2] Operation: 63-61=2 Exploring Operation: 63-27=36, Resulting Numbers: [61, 36] Generated Node #0,2,2: 56:[61, 36] Operation: 63-27=36 Exploring Operation: 63+27=90, Resulting Numbers: [61, 90] Generated Node #0,2,3: 56:[61, 90] Operation: 63+27=90 Exploring Operation: 61+27=88, Resulting Numbers: [63, 88] Generated Node #0,2,4: 56:[63, 88] Operation: 61+27=88 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 56:[27, 2], Operations: ['66-39=27', '63-61=2'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 56:[63, 34], Operations: ['66-39=27', '61-27=34'] Exploring Operation: 63-34=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 63+34=97, Resulting Numbers: [97] 97,56 unequal: No Solution Exploring Operation: 63*34=2142, Resulting Numbers: [2142] 2142,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 56:[61, 36], Operations: ['66-39=27', '63-27=36'] Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 61*36=2196, Resulting Numbers: [2196] 2196,56 unequal: No Solution Exploring Operation: 61+36=97, Resulting Numbers: [97] 97,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 56:[61, 90], Operations: ['66-39=27', '63+27=90'] Exploring Operation: 90-61=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 61+90=151, Resulting Numbers: [151] 151,56 unequal: No Solution Exploring Operation: 61*90=5490, Resulting Numbers: [5490] 5490,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 56:[63, 88], Operations: ['66-39=27', '61+27=88'] Exploring Operation: 88-63=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 63+88=151, Resulting Numbers: [151] 151,56 unequal: No Solution Exploring Operation: 63*88=5544, Resulting Numbers: [5544] 5544,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[39, 61, 3], Operations: ['66-63=3'] Exploring Operation: 39+3=42, Resulting Numbers: [61, 42] Generated Node #0,0,0: 56:[61, 42] Operation: 39+3=42 Exploring Operation: 39-3=36, Resulting Numbers: [61, 36] Generated Node #0,0,1: 56:[61, 36] Operation: 39-3=36 Exploring Operation: 61-39=22, Resulting Numbers: [3, 22] Generated Node #0,0,2: 56:[3, 22] Operation: 61-39=22 Exploring Operation: 39/3=13, Resulting Numbers: [61, 13] Generated Node #0,0,3: 56:[61, 13] Operation: 39/3=13 Exploring Operation: 61-3=58, Resulting Numbers: [39, 58] Generated Node #0,0,4: 56:[39, 58] Operation: 61-3=58 Moving to Node #0,0,3 Current State: 56:[61, 13], Operations: ['66-63=3', '39/3=13'] Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,56 unequal: No Solution Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,56 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[3, 22], Operations: ['66-63=3', '61-39=22'] Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[61, 36], Operations: ['66-63=3', '39-3=36'] Exploring Operation: 61+36=97, Resulting Numbers: [97] 97,56 unequal: No Solution Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 61*36=2196, Resulting Numbers: [2196] 2196,56 unequal: No Solution Moving to Node #0,0,4 Current State: 56:[39, 58], Operations: ['66-63=3', '61-3=58'] Exploring Operation: 39*58=2262, Resulting Numbers: [2262] 2262,56 unequal: No Solution Exploring Operation: 39+58=97, Resulting Numbers: [97] 97,56 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[61, 42], Operations: ['66-63=3', '39+3=42'] Exploring Operation: 61*42=2562, Resulting Numbers: [2562] 2562,56 unequal: No Solution Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 61+42=103, Resulting Numbers: [103] 103,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[66, 61, 24], Operations: ['63-39=24'] Exploring Operation: 66-61=5, Resulting Numbers: [24, 5] Generated Node #0,1,0: 56:[24, 5] Operation: 66-61=5 Exploring Operation: 66-24=42, Resulting Numbers: [61, 42] Generated Node #0,1,1: 56:[61, 42] Operation: 66-24=42 Exploring Operation: 66+24=90, Resulting Numbers: [61, 90] Generated Node #0,1,2: 56:[61, 90] Operation: 66+24=90 Exploring Operation: 61-24=37, Resulting Numbers: [66, 37] Generated Node #0,1,3: 56:[66, 37] Operation: 61-24=37 Exploring Operation: 61+24=85, Resulting Numbers: [66, 85] Generated Node #0,1,4: 56:[66, 85] Operation: 61+24=85 Moving to Node #0,1,0 Current State: 56:[24, 5], Operations: ['63-39=24', '66-61=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,56 unequal: No Solution Moving to Node #0,1,3 Current State: 56:[66, 37], Operations: ['63-39=24', '61-24=37'] Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 66*37=2442, Resulting Numbers: [2442] 2442,56 unequal: No Solution Exploring Operation: 66+37=103, Resulting Numbers: [103] 103,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[61, 42], Operations: ['63-39=24', '66-24=42'] Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 61+42=103, Resulting Numbers: [103] 103,56 unequal: No Solution Exploring Operation: 61*42=2562, Resulting Numbers: [2562] 2562,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[61, 90], Operations: ['63-39=24', '66+24=90'] Exploring Operation: 61+90=151, Resulting Numbers: [151] 151,56 unequal: No Solution Exploring Operation: 61*90=5490, Resulting Numbers: [5490] 5490,56 unequal: No Solution Exploring Operation: 90-61=29, Resulting Numbers: [29] 29,56 unequal: No Solution Moving to Node #0,1,4 Current State: 56:[66, 85], Operations: ['63-39=24', '61+24=85'] Exploring Operation: 85-66=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 66*85=5610, Resulting Numbers: [5610] 5610,56 unequal: No Solution Exploring Operation: 66+85=151, Resulting Numbers: [151] 151,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 56:[63, 39, 5], Operations: ['66-61=5'] Exploring Operation: 63+5=68, Resulting Numbers: [39, 68] Generated Node #0,4,0: 56:[39, 68] Operation: 63+5=68 Exploring Operation: 39-5=34, Resulting Numbers: [63, 34] Generated Node #0,4,1: 56:[63, 34] Operation: 39-5=34 Exploring Operation: 63-5=58, Resulting Numbers: [39, 58] Generated Node #0,4,2: 56:[39, 58] Operation: 63-5=58 Exploring Operation: 63-39=24, Resulting Numbers: [5, 24] Generated Node #0,4,3: 56:[5, 24] Operation: 63-39=24 Exploring Operation: 39+5=44, Resulting Numbers: [63, 44] Generated Node #0,4,4: 56:[63, 44] Operation: 39+5=44 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 56:[5, 24], Operations: ['66-61=5', '63-39=24'] Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,56 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 56:[63, 34], Operations: ['66-61=5', '39-5=34'] Exploring Operation: 63*34=2142, Resulting Numbers: [2142] 2142,56 unequal: No Solution Exploring Operation: 63-34=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 63+34=97, Resulting Numbers: [97] 97,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 56:[39, 58], Operations: ['66-61=5', '63-5=58'] Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 39*58=2262, Resulting Numbers: [2262] 2262,56 unequal: No Solution Exploring Operation: 39+58=97, Resulting Numbers: [97] 97,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 56:[63, 44], Operations: ['66-61=5', '39+5=44'] Exploring Operation: 63+44=107, Resulting Numbers: [107] 107,56 unequal: No Solution Exploring Operation: 63*44=2772, Resulting Numbers: [2772] 2772,56 unequal: No Solution Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 56:[39, 68], Operations: ['66-61=5', '63+5=68'] Exploring Operation: 39*68=2652, Resulting Numbers: [2652] 2652,56 unequal: No Solution Exploring Operation: 68-39=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 39+68=107, Resulting Numbers: [107] 107,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[66, 39, 2], Operations: ['63-61=2'] Exploring Operation: 66+2=68, Resulting Numbers: [39, 68] Generated Node #0,3,0: 56:[39, 68] Operation: 66+2=68 Exploring Operation: 66-39=27, Resulting Numbers: [2, 27] Generated Node #0,3,1: 56:[2, 27] Operation: 66-39=27 Exploring Operation: 39-2=37, Resulting Numbers: [66, 37] Generated Node #0,3,2: 56:[66, 37] Operation: 39-2=37 Exploring Operation: 66-2=64, Resulting Numbers: [39, 64] Generated Node #0,3,3: 56:[39, 64] Operation: 66-2=64 Exploring Operation: 66/2=33, Resulting Numbers: [39, 33] Generated Node #0,3,4: 56:[39, 33] Operation: 66/2=33 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 56:[2, 27], Operations: ['63-61=2', '66-39=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,56 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 56:[39, 33], Operations: ['63-61=2', '66/2=33'] Exploring Operation: 39+33=72, Resulting Numbers: [72] 72,56 unequal: No Solution Exploring Operation: 39*33=1287, Resulting Numbers: [1287] 1287,56 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 56:[66, 37], Operations: ['63-61=2', '39-2=37'] Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 66*37=2442, Resulting Numbers: [2442] 2442,56 unequal: No Solution Exploring Operation: 66+37=103, Resulting Numbers: [103] 103,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 56:[39, 64], Operations: ['63-61=2', '66-2=64'] Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 39*64=2496, Resulting Numbers: [2496] 2496,56 unequal: No Solution Exploring Operation: 39+64=103, Resulting Numbers: [103] 103,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 56:[39, 68], Operations: ['63-61=2', '66+2=68'] Exploring Operation: 68-39=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 39*68=2652, Resulting Numbers: [2652] 2652,56 unequal: No Solution Exploring Operation: 39+68=107, Resulting Numbers: [107] 107,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 90, 72, 36, 88 ]
18
[ "90-88=2", "72-36=36", "36/2=18" ]
Current State: 18:[90, 72, 36, 88], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [72, 36, 2] Generated Node #2: [72, 36, 2] from Operation: 90-88=2 Current State: 18:[72, 36, 2], Operations: ['90-88=2'] Exploring Operation: 72-36=36, Resulting Numbers: [2, 36] Generated Node #3: [2, 36] from Operation: 72-36=36 Current State: 18:[2, 36], Operations: ['90-88=2', '72-36=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[90, 72, 36, 88], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [90, 88, 2] Generated Node #0,0: 18:[90, 88, 2] Operation: 72/36=2 Exploring Operation: 90-72=18, Resulting Numbers: [36, 88, 18] Generated Node #0,1: 18:[36, 88, 18] Operation: 90-72=18 Exploring Operation: 90-88=2, Resulting Numbers: [72, 36, 2] Generated Node #0,2: 18:[72, 36, 2] Operation: 90-88=2 Exploring Operation: 88-72=16, Resulting Numbers: [90, 36, 16] Generated Node #0,3: 18:[90, 36, 16] Operation: 88-72=16 Moving to Node #0,2 Current State: 18:[72, 36, 2], Operations: ['90-88=2'] Exploring Operation: 36/2=18, Resulting Numbers: [72, 18] Generated Node #0,2,0: 18:[72, 18] Operation: 36/2=18 Exploring Operation: 72/2=36, Resulting Numbers: [36, 36] Generated Node #0,2,1: 18:[36, 36] Operation: 72/2=36 Exploring Operation: 72-36=36, Resulting Numbers: [2, 36] Generated Node #0,2,2: 18:[2, 36] Operation: 72-36=36 Exploring Operation: 72/36=2, Resulting Numbers: [2, 2] Generated Node #0,2,3: 18:[2, 2] Operation: 72/36=2 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[2, 2], Operations: ['90-88=2', '72/36=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,18 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,18 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:[2, 36], Operations: ['90-88=2', '72-36=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[90, 72, 36, 88], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [72, 36, 2] Generated Node #0,2: 18:[72, 36, 2] Operation: 90-88=2 Moving to Node #0,2 Current State: 18:[72, 36, 2], Operations: ['90-88=2'] Exploring Operation: 72-36=36, Resulting Numbers: [2, 36] Generated Node #0,2,2: 18:[2, 36] Operation: 72-36=36 Moving to Node #0,2,2 Current State: 18:[2, 36], Operations: ['90-88=2', '72-36=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 9, 18, 12, 84 ]
74
[ "18/9=2", "84-12=72", "2+72=74" ]
Current State: 74:[9, 18, 12, 84], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [12, 84, 2] Generated Node #2: [12, 84, 2] from Operation: 18/9=2 Current State: 74:[12, 84, 2], Operations: ['18/9=2'] Exploring Operation: 84-12=72, Resulting Numbers: [2, 72] Generated Node #3: [2, 72] from Operation: 84-12=72 Current State: 74:[2, 72], Operations: ['18/9=2', '84-12=72'] Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[9, 18, 12, 84], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [12, 84, 2] Generated Node #0,0: 74:[12, 84, 2] Operation: 18/9=2 Moving to Node #0,0 Current State: 74:[12, 84, 2], Operations: ['18/9=2'] Exploring Operation: 84-12=72, Resulting Numbers: [2, 72] Generated Node #0,0,0: 74:[2, 72] Operation: 84-12=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[2, 72], Operations: ['18/9=2', '84-12=72'] Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[9, 18, 12, 84], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [12, 84, 2] Generated Node #0,0: 74:[12, 84, 2] Operation: 18/9=2 Moving to Node #0,0 Current State: 74:[12, 84, 2], Operations: ['18/9=2'] Exploring Operation: 84-12=72, Resulting Numbers: [2, 72] Generated Node #0,0,0: 74:[2, 72] Operation: 84-12=72 Moving to Node #0,0,0 Current State: 74:[2, 72], Operations: ['18/9=2', '84-12=72'] Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 29, 75, 68, 13 ]
62
[ "75-68=7", "13*7=91", "91-29=62" ]
Current State: 62:[29, 75, 68, 13], Operations: [] Exploring Operation: 75-68=7, Resulting Numbers: [29, 13, 7] Generated Node #2: [29, 13, 7] from Operation: 75-68=7 Current State: 62:[29, 13, 7], Operations: ['75-68=7'] Exploring Operation: 13*7=91, Resulting Numbers: [29, 91] Generated Node #3: [29, 91] from Operation: 13*7=91 Current State: 62:[29, 91], Operations: ['75-68=7', '13*7=91'] Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[29, 75, 68, 13], Operations: [] Exploring Operation: 75-13=62, Resulting Numbers: [29, 68, 62] Generated Node #0,0: 62:[29, 68, 62] Operation: 75-13=62 Exploring Operation: 68-13=55, Resulting Numbers: [29, 75, 55] Generated Node #0,1: 62:[29, 75, 55] Operation: 68-13=55 Exploring Operation: 75-68=7, Resulting Numbers: [29, 13, 7] Generated Node #0,2: 62:[29, 13, 7] Operation: 75-68=7 Moving to Node #0,0 Current State: 62:[29, 68, 62], Operations: ['75-13=62'] Exploring Operation: 68-29=39, Resulting Numbers: [62, 39] Generated Node #0,0,0: 62:[62, 39] Operation: 68-29=39 Exploring Operation: 62-29=33, Resulting Numbers: [68, 33] Generated Node #0,0,1: 62:[68, 33] Operation: 62-29=33 Exploring Operation: 68-62=6, Resulting Numbers: [29, 6] Generated Node #0,0,2: 62:[29, 6] Operation: 68-62=6 Moving to Node #0,2 Current State: 62:[29, 13, 7], Operations: ['75-68=7'] Exploring Operation: 13-7=6, Resulting Numbers: [29, 6] Generated Node #0,2,0: 62:[29, 6] Operation: 13-7=6 Exploring Operation: 13+7=20, Resulting Numbers: [29, 20] Generated Node #0,2,1: 62:[29, 20] Operation: 13+7=20 Exploring Operation: 29+13=42, Resulting Numbers: [7, 42] Generated Node #0,2,2: 62:[7, 42] Operation: 29+13=42 Moving to Node #0,1 Current State: 62:[29, 75, 55], Operations: ['68-13=55'] Exploring Operation: 55-29=26, Resulting Numbers: [75, 26] Generated Node #0,1,0: 62:[75, 26] Operation: 55-29=26 Exploring Operation: 75-55=20, Resulting Numbers: [29, 20] Generated Node #0,1,1: 62:[29, 20] Operation: 75-55=20 Exploring Operation: 75-29=46, Resulting Numbers: [55, 46] Generated Node #0,1,2: 62:[55, 46] Operation: 75-29=46 Moving to Node #0,0,2 Current State: 62:[29, 6], Operations: ['75-13=62', '68-62=6'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[29, 6], Operations: ['75-68=7', '13-7=6'] Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,62 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[68, 33], Operations: ['75-13=62', '62-29=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 68*33=2244, Resulting Numbers: [2244] 2244,62 unequal: No Solution Exploring Operation: 68+33=101, Resulting Numbers: [101] 101,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[62, 39], Operations: ['75-13=62', '68-29=39'] Exploring Operation: 62+39=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 62*39=2418, Resulting Numbers: [2418] 2418,62 unequal: No Solution Exploring Operation: 62-39=23, Resulting Numbers: [23] 23,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[29, 20], Operations: ['68-13=55', '75-55=20'] Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,62 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[29, 20], Operations: ['75-68=7', '13+7=20'] Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,62 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,62 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[7, 42], Operations: ['75-68=7', '29+13=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,62 unequal: No Solution Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[75, 26], Operations: ['68-13=55', '55-29=26'] Exploring Operation: 75+26=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,62 unequal: No Solution Exploring Operation: 75*26=1950, Resulting Numbers: [1950] 1950,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[55, 46], Operations: ['68-13=55', '75-29=46'] Exploring Operation: 55-46=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 55+46=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 55*46=2530, Resulting Numbers: [2530] 2530,62 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 78, 98, 51, 90 ]
19
[ "98-78=20", "90-51=39", "39-20=19" ]
Current State: 19:[78, 98, 51, 90], Operations: [] Exploring Operation: 98-78=20, Resulting Numbers: [51, 90, 20] Generated Node #2: [51, 90, 20] from Operation: 98-78=20 Current State: 19:[51, 90, 20], Operations: ['98-78=20'] Exploring Operation: 90-51=39, Resulting Numbers: [20, 39] Generated Node #3: [20, 39] from Operation: 90-51=39 Current State: 19:[20, 39], Operations: ['98-78=20', '90-51=39'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[78, 98, 51, 90], Operations: [] Exploring Operation: 98-51=47, Resulting Numbers: [78, 90, 47] Generated Node #0,0: 19:[78, 90, 47] Operation: 98-51=47 Exploring Operation: 78-51=27, Resulting Numbers: [98, 90, 27] Generated Node #0,1: 19:[98, 90, 27] Operation: 78-51=27 Exploring Operation: 98-90=8, Resulting Numbers: [78, 51, 8] Generated Node #0,2: 19:[78, 51, 8] Operation: 98-90=8 Exploring Operation: 90-78=12, Resulting Numbers: [98, 51, 12] Generated Node #0,3: 19:[98, 51, 12] Operation: 90-78=12 Exploring Operation: 98-78=20, Resulting Numbers: [51, 90, 20] Generated Node #0,4: 19:[51, 90, 20] Operation: 98-78=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[78, 51, 8], Operations: ['98-90=8'] Exploring Operation: 51+8=59, Resulting Numbers: [78, 59] Generated Node #0,2,0: 19:[78, 59] Operation: 51+8=59 Exploring Operation: 78+8=86, Resulting Numbers: [51, 86] Generated Node #0,2,1: 19:[51, 86] Operation: 78+8=86 Exploring Operation: 78-51=27, Resulting Numbers: [8, 27] Generated Node #0,2,2: 19:[8, 27] Operation: 78-51=27 Exploring Operation: 51-8=43, Resulting Numbers: [78, 43] Generated Node #0,2,3: 19:[78, 43] Operation: 51-8=43 Exploring Operation: 78-8=70, Resulting Numbers: [51, 70] Generated Node #0,2,4: 19:[51, 70] Operation: 78-8=70 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 19:[8, 27], Operations: ['98-90=8', '78-51=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[78, 98, 51, 90], Operations: [] Exploring Operation: 98-90=8, Resulting Numbers: [78, 51, 8] Generated Node #0,2: 19:[78, 51, 8] Operation: 98-90=8 Moving to Node #0,2 Current State: 19:[78, 51, 8], Operations: ['98-90=8'] Exploring Operation: 78-51=27, Resulting Numbers: [8, 27] Generated Node #0,2,2: 19:[8, 27] Operation: 78-51=27 Moving to Node #0,2,2 Current State: 19:[8, 27], Operations: ['98-90=8', '78-51=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 24, 33, 70, 40 ]
21
[ "33-24=9", "70-40=30", "30-9=21" ]
Current State: 21:[24, 33, 70, 40], Operations: [] Exploring Operation: 33-24=9, Resulting Numbers: [70, 40, 9] Generated Node #2: [70, 40, 9] from Operation: 33-24=9 Current State: 21:[70, 40, 9], Operations: ['33-24=9'] Exploring Operation: 70-40=30, Resulting Numbers: [9, 30] Generated Node #3: [9, 30] from Operation: 70-40=30 Current State: 21:[9, 30], Operations: ['33-24=9', '70-40=30'] Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[24, 33, 70, 40], Operations: [] Exploring Operation: 70-33=37, Resulting Numbers: [24, 40, 37] Generated Node #0,0: 21:[24, 40, 37] Operation: 70-33=37 Exploring Operation: 40-33=7, Resulting Numbers: [24, 70, 7] Generated Node #0,1: 21:[24, 70, 7] Operation: 40-33=7 Exploring Operation: 70-24=46, Resulting Numbers: [33, 40, 46] Generated Node #0,2: 21:[33, 40, 46] Operation: 70-24=46 Exploring Operation: 70-40=30, Resulting Numbers: [24, 33, 30] Generated Node #0,3: 21:[24, 33, 30] Operation: 70-40=30 Moving to Node #0,3 Current State: 21:[24, 33, 30], Operations: ['70-40=30'] Exploring Operation: 33-24=9, Resulting Numbers: [30, 9] Generated Node #0,3,0: 21:[30, 9] Operation: 33-24=9 Exploring Operation: 24+33=57, Resulting Numbers: [30, 57] Generated Node #0,3,1: 21:[30, 57] Operation: 24+33=57 Exploring Operation: 33-30=3, Resulting Numbers: [24, 3] Generated Node #0,3,2: 21:[24, 3] Operation: 33-30=3 Exploring Operation: 30-24=6, Resulting Numbers: [33, 6] Generated Node #0,3,3: 21:[33, 6] Operation: 30-24=6 Moving to Node #0,0 Current State: 21:[24, 40, 37], Operations: ['70-33=37'] Exploring Operation: 40-24=16, Resulting Numbers: [37, 16] Generated Node #0,0,0: 21:[37, 16] Operation: 40-24=16 Exploring Operation: 40-37=3, Resulting Numbers: [24, 3] Generated Node #0,0,1: 21:[24, 3] Operation: 40-37=3 Exploring Operation: 37-24=13, Resulting Numbers: [40, 13] Generated Node #0,0,2: 21:[40, 13] Operation: 37-24=13 Exploring Operation: 24+40=64, Resulting Numbers: [37, 64] Generated Node #0,0,3: 21:[37, 64] Operation: 24+40=64 Moving to Node #0,1 Current State: 21:[24, 70, 7], Operations: ['40-33=7'] Exploring Operation: 24-7=17, Resulting Numbers: [70, 17] Generated Node #0,1,0: 21:[70, 17] Operation: 24-7=17 Exploring Operation: 70-24=46, Resulting Numbers: [7, 46] Generated Node #0,1,1: 21:[7, 46] Operation: 70-24=46 Exploring Operation: 70-7=63, Resulting Numbers: [24, 63] Generated Node #0,1,2: 21:[24, 63] Operation: 70-7=63 Exploring Operation: 70/7=10, Resulting Numbers: [24, 10] Generated Node #0,1,3: 21:[24, 10] Operation: 70/7=10 Moving to Node #0,2 Current State: 21:[33, 40, 46], Operations: ['70-24=46'] Exploring Operation: 46-33=13, Resulting Numbers: [40, 13] Generated Node #0,2,0: 21:[40, 13] Operation: 46-33=13 Exploring Operation: 33+40=73, Resulting Numbers: [46, 73] Generated Node #0,2,1: 21:[46, 73] Operation: 33+40=73 Exploring Operation: 46-40=6, Resulting Numbers: [33, 6] Generated Node #0,2,2: 21:[33, 6] Operation: 46-40=6 Exploring Operation: 40-33=7, Resulting Numbers: [46, 7] Generated Node #0,2,3: 21:[46, 7] Operation: 40-33=7 Moving to Node #0,3,2 Current State: 21:[24, 3], Operations: ['70-40=30', '33-30=3'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[24, 33, 70, 40], Operations: [] Exploring Operation: 70-40=30, Resulting Numbers: [24, 33, 30] Generated Node #0,3: 21:[24, 33, 30] Operation: 70-40=30 Moving to Node #0,3 Current State: 21:[24, 33, 30], Operations: ['70-40=30'] Exploring Operation: 33-30=3, Resulting Numbers: [24, 3] Generated Node #0,3,2: 21:[24, 3] Operation: 33-30=3 Moving to Node #0,3,2 Current State: 21:[24, 3], Operations: ['70-40=30', '33-30=3'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.978299
hs_4
sum_heuristic
[ 12, 46, 89, 44 ]
95
[ "46-44=2", "12/2=6", "89+6=95" ]
Current State: 95:[12, 46, 89, 44], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [12, 89, 2] Generated Node #2: [12, 89, 2] from Operation: 46-44=2 Current State: 95:[12, 89, 2], Operations: ['46-44=2'] Exploring Operation: 12/2=6, Resulting Numbers: [89, 6] Generated Node #3: [89, 6] from Operation: 12/2=6 Current State: 95:[89, 6], Operations: ['46-44=2', '12/2=6'] Exploring Operation: 89+6=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[12, 46, 89, 44], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [12, 89, 2] Generated Node #0,0: 95:[12, 89, 2] Operation: 46-44=2 Exploring Operation: 46+44=90, Resulting Numbers: [12, 89, 90] Generated Node #0,1: 95:[12, 89, 90] Operation: 46+44=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[12, 89, 2], Operations: ['46-44=2'] Exploring Operation: 12+89=101, Resulting Numbers: [2, 101] Generated Node #0,0,0: 95:[2, 101] Operation: 12+89=101 Exploring Operation: 12/2=6, Resulting Numbers: [89, 6] Generated Node #0,0,1: 95:[89, 6] Operation: 12/2=6 Moving to Node #0,0,1 Current State: 95:[89, 6], Operations: ['46-44=2', '12/2=6'] Exploring Operation: 89+6=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[12, 46, 89, 44], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [12, 89, 2] Generated Node #0,0: 95:[12, 89, 2] Operation: 46-44=2 Moving to Node #0,0 Current State: 95:[12, 89, 2], Operations: ['46-44=2'] Exploring Operation: 12/2=6, Resulting Numbers: [89, 6] Generated Node #0,0,1: 95:[89, 6] Operation: 12/2=6 Moving to Node #0,0,1 Current State: 95:[89, 6], Operations: ['46-44=2', '12/2=6'] Exploring Operation: 89+6=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 38, 2, 99, 9 ]
29
[ "38+2=40", "99/9=11", "40-11=29" ]
Current State: 29:[38, 2, 99, 9], Operations: [] Exploring Operation: 38+2=40, Resulting Numbers: [99, 9, 40] Generated Node #2: [99, 9, 40] from Operation: 38+2=40 Current State: 29:[99, 9, 40], Operations: ['38+2=40'] Exploring Operation: 99/9=11, Resulting Numbers: [40, 11] Generated Node #3: [40, 11] from Operation: 99/9=11 Current State: 29:[40, 11], Operations: ['38+2=40', '99/9=11'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[38, 2, 99, 9], Operations: [] Exploring Operation: 99-38=61, Resulting Numbers: [2, 9, 61] Generated Node #0,0: 29:[2, 9, 61] Operation: 99-38=61 Exploring Operation: 99/9=11, Resulting Numbers: [38, 2, 11] Generated Node #0,1: 29:[38, 2, 11] Operation: 99/9=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[38, 2, 11], Operations: ['99/9=11'] Exploring Operation: 38-2=36, Resulting Numbers: [11, 36] Generated Node #0,1,0: 29:[11, 36] Operation: 38-2=36 Exploring Operation: 2*11=22, Resulting Numbers: [38, 22] Generated Node #0,1,1: 29:[38, 22] Operation: 2*11=22 Moving to Node #0,1,1 Current State: 29:[38, 22], Operations: ['99/9=11', '2*11=22'] Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[11, 36], Operations: ['99/9=11', '38-2=36'] Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,29 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[2, 9, 61], Operations: ['99-38=61'] Exploring Operation: 2*9=18, Resulting Numbers: [61, 18] Generated Node #0,0,0: 29:[61, 18] Operation: 2*9=18 Exploring Operation: 2+9=11, Resulting Numbers: [61, 11] Generated Node #0,0,1: 29:[61, 11] Operation: 2+9=11 Moving to Node #0,0,0 Current State: 29:[61, 18], Operations: ['99-38=61', '2*9=18'] Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,29 unequal: No Solution Exploring Operation: 61+18=79, Resulting Numbers: [79] 79,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[61, 11], Operations: ['99-38=61', '2+9=11'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 61+11=72, Resulting Numbers: [72] 72,29 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
[ 42, 48, 69, 38 ]
37
[ "48-42=6", "69-38=31", "6+31=37" ]
Current State: 37:[42, 48, 69, 38], Operations: [] Exploring Operation: 48-42=6, Resulting Numbers: [69, 38, 6] Generated Node #2: [69, 38, 6] from Operation: 48-42=6 Current State: 37:[69, 38, 6], Operations: ['48-42=6'] Exploring Operation: 69-38=31, Resulting Numbers: [6, 31] Generated Node #3: [6, 31] from Operation: 69-38=31 Current State: 37:[6, 31], Operations: ['48-42=6', '69-38=31'] Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[42, 48, 69, 38], Operations: [] Exploring Operation: 69-42=27, Resulting Numbers: [48, 38, 27] Generated Node #0,0: 37:[48, 38, 27] Operation: 69-42=27 Exploring Operation: 69-48=21, Resulting Numbers: [42, 38, 21] Generated Node #0,1: 37:[42, 38, 21] Operation: 69-48=21 Moving to Node #0,0 Current State: 37:[48, 38, 27], Operations: ['69-42=27'] Exploring Operation: 48-38=10, Resulting Numbers: [27, 10] Generated Node #0,0,0: 37:[27, 10] Operation: 48-38=10 Exploring Operation: 48-27=21, Resulting Numbers: [38, 21] Generated Node #0,0,1: 37:[38, 21] Operation: 48-27=21 Moving to Node #0,1 Current State: 37:[42, 38, 21], Operations: ['69-48=21'] Exploring Operation: 38-21=17, Resulting Numbers: [42, 17] Generated Node #0,1,0: 37:[42, 17] Operation: 38-21=17 Exploring Operation: 42-21=21, Resulting Numbers: [38, 21] Generated Node #0,1,1: 37:[38, 21] Operation: 42-21=21 Moving to Node #0,0,1 Current State: 37:[38, 21], Operations: ['69-42=27', '48-27=21'] Exploring Operation: 38+21=59, Resulting Numbers: [59] 59,37 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[38, 21], Operations: ['69-48=21', '42-21=21'] Exploring Operation: 38+21=59, Resulting Numbers: [59] 59,37 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[42, 17], Operations: ['69-48=21', '38-21=17'] Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,37 unequal: No Solution Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[27, 10], Operations: ['69-42=27', '48-38=10'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[42, 48, 69, 38], Operations: [] Exploring Operation: 69-42=27, Resulting Numbers: [48, 38, 27] Generated Node #0,0: 37:[48, 38, 27] Operation: 69-42=27 Moving to Node #0,0 Current State: 37:[48, 38, 27], Operations: ['69-42=27'] Exploring Operation: 48-38=10, Resulting Numbers: [27, 10] Generated Node #0,0,0: 37:[27, 10] Operation: 48-38=10 Moving to Node #0,0,0 Current State: 37:[27, 10], Operations: ['69-42=27', '48-38=10'] Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 44, 15, 35, 40 ]
20
[ "44*15=660", "40+660=700", "700/35=20" ]
Current State: 20:[44, 15, 35, 40], Operations: [] Exploring Operation: 44*15=660, Resulting Numbers: [35, 40, 660] Generated Node #2: [35, 40, 660] from Operation: 44*15=660 Current State: 20:[35, 40, 660], Operations: ['44*15=660'] Exploring Operation: 40+660=700, Resulting Numbers: [35, 700] Generated Node #3: [35, 700] from Operation: 40+660=700 Current State: 20:[35, 700], Operations: ['44*15=660', '40+660=700'] Exploring Operation: 700/35=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[44, 15, 35, 40], Operations: [] Exploring Operation: 44-35=9, Resulting Numbers: [15, 40, 9] Generated Node #0,0: 20:[15, 40, 9] Operation: 44-35=9 Exploring Operation: 35-15=20, Resulting Numbers: [44, 40, 20] Generated Node #0,1: 20:[44, 40, 20] Operation: 35-15=20 Exploring Operation: 40-35=5, Resulting Numbers: [44, 15, 5] Generated Node #0,2: 20:[44, 15, 5] Operation: 40-35=5 Exploring Operation: 44-15=29, Resulting Numbers: [35, 40, 29] Generated Node #0,3: 20:[35, 40, 29] Operation: 44-15=29 Exploring Operation: 44-40=4, Resulting Numbers: [15, 35, 4] Generated Node #0,4: 20:[15, 35, 4] Operation: 44-40=4 Moving to Node #0,4 Current State: 20:[15, 35, 4], Operations: ['44-40=4'] Exploring Operation: 35-4=31, Resulting Numbers: [15, 31] Generated Node #0,4,0: 20:[15, 31] Operation: 35-4=31 Exploring Operation: 35-15=20, Resulting Numbers: [4, 20] Generated Node #0,4,1: 20:[4, 20] Operation: 35-15=20 Exploring Operation: 15-4=11, Resulting Numbers: [35, 11] Generated Node #0,4,2: 20:[35, 11] Operation: 15-4=11 Exploring Operation: 35+4=39, Resulting Numbers: [15, 39] Generated Node #0,4,3: 20:[15, 39] Operation: 35+4=39 Exploring Operation: 15+4=19, Resulting Numbers: [35, 19] Generated Node #0,4,4: 20:[35, 19] Operation: 15+4=19 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 20:[4, 20], Operations: ['44-40=4', '35-15=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,20 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 #0,4,0 Current State: 20:[15, 31], Operations: ['44-40=4', '35-4=31'] Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,20 unequal: No Solution Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,20 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 #0,4,2 Current State: 20:[35, 11], Operations: ['44-40=4', '15-4=11'] Exploring Operation: 35*11=385, Resulting Numbers: [385] 385,20 unequal: No Solution Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 35+11=46, Resulting Numbers: [46] 46,20 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 #0,4,4 Current State: 20:[35, 19], Operations: ['44-40=4', '15+4=19'] Exploring Operation: 35*19=665, Resulting Numbers: [665] 665,20 unequal: No Solution Exploring Operation: 35+19=54, Resulting Numbers: [54] 54,20 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,20 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 #0,4,3 Current State: 20:[15, 39], Operations: ['44-40=4', '35+4=39'] Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,20 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 20:[15, 40, 9], Operations: ['44-35=9'] Exploring Operation: 40-9=31, Resulting Numbers: [15, 31] Generated Node #0,0,0: 20:[15, 31] Operation: 40-9=31 Exploring Operation: 15+9=24, Resulting Numbers: [40, 24] Generated Node #0,0,1: 20:[40, 24] Operation: 15+9=24 Exploring Operation: 40+9=49, Resulting Numbers: [15, 49] Generated Node #0,0,2: 20:[15, 49] Operation: 40+9=49 Exploring Operation: 40-15=25, Resulting Numbers: [9, 25] Generated Node #0,0,3: 20:[9, 25] Operation: 40-15=25 Exploring Operation: 15-9=6, Resulting Numbers: [40, 6] Generated Node #0,0,4: 20:[40, 6] Operation: 15-9=6 Moving to Node #0,2 Current State: 20:[44, 15, 5], Operations: ['40-35=5'] Exploring Operation: 44-5=39, Resulting Numbers: [15, 39] Generated Node #0,2,0: 20:[15, 39] Operation: 44-5=39 Exploring Operation: 15/5=3, Resulting Numbers: [44, 3] Generated Node #0,2,1: 20:[44, 3] Operation: 15/5=3 Exploring Operation: 15-5=10, Resulting Numbers: [44, 10] Generated Node #0,2,2: 20:[44, 10] Operation: 15-5=10 Exploring Operation: 44-15=29, Resulting Numbers: [5, 29] Generated Node #0,2,3: 20:[5, 29] Operation: 44-15=29 Exploring Operation: 15+5=20, Resulting Numbers: [44, 20] Generated Node #0,2,4: 20:[44, 20] Operation: 15+5=20 Moving to Node #0,1 Current State: 20:[44, 40, 20], Operations: ['35-15=20'] Exploring Operation: 44-20=24, Resulting Numbers: [40, 24] Generated Node #0,1,0: 20:[40, 24] Operation: 44-20=24 Exploring Operation: 44-40=4, Resulting Numbers: [20, 4] Generated Node #0,1,1: 20:[20, 4] Operation: 44-40=4 Exploring Operation: 44+40=84, Resulting Numbers: [20, 84] Generated Node #0,1,2: 20:[20, 84] Operation: 44+40=84 Exploring Operation: 40-20=20, Resulting Numbers: [44, 20] Generated Node #0,1,3: 20:[44, 20] Operation: 40-20=20 Exploring Operation: 40/20=2, Resulting Numbers: [44, 2] Generated Node #0,1,4: 20:[44, 2] Operation: 40/20=2 Moving to Node #0,3 Current State: 20:[35, 40, 29], Operations: ['44-15=29'] Exploring Operation: 40-29=11, Resulting Numbers: [35, 11] Generated Node #0,3,0: 20:[35, 11] Operation: 40-29=11 Exploring Operation: 35-29=6, Resulting Numbers: [40, 6] Generated Node #0,3,1: 20:[40, 6] Operation: 35-29=6 Exploring Operation: 40-35=5, Resulting Numbers: [29, 5] Generated Node #0,3,2: 20:[29, 5] Operation: 40-35=5 Exploring Operation: 35+40=75, Resulting Numbers: [29, 75] Generated Node #0,3,3: 20:[29, 75] Operation: 35+40=75 Exploring Operation: 35+29=64, Resulting Numbers: [40, 64] Generated Node #0,3,4: 20:[40, 64] Operation: 35+29=64 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 20:[29, 5], Operations: ['44-15=29', '40-35=5'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,20 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 #0,3,0 Current State: 20:[35, 11], Operations: ['44-15=29', '40-29=11'] Exploring Operation: 35+11=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 35*11=385, Resulting Numbers: [385] 385,20 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 #0,3,1 Current State: 20:[40, 6], Operations: ['44-15=29', '35-29=6'] Exploring Operation: 40*6=240, Resulting Numbers: [240] 240,20 unequal: No Solution Exploring Operation: 40+6=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,20 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 #0,3,3 Current State: 20:[29, 75], Operations: ['44-15=29', '35+40=75'] Exploring Operation: 29+75=104, Resulting Numbers: [104] 104,20 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 29*75=2175, Resulting Numbers: [2175] 2175,20 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 #0,3,4 Current State: 20:[40, 64], Operations: ['44-15=29', '35+29=64'] Exploring Operation: 40+64=104, Resulting Numbers: [104] 104,20 unequal: No Solution Exploring Operation: 64-40=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 40*64=2560, Resulting Numbers: [2560] 2560,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 20:[20, 4], Operations: ['35-15=20', '44-40=4'] Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,20 unequal: No Solution Moving to Node #0,0,3 Current State: 20:[9, 25], Operations: ['44-35=9', '40-15=25'] Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 9*25=225, Resulting Numbers: [225] 225,20 unequal: No Solution Moving to Node #0,2,3 Current State: 20:[5, 29], Operations: ['40-35=5', '44-15=29'] Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,20 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[15, 31], Operations: ['44-35=9', '40-9=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,20 unequal: No Solution Moving to Node #0,0,4 Current State: 20:[40, 6], Operations: ['44-35=9', '15-9=6'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 40+6=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 40*6=240, Resulting Numbers: [240] 240,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[15, 39], Operations: ['40-35=5', '44-5=39'] Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,20 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[40, 24], Operations: ['35-15=20', '44-20=24'] Exploring Operation: 40*24=960, Resulting Numbers: [960] 960,20 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,20 unequal: No Solution Moving to Node #0,1,3 Current State: 20:[44, 20], Operations: ['35-15=20', '40-20=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,20 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,20 unequal: No Solution Moving to Node #0,1,4 Current State: 20:[44, 2], Operations: ['35-15=20', '40/20=2'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[44, 10], Operations: ['40-35=5', '15-5=10'] Exploring Operation: 44+10=54, Resulting Numbers: [54] 54,20 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 44*10=440, Resulting Numbers: [440] 440,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[40, 24], Operations: ['44-35=9', '15+9=24'] Exploring Operation: 40*24=960, Resulting Numbers: [960] 960,20 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,20 unequal: No Solution Moving to Node #0,2,4 Current State: 20:[44, 20], Operations: ['40-35=5', '15+5=20'] Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,20 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[44, 3], Operations: ['40-35=5', '15/5=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,20 unequal: No Solution Exploring Operation: 44*3=132, Resulting Numbers: [132] 132,20 unequal: No Solution Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,20 unequal: No Solution Moving to Node #0,0,2 Current State: 20:[15, 49], Operations: ['44-35=9', '40+9=49'] Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 15*49=735, Resulting Numbers: [735] 735,20 unequal: No Solution Exploring Operation: 15+49=64, Resulting Numbers: [64] 64,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[20, 84], Operations: ['35-15=20', '44+40=84'] Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,20 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,20 unequal: No Solution Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,20 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 89, 33, 1, 19 ]
36
[ "89-33=56", "1+19=20", "56-20=36" ]
Current State: 36:[89, 33, 1, 19], Operations: [] Exploring Operation: 89-33=56, Resulting Numbers: [1, 19, 56] Generated Node #2: [1, 19, 56] from Operation: 89-33=56 Current State: 36:[1, 19, 56], Operations: ['89-33=56'] Exploring Operation: 1+19=20, Resulting Numbers: [56, 20] Generated Node #3: [56, 20] from Operation: 1+19=20 Current State: 36:[56, 20], Operations: ['89-33=56', '1+19=20'] Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[89, 33, 1, 19], Operations: [] Exploring Operation: 89-33=56, Resulting Numbers: [1, 19, 56] Generated Node #0,0: 36:[1, 19, 56] Operation: 89-33=56 Moving to Node #0,0 Current State: 36:[1, 19, 56], Operations: ['89-33=56'] Exploring Operation: 56-19=37, Resulting Numbers: [1, 37] Generated Node #0,0,0: 36:[1, 37] Operation: 56-19=37 Moving to Node #0,0,0 Current State: 36:[1, 37], Operations: ['89-33=56', '56-19=37'] Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[89, 33, 1, 19], Operations: [] Exploring Operation: 89-33=56, Resulting Numbers: [1, 19, 56] Generated Node #0,0: 36:[1, 19, 56] Operation: 89-33=56 Moving to Node #0,0 Current State: 36:[1, 19, 56], Operations: ['89-33=56'] Exploring Operation: 56-19=37, Resulting Numbers: [1, 37] Generated Node #0,0,0: 36:[1, 37] Operation: 56-19=37 Moving to Node #0,0,0 Current State: 36:[1, 37], Operations: ['89-33=56', '56-19=37'] Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 71, 56, 99, 17 ]
11
[ "71+56=127", "99+17=116", "127-116=11" ]
Current State: 11:[71, 56, 99, 17], Operations: [] Exploring Operation: 71+56=127, Resulting Numbers: [99, 17, 127] Generated Node #2: [99, 17, 127] from Operation: 71+56=127 Current State: 11:[99, 17, 127], Operations: ['71+56=127'] Exploring Operation: 99+17=116, Resulting Numbers: [127, 116] Generated Node #3: [127, 116] from Operation: 99+17=116 Current State: 11:[127, 116], Operations: ['71+56=127', '99+17=116'] Exploring Operation: 127-116=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[71, 56, 99, 17], Operations: [] Exploring Operation: 71-56=15, Resulting Numbers: [99, 17, 15] Generated Node #0,0: 11:[99, 17, 15] Operation: 71-56=15 Exploring Operation: 99-71=28, Resulting Numbers: [56, 17, 28] Generated Node #0,1: 11:[56, 17, 28] Operation: 99-71=28 Exploring Operation: 99-56=43, Resulting Numbers: [71, 17, 43] Generated Node #0,2: 11:[71, 17, 43] Operation: 99-56=43 Moving to Node #0,1 Current State: 11:[56, 17, 28], Operations: ['99-71=28'] Exploring Operation: 56-28=28, Resulting Numbers: [17, 28] Generated Node #0,1,0: 11:[17, 28] Operation: 56-28=28 Exploring Operation: 56/28=2, Resulting Numbers: [17, 2] Generated Node #0,1,1: 11:[17, 2] Operation: 56/28=2 Exploring Operation: 56-17=39, Resulting Numbers: [28, 39] Generated Node #0,1,2: 11:[28, 39] Operation: 56-17=39 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[17, 2], Operations: ['99-71=28', '56/28=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[17, 28], Operations: ['99-71=28', '56-28=28'] Exploring Operation: 17*28=476, Resulting Numbers: [476] 476,11 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[71, 56, 99, 17], Operations: [] Exploring Operation: 99-71=28, Resulting Numbers: [56, 17, 28] Generated Node #0,1: 11:[56, 17, 28] Operation: 99-71=28 Moving to Node #0,1 Current State: 11:[56, 17, 28], Operations: ['99-71=28'] Exploring Operation: 56-28=28, Resulting Numbers: [17, 28] Generated Node #0,1,0: 11:[17, 28] Operation: 56-28=28 Moving to Node #0,1,0 Current State: 11:[17, 28], Operations: ['99-71=28', '56-28=28'] Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 9, 10, 93, 81 ]
12
[ "10-9=1", "93-81=12", "1*12=12" ]
Current State: 12:[9, 10, 93, 81], Operations: [] Exploring Operation: 10-9=1, Resulting Numbers: [93, 81, 1] Generated Node #2: [93, 81, 1] from Operation: 10-9=1 Current State: 12:[93, 81, 1], Operations: ['10-9=1'] Exploring Operation: 93-81=12, Resulting Numbers: [1, 12] Generated Node #3: [1, 12] from Operation: 93-81=12 Current State: 12:[1, 12], Operations: ['10-9=1', '93-81=12'] Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[9, 10, 93, 81], Operations: [] Exploring Operation: 81/9=9, Resulting Numbers: [10, 93, 9] Generated Node #0,0: 12:[10, 93, 9] Operation: 81/9=9 Exploring Operation: 93-81=12, Resulting Numbers: [9, 10, 12] Generated Node #0,1: 12:[9, 10, 12] Operation: 93-81=12 Moving to Node #0,1 Current State: 12:[9, 10, 12], Operations: ['93-81=12'] Exploring Operation: 12-9=3, Resulting Numbers: [10, 3] Generated Node #0,1,0: 12:[10, 3] Operation: 12-9=3 Exploring Operation: 10-9=1, Resulting Numbers: [12, 1] Generated Node #0,1,1: 12:[12, 1] Operation: 10-9=1 Moving to Node #0,0 Current State: 12:[10, 93, 9], Operations: ['81/9=9'] Exploring Operation: 93-9=84, Resulting Numbers: [10, 84] Generated Node #0,0,0: 12:[10, 84] Operation: 93-9=84 Exploring Operation: 93-10=83, Resulting Numbers: [9, 83] Generated Node #0,0,1: 12:[9, 83] Operation: 93-10=83 Moving to Node #0,1,1 Current State: 12:[12, 1], Operations: ['93-81=12', '10-9=1'] Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[9, 10, 93, 81], Operations: [] Exploring Operation: 93-81=12, Resulting Numbers: [9, 10, 12] Generated Node #0,1: 12:[9, 10, 12] Operation: 93-81=12 Moving to Node #0,1 Current State: 12:[9, 10, 12], Operations: ['93-81=12'] Exploring Operation: 10-9=1, Resulting Numbers: [12, 1] Generated Node #0,1,1: 12:[12, 1] Operation: 10-9=1 Moving to Node #0,1,1 Current State: 12:[12, 1], Operations: ['93-81=12', '10-9=1'] Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 14, 48, 76, 36 ]
34
[ "76-48=28", "28/14=2", "36-2=34" ]
Current State: 34:[14, 48, 76, 36], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [14, 36, 28] Generated Node #2: [14, 36, 28] from Operation: 76-48=28 Current State: 34:[14, 36, 28], Operations: ['76-48=28'] Exploring Operation: 28/14=2, Resulting Numbers: [36, 2] Generated Node #3: [36, 2] from Operation: 28/14=2 Current State: 34:[36, 2], Operations: ['76-48=28', '28/14=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[14, 48, 76, 36], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [14, 36, 28] Generated Node #0,0: 34:[14, 36, 28] Operation: 76-48=28 Exploring Operation: 76-36=40, Resulting Numbers: [14, 48, 40] Generated Node #0,1: 34:[14, 48, 40] Operation: 76-36=40 Exploring Operation: 48-14=34, Resulting Numbers: [76, 36, 34] Generated Node #0,2: 34:[76, 36, 34] Operation: 48-14=34 Moving to Node #0,0 Current State: 34:[14, 36, 28], Operations: ['76-48=28'] Exploring Operation: 28/14=2, Resulting Numbers: [36, 2] Generated Node #0,0,0: 34:[36, 2] Operation: 28/14=2 Exploring Operation: 36-28=8, Resulting Numbers: [14, 8] Generated Node #0,0,1: 34:[14, 8] Operation: 36-28=8 Exploring Operation: 28-14=14, Resulting Numbers: [36, 14] Generated Node #0,0,2: 34:[36, 14] Operation: 28-14=14 Moving to Node #0,1 Current State: 34:[14, 48, 40], Operations: ['76-36=40'] Exploring Operation: 48-40=8, Resulting Numbers: [14, 8] Generated Node #0,1,0: 34:[14, 8] Operation: 48-40=8 Exploring Operation: 48-14=34, Resulting Numbers: [40, 34] Generated Node #0,1,1: 34:[40, 34] Operation: 48-14=34 Exploring Operation: 40-14=26, Resulting Numbers: [48, 26] Generated Node #0,1,2: 34:[48, 26] Operation: 40-14=26 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[40, 34], Operations: ['76-36=40', '48-14=34'] Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,34 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[14, 8], Operations: ['76-36=40', '48-40=8'] Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,34 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 34:[48, 26], Operations: ['76-36=40', '40-14=26'] Exploring Operation: 48*26=1248, Resulting Numbers: [1248] 1248,34 unequal: No Solution Exploring Operation: 48+26=74, Resulting Numbers: [74] 74,34 unequal: No Solution Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,34 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: 34:[76, 36, 34], Operations: ['48-14=34'] Exploring Operation: 76-34=42, Resulting Numbers: [36, 42] Generated Node #0,2,0: 34:[36, 42] Operation: 76-34=42 Exploring Operation: 36-34=2, Resulting Numbers: [76, 2] Generated Node #0,2,1: 34:[76, 2] Operation: 36-34=2 Exploring Operation: 76-36=40, Resulting Numbers: [34, 40] Generated Node #0,2,2: 34:[34, 40] Operation: 76-36=40 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 34:[34, 40], Operations: ['48-14=34', '76-36=40'] Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,34 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 34:[36, 42], Operations: ['48-14=34', '76-34=42'] Exploring Operation: 36+42=78, Resulting Numbers: [78] 78,34 unequal: No Solution Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 36*42=1512, Resulting Numbers: [1512] 1512,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 34:[76, 2], Operations: ['48-14=34', '36-34=2'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,34 unequal: No Solution Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,34 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: 34:[36, 2], Operations: ['76-48=28', '28/14=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[14, 48, 76, 36], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [14, 36, 28] Generated Node #0,0: 34:[14, 36, 28] Operation: 76-48=28 Moving to Node #0,0 Current State: 34:[14, 36, 28], Operations: ['76-48=28'] Exploring Operation: 28/14=2, Resulting Numbers: [36, 2] Generated Node #0,0,0: 34:[36, 2] Operation: 28/14=2 Moving to Node #0,0,0 Current State: 34:[36, 2], Operations: ['76-48=28', '28/14=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.967882
hs_3
sum_heuristic
[ 61, 22, 53, 61 ]
74
[ "61/61=1", "22+53=75", "75-1=74" ]
Current State: 74:[61, 22, 53, 61], Operations: [] Exploring Operation: 61/61=1, Resulting Numbers: [22, 53, 1] Generated Node #2: [22, 53, 1] from Operation: 61/61=1 Current State: 74:[22, 53, 1], Operations: ['61/61=1'] Exploring Operation: 22+53=75, Resulting Numbers: [1, 75] Generated Node #3: [1, 75] from Operation: 22+53=75 Current State: 74:[1, 75], Operations: ['61/61=1', '22+53=75'] Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[61, 22, 53, 61], Operations: [] Exploring Operation: 22+53=75, Resulting Numbers: [61, 61, 75] Generated Node #0,0: 74:[61, 61, 75] Operation: 22+53=75 Exploring Operation: 53-22=31, Resulting Numbers: [61, 61, 31] Generated Node #0,1: 74:[61, 61, 31] Operation: 53-22=31 Exploring Operation: 61/61=1, Resulting Numbers: [22, 53, 1] Generated Node #0,2: 74:[22, 53, 1] Operation: 61/61=1 Exploring Operation: 61-22=39, Resulting Numbers: [61, 53, 39] Generated Node #0,3: 74:[61, 53, 39] Operation: 61-22=39 Exploring Operation: 61-22=39, Resulting Numbers: [53, 61, 39] Generated Node #0,4: 74:[53, 61, 39] Operation: 61-22=39 Moving to Node #0,0 Current State: 74:[61, 61, 75], Operations: ['22+53=75'] Exploring Operation: 61+61=122, Resulting Numbers: [75, 122] Generated Node #0,0,0: 74:[75, 122] Operation: 61+61=122 Exploring Operation: 75-61=14, Resulting Numbers: [61, 14] Generated Node #0,0,1: 74:[61, 14] Operation: 75-61=14 Exploring Operation: 61-61=0, Resulting Numbers: [75, 0] Generated Node #0,0,2: 74:[75, 0] Operation: 61-61=0 Exploring Operation: 75-61=14, Resulting Numbers: [61, 14] Generated Node #0,0,3: 74:[61, 14] Operation: 75-61=14 Exploring Operation: 61/61=1, Resulting Numbers: [75, 1] Generated Node #0,0,4: 74:[75, 1] Operation: 61/61=1 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 74:[75, 1], Operations: ['22+53=75', '61/61=1'] Exploring Operation: 75*1=75, Resulting Numbers: [75] 75,74 unequal: No Solution Exploring Operation: 75+1=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,74 unequal: No Solution Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[61, 22, 53, 61], Operations: [] Exploring Operation: 22+53=75, Resulting Numbers: [61, 61, 75] Generated Node #0,0: 74:[61, 61, 75] Operation: 22+53=75 Moving to Node #0,0 Current State: 74:[61, 61, 75], Operations: ['22+53=75'] Exploring Operation: 61/61=1, Resulting Numbers: [75, 1] Generated Node #0,0,4: 74:[75, 1] Operation: 61/61=1 Moving to Node #0,0,4 Current State: 74:[75, 1], Operations: ['22+53=75', '61/61=1'] Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 13, 48, 40, 65 ]
56
[ "13*40=520", "520/65=8", "48+8=56" ]
Current State: 56:[13, 48, 40, 65], Operations: [] Exploring Operation: 13*40=520, Resulting Numbers: [48, 65, 520] Generated Node #2: [48, 65, 520] from Operation: 13*40=520 Current State: 56:[48, 65, 520], Operations: ['13*40=520'] Exploring Operation: 520/65=8, Resulting Numbers: [48, 8] Generated Node #3: [48, 8] from Operation: 520/65=8 Current State: 56:[48, 8], Operations: ['13*40=520', '520/65=8'] Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[13, 48, 40, 65], Operations: [] Exploring Operation: 48-40=8, Resulting Numbers: [13, 65, 8] Generated Node #0,0: 56:[13, 65, 8] Operation: 48-40=8 Moving to Node #0,0 Current State: 56:[13, 65, 8], Operations: ['48-40=8'] Exploring Operation: 65/13=5, Resulting Numbers: [8, 5] Generated Node #0,0,0: 56:[8, 5] Operation: 65/13=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[8, 5], Operations: ['48-40=8', '65/13=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,56 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
[ 56, 6, 25, 21 ]
19
[ "56-6=50", "50/25=2", "21-2=19" ]
Current State: 19:[56, 6, 25, 21], Operations: [] Exploring Operation: 56-6=50, Resulting Numbers: [25, 21, 50] Generated Node #2: [25, 21, 50] from Operation: 56-6=50 Current State: 19:[25, 21, 50], Operations: ['56-6=50'] Exploring Operation: 50/25=2, Resulting Numbers: [21, 2] Generated Node #3: [21, 2] from Operation: 50/25=2 Current State: 19:[21, 2], Operations: ['56-6=50', '50/25=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[56, 6, 25, 21], Operations: [] Exploring Operation: 56-21=35, Resulting Numbers: [6, 25, 35] Generated Node #0,0: 19:[6, 25, 35] Operation: 56-21=35 Exploring Operation: 56-25=31, Resulting Numbers: [6, 21, 31] Generated Node #0,1: 19:[6, 21, 31] Operation: 56-25=31 Moving to Node #0,1 Current State: 19:[6, 21, 31], Operations: ['56-25=31'] Exploring Operation: 21-6=15, Resulting Numbers: [31, 15] Generated Node #0,1,0: 19:[31, 15] Operation: 21-6=15 Exploring Operation: 31-6=25, Resulting Numbers: [21, 25] Generated Node #0,1,1: 19:[21, 25] Operation: 31-6=25 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[21, 25], Operations: ['56-25=31', '31-6=25'] Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[31, 15], Operations: ['56-25=31', '21-6=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 19:[6, 25, 35], Operations: ['56-21=35'] Exploring Operation: 25-6=19, Resulting Numbers: [35, 19] Generated Node #0,0,0: 19:[35, 19] Operation: 25-6=19 Exploring Operation: 35-6=29, Resulting Numbers: [25, 29] Generated Node #0,0,1: 19:[25, 29] Operation: 35-6=29 Moving to Node #0,0,0 Current State: 19:[35, 19], Operations: ['56-21=35', '25-6=19'] Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 35+19=54, Resulting Numbers: [54] 54,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[25, 29], Operations: ['56-21=35', '35-6=29'] Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,19 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 74, 24, 93, 95 ]
52
[ "74-24=50", "95-93=2", "50+2=52" ]
Current State: 52:[74, 24, 93, 95], Operations: [] Exploring Operation: 74-24=50, Resulting Numbers: [93, 95, 50] Generated Node #2: [93, 95, 50] from Operation: 74-24=50 Current State: 52:[93, 95, 50], Operations: ['74-24=50'] Exploring Operation: 95-93=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 95-93=2 Current State: 52:[50, 2], Operations: ['74-24=50', '95-93=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[74, 24, 93, 95], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [74, 24, 2] Generated Node #0,0: 52:[74, 24, 2] Operation: 95-93=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[74, 24, 2], Operations: ['95-93=2'] Exploring Operation: 74-24=50, Resulting Numbers: [2, 50] Generated Node #0,0,0: 52:[2, 50] Operation: 74-24=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[2, 50], Operations: ['95-93=2', '74-24=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[74, 24, 93, 95], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [74, 24, 2] Generated Node #0,0: 52:[74, 24, 2] Operation: 95-93=2 Moving to Node #0,0 Current State: 52:[74, 24, 2], Operations: ['95-93=2'] Exploring Operation: 74-24=50, Resulting Numbers: [2, 50] Generated Node #0,0,0: 52:[2, 50] Operation: 74-24=50 Moving to Node #0,0,0 Current State: 52:[2, 50], Operations: ['95-93=2', '74-24=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 32, 42, 43, 85 ]
31
[ "42+43=85", "85/85=1", "32-1=31" ]
Current State: 31:[32, 42, 43, 85], Operations: [] Exploring Operation: 42+43=85, Resulting Numbers: [32, 85, 85] Generated Node #2: [32, 85, 85] from Operation: 42+43=85 Current State: 31:[32, 85, 85], Operations: ['42+43=85'] Exploring Operation: 85/85=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 85/85=1 Current State: 31:[32, 1], Operations: ['42+43=85', '85/85=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[32, 42, 43, 85], Operations: [] Exploring Operation: 85-42=43, Resulting Numbers: [32, 43, 43] Generated Node #0,0: 31:[32, 43, 43] Operation: 85-42=43 Exploring Operation: 85-43=42, Resulting Numbers: [32, 42, 42] Generated Node #0,1: 31:[32, 42, 42] Operation: 85-43=42 Exploring Operation: 85-32=53, Resulting Numbers: [42, 43, 53] Generated Node #0,2: 31:[42, 43, 53] Operation: 85-32=53 Moving to Node #0,1 Current State: 31:[32, 42, 42], Operations: ['85-43=42'] Exploring Operation: 42/42=1, Resulting Numbers: [32, 1] Generated Node #0,1,0: 31:[32, 1] Operation: 42/42=1 Exploring Operation: 42-32=10, Resulting Numbers: [42, 10] Generated Node #0,1,1: 31:[42, 10] Operation: 42-32=10 Exploring Operation: 42-32=10, Resulting Numbers: [42, 10] Generated Node #0,1,2: 31:[42, 10] Operation: 42-32=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[32, 1], Operations: ['85-43=42', '42/42=1'] Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[32, 42, 43, 85], Operations: [] Exploring Operation: 85-43=42, Resulting Numbers: [32, 42, 42] Generated Node #0,1: 31:[32, 42, 42] Operation: 85-43=42 Moving to Node #0,1 Current State: 31:[32, 42, 42], Operations: ['85-43=42'] Exploring Operation: 42/42=1, Resulting Numbers: [32, 1] Generated Node #0,1,0: 31:[32, 1] Operation: 42/42=1 Moving to Node #0,1,0 Current State: 31:[32, 1], Operations: ['85-43=42', '42/42=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 64, 37, 2, 2 ]
89
[ "64*2=128", "37+2=39", "128-39=89" ]
Current State: 89:[64, 37, 2, 2], Operations: [] Exploring Operation: 64*2=128, Resulting Numbers: [37, 128] Generated Node #2: [37, 128] from Operation: 64*2=128 Current State: 89:[37, 128], Operations: ['64*2=128'] Exploring Operation: 37+2=39, Resulting Numbers: [128, 39] Generated Node #3: [128, 39] from Operation: 37+2=39 Current State: 89:[128, 39], Operations: ['64*2=128', '37+2=39'] Exploring Operation: 128-39=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[64, 37, 2, 2], Operations: [] Exploring Operation: 37*2=74, Resulting Numbers: [64, 2, 74] Generated Node #0,0: 89:[64, 2, 74] Operation: 37*2=74 Exploring Operation: 64+2=66, Resulting Numbers: [37, 2, 66] Generated Node #0,1: 89:[37, 2, 66] Operation: 64+2=66 Exploring Operation: 64+2=66, Resulting Numbers: [37, 2, 66] Generated Node #0,2: 89:[37, 2, 66] Operation: 64+2=66 Exploring Operation: 37*2=74, Resulting Numbers: [64, 2, 74] Generated Node #0,3: 89:[64, 2, 74] Operation: 37*2=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[64, 2, 74], Operations: ['37*2=74'] Exploring Operation: 2+74=76, Resulting Numbers: [64, 76] Generated Node #0,0,0: 89:[64, 76] Operation: 2+74=76 Exploring Operation: 64+2=66, Resulting Numbers: [74, 66] Generated Node #0,0,1: 89:[74, 66] Operation: 64+2=66 Exploring Operation: 64-2=62, Resulting Numbers: [74, 62] Generated Node #0,0,2: 89:[74, 62] Operation: 64-2=62 Exploring Operation: 74-2=72, Resulting Numbers: [64, 72] Generated Node #0,0,3: 89:[64, 72] Operation: 74-2=72 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[64, 76], Operations: ['37*2=74', '2+74=76'] Exploring Operation: 76-64=12, Resulting Numbers: [12] 12,89 unequal: No Solution Exploring Operation: 64*76=4864, Resulting Numbers: [4864] 4864,89 unequal: No Solution Exploring Operation: 64+76=140, Resulting Numbers: [140] 140,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[74, 66], Operations: ['37*2=74', '64+2=66'] Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 74+66=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 74*66=4884, Resulting Numbers: [4884] 4884,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[74, 62], Operations: ['37*2=74', '64-2=62'] Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,89 unequal: No Solution Exploring Operation: 74+62=136, Resulting Numbers: [136] 136,89 unequal: No Solution Exploring Operation: 74*62=4588, Resulting Numbers: [4588] 4588,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 89:[64, 72], Operations: ['37*2=74', '74-2=72'] Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,89 unequal: No Solution Exploring Operation: 64*72=4608, Resulting Numbers: [4608] 4608,89 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: 89:[64, 2, 74], Operations: ['37*2=74'] Exploring Operation: 2+74=76, Resulting Numbers: [64, 76] Generated Node #0,3,0: 89:[64, 76] Operation: 2+74=76 Exploring Operation: 74-2=72, Resulting Numbers: [64, 72] Generated Node #0,3,1: 89:[64, 72] Operation: 74-2=72 Exploring Operation: 64-2=62, Resulting Numbers: [74, 62] Generated Node #0,3,2: 89:[74, 62] Operation: 64-2=62 Exploring Operation: 64+2=66, Resulting Numbers: [74, 66] Generated Node #0,3,3: 89:[74, 66] Operation: 64+2=66 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 89:[64, 76], Operations: ['37*2=74', '2+74=76'] Exploring Operation: 64+76=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 76-64=12, Resulting Numbers: [12] 12,89 unequal: No Solution Exploring Operation: 64*76=4864, Resulting Numbers: [4864] 4864,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 89:[74, 66], Operations: ['37*2=74', '64+2=66'] Exploring Operation: 74+66=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 74*66=4884, Resulting Numbers: [4884] 4884,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 89:[64, 72], Operations: ['37*2=74', '74-2=72'] Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 64*72=4608, Resulting Numbers: [4608] 4608,89 unequal: No Solution Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 89:[74, 62], Operations: ['37*2=74', '64-2=62'] Exploring Operation: 74+62=136, Resulting Numbers: [136] 136,89 unequal: No Solution Exploring Operation: 74*62=4588, Resulting Numbers: [4588] 4588,89 unequal: No Solution Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,89 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: 89:[37, 2, 66], Operations: ['64+2=66'] Exploring Operation: 37+2=39, Resulting Numbers: [66, 39] Generated Node #0,1,0: 89:[66, 39] Operation: 37+2=39 Exploring Operation: 37-2=35, Resulting Numbers: [66, 35] Generated Node #0,1,1: 89:[66, 35] Operation: 37-2=35 Exploring Operation: 37*2=74, Resulting Numbers: [66, 74] Generated Node #0,1,2: 89:[66, 74] Operation: 37*2=74 Exploring Operation: 2+66=68, Resulting Numbers: [37, 68] Generated Node #0,1,3: 89:[37, 68] Operation: 2+66=68 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[66, 74], Operations: ['64+2=66', '37*2=74'] Exploring Operation: 66+74=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 66*74=4884, Resulting Numbers: [4884] 4884,89 unequal: No Solution Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[66, 39], Operations: ['64+2=66', '37+2=39'] Exploring Operation: 66+39=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,89 unequal: No Solution Exploring Operation: 66*39=2574, Resulting Numbers: [2574] 2574,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 89:[37, 68], Operations: ['64+2=66', '2+66=68'] Exploring Operation: 37*68=2516, Resulting Numbers: [2516] 2516,89 unequal: No Solution Exploring Operation: 37+68=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[66, 35], Operations: ['64+2=66', '37-2=35'] Exploring Operation: 66+35=101, Resulting Numbers: [101] 101,89 unequal: No Solution Exploring Operation: 66*35=2310, Resulting Numbers: [2310] 2310,89 unequal: No Solution Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,89 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: 89:[37, 2, 66], Operations: ['64+2=66'] Exploring Operation: 37+2=39, Resulting Numbers: [66, 39] Generated Node #0,2,0: 89:[66, 39] Operation: 37+2=39 Exploring Operation: 37-2=35, Resulting Numbers: [66, 35] Generated Node #0,2,1: 89:[66, 35] Operation: 37-2=35 Exploring Operation: 2+66=68, Resulting Numbers: [37, 68] Generated Node #0,2,2: 89:[37, 68] Operation: 2+66=68 Exploring Operation: 37*2=74, Resulting Numbers: [66, 74] Generated Node #0,2,3: 89:[66, 74] Operation: 37*2=74 Moving to Node #0,2,3 Current State: 89:[66, 74], Operations: ['64+2=66', '37*2=74'] Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 66+74=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 66*74=4884, Resulting Numbers: [4884] 4884,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[37, 68], Operations: ['64+2=66', '2+66=68'] Exploring Operation: 37+68=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 37*68=2516, Resulting Numbers: [2516] 2516,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[66, 39], Operations: ['64+2=66', '37+2=39'] Exploring Operation: 66*39=2574, Resulting Numbers: [2574] 2574,89 unequal: No Solution Exploring Operation: 66+39=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[66, 35], Operations: ['64+2=66', '37-2=35'] Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 66+35=101, Resulting Numbers: [101] 101,89 unequal: No Solution Exploring Operation: 66*35=2310, Resulting Numbers: [2310] 2310,89 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
[ 15, 33, 3, 81 ]
43
[ "15+33=48", "81+48=129", "129/3=43" ]
Current State: 43:[15, 33, 3, 81], Operations: [] Exploring Operation: 15+33=48, Resulting Numbers: [3, 81, 48] Generated Node #2: [3, 81, 48] from Operation: 15+33=48 Current State: 43:[3, 81, 48], Operations: ['15+33=48'] Exploring Operation: 81+48=129, Resulting Numbers: [3, 129] Generated Node #3: [3, 129] from Operation: 81+48=129 Current State: 43:[3, 129], Operations: ['15+33=48', '81+48=129'] Exploring Operation: 129/3=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[15, 33, 3, 81], Operations: [] Exploring Operation: 15*3=45, Resulting Numbers: [33, 81, 45] Generated Node #0,0: 43:[33, 81, 45] Operation: 15*3=45 Exploring Operation: 81/3=27, Resulting Numbers: [15, 33, 27] Generated Node #0,1: 43:[15, 33, 27] Operation: 81/3=27 Exploring Operation: 15+3=18, Resulting Numbers: [33, 81, 18] Generated Node #0,2: 43:[33, 81, 18] Operation: 15+3=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[33, 81, 45], Operations: ['15*3=45'] Exploring Operation: 45-33=12, Resulting Numbers: [81, 12] Generated Node #0,0,0: 43:[81, 12] Operation: 45-33=12 Exploring Operation: 81-45=36, Resulting Numbers: [33, 36] Generated Node #0,0,1: 43:[33, 36] Operation: 81-45=36 Exploring Operation: 81-33=48, Resulting Numbers: [45, 48] Generated Node #0,0,2: 43:[45, 48] Operation: 81-33=48 Moving to Node #0,0,2 Current State: 43:[45, 48], Operations: ['15*3=45', '81-33=48'] Exploring Operation: 45*48=2160, Resulting Numbers: [2160] 2160,43 unequal: No Solution Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 45+48=93, Resulting Numbers: [93] 93,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[33, 36], Operations: ['15*3=45', '81-45=36'] Exploring Operation: 33+36=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 33*36=1188, Resulting Numbers: [1188] 1188,43 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[81, 12], Operations: ['15*3=45', '45-33=12'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 81*12=972, Resulting Numbers: [972] 972,43 unequal: No Solution Exploring Operation: 81+12=93, Resulting Numbers: [93] 93,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[15, 33, 27], Operations: ['81/3=27'] Exploring Operation: 15+27=42, Resulting Numbers: [33, 42] Generated Node #0,1,0: 43:[33, 42] Operation: 15+27=42 Exploring Operation: 33-15=18, Resulting Numbers: [27, 18] Generated Node #0,1,1: 43:[27, 18] Operation: 33-15=18 Exploring Operation: 15+33=48, Resulting Numbers: [27, 48] Generated Node #0,1,2: 43:[27, 48] Operation: 15+33=48 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[33, 42], Operations: ['81/3=27', '15+27=42'] Exploring Operation: 33+42=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 33*42=1386, Resulting Numbers: [1386] 1386,43 unequal: No Solution Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 43:[27, 48], Operations: ['81/3=27', '15+33=48'] Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 27*48=1296, Resulting Numbers: [1296] 1296,43 unequal: No Solution Exploring Operation: 27+48=75, Resulting Numbers: [75] 75,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[27, 18], Operations: ['81/3=27', '33-15=18'] Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[33, 81, 18], Operations: ['15+3=18'] Exploring Operation: 81-33=48, Resulting Numbers: [18, 48] Generated Node #0,2,0: 43:[18, 48] Operation: 81-33=48 Exploring Operation: 33+18=51, Resulting Numbers: [81, 51] Generated Node #0,2,1: 43:[81, 51] Operation: 33+18=51 Exploring Operation: 81-18=63, Resulting Numbers: [33, 63] Generated Node #0,2,2: 43:[33, 63] Operation: 81-18=63 Moving to Node #0,2,0 Current State: 43:[18, 48], Operations: ['15+3=18', '81-33=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,43 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[33, 63], Operations: ['15+3=18', '81-18=63'] Exploring Operation: 33*63=2079, Resulting Numbers: [2079] 2079,43 unequal: No Solution Exploring Operation: 33+63=96, Resulting Numbers: [96] 96,43 unequal: No Solution Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[81, 51], Operations: ['15+3=18', '33+18=51'] Exploring Operation: 81*51=4131, Resulting Numbers: [4131] 4131,43 unequal: No Solution Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,43 unequal: No Solution Exploring Operation: 81+51=132, Resulting Numbers: [132] 132,43 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
[ 2, 9, 49, 3 ]
64
[ "2*9=18", "49-3=46", "18+46=64" ]
Current State: 64:[2, 9, 49, 3], Operations: [] Exploring Operation: 2*9=18, Resulting Numbers: [49, 3, 18] Generated Node #2: [49, 3, 18] from Operation: 2*9=18 Current State: 64:[49, 3, 18], Operations: ['2*9=18'] Exploring Operation: 49-3=46, Resulting Numbers: [18, 46] Generated Node #3: [18, 46] from Operation: 49-3=46 Current State: 64:[18, 46], Operations: ['2*9=18', '49-3=46'] Exploring Operation: 18+46=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[2, 9, 49, 3], Operations: [] Exploring Operation: 9+49=58, Resulting Numbers: [2, 3, 58] Generated Node #0,0: 64:[2, 3, 58] Operation: 9+49=58 Exploring Operation: 49-9=40, Resulting Numbers: [2, 3, 40] Generated Node #0,1: 64:[2, 3, 40] Operation: 49-9=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[2, 3, 58], Operations: ['9+49=58'] Exploring Operation: 58/2=29, Resulting Numbers: [3, 29] Generated Node #0,0,0: 64:[3, 29] Operation: 58/2=29 Exploring Operation: 3+58=61, Resulting Numbers: [2, 61] Generated Node #0,0,1: 64:[2, 61] Operation: 3+58=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 64:[2, 61], Operations: ['9+49=58', '3+58=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,64 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[3, 29], Operations: ['9+49=58', '58/2=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[2, 3, 40], Operations: ['49-9=40'] Exploring Operation: 40/2=20, Resulting Numbers: [3, 20] Generated Node #0,1,0: 64:[3, 20] Operation: 40/2=20 Exploring Operation: 40-3=37, Resulting Numbers: [2, 37] Generated Node #0,1,1: 64:[2, 37] Operation: 40-3=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[3, 20], Operations: ['49-9=40', '40/2=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,64 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[2, 37], Operations: ['49-9=40', '40-3=37'] Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,64 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 74, 21, 80 ]
15
[ "80-74=6", "6*6=36", "36-21=15" ]
Current State: 15:[6, 74, 21, 80], Operations: [] Exploring Operation: 80-74=6, Resulting Numbers: [6, 21, 6] Generated Node #2: [6, 21, 6] from Operation: 80-74=6 Current State: 15:[6, 21, 6], Operations: ['80-74=6'] Exploring Operation: 6*6=36, Resulting Numbers: [21, 36] Generated Node #3: [21, 36] from Operation: 6*6=36 Current State: 15:[21, 36], Operations: ['80-74=6', '6*6=36'] Exploring Operation: 36-21=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[6, 74, 21, 80], Operations: [] Exploring Operation: 80-74=6, Resulting Numbers: [6, 21, 6] Generated Node #0,0: 15:[6, 21, 6] Operation: 80-74=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[6, 21, 6], Operations: ['80-74=6'] Exploring Operation: 21-6=15, Resulting Numbers: [6, 15] Generated Node #0,0,0: 15:[6, 15] Operation: 21-6=15 Moving to Node #0,0,0 Current State: 15:[6, 15], Operations: ['80-74=6', '21-6=15'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,15 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
[ 62, 84, 81, 48 ]
82
[ "84-81=3", "48*3=144", "144-62=82" ]
Current State: 82:[62, 84, 81, 48], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [62, 48, 3] Generated Node #2: [62, 48, 3] from Operation: 84-81=3 Current State: 82:[62, 48, 3], Operations: ['84-81=3'] Exploring Operation: 48*3=144, Resulting Numbers: [62, 144] Generated Node #3: [62, 144] from Operation: 48*3=144 Current State: 82:[62, 144], Operations: ['84-81=3', '48*3=144'] Exploring Operation: 144-62=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[62, 84, 81, 48], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [84, 81, 14] Generated Node #0,0: 82:[84, 81, 14] Operation: 62-48=14 Exploring Operation: 84-48=36, Resulting Numbers: [62, 81, 36] Generated Node #0,1: 82:[62, 81, 36] Operation: 84-48=36 Exploring Operation: 81-62=19, Resulting Numbers: [84, 48, 19] Generated Node #0,2: 82:[84, 48, 19] Operation: 81-62=19 Moving to Node #0,0 Current State: 82:[84, 81, 14], Operations: ['62-48=14'] Exploring Operation: 84/14=6, Resulting Numbers: [81, 6] Generated Node #0,0,0: 82:[81, 6] Operation: 84/14=6 Exploring Operation: 84-14=70, Resulting Numbers: [81, 70] Generated Node #0,0,1: 82:[81, 70] Operation: 84-14=70 Exploring Operation: 84-81=3, Resulting Numbers: [14, 3] Generated Node #0,0,2: 82:[14, 3] Operation: 84-81=3 Moving to Node #0,1 Current State: 82:[62, 81, 36], Operations: ['84-48=36'] Exploring Operation: 81-62=19, Resulting Numbers: [36, 19] Generated Node #0,1,0: 82:[36, 19] Operation: 81-62=19 Exploring Operation: 62+36=98, Resulting Numbers: [81, 98] Generated Node #0,1,1: 82:[81, 98] Operation: 62+36=98 Exploring Operation: 62-36=26, Resulting Numbers: [81, 26] Generated Node #0,1,2: 82:[81, 26] Operation: 62-36=26 Moving to Node #0,2 Current State: 82:[84, 48, 19], Operations: ['81-62=19'] Exploring Operation: 48-19=29, Resulting Numbers: [84, 29] Generated Node #0,2,0: 82:[84, 29] Operation: 48-19=29 Exploring Operation: 48+19=67, Resulting Numbers: [84, 67] Generated Node #0,2,1: 82:[84, 67] Operation: 48+19=67 Exploring Operation: 84-48=36, Resulting Numbers: [19, 36] Generated Node #0,2,2: 82:[19, 36] Operation: 84-48=36 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 82:[84, 29], Operations: ['81-62=19', '48-19=29'] Exploring Operation: 84*29=2436, Resulting Numbers: [2436] 2436,82 unequal: No Solution Exploring Operation: 84+29=113, Resulting Numbers: [113] 113,82 unequal: No Solution Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,82 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 #0,2,1 Current State: 82:[84, 67], Operations: ['81-62=19', '48+19=67'] Exploring Operation: 84+67=151, Resulting Numbers: [151] 151,82 unequal: No Solution Exploring Operation: 84-67=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 84*67=5628, Resulting Numbers: [5628] 5628,82 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 #0,2,2 Current State: 82:[19, 36], Operations: ['81-62=19', '84-48=36'] Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,82 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,82 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,82 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: 82:[81, 6], Operations: ['62-48=14', '84/14=6'] Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,82 unequal: No Solution Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,82 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[14, 3], Operations: ['62-48=14', '84-81=3'] Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[81, 70], Operations: ['62-48=14', '84-14=70'] Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 81*70=5670, Resulting Numbers: [5670] 5670,82 unequal: No Solution Exploring Operation: 81+70=151, Resulting Numbers: [151] 151,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[81, 26], Operations: ['84-48=36', '62-36=26'] Exploring Operation: 81*26=2106, Resulting Numbers: [2106] 2106,82 unequal: No Solution Exploring Operation: 81+26=107, Resulting Numbers: [107] 107,82 unequal: No Solution Exploring Operation: 81-26=55, Resulting Numbers: [55] 55,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[81, 98], Operations: ['84-48=36', '62+36=98'] Exploring Operation: 98-81=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 81+98=179, Resulting Numbers: [179] 179,82 unequal: No Solution Exploring Operation: 81*98=7938, Resulting Numbers: [7938] 7938,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[36, 19], Operations: ['84-48=36', '81-62=19'] Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,82 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,82 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 82, 10, 71, 80 ]
30
[ "82-71=11", "10*11=110", "110-80=30" ]
Current State: 30:[82, 10, 71, 80], Operations: [] Exploring Operation: 82-71=11, Resulting Numbers: [10, 80, 11] Generated Node #2: [10, 80, 11] from Operation: 82-71=11 Current State: 30:[10, 80, 11], Operations: ['82-71=11'] Exploring Operation: 10*11=110, Resulting Numbers: [80, 110] Generated Node #3: [80, 110] from Operation: 10*11=110 Current State: 30:[80, 110], Operations: ['82-71=11', '10*11=110'] Exploring Operation: 110-80=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[82, 10, 71, 80], Operations: [] Exploring Operation: 82-80=2, Resulting Numbers: [10, 71, 2] Generated Node #0,0: 30:[10, 71, 2] Operation: 82-80=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[10, 71, 2], Operations: ['82-80=2'] Exploring Operation: 71-10=61, Resulting Numbers: [2, 61] Generated Node #0,0,0: 30:[2, 61] Operation: 71-10=61 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[2, 61], Operations: ['82-80=2', '71-10=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 64, 48, 60, 3 ]
100
[ "48+60=108", "108/3=36", "64+36=100" ]
Current State: 100:[64, 48, 60, 3], Operations: [] Exploring Operation: 48+60=108, Resulting Numbers: [64, 3, 108] Generated Node #2: [64, 3, 108] from Operation: 48+60=108 Current State: 100:[64, 3, 108], Operations: ['48+60=108'] Exploring Operation: 108/3=36, Resulting Numbers: [64, 36] Generated Node #3: [64, 36] from Operation: 108/3=36 Current State: 100:[64, 36], Operations: ['48+60=108', '108/3=36'] Exploring Operation: 64+36=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[64, 48, 60, 3], Operations: [] Exploring Operation: 60-48=12, Resulting Numbers: [64, 3, 12] Generated Node #0,0: 100:[64, 3, 12] Operation: 60-48=12 Exploring Operation: 64-60=4, Resulting Numbers: [48, 3, 4] Generated Node #0,1: 100:[48, 3, 4] Operation: 64-60=4 Exploring Operation: 64+48=112, Resulting Numbers: [60, 3, 112] Generated Node #0,2: 100:[60, 3, 112] Operation: 64+48=112 Exploring Operation: 64-48=16, Resulting Numbers: [60, 3, 16] Generated Node #0,3: 100:[60, 3, 16] Operation: 64-48=16 Exploring Operation: 60/3=20, Resulting Numbers: [64, 48, 20] Generated Node #0,4: 100:[64, 48, 20] Operation: 60/3=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[48, 3, 4], Operations: ['64-60=4'] Exploring Operation: 48/4=12, Resulting Numbers: [3, 12] Generated Node #0,1,0: 100:[3, 12] Operation: 48/4=12 Exploring Operation: 48+3=51, Resulting Numbers: [4, 51] Generated Node #0,1,1: 100:[4, 51] Operation: 48+3=51 Exploring Operation: 48/3=16, Resulting Numbers: [4, 16] Generated Node #0,1,2: 100:[4, 16] Operation: 48/3=16 Exploring Operation: 48+4=52, Resulting Numbers: [3, 52] Generated Node #0,1,3: 100:[3, 52] Operation: 48+4=52 Exploring Operation: 4-3=1, Resulting Numbers: [48, 1] Generated Node #0,1,4: 100:[48, 1] Operation: 4-3=1 Moving to Node #0,1,1 Current State: 100:[4, 51], Operations: ['64-60=4', '48+3=51'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,100 unequal: No Solution Exploring Operation: 4*51=204, Resulting Numbers: [204] 204,100 unequal: No Solution Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[3, 52], Operations: ['64-60=4', '48+4=52'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[3, 12], Operations: ['64-60=4', '48/4=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,100 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,100 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,100 unequal: No Solution Moving to Node #0,1,4 Current State: 100:[48, 1], Operations: ['64-60=4', '4-3=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[4, 16], Operations: ['64-60=4', '48/3=16'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,100 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[60, 3, 16], Operations: ['64-48=16'] Exploring Operation: 3+16=19, Resulting Numbers: [60, 19] Generated Node #0,3,0: 100:[60, 19] Operation: 3+16=19 Exploring Operation: 60-16=44, Resulting Numbers: [3, 44] Generated Node #0,3,1: 100:[3, 44] Operation: 60-16=44 Exploring Operation: 60/3=20, Resulting Numbers: [16, 20] Generated Node #0,3,2: 100:[16, 20] Operation: 60/3=20 Exploring Operation: 60-3=57, Resulting Numbers: [16, 57] Generated Node #0,3,3: 100:[16, 57] Operation: 60-3=57 Exploring Operation: 3*16=48, Resulting Numbers: [60, 48] Generated Node #0,3,4: 100:[60, 48] Operation: 3*16=48 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 100:[16, 20], Operations: ['64-48=16', '60/3=20'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 16*20=320, Resulting Numbers: [320] 320,100 unequal: No Solution Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 100:[3, 44], Operations: ['64-48=16', '60-16=44'] Exploring Operation: 3*44=132, Resulting Numbers: [132] 132,100 unequal: No Solution Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,100 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 100:[60, 19], Operations: ['64-48=16', '3+16=19'] Exploring Operation: 60+19=79, Resulting Numbers: [79] 79,100 unequal: No Solution Exploring Operation: 60*19=1140, Resulting Numbers: [1140] 1140,100 unequal: No Solution Exploring Operation: 60-19=41, Resulting Numbers: [41] 41,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 100:[16, 57], Operations: ['64-48=16', '60-3=57'] Exploring Operation: 16+57=73, Resulting Numbers: [73] 73,100 unequal: No Solution Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,100 unequal: No Solution Exploring Operation: 16*57=912, Resulting Numbers: [912] 912,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 100:[60, 48], Operations: ['64-48=16', '3*16=48'] Exploring Operation: 60+48=108, Resulting Numbers: [108] 108,100 unequal: No Solution Exploring Operation: 60*48=2880, Resulting Numbers: [2880] 2880,100 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 100:[64, 48, 20], Operations: ['60/3=20'] Exploring Operation: 64-48=16, Resulting Numbers: [20, 16] Generated Node #0,4,0: 100:[20, 16] Operation: 64-48=16 Exploring Operation: 64+48=112, Resulting Numbers: [20, 112] Generated Node #0,4,1: 100:[20, 112] Operation: 64+48=112 Exploring Operation: 48-20=28, Resulting Numbers: [64, 28] Generated Node #0,4,2: 100:[64, 28] Operation: 48-20=28 Exploring Operation: 64+20=84, Resulting Numbers: [48, 84] Generated Node #0,4,3: 100:[48, 84] Operation: 64+20=84 Exploring Operation: 64-20=44, Resulting Numbers: [48, 44] Generated Node #0,4,4: 100:[48, 44] Operation: 64-20=44 Moving to Node #0,4,0 Current State: 100:[20, 16], Operations: ['60/3=20', '64-48=16'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,100 unequal: No Solution Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,100 unequal: No Solution Moving to Node #0,4,4 Current State: 100:[48, 44], Operations: ['60/3=20', '64-20=44'] Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,100 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,100 unequal: No Solution Moving to Node #0,4,1 Current State: 100:[20, 112], Operations: ['60/3=20', '64+48=112'] Exploring Operation: 20*112=2240, Resulting Numbers: [2240] 2240,100 unequal: No Solution Exploring Operation: 112-20=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 20+112=132, Resulting Numbers: [132] 132,100 unequal: No Solution Moving to Node #0,4,2 Current State: 100:[64, 28], Operations: ['60/3=20', '48-20=28'] Exploring Operation: 64+28=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 64-28=36, Resulting Numbers: [36] 36,100 unequal: No Solution Exploring Operation: 64*28=1792, Resulting Numbers: [1792] 1792,100 unequal: No Solution Moving to Node #0,4,3 Current State: 100:[48, 84], Operations: ['60/3=20', '64+20=84'] Exploring Operation: 84-48=36, Resulting Numbers: [36] 36,100 unequal: No Solution Exploring Operation: 48*84=4032, Resulting Numbers: [4032] 4032,100 unequal: No Solution Exploring Operation: 48+84=132, Resulting Numbers: [132] 132,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[64, 3, 12], Operations: ['60-48=12'] Exploring Operation: 64+3=67, Resulting Numbers: [12, 67] Generated Node #0,0,0: 100:[12, 67] Operation: 64+3=67 Exploring Operation: 64-12=52, Resulting Numbers: [3, 52] Generated Node #0,0,1: 100:[3, 52] Operation: 64-12=52 Exploring Operation: 12-3=9, Resulting Numbers: [64, 9] Generated Node #0,0,2: 100:[64, 9] Operation: 12-3=9 Exploring Operation: 12/3=4, Resulting Numbers: [64, 4] Generated Node #0,0,3: 100:[64, 4] Operation: 12/3=4 Exploring Operation: 64-3=61, Resulting Numbers: [12, 61] Generated Node #0,0,4: 100:[12, 61] Operation: 64-3=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 100:[3, 52], Operations: ['60-48=12', '64-12=52'] Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,100 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,100 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 #0,0,4 Current State: 100:[12, 61], Operations: ['60-48=12', '64-3=61'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 12*61=732, Resulting Numbers: [732] 732,100 unequal: No Solution Exploring Operation: 12+61=73, Resulting Numbers: [73] 73,100 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 #0,0,3 Current State: 100:[64, 4], Operations: ['60-48=12', '12/3=4'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 64*4=256, Resulting Numbers: [256] 256,100 unequal: No Solution Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,100 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 #0,0,2 Current State: 100:[64, 9], Operations: ['60-48=12', '12-3=9'] Exploring Operation: 64*9=576, Resulting Numbers: [576] 576,100 unequal: No Solution Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,100 unequal: No Solution Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 100:[12, 67], Operations: ['60-48=12', '64+3=67'] Exploring Operation: 12+67=79, Resulting Numbers: [79] 79,100 unequal: No Solution Exploring Operation: 12*67=804, Resulting Numbers: [804] 804,100 unequal: No Solution Exploring Operation: 67-12=55, Resulting Numbers: [55] 55,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[60, 3, 112], Operations: ['64+48=112'] Exploring Operation: 112-60=52, Resulting Numbers: [3, 52] Generated Node #0,2,0: 100:[3, 52] Operation: 112-60=52 Exploring Operation: 60+3=63, Resulting Numbers: [112, 63] Generated Node #0,2,1: 100:[112, 63] Operation: 60+3=63 Exploring Operation: 60-3=57, Resulting Numbers: [112, 57] Generated Node #0,2,2: 100:[112, 57] Operation: 60-3=57 Exploring Operation: 60/3=20, Resulting Numbers: [112, 20] Generated Node #0,2,3: 100:[112, 20] Operation: 60/3=20 Exploring Operation: 112-3=109, Resulting Numbers: [60, 109] Generated Node #0,2,4: 100:[60, 109] Operation: 112-3=109 Moving to Node #0,2,0 Current State: 100:[3, 52], Operations: ['64+48=112', '112-60=52'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,100 unequal: No Solution Moving to Node #0,2,3 Current State: 100:[112, 20], Operations: ['64+48=112', '60/3=20'] Exploring Operation: 112+20=132, Resulting Numbers: [132] 132,100 unequal: No Solution Exploring Operation: 112*20=2240, Resulting Numbers: [2240] 2240,100 unequal: No Solution Exploring Operation: 112-20=92, Resulting Numbers: [92] 92,100 unequal: No Solution Moving to Node #0,2,2 Current State: 100:[112, 57], Operations: ['64+48=112', '60-3=57'] Exploring Operation: 112*57=6384, Resulting Numbers: [6384] 6384,100 unequal: No Solution Exploring Operation: 112+57=169, Resulting Numbers: [169] 169,100 unequal: No Solution Exploring Operation: 112-57=55, Resulting Numbers: [55] 55,100 unequal: No Solution Moving to Node #0,2,4 Current State: 100:[60, 109], Operations: ['64+48=112', '112-3=109'] Exploring Operation: 60*109=6540, Resulting Numbers: [6540] 6540,100 unequal: No Solution Exploring Operation: 60+109=169, Resulting Numbers: [169] 169,100 unequal: No Solution Exploring Operation: 109-60=49, Resulting Numbers: [49] 49,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[112, 63], Operations: ['64+48=112', '60+3=63'] Exploring Operation: 112-63=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 112+63=175, Resulting Numbers: [175] 175,100 unequal: No Solution Exploring Operation: 112*63=7056, Resulting Numbers: [7056] 7056,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 65, 8, 54, 15 ]
12
[ "65-8=57", "54+15=69", "69-57=12" ]
Current State: 12:[65, 8, 54, 15], Operations: [] Exploring Operation: 65-8=57, Resulting Numbers: [54, 15, 57] Generated Node #2: [54, 15, 57] from Operation: 65-8=57 Current State: 12:[54, 15, 57], Operations: ['65-8=57'] Exploring Operation: 54+15=69, Resulting Numbers: [57, 69] Generated Node #3: [57, 69] from Operation: 54+15=69 Current State: 12:[57, 69], Operations: ['65-8=57', '54+15=69'] Exploring Operation: 69-57=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[65, 8, 54, 15], Operations: [] Exploring Operation: 54-15=39, Resulting Numbers: [65, 8, 39] Generated Node #0,0: 12:[65, 8, 39] Operation: 54-15=39 Exploring Operation: 65-15=50, Resulting Numbers: [8, 54, 50] Generated Node #0,1: 12:[8, 54, 50] Operation: 65-15=50 Exploring Operation: 65-54=11, Resulting Numbers: [8, 15, 11] Generated Node #0,2: 12:[8, 15, 11] Operation: 65-54=11 Moving to Node #0,2 Current State: 12:[8, 15, 11], Operations: ['65-54=11'] Exploring Operation: 15-11=4, Resulting Numbers: [8, 4] Generated Node #0,2,0: 12:[8, 4] Operation: 15-11=4 Exploring Operation: 15-8=7, Resulting Numbers: [11, 7] Generated Node #0,2,1: 12:[11, 7] Operation: 15-8=7 Exploring Operation: 11-8=3, Resulting Numbers: [15, 3] Generated Node #0,2,2: 12:[15, 3] Operation: 11-8=3 Moving to Node #0,0 Current State: 12:[65, 8, 39], Operations: ['54-15=39'] Exploring Operation: 39-8=31, Resulting Numbers: [65, 31] Generated Node #0,0,0: 12:[65, 31] Operation: 39-8=31 Exploring Operation: 65-39=26, Resulting Numbers: [8, 26] Generated Node #0,0,1: 12:[8, 26] Operation: 65-39=26 Exploring Operation: 65-8=57, Resulting Numbers: [39, 57] Generated Node #0,0,2: 12:[39, 57] Operation: 65-8=57 Moving to Node #0,1 Current State: 12:[8, 54, 50], Operations: ['65-15=50'] Exploring Operation: 50-8=42, Resulting Numbers: [54, 42] Generated Node #0,1,0: 12:[54, 42] Operation: 50-8=42 Exploring Operation: 54-8=46, Resulting Numbers: [50, 46] Generated Node #0,1,1: 12:[50, 46] Operation: 54-8=46 Exploring Operation: 54-50=4, Resulting Numbers: [8, 4] Generated Node #0,1,2: 12:[8, 4] Operation: 54-50=4 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 12:[8, 4], Operations: ['65-15=50', '54-50=4'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[65, 8, 54, 15], Operations: [] Exploring Operation: 65-15=50, Resulting Numbers: [8, 54, 50] Generated Node #0,1: 12:[8, 54, 50] Operation: 65-15=50 Moving to Node #0,1 Current State: 12:[8, 54, 50], Operations: ['65-15=50'] Exploring Operation: 54-50=4, Resulting Numbers: [8, 4] Generated Node #0,1,2: 12:[8, 4] Operation: 54-50=4 Moving to Node #0,1,2 Current State: 12:[8, 4], Operations: ['65-15=50', '54-50=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 39, 63, 22, 3 ]
72
[ "39/3=13", "63+22=85", "85-13=72" ]
Current State: 72:[39, 63, 22, 3], Operations: [] Exploring Operation: 39/3=13, Resulting Numbers: [63, 22, 13] Generated Node #2: [63, 22, 13] from Operation: 39/3=13 Current State: 72:[63, 22, 13], Operations: ['39/3=13'] Exploring Operation: 63+22=85, Resulting Numbers: [13, 85] Generated Node #3: [13, 85] from Operation: 63+22=85 Current State: 72:[13, 85], Operations: ['39/3=13', '63+22=85'] Exploring Operation: 85-13=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[39, 63, 22, 3], Operations: [] Exploring Operation: 63-39=24, Resulting Numbers: [22, 3, 24] Generated Node #0,0: 72:[22, 3, 24] Operation: 63-39=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[22, 3, 24], Operations: ['63-39=24'] Exploring Operation: 24-22=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 72:[3, 2] Operation: 24-22=2 Moving to Node #0,0,0 Current State: 72:[3, 2], Operations: ['63-39=24', '24-22=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 77, 28, 64, 58 ]
99
[ "77+28=105", "64-58=6", "105-6=99" ]
Current State: 99:[77, 28, 64, 58], Operations: [] Exploring Operation: 77+28=105, Resulting Numbers: [64, 58, 105] Generated Node #2: [64, 58, 105] from Operation: 77+28=105 Current State: 99:[64, 58, 105], Operations: ['77+28=105'] Exploring Operation: 64-58=6, Resulting Numbers: [105, 6] Generated Node #3: [105, 6] from Operation: 64-58=6 Current State: 99:[105, 6], Operations: ['77+28=105', '64-58=6'] Exploring Operation: 105-6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[77, 28, 64, 58], Operations: [] Exploring Operation: 77-64=13, Resulting Numbers: [28, 58, 13] Generated Node #0,0: 99:[28, 58, 13] Operation: 77-64=13 Exploring Operation: 64-58=6, Resulting Numbers: [77, 28, 6] Generated Node #0,1: 99:[77, 28, 6] Operation: 64-58=6 Exploring Operation: 77-58=19, Resulting Numbers: [28, 64, 19] Generated Node #0,2: 99:[28, 64, 19] Operation: 77-58=19 Exploring Operation: 64-28=36, Resulting Numbers: [77, 58, 36] Generated Node #0,3: 99:[77, 58, 36] Operation: 64-28=36 Moving to Node #0,1 Current State: 99:[77, 28, 6], Operations: ['64-58=6'] Exploring Operation: 77-28=49, Resulting Numbers: [6, 49] Generated Node #0,1,0: 99:[6, 49] Operation: 77-28=49 Exploring Operation: 77+6=83, Resulting Numbers: [28, 83] Generated Node #0,1,1: 99:[28, 83] Operation: 77+6=83 Exploring Operation: 28+6=34, Resulting Numbers: [77, 34] Generated Node #0,1,2: 99:[77, 34] Operation: 28+6=34 Exploring Operation: 77+28=105, Resulting Numbers: [6, 105] Generated Node #0,1,3: 99:[6, 105] Operation: 77+28=105 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[6, 105], Operations: ['64-58=6', '77+28=105'] Exploring Operation: 6+105=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 6*105=630, Resulting Numbers: [630] 630,99 unequal: No Solution Exploring Operation: 105-6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[77, 28, 64, 58], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [77, 28, 6] Generated Node #0,1: 99:[77, 28, 6] Operation: 64-58=6 Moving to Node #0,1 Current State: 99:[77, 28, 6], Operations: ['64-58=6'] Exploring Operation: 77+28=105, Resulting Numbers: [6, 105] Generated Node #0,1,3: 99:[6, 105] Operation: 77+28=105 Moving to Node #0,1,3 Current State: 99:[6, 105], Operations: ['64-58=6', '77+28=105'] Exploring Operation: 105-6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 98, 41, 31, 1 ]
27
[ "98-41=57", "31-1=30", "57-30=27" ]
Current State: 27:[98, 41, 31, 1], Operations: [] Exploring Operation: 98-41=57, Resulting Numbers: [31, 1, 57] Generated Node #2: [31, 1, 57] from Operation: 98-41=57 Current State: 27:[31, 1, 57], Operations: ['98-41=57'] Exploring Operation: 31-1=30, Resulting Numbers: [57, 30] Generated Node #3: [57, 30] from Operation: 31-1=30 Current State: 27:[57, 30], Operations: ['98-41=57', '31-1=30'] Exploring Operation: 57-30=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[98, 41, 31, 1], Operations: [] Exploring Operation: 98-41=57, Resulting Numbers: [31, 1, 57] Generated Node #0,0: 27:[31, 1, 57] Operation: 98-41=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[31, 1, 57], Operations: ['98-41=57'] Exploring Operation: 57-31=26, Resulting Numbers: [1, 26] Generated Node #0,0,0: 27:[1, 26] Operation: 57-31=26 Moving to Node #0,0,0 Current State: 27:[1, 26], Operations: ['98-41=57', '57-31=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[98, 41, 31, 1], Operations: [] Exploring Operation: 98-41=57, Resulting Numbers: [31, 1, 57] Generated Node #0,0: 27:[31, 1, 57] Operation: 98-41=57 Moving to Node #0,0 Current State: 27:[31, 1, 57], Operations: ['98-41=57'] Exploring Operation: 57-31=26, Resulting Numbers: [1, 26] Generated Node #0,0,0: 27:[1, 26] Operation: 57-31=26 Moving to Node #0,0,0 Current State: 27:[1, 26], Operations: ['98-41=57', '57-31=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 51, 48, 32, 44 ]
15
[ "51-48=3", "44-32=12", "3+12=15" ]
Current State: 15:[51, 48, 32, 44], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [32, 44, 3] Generated Node #2: [32, 44, 3] from Operation: 51-48=3 Current State: 15:[32, 44, 3], Operations: ['51-48=3'] Exploring Operation: 44-32=12, Resulting Numbers: [3, 12] Generated Node #3: [3, 12] from Operation: 44-32=12 Current State: 15:[3, 12], Operations: ['51-48=3', '44-32=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[51, 48, 32, 44], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [32, 44, 3] Generated Node #0,0: 15:[32, 44, 3] Operation: 51-48=3 Exploring Operation: 51-44=7, Resulting Numbers: [48, 32, 7] Generated Node #0,1: 15:[48, 32, 7] Operation: 51-44=7 Moving to Node #0,0 Current State: 15:[32, 44, 3], Operations: ['51-48=3'] Exploring Operation: 44-32=12, Resulting Numbers: [3, 12] Generated Node #0,0,0: 15:[3, 12] Operation: 44-32=12 Exploring Operation: 32-3=29, Resulting Numbers: [44, 29] Generated Node #0,0,1: 15:[44, 29] Operation: 32-3=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[3, 12], Operations: ['51-48=3', '44-32=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[51, 48, 32, 44], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [32, 44, 3] Generated Node #0,0: 15:[32, 44, 3] Operation: 51-48=3 Moving to Node #0,0 Current State: 15:[32, 44, 3], Operations: ['51-48=3'] Exploring Operation: 44-32=12, Resulting Numbers: [3, 12] Generated Node #0,0,0: 15:[3, 12] Operation: 44-32=12 Moving to Node #0,0,0 Current State: 15:[3, 12], Operations: ['51-48=3', '44-32=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 77, 9, 48, 18 ]
31
[ "77-48=29", "18/9=2", "29+2=31" ]
Current State: 31:[77, 9, 48, 18], Operations: [] Exploring Operation: 77-48=29, Resulting Numbers: [9, 18, 29] Generated Node #2: [9, 18, 29] from Operation: 77-48=29 Current State: 31:[9, 18, 29], Operations: ['77-48=29'] Exploring Operation: 18/9=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 18/9=2 Current State: 31:[29, 2], Operations: ['77-48=29', '18/9=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[77, 9, 48, 18], Operations: [] Exploring Operation: 77-18=59, Resulting Numbers: [9, 48, 59] Generated Node #0,0: 31:[9, 48, 59] Operation: 77-18=59 Exploring Operation: 77-48=29, Resulting Numbers: [9, 18, 29] Generated Node #0,1: 31:[9, 18, 29] Operation: 77-48=29 Exploring Operation: 77-9=68, Resulting Numbers: [48, 18, 68] Generated Node #0,2: 31:[48, 18, 68] Operation: 77-9=68 Exploring Operation: 48-9=39, Resulting Numbers: [77, 18, 39] Generated Node #0,3: 31:[77, 18, 39] Operation: 48-9=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[9, 18, 29], Operations: ['77-48=29'] Exploring Operation: 9+18=27, Resulting Numbers: [29, 27] Generated Node #0,1,0: 31:[29, 27] Operation: 9+18=27 Exploring Operation: 29-9=20, Resulting Numbers: [18, 20] Generated Node #0,1,1: 31:[18, 20] Operation: 29-9=20 Exploring Operation: 18-9=9, Resulting Numbers: [29, 9] Generated Node #0,1,2: 31:[29, 9] Operation: 18-9=9 Exploring Operation: 9+29=38, Resulting Numbers: [18, 38] Generated Node #0,1,3: 31:[18, 38] Operation: 9+29=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[29, 27], Operations: ['77-48=29', '9+18=27'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 31:[18, 38], Operations: ['77-48=29', '9+29=38'] Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,31 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 31:[18, 20], Operations: ['77-48=29', '29-9=20'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 31:[29, 9], Operations: ['77-48=29', '18-9=9'] Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,31 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[9, 48, 59], Operations: ['77-18=59'] Exploring Operation: 59-9=50, Resulting Numbers: [48, 50] Generated Node #0,0,0: 31:[48, 50] Operation: 59-9=50 Exploring Operation: 9+48=57, Resulting Numbers: [59, 57] Generated Node #0,0,1: 31:[59, 57] Operation: 9+48=57 Exploring Operation: 48-9=39, Resulting Numbers: [59, 39] Generated Node #0,0,2: 31:[59, 39] Operation: 48-9=39 Exploring Operation: 59-48=11, Resulting Numbers: [9, 11] Generated Node #0,0,3: 31:[9, 11] Operation: 59-48=11 Moving to Node #0,0,0 Current State: 31:[48, 50], Operations: ['77-18=59', '59-9=50'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[59, 39], Operations: ['77-18=59', '48-9=39'] Exploring Operation: 59+39=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 59-39=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 59*39=2301, Resulting Numbers: [2301] 2301,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[9, 11], Operations: ['77-18=59', '59-48=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[59, 57], Operations: ['77-18=59', '9+48=57'] Exploring Operation: 59+57=116, Resulting Numbers: [116] 116,31 unequal: No Solution Exploring Operation: 59*57=3363, Resulting Numbers: [3363] 3363,31 unequal: No Solution Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[48, 18, 68], Operations: ['77-9=68'] Exploring Operation: 48-18=30, Resulting Numbers: [68, 30] Generated Node #0,2,0: 31:[68, 30] Operation: 48-18=30 Exploring Operation: 68-48=20, Resulting Numbers: [18, 20] Generated Node #0,2,1: 31:[18, 20] Operation: 68-48=20 Exploring Operation: 68-18=50, Resulting Numbers: [48, 50] Generated Node #0,2,2: 31:[48, 50] Operation: 68-18=50 Exploring Operation: 48+18=66, Resulting Numbers: [68, 66] Generated Node #0,2,3: 31:[68, 66] Operation: 48+18=66 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 31:[18, 20], Operations: ['77-9=68', '68-48=20'] Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,31 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 31:[48, 50], Operations: ['77-9=68', '68-18=50'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,31 unequal: No Solution Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 31:[68, 30], Operations: ['77-9=68', '48-18=30'] Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 31:[68, 66], Operations: ['77-9=68', '48+18=66'] Exploring Operation: 68-66=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 68*66=4488, Resulting Numbers: [4488] 4488,31 unequal: No Solution Exploring Operation: 68+66=134, Resulting Numbers: [134] 134,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 31:[77, 18, 39], Operations: ['48-9=39'] Exploring Operation: 77-18=59, Resulting Numbers: [39, 59] Generated Node #0,3,0: 31:[39, 59] Operation: 77-18=59 Exploring Operation: 39-18=21, Resulting Numbers: [77, 21] Generated Node #0,3,1: 31:[77, 21] Operation: 39-18=21 Exploring Operation: 77-39=38, Resulting Numbers: [18, 38] Generated Node #0,3,2: 31:[18, 38] Operation: 77-39=38 Exploring Operation: 77+18=95, Resulting Numbers: [39, 95] Generated Node #0,3,3: 31:[39, 95] Operation: 77+18=95 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 31:[18, 38], Operations: ['48-9=39', '77-39=38'] Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,31 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 31:[39, 59], Operations: ['48-9=39', '77-18=59'] Exploring Operation: 39+59=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 39*59=2301, Resulting Numbers: [2301] 2301,31 unequal: No Solution Exploring Operation: 59-39=20, Resulting Numbers: [20] 20,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 31:[77, 21], Operations: ['48-9=39', '39-18=21'] Exploring Operation: 77+21=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 77*21=1617, Resulting Numbers: [1617] 1617,31 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 31:[39, 95], Operations: ['48-9=39', '77+18=95'] Exploring Operation: 39+95=134, Resulting Numbers: [134] 134,31 unequal: No Solution Exploring Operation: 39*95=3705, Resulting Numbers: [3705] 3705,31 unequal: No Solution Exploring Operation: 95-39=56, Resulting Numbers: [56] 56,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 24, 26, 7, 91 ]
22
[ "26*7=182", "182/91=2", "24-2=22" ]
Current State: 22:[24, 26, 7, 91], Operations: [] Exploring Operation: 26*7=182, Resulting Numbers: [24, 91, 182] Generated Node #2: [24, 91, 182] from Operation: 26*7=182 Current State: 22:[24, 91, 182], Operations: ['26*7=182'] Exploring Operation: 182/91=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 182/91=2 Current State: 22:[24, 2], Operations: ['26*7=182', '182/91=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[24, 26, 7, 91], Operations: [] Exploring Operation: 91-26=65, Resulting Numbers: [24, 7, 65] Generated Node #0,0: 22:[24, 7, 65] Operation: 91-26=65 Exploring Operation: 91-7=84, Resulting Numbers: [24, 26, 84] Generated Node #0,1: 22:[24, 26, 84] Operation: 91-7=84 Exploring Operation: 91-24=67, Resulting Numbers: [26, 7, 67] Generated Node #0,2: 22:[26, 7, 67] Operation: 91-24=67 Exploring Operation: 91/7=13, Resulting Numbers: [24, 26, 13] Generated Node #0,3: 22:[24, 26, 13] Operation: 91/7=13 Moving to Node #0,3 Current State: 22:[24, 26, 13], Operations: ['91/7=13'] Exploring Operation: 24-13=11, Resulting Numbers: [26, 11] Generated Node #0,3,0: 22:[26, 11] Operation: 24-13=11 Exploring Operation: 26-24=2, Resulting Numbers: [13, 2] Generated Node #0,3,1: 22:[13, 2] Operation: 26-24=2 Exploring Operation: 26/13=2, Resulting Numbers: [24, 2] Generated Node #0,3,2: 22:[24, 2] Operation: 26/13=2 Exploring Operation: 26-13=13, Resulting Numbers: [24, 13] Generated Node #0,3,3: 22:[24, 13] Operation: 26-13=13 Moving to Node #0,0 Current State: 22:[24, 7, 65], Operations: ['91-26=65'] Exploring Operation: 24+7=31, Resulting Numbers: [65, 31] Generated Node #0,0,0: 22:[65, 31] Operation: 24+7=31 Exploring Operation: 24-7=17, Resulting Numbers: [65, 17] Generated Node #0,0,1: 22:[65, 17] Operation: 24-7=17 Exploring Operation: 65-7=58, Resulting Numbers: [24, 58] Generated Node #0,0,2: 22:[24, 58] Operation: 65-7=58 Exploring Operation: 65-24=41, Resulting Numbers: [7, 41] Generated Node #0,0,3: 22:[7, 41] Operation: 65-24=41 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 22:[7, 41], Operations: ['91-26=65', '65-24=41'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,22 unequal: No Solution Exploring Operation: 7*41=287, Resulting Numbers: [287] 287,22 unequal: No Solution Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,22 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 #0,0,2 Current State: 22:[24, 58], Operations: ['91-26=65', '65-7=58'] Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,22 unequal: No Solution Exploring Operation: 24+58=82, Resulting Numbers: [82] 82,22 unequal: No Solution Exploring Operation: 24*58=1392, Resulting Numbers: [1392] 1392,22 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 #0,0,1 Current State: 22:[65, 17], Operations: ['91-26=65', '24-7=17'] Exploring Operation: 65*17=1105, Resulting Numbers: [1105] 1105,22 unequal: No Solution Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 65+17=82, Resulting Numbers: [82] 82,22 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 #0,0,0 Current State: 22:[65, 31], Operations: ['91-26=65', '24+7=31'] Exploring Operation: 65+31=96, Resulting Numbers: [96] 96,22 unequal: No Solution Exploring Operation: 65*31=2015, Resulting Numbers: [2015] 2015,22 unequal: No Solution Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,22 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: 22:[26, 7, 67], Operations: ['91-24=67'] Exploring Operation: 26-7=19, Resulting Numbers: [67, 19] Generated Node #0,2,0: 22:[67, 19] Operation: 26-7=19 Exploring Operation: 26+7=33, Resulting Numbers: [67, 33] Generated Node #0,2,1: 22:[67, 33] Operation: 26+7=33 Exploring Operation: 67-26=41, Resulting Numbers: [7, 41] Generated Node #0,2,2: 22:[7, 41] Operation: 67-26=41 Exploring Operation: 67-7=60, Resulting Numbers: [26, 60] Generated Node #0,2,3: 22:[26, 60] Operation: 67-7=60 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[7, 41], Operations: ['91-24=67', '67-26=41'] Exploring Operation: 7*41=287, Resulting Numbers: [287] 287,22 unequal: No Solution Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,22 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:[26, 60], Operations: ['91-24=67', '67-7=60'] Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,22 unequal: No Solution Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,22 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,22 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:[67, 19], Operations: ['91-24=67', '26-7=19'] Exploring Operation: 67+19=86, Resulting Numbers: [86] 86,22 unequal: No Solution Exploring Operation: 67*19=1273, Resulting Numbers: [1273] 1273,22 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,22 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:[67, 33], Operations: ['91-24=67', '26+7=33'] Exploring Operation: 67*33=2211, Resulting Numbers: [2211] 2211,22 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,22 unequal: No Solution Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,22 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:[24, 26, 84], Operations: ['91-7=84'] Exploring Operation: 84-26=58, Resulting Numbers: [24, 58] Generated Node #0,1,0: 22:[24, 58] Operation: 84-26=58 Exploring Operation: 26-24=2, Resulting Numbers: [84, 2] Generated Node #0,1,1: 22:[84, 2] Operation: 26-24=2 Exploring Operation: 24+26=50, Resulting Numbers: [84, 50] Generated Node #0,1,2: 22:[84, 50] Operation: 24+26=50 Exploring Operation: 84-24=60, Resulting Numbers: [26, 60] Generated Node #0,1,3: 22:[26, 60] Operation: 84-24=60 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[24, 58], Operations: ['91-7=84', '84-26=58'] Exploring Operation: 24+58=82, Resulting Numbers: [82] 82,22 unequal: No Solution Exploring Operation: 24*58=1392, Resulting Numbers: [1392] 1392,22 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,22 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:[26, 60], Operations: ['91-7=84', '84-24=60'] Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,22 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,22 unequal: No Solution Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,22 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:[84, 2], Operations: ['91-7=84', '26-24=2'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,22 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,22 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,22 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:[84, 50], Operations: ['91-7=84', '24+26=50'] Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,22 unequal: No Solution Exploring Operation: 84*50=4200, Resulting Numbers: [4200] 4200,22 unequal: No Solution Exploring Operation: 84+50=134, Resulting Numbers: [134] 134,22 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: 22:[13, 2], Operations: ['91/7=13', '26-24=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[24, 2], Operations: ['91/7=13', '26/13=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[24, 26, 7, 91], Operations: [] Exploring Operation: 91/7=13, Resulting Numbers: [24, 26, 13] Generated Node #0,3: 22:[24, 26, 13] Operation: 91/7=13 Moving to Node #0,3 Current State: 22:[24, 26, 13], Operations: ['91/7=13'] Exploring Operation: 26/13=2, Resulting Numbers: [24, 2] Generated Node #0,3,2: 22:[24, 2] Operation: 26/13=2 Moving to Node #0,3,2 Current State: 22:[24, 2], Operations: ['91/7=13', '26/13=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.943576
hs_4
sum_heuristic
[ 49, 54, 64, 10 ]
51
[ "64-54=10", "10*10=100", "100-49=51" ]
Current State: 51:[49, 54, 64, 10], Operations: [] Exploring Operation: 64-54=10, Resulting Numbers: [49, 10, 10] Generated Node #2: [49, 10, 10] from Operation: 64-54=10 Current State: 51:[49, 10, 10], Operations: ['64-54=10'] Exploring Operation: 10*10=100, Resulting Numbers: [49, 100] Generated Node #3: [49, 100] from Operation: 10*10=100 Current State: 51:[49, 100], Operations: ['64-54=10', '10*10=100'] Exploring Operation: 100-49=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[49, 54, 64, 10], Operations: [] Exploring Operation: 64-10=54, Resulting Numbers: [49, 54, 54] Generated Node #0,0: 51:[49, 54, 54] Operation: 64-10=54 Exploring Operation: 64-49=15, Resulting Numbers: [54, 10, 15] Generated Node #0,1: 51:[54, 10, 15] Operation: 64-49=15 Moving to Node #0,0 Current State: 51:[49, 54, 54], Operations: ['64-10=54'] Exploring Operation: 54-49=5, Resulting Numbers: [54, 5] Generated Node #0,0,0: 51:[54, 5] Operation: 54-49=5 Exploring Operation: 54/54=1, Resulting Numbers: [49, 1] Generated Node #0,0,1: 51:[49, 1] Operation: 54/54=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[49, 1], Operations: ['64-10=54', '54/54=1'] Exploring Operation: 49+1=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[54, 5], Operations: ['64-10=54', '54-49=5'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,51 unequal: No Solution Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 51:[54, 10, 15], Operations: ['64-49=15'] Exploring Operation: 54-10=44, Resulting Numbers: [15, 44] Generated Node #0,1,0: 51:[15, 44] Operation: 54-10=44 Exploring Operation: 15-10=5, Resulting Numbers: [54, 5] Generated Node #0,1,1: 51:[54, 5] Operation: 15-10=5 Moving to Node #0,1,1 Current State: 51:[54, 5], Operations: ['64-49=15', '15-10=5'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,51 unequal: No Solution Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[15, 44], Operations: ['64-49=15', '54-10=44'] Exploring Operation: 15+44=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,51 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 73, 82, 93, 1 ]
63
[ "73+82=155", "93-1=92", "155-92=63" ]
Current State: 63:[73, 82, 93, 1], Operations: [] Exploring Operation: 73+82=155, Resulting Numbers: [93, 1, 155] Generated Node #2: [93, 1, 155] from Operation: 73+82=155 Current State: 63:[93, 1, 155], Operations: ['73+82=155'] Exploring Operation: 93-1=92, Resulting Numbers: [155, 92] Generated Node #3: [155, 92] from Operation: 93-1=92 Current State: 63:[155, 92], Operations: ['73+82=155', '93-1=92'] Exploring Operation: 155-92=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[73, 82, 93, 1], Operations: [] Exploring Operation: 73-1=72, Resulting Numbers: [82, 93, 72] Generated Node #0,0: 63:[82, 93, 72] Operation: 73-1=72 Exploring Operation: 82-73=9, Resulting Numbers: [93, 1, 9] Generated Node #0,1: 63:[93, 1, 9] Operation: 82-73=9 Exploring Operation: 82-1=81, Resulting Numbers: [73, 93, 81] Generated Node #0,2: 63:[73, 93, 81] Operation: 82-1=81 Exploring Operation: 93-73=20, Resulting Numbers: [82, 1, 20] Generated Node #0,3: 63:[82, 1, 20] Operation: 93-73=20 Exploring Operation: 93-82=11, Resulting Numbers: [73, 1, 11] Generated Node #0,4: 63:[73, 1, 11] Operation: 93-82=11 Moving to Node #0,4 Current State: 63:[73, 1, 11], Operations: ['93-82=11'] Exploring Operation: 11-1=10, Resulting Numbers: [73, 10] Generated Node #0,4,0: 63:[73, 10] Operation: 11-1=10 Exploring Operation: 73*1=73, Resulting Numbers: [11, 73] Generated Node #0,4,1: 63:[11, 73] Operation: 73*1=73 Exploring Operation: 73-11=62, Resulting Numbers: [1, 62] Generated Node #0,4,2: 63:[1, 62] Operation: 73-11=62 Exploring Operation: 73-1=72, Resulting Numbers: [11, 72] Generated Node #0,4,3: 63:[11, 72] Operation: 73-1=72 Exploring Operation: 73/1=73, Resulting Numbers: [11, 73] Generated Node #0,4,4: 63:[11, 73] Operation: 73/1=73 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 63:[1, 62], Operations: ['93-82=11', '73-11=62'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[73, 82, 93, 1], Operations: [] Exploring Operation: 93-82=11, Resulting Numbers: [73, 1, 11] Generated Node #0,4: 63:[73, 1, 11] Operation: 93-82=11 Moving to Node #0,4 Current State: 63:[73, 1, 11], Operations: ['93-82=11'] Exploring Operation: 73-11=62, Resulting Numbers: [1, 62] Generated Node #0,4,2: 63:[1, 62] Operation: 73-11=62 Moving to Node #0,4,2 Current State: 63:[1, 62], Operations: ['93-82=11', '73-11=62'] Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 35, 45, 70, 9 ]
71
[ "45-35=10", "70-9=61", "10+61=71" ]
Current State: 71:[35, 45, 70, 9], Operations: [] Exploring Operation: 45-35=10, Resulting Numbers: [70, 9, 10] Generated Node #2: [70, 9, 10] from Operation: 45-35=10 Current State: 71:[70, 9, 10], Operations: ['45-35=10'] Exploring Operation: 70-9=61, Resulting Numbers: [10, 61] Generated Node #3: [10, 61] from Operation: 70-9=61 Current State: 71:[10, 61], Operations: ['45-35=10', '70-9=61'] Exploring Operation: 10+61=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[35, 45, 70, 9], Operations: [] Exploring Operation: 35+9=44, Resulting Numbers: [45, 70, 44] Generated Node #0,0: 71:[45, 70, 44] Operation: 35+9=44 Exploring Operation: 45+9=54, Resulting Numbers: [35, 70, 54] Generated Node #0,1: 71:[35, 70, 54] Operation: 45+9=54 Moving to Node #0,0 Current State: 71:[45, 70, 44], Operations: ['35+9=44'] Exploring Operation: 70+44=114, Resulting Numbers: [45, 114] Generated Node #0,0,0: 71:[45, 114] Operation: 70+44=114 Exploring Operation: 45+44=89, Resulting Numbers: [70, 89] Generated Node #0,0,1: 71:[70, 89] Operation: 45+44=89 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[70, 89], Operations: ['35+9=44', '45+44=89'] Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 70+89=159, Resulting Numbers: [159] 159,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[45, 114], Operations: ['35+9=44', '70+44=114'] Exploring Operation: 45+114=159, Resulting Numbers: [159] 159,71 unequal: No Solution Exploring Operation: 114-45=69, Resulting Numbers: [69] 69,71 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:[35, 70, 54], Operations: ['45+9=54'] Exploring Operation: 35+70=105, Resulting Numbers: [54, 105] Generated Node #0,1,0: 71:[54, 105] Operation: 35+70=105 Exploring Operation: 35+54=89, Resulting Numbers: [70, 89] Generated Node #0,1,1: 71:[70, 89] Operation: 35+54=89 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[70, 89], Operations: ['45+9=54', '35+54=89'] Exploring Operation: 70+89=159, Resulting Numbers: [159] 159,71 unequal: No Solution Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,71 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 #0,1,0 Current State: 71:[54, 105], Operations: ['45+9=54', '35+70=105'] Exploring Operation: 105-54=51, Resulting Numbers: [51] 51,71 unequal: No Solution Exploring Operation: 54+105=159, Resulting Numbers: [159] 159,71 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
[ 50, 46, 51, 53 ]
15
[ "53-50=3", "51-46=5", "3*5=15" ]
Current State: 15:[50, 46, 51, 53], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [46, 51, 3] Generated Node #2: [46, 51, 3] from Operation: 53-50=3 Current State: 15:[46, 51, 3], Operations: ['53-50=3'] Exploring Operation: 51-46=5, Resulting Numbers: [3, 5] Generated Node #3: [3, 5] from Operation: 51-46=5 Current State: 15:[3, 5], Operations: ['53-50=3', '51-46=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[50, 46, 51, 53], Operations: [] Exploring Operation: 51-46=5, Resulting Numbers: [50, 53, 5] Generated Node #0,0: 15:[50, 53, 5] Operation: 51-46=5 Exploring Operation: 53-46=7, Resulting Numbers: [50, 51, 7] Generated Node #0,1: 15:[50, 51, 7] Operation: 53-46=7 Exploring Operation: 53-50=3, Resulting Numbers: [46, 51, 3] Generated Node #0,2: 15:[46, 51, 3] Operation: 53-50=3 Exploring Operation: 51-50=1, Resulting Numbers: [46, 53, 1] Generated Node #0,3: 15:[46, 53, 1] Operation: 51-50=1 Exploring Operation: 53-51=2, Resulting Numbers: [50, 46, 2] Generated Node #0,4: 15:[50, 46, 2] Operation: 53-51=2 Moving to Node #0,2 Current State: 15:[46, 51, 3], Operations: ['53-50=3'] Exploring Operation: 46+3=49, Resulting Numbers: [51, 49] Generated Node #0,2,0: 15:[51, 49] Operation: 46+3=49 Exploring Operation: 46-3=43, Resulting Numbers: [51, 43] Generated Node #0,2,1: 15:[51, 43] Operation: 46-3=43 Exploring Operation: 51-3=48, Resulting Numbers: [46, 48] Generated Node #0,2,2: 15:[46, 48] Operation: 51-3=48 Exploring Operation: 51-46=5, Resulting Numbers: [3, 5] Generated Node #0,2,3: 15:[3, 5] Operation: 51-46=5 Exploring Operation: 51/3=17, Resulting Numbers: [46, 17] Generated Node #0,2,4: 15:[46, 17] Operation: 51/3=17 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 15:[3, 5], Operations: ['53-50=3', '51-46=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[50, 46, 51, 53], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [46, 51, 3] Generated Node #0,2: 15:[46, 51, 3] Operation: 53-50=3 Moving to Node #0,2 Current State: 15:[46, 51, 3], Operations: ['53-50=3'] Exploring Operation: 51-46=5, Resulting Numbers: [3, 5] Generated Node #0,2,3: 15:[3, 5] Operation: 51-46=5 Moving to Node #0,2,3 Current State: 15:[3, 5], Operations: ['53-50=3', '51-46=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 83, 7, 79, 18 ]
84
[ "83+7=90", "90/18=5", "79+5=84" ]
Current State: 84:[83, 7, 79, 18], Operations: [] Exploring Operation: 83+7=90, Resulting Numbers: [79, 18, 90] Generated Node #2: [79, 18, 90] from Operation: 83+7=90 Current State: 84:[79, 18, 90], Operations: ['83+7=90'] Exploring Operation: 90/18=5, Resulting Numbers: [79, 5] Generated Node #3: [79, 5] from Operation: 90/18=5 Current State: 84:[79, 5], Operations: ['83+7=90', '90/18=5'] Exploring Operation: 79+5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[83, 7, 79, 18], Operations: [] Exploring Operation: 83-79=4, Resulting Numbers: [7, 18, 4] Generated Node #0,0: 84:[7, 18, 4] Operation: 83-79=4 Exploring Operation: 18-7=11, Resulting Numbers: [83, 79, 11] Generated Node #0,1: 84:[83, 79, 11] Operation: 18-7=11 Exploring Operation: 7+79=86, Resulting Numbers: [83, 18, 86] Generated Node #0,2: 84:[83, 18, 86] Operation: 7+79=86 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[7, 18, 4], Operations: ['83-79=4'] Exploring Operation: 18+4=22, Resulting Numbers: [7, 22] Generated Node #0,0,0: 84:[7, 22] Operation: 18+4=22 Exploring Operation: 18-4=14, Resulting Numbers: [7, 14] Generated Node #0,0,1: 84:[7, 14] Operation: 18-4=14 Exploring Operation: 18-7=11, Resulting Numbers: [4, 11] Generated Node #0,0,2: 84:[4, 11] Operation: 18-7=11 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 84:[7, 14], Operations: ['83-79=4', '18-4=14'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,84 unequal: No Solution No 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: 84:[7, 22], Operations: ['83-79=4', '18+4=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,84 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,84 unequal: No Solution No 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: 84:[4, 11], Operations: ['83-79=4', '18-7=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,84 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,84 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[83, 18, 86], Operations: ['7+79=86'] Exploring Operation: 86-18=68, Resulting Numbers: [83, 68] Generated Node #0,2,0: 84:[83, 68] Operation: 86-18=68 Exploring Operation: 86-83=3, Resulting Numbers: [18, 3] Generated Node #0,2,1: 84:[18, 3] Operation: 86-83=3 Exploring Operation: 83+18=101, Resulting Numbers: [86, 101] Generated Node #0,2,2: 84:[86, 101] Operation: 83+18=101 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 84:[18, 3], Operations: ['7+79=86', '86-83=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,84 unequal: No Solution No 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: 84:[83, 68], Operations: ['7+79=86', '86-18=68'] Exploring Operation: 83-68=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 83+68=151, Resulting Numbers: [151] 151,84 unequal: No Solution Exploring Operation: 83*68=5644, Resulting Numbers: [5644] 5644,84 unequal: No Solution No 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: 84:[86, 101], Operations: ['7+79=86', '83+18=101'] Exploring Operation: 86*101=8686, Resulting Numbers: [8686] 8686,84 unequal: No Solution Exploring Operation: 86+101=187, Resulting Numbers: [187] 187,84 unequal: No Solution Exploring Operation: 101-86=15, Resulting Numbers: [15] 15,84 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[83, 79, 11], Operations: ['18-7=11'] Exploring Operation: 79+11=90, Resulting Numbers: [83, 90] Generated Node #0,1,0: 84:[83, 90] Operation: 79+11=90 Exploring Operation: 83+11=94, Resulting Numbers: [79, 94] Generated Node #0,1,1: 84:[79, 94] Operation: 83+11=94 Exploring Operation: 83-79=4, Resulting Numbers: [11, 4] Generated Node #0,1,2: 84:[11, 4] Operation: 83-79=4 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 84:[11, 4], Operations: ['18-7=11', '83-79=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,84 unequal: No Solution No 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: 84:[83, 90], Operations: ['18-7=11', '79+11=90'] Exploring Operation: 90-83=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 83*90=7470, Resulting Numbers: [7470] 7470,84 unequal: No Solution Exploring Operation: 83+90=173, Resulting Numbers: [173] 173,84 unequal: No Solution No 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: 84:[79, 94], Operations: ['18-7=11', '83+11=94'] Exploring Operation: 79+94=173, Resulting Numbers: [173] 173,84 unequal: No Solution Exploring Operation: 94-79=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 79*94=7426, Resulting Numbers: [7426] 7426,84 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_3
mult_heuristic
[ 52, 48, 9, 1 ]
92
[ "52+48=100", "9-1=8", "100-8=92" ]
Current State: 92:[52, 48, 9, 1], Operations: [] Exploring Operation: 52+48=100, Resulting Numbers: [9, 1, 100] Generated Node #2: [9, 1, 100] from Operation: 52+48=100 Current State: 92:[9, 1, 100], Operations: ['52+48=100'] Exploring Operation: 9-1=8, Resulting Numbers: [100, 8] Generated Node #3: [100, 8] from Operation: 9-1=8 Current State: 92:[100, 8], Operations: ['52+48=100', '9-1=8'] Exploring Operation: 100-8=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[52, 48, 9, 1], Operations: [] Exploring Operation: 52-9=43, Resulting Numbers: [48, 1, 43] Generated Node #0,0: 92:[48, 1, 43] Operation: 52-9=43 Exploring Operation: 52-1=51, Resulting Numbers: [48, 9, 51] Generated Node #0,1: 92:[48, 9, 51] Operation: 52-1=51 Exploring Operation: 9-1=8, Resulting Numbers: [52, 48, 8] Generated Node #0,2: 92:[52, 48, 8] Operation: 9-1=8 Exploring Operation: 52-48=4, Resulting Numbers: [9, 1, 4] Generated Node #0,3: 92:[9, 1, 4] Operation: 52-48=4 Exploring Operation: 48-1=47, Resulting Numbers: [52, 9, 47] Generated Node #0,4: 92:[52, 9, 47] Operation: 48-1=47 Moving to Node #0,0 Current State: 92:[48, 1, 43], Operations: ['52-9=43'] Exploring Operation: 1+43=44, Resulting Numbers: [48, 44] Generated Node #0,0,0: 92:[48, 44] Operation: 1+43=44 Exploring Operation: 48+43=91, Resulting Numbers: [1, 91] Generated Node #0,0,1: 92:[1, 91] Operation: 48+43=91 Exploring Operation: 48*1=48, Resulting Numbers: [43, 48] Generated Node #0,0,2: 92:[43, 48] Operation: 48*1=48 Exploring Operation: 48-1=47, Resulting Numbers: [43, 47] Generated Node #0,0,3: 92:[43, 47] Operation: 48-1=47 Exploring Operation: 48-43=5, Resulting Numbers: [1, 5] Generated Node #0,0,4: 92:[1, 5] Operation: 48-43=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[1, 91], Operations: ['52-9=43', '48+43=91'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,92 unequal: No Solution Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,92 unequal: No Solution Exploring Operation: 1+91=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[52, 48, 9, 1], Operations: [] Exploring Operation: 52-9=43, Resulting Numbers: [48, 1, 43] Generated Node #0,0: 92:[48, 1, 43] Operation: 52-9=43 Moving to Node #0,0 Current State: 92:[48, 1, 43], Operations: ['52-9=43'] Exploring Operation: 48+43=91, Resulting Numbers: [1, 91] Generated Node #0,0,1: 92:[1, 91] Operation: 48+43=91 Moving to Node #0,0,1 Current State: 92:[1, 91], Operations: ['52-9=43', '48+43=91'] Exploring Operation: 1+91=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 36, 2, 36, 60 ]
57
[ "36/36=1", "60-2=58", "58-1=57" ]
Current State: 57:[36, 2, 36, 60], Operations: [] Exploring Operation: 36/36=1, Resulting Numbers: [2, 60, 1] Generated Node #2: [2, 60, 1] from Operation: 36/36=1 Current State: 57:[2, 60, 1], Operations: ['36/36=1'] Exploring Operation: 60-2=58, Resulting Numbers: [1, 58] Generated Node #3: [1, 58] from Operation: 60-2=58 Current State: 57:[1, 58], Operations: ['36/36=1', '60-2=58'] Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[36, 2, 36, 60], Operations: [] Exploring Operation: 36-36=0, Resulting Numbers: [2, 60, 0] Generated Node #0,0: 57:[2, 60, 0] Operation: 36-36=0 Exploring Operation: 36/2=18, Resulting Numbers: [36, 60, 18] Generated Node #0,1: 57:[36, 60, 18] Operation: 36/2=18 Exploring Operation: 36/2=18, Resulting Numbers: [36, 60, 18] Generated Node #0,2: 57:[36, 60, 18] Operation: 36/2=18 Exploring Operation: 36/36=1, Resulting Numbers: [2, 60, 1] Generated Node #0,3: 57:[2, 60, 1] Operation: 36/36=1 Exploring Operation: 36+36=72, Resulting Numbers: [2, 60, 72] Generated Node #0,4: 57:[2, 60, 72] Operation: 36+36=72 Start Sub Search at level 1: Moving to Node #0,3 Current State: 57:[2, 60, 1], Operations: ['36/36=1'] Exploring Operation: 2+1=3, Resulting Numbers: [60, 3] Generated Node #0,3,0: 57:[60, 3] Operation: 2+1=3 Exploring Operation: 60-1=59, Resulting Numbers: [2, 59] Generated Node #0,3,1: 57:[2, 59] Operation: 60-1=59 Exploring Operation: 2/1=2, Resulting Numbers: [60, 2] Generated Node #0,3,2: 57:[60, 2] Operation: 2/1=2 Exploring Operation: 2*1=2, Resulting Numbers: [60, 2] Generated Node #0,3,3: 57:[60, 2] Operation: 2*1=2 Exploring Operation: 60-2=58, Resulting Numbers: [1, 58] Generated Node #0,3,4: 57:[1, 58] Operation: 60-2=58 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 57:[60, 3], Operations: ['36/36=1', '2+1=3'] Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,57 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[36, 2, 36, 60], Operations: [] Exploring Operation: 36/36=1, Resulting Numbers: [2, 60, 1] Generated Node #0,3: 57:[2, 60, 1] Operation: 36/36=1 Moving to Node #0,3 Current State: 57:[2, 60, 1], Operations: ['36/36=1'] Exploring Operation: 2+1=3, Resulting Numbers: [60, 3] Generated Node #0,3,0: 57:[60, 3] Operation: 2+1=3 Moving to Node #0,3,0 Current State: 57:[60, 3], Operations: ['36/36=1', '2+1=3'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 40, 55, 8, 2 ]
79
[ "40+55=95", "8*2=16", "95-16=79" ]
Current State: 79:[40, 55, 8, 2], Operations: [] Exploring Operation: 40+55=95, Resulting Numbers: [8, 2, 95] Generated Node #2: [8, 2, 95] from Operation: 40+55=95 Current State: 79:[8, 2, 95], Operations: ['40+55=95'] Exploring Operation: 8*2=16, Resulting Numbers: [95, 16] Generated Node #3: [95, 16] from Operation: 8*2=16 Current State: 79:[95, 16], Operations: ['40+55=95', '8*2=16'] Exploring Operation: 95-16=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[40, 55, 8, 2], Operations: [] Exploring Operation: 40*2=80, Resulting Numbers: [55, 8, 80] Generated Node #0,0: 79:[55, 8, 80] Operation: 40*2=80 Moving to Node #0,0 Current State: 79:[55, 8, 80], Operations: ['40*2=80'] Exploring Operation: 55+8=63, Resulting Numbers: [80, 63] Generated Node #0,0,0: 79:[80, 63] Operation: 55+8=63 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[80, 63], Operations: ['40*2=80', '55+8=63'] Exploring Operation: 80-63=17, Resulting Numbers: [17] 17,79 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
[ 28, 9, 47, 8 ]
92
[ "28+9=37", "47+8=55", "37+55=92" ]
Current State: 92:[28, 9, 47, 8], Operations: [] Exploring Operation: 28+9=37, Resulting Numbers: [47, 8, 37] Generated Node #2: [47, 8, 37] from Operation: 28+9=37 Current State: 92:[47, 8, 37], Operations: ['28+9=37'] Exploring Operation: 47+8=55, Resulting Numbers: [37, 55] Generated Node #3: [37, 55] from Operation: 47+8=55 Current State: 92:[37, 55], Operations: ['28+9=37', '47+8=55'] Exploring Operation: 37+55=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[28, 9, 47, 8], Operations: [] Exploring Operation: 9-8=1, Resulting Numbers: [28, 47, 1] Generated Node #0,0: 92:[28, 47, 1] Operation: 9-8=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[28, 47, 1], Operations: ['9-8=1'] Exploring Operation: 47-28=19, Resulting Numbers: [1, 19] Generated Node #0,0,0: 92:[1, 19] Operation: 47-28=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[1, 19], Operations: ['9-8=1', '47-28=19'] Exploring Operation: 1+19=20, Resulting Numbers: [20] 20,92 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 No solution found.
0
hs_1
sum_heuristic
[ 42, 6, 53, 14 ]
74
[ "42/6=7", "53+14=67", "7+67=74" ]
Current State: 74:[42, 6, 53, 14], Operations: [] Exploring Operation: 42/6=7, Resulting Numbers: [53, 14, 7] Generated Node #2: [53, 14, 7] from Operation: 42/6=7 Current State: 74:[53, 14, 7], Operations: ['42/6=7'] Exploring Operation: 53+14=67, Resulting Numbers: [7, 67] Generated Node #3: [7, 67] from Operation: 53+14=67 Current State: 74:[7, 67], Operations: ['42/6=7', '53+14=67'] Exploring Operation: 7+67=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[42, 6, 53, 14], Operations: [] Exploring Operation: 53-14=39, Resulting Numbers: [42, 6, 39] Generated Node #0,0: 74:[42, 6, 39] Operation: 53-14=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[42, 6, 39], Operations: ['53-14=39'] Exploring Operation: 42-6=36, Resulting Numbers: [39, 36] Generated Node #0,0,0: 74:[39, 36] Operation: 42-6=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[39, 36], Operations: ['53-14=39', '42-6=36'] Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,74 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
[ 69, 46, 24, 7 ]
98
[ "69+46=115", "24-7=17", "115-17=98" ]
Current State: 98:[69, 46, 24, 7], Operations: [] Exploring Operation: 69+46=115, Resulting Numbers: [24, 7, 115] Generated Node #2: [24, 7, 115] from Operation: 69+46=115 Current State: 98:[24, 7, 115], Operations: ['69+46=115'] Exploring Operation: 24-7=17, Resulting Numbers: [115, 17] Generated Node #3: [115, 17] from Operation: 24-7=17 Current State: 98:[115, 17], Operations: ['69+46=115', '24-7=17'] Exploring Operation: 115-17=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[69, 46, 24, 7], Operations: [] Exploring Operation: 69+24=93, Resulting Numbers: [46, 7, 93] Generated Node #0,0: 98:[46, 7, 93] Operation: 69+24=93 Exploring Operation: 69-24=45, Resulting Numbers: [46, 7, 45] Generated Node #0,1: 98:[46, 7, 45] Operation: 69-24=45 Moving to Node #0,1 Current State: 98:[46, 7, 45], Operations: ['69-24=45'] Exploring Operation: 46-45=1, Resulting Numbers: [7, 1] Generated Node #0,1,0: 98:[7, 1] Operation: 46-45=1 Exploring Operation: 7+45=52, Resulting Numbers: [46, 52] Generated Node #0,1,1: 98:[46, 52] Operation: 7+45=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 98:[7, 1], Operations: ['69-24=45', '46-45=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,98 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 #0,1,1 Current State: 98:[46, 52], Operations: ['69-24=45', '7+45=52'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 46+52=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[69, 46, 24, 7], Operations: [] Exploring Operation: 69-24=45, Resulting Numbers: [46, 7, 45] Generated Node #0,1: 98:[46, 7, 45] Operation: 69-24=45 Moving to Node #0,1 Current State: 98:[46, 7, 45], Operations: ['69-24=45'] Exploring Operation: 7+45=52, Resulting Numbers: [46, 52] Generated Node #0,1,1: 98:[46, 52] Operation: 7+45=52 Moving to Node #0,1,1 Current State: 98:[46, 52], Operations: ['69-24=45', '7+45=52'] Exploring Operation: 46+52=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 24, 23, 17, 82 ]
99
[ "24-23=1", "17+82=99", "1*99=99" ]
Current State: 99:[24, 23, 17, 82], Operations: [] Exploring Operation: 24-23=1, Resulting Numbers: [17, 82, 1] Generated Node #2: [17, 82, 1] from Operation: 24-23=1 Current State: 99:[17, 82, 1], Operations: ['24-23=1'] Exploring Operation: 17+82=99, Resulting Numbers: [1, 99] Generated Node #3: [1, 99] from Operation: 17+82=99 Current State: 99:[1, 99], Operations: ['24-23=1', '17+82=99'] Exploring Operation: 1*99=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[24, 23, 17, 82], Operations: [] Exploring Operation: 17+82=99, Resulting Numbers: [24, 23, 99] Generated Node #0,0: 99:[24, 23, 99] Operation: 17+82=99 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[24, 23, 99], Operations: ['17+82=99'] Exploring Operation: 24-23=1, Resulting Numbers: [99, 1] Generated Node #0,0,0: 99:[99, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 99:[99, 1], Operations: ['17+82=99', '24-23=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[24, 23, 17, 82], Operations: [] Exploring Operation: 17+82=99, Resulting Numbers: [24, 23, 99] Generated Node #0,0: 99:[24, 23, 99] Operation: 17+82=99 Moving to Node #0,0 Current State: 99:[24, 23, 99], Operations: ['17+82=99'] Exploring Operation: 24-23=1, Resulting Numbers: [99, 1] Generated Node #0,0,0: 99:[99, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 99:[99, 1], Operations: ['17+82=99', '24-23=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 95, 58, 72, 21 ]
60
[ "95+58=153", "72+21=93", "153-93=60" ]
Current State: 60:[95, 58, 72, 21], Operations: [] Exploring Operation: 95+58=153, Resulting Numbers: [72, 21, 153] Generated Node #2: [72, 21, 153] from Operation: 95+58=153 Current State: 60:[72, 21, 153], Operations: ['95+58=153'] Exploring Operation: 72+21=93, Resulting Numbers: [153, 93] Generated Node #3: [153, 93] from Operation: 72+21=93 Current State: 60:[153, 93], Operations: ['95+58=153', '72+21=93'] Exploring Operation: 153-93=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[95, 58, 72, 21], Operations: [] Exploring Operation: 95-58=37, Resulting Numbers: [72, 21, 37] Generated Node #0,0: 60:[72, 21, 37] Operation: 95-58=37 Exploring Operation: 95-72=23, Resulting Numbers: [58, 21, 23] Generated Node #0,1: 60:[58, 21, 23] Operation: 95-72=23 Exploring Operation: 72-58=14, Resulting Numbers: [95, 21, 14] Generated Node #0,2: 60:[95, 21, 14] Operation: 72-58=14 Exploring Operation: 95-21=74, Resulting Numbers: [58, 72, 74] Generated Node #0,3: 60:[58, 72, 74] Operation: 95-21=74 Moving to Node #0,1 Current State: 60:[58, 21, 23], Operations: ['95-72=23'] Exploring Operation: 58-23=35, Resulting Numbers: [21, 35] Generated Node #0,1,0: 60:[21, 35] Operation: 58-23=35 Exploring Operation: 58-21=37, Resulting Numbers: [23, 37] Generated Node #0,1,1: 60:[23, 37] Operation: 58-21=37 Exploring Operation: 23-21=2, Resulting Numbers: [58, 2] Generated Node #0,1,2: 60:[58, 2] Operation: 23-21=2 Exploring Operation: 21+23=44, Resulting Numbers: [58, 44] Generated Node #0,1,3: 60:[58, 44] Operation: 21+23=44 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[58, 2], Operations: ['95-72=23', '23-21=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,60 unequal: No Solution Exploring Operation: 58*2=116, Resulting Numbers: [116] 116,60 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[95, 58, 72, 21], Operations: [] Exploring Operation: 95-72=23, Resulting Numbers: [58, 21, 23] Generated Node #0,1: 60:[58, 21, 23] Operation: 95-72=23 Moving to Node #0,1 Current State: 60:[58, 21, 23], Operations: ['95-72=23'] Exploring Operation: 23-21=2, Resulting Numbers: [58, 2] Generated Node #0,1,2: 60:[58, 2] Operation: 23-21=2 Moving to Node #0,1,2 Current State: 60:[58, 2], Operations: ['95-72=23', '23-21=2'] Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 3, 75, 59, 97 ]
39
[ "97-59=38", "3*38=114", "114-75=39" ]
Current State: 39:[3, 75, 59, 97], Operations: [] Exploring Operation: 97-59=38, Resulting Numbers: [3, 75, 38] Generated Node #2: [3, 75, 38] from Operation: 97-59=38 Current State: 39:[3, 75, 38], Operations: ['97-59=38'] Exploring Operation: 3*38=114, Resulting Numbers: [75, 114] Generated Node #3: [75, 114] from Operation: 3*38=114 Current State: 39:[75, 114], Operations: ['97-59=38', '3*38=114'] Exploring Operation: 114-75=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[3, 75, 59, 97], Operations: [] Exploring Operation: 97-75=22, Resulting Numbers: [3, 59, 22] Generated Node #0,0: 39:[3, 59, 22] Operation: 97-75=22 Exploring Operation: 97-59=38, Resulting Numbers: [3, 75, 38] Generated Node #0,1: 39:[3, 75, 38] Operation: 97-59=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[3, 59, 22], Operations: ['97-75=22'] Exploring Operation: 59-3=56, Resulting Numbers: [22, 56] Generated Node #0,0,0: 39:[22, 56] Operation: 59-3=56 Exploring Operation: 59-22=37, Resulting Numbers: [3, 37] Generated Node #0,0,1: 39:[3, 37] Operation: 59-22=37 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[3, 37], Operations: ['97-75=22', '59-22=37'] Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,39 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[22, 56], Operations: ['97-75=22', '59-3=56'] Exploring Operation: 22+56=78, Resulting Numbers: [78] 78,39 unequal: No Solution Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,39 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: 39:[3, 75, 38], Operations: ['97-59=38'] Exploring Operation: 75/3=25, Resulting Numbers: [38, 25] Generated Node #0,1,0: 39:[38, 25] Operation: 75/3=25 Exploring Operation: 75-38=37, Resulting Numbers: [3, 37] Generated Node #0,1,1: 39:[3, 37] Operation: 75-38=37 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[3, 37], Operations: ['97-59=38', '75-38=37'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[38, 25], Operations: ['97-59=38', '75/3=25'] Exploring Operation: 38+25=63, Resulting Numbers: [63] 63,39 unequal: No Solution Exploring Operation: 38-25=13, Resulting Numbers: [13] 13,39 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
[ 47, 87, 14, 94 ]
26
[ "47+87=134", "14+94=108", "134-108=26" ]
Current State: 26:[47, 87, 14, 94], Operations: [] Exploring Operation: 47+87=134, Resulting Numbers: [14, 94, 134] Generated Node #2: [14, 94, 134] from Operation: 47+87=134 Current State: 26:[14, 94, 134], Operations: ['47+87=134'] Exploring Operation: 14+94=108, Resulting Numbers: [134, 108] Generated Node #3: [134, 108] from Operation: 14+94=108 Current State: 26:[134, 108], Operations: ['47+87=134', '14+94=108'] Exploring Operation: 134-108=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[47, 87, 14, 94], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [47, 14, 7] Generated Node #0,0: 26:[47, 14, 7] Operation: 94-87=7 Exploring Operation: 94/47=2, Resulting Numbers: [87, 14, 2] Generated Node #0,1: 26:[87, 14, 2] Operation: 94/47=2 Exploring Operation: 87-47=40, Resulting Numbers: [14, 94, 40] Generated Node #0,2: 26:[14, 94, 40] Operation: 87-47=40 Moving to Node #0,0 Current State: 26:[47, 14, 7], Operations: ['94-87=7'] Exploring Operation: 47-14=33, Resulting Numbers: [7, 33] Generated Node #0,0,0: 26:[7, 33] Operation: 47-14=33 Exploring Operation: 47-7=40, Resulting Numbers: [14, 40] Generated Node #0,0,1: 26:[14, 40] Operation: 47-7=40 Exploring Operation: 14/7=2, Resulting Numbers: [47, 2] Generated Node #0,0,2: 26:[47, 2] Operation: 14/7=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[7, 33], Operations: ['94-87=7', '47-14=33'] Exploring Operation: 7+33=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 7*33=231, Resulting Numbers: [231] 231,26 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[47, 87, 14, 94], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [47, 14, 7] Generated Node #0,0: 26:[47, 14, 7] Operation: 94-87=7 Moving to Node #0,0 Current State: 26:[47, 14, 7], Operations: ['94-87=7'] Exploring Operation: 47-14=33, Resulting Numbers: [7, 33] Generated Node #0,0,0: 26:[7, 33] Operation: 47-14=33 Moving to Node #0,0,0 Current State: 26:[7, 33], Operations: ['94-87=7', '47-14=33'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 97, 48, 84, 27 ]
62
[ "97-48=49", "84+27=111", "111-49=62" ]
Current State: 62:[97, 48, 84, 27], Operations: [] Exploring Operation: 97-48=49, Resulting Numbers: [84, 27, 49] Generated Node #2: [84, 27, 49] from Operation: 97-48=49 Current State: 62:[84, 27, 49], Operations: ['97-48=49'] Exploring Operation: 84+27=111, Resulting Numbers: [49, 111] Generated Node #3: [49, 111] from Operation: 84+27=111 Current State: 62:[49, 111], Operations: ['97-48=49', '84+27=111'] Exploring Operation: 111-49=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[97, 48, 84, 27], Operations: [] Exploring Operation: 97-48=49, Resulting Numbers: [84, 27, 49] Generated Node #0,0: 62:[84, 27, 49] Operation: 97-48=49 Exploring Operation: 97-84=13, Resulting Numbers: [48, 27, 13] Generated Node #0,1: 62:[48, 27, 13] Operation: 97-84=13 Moving to Node #0,1 Current State: 62:[48, 27, 13], Operations: ['97-84=13'] Exploring Operation: 48-13=35, Resulting Numbers: [27, 35] Generated Node #0,1,0: 62:[27, 35] Operation: 48-13=35 Exploring Operation: 48+13=61, Resulting Numbers: [27, 61] Generated Node #0,1,1: 62:[27, 61] Operation: 48+13=61 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[27, 61], Operations: ['97-84=13', '48+13=61'] Exploring Operation: 61-27=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 27+61=88, Resulting Numbers: [88] 88,62 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 #0,1,0 Current State: 62:[27, 35], Operations: ['97-84=13', '48-13=35'] Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,62 unequal: No Solution Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[97, 48, 84, 27], Operations: [] Exploring Operation: 97-84=13, Resulting Numbers: [48, 27, 13] Generated Node #0,1: 62:[48, 27, 13] Operation: 97-84=13 Moving to Node #0,1 Current State: 62:[48, 27, 13], Operations: ['97-84=13'] Exploring Operation: 48-13=35, Resulting Numbers: [27, 35] Generated Node #0,1,0: 62:[27, 35] Operation: 48-13=35 Moving to Node #0,1,0 Current State: 62:[27, 35], Operations: ['97-84=13', '48-13=35'] Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 12, 11, 71, 2 ]
68
[ "12-11=1", "71-2=69", "69-1=68" ]
Current State: 68:[12, 11, 71, 2], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [71, 2, 1] Generated Node #2: [71, 2, 1] from Operation: 12-11=1 Current State: 68:[71, 2, 1], Operations: ['12-11=1'] Exploring Operation: 71-2=69, Resulting Numbers: [1, 69] Generated Node #3: [1, 69] from Operation: 71-2=69 Current State: 68:[1, 69], Operations: ['12-11=1', '71-2=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[12, 11, 71, 2], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [71, 2, 1] Generated Node #0,0: 68:[71, 2, 1] Operation: 12-11=1 Exploring Operation: 12+11=23, Resulting Numbers: [71, 2, 23] Generated Node #0,1: 68:[71, 2, 23] Operation: 12+11=23 Moving to Node #0,0 Current State: 68:[71, 2, 1], Operations: ['12-11=1'] Exploring Operation: 71-2=69, Resulting Numbers: [1, 69] Generated Node #0,0,0: 68:[1, 69] Operation: 71-2=69 Exploring Operation: 71-1=70, Resulting Numbers: [2, 70] Generated Node #0,0,1: 68:[2, 70] Operation: 71-1=70 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[1, 69], Operations: ['12-11=1', '71-2=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[12, 11, 71, 2], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [71, 2, 1] Generated Node #0,0: 68:[71, 2, 1] Operation: 12-11=1 Moving to Node #0,0 Current State: 68:[71, 2, 1], Operations: ['12-11=1'] Exploring Operation: 71-2=69, Resulting Numbers: [1, 69] Generated Node #0,0,0: 68:[1, 69] Operation: 71-2=69 Moving to Node #0,0,0 Current State: 68:[1, 69], Operations: ['12-11=1', '71-2=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 8, 7, 22, 92 ]
46
[ "22-8=14", "7*92=644", "644/14=46" ]
Current State: 46:[8, 7, 22, 92], Operations: [] Exploring Operation: 22-8=14, Resulting Numbers: [7, 92, 14] Generated Node #2: [7, 92, 14] from Operation: 22-8=14 Current State: 46:[7, 92, 14], Operations: ['22-8=14'] Exploring Operation: 7*92=644, Resulting Numbers: [14, 644] Generated Node #3: [14, 644] from Operation: 7*92=644 Current State: 46:[14, 644], Operations: ['22-8=14', '7*92=644'] Exploring Operation: 644/14=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[8, 7, 22, 92], Operations: [] Exploring Operation: 92-7=85, Resulting Numbers: [8, 22, 85] Generated Node #0,0: 46:[8, 22, 85] Operation: 92-7=85 Exploring Operation: 8+7=15, Resulting Numbers: [22, 92, 15] Generated Node #0,1: 46:[22, 92, 15] Operation: 8+7=15 Exploring Operation: 92-8=84, Resulting Numbers: [7, 22, 84] Generated Node #0,2: 46:[7, 22, 84] Operation: 92-8=84 Exploring Operation: 8-7=1, Resulting Numbers: [22, 92, 1] Generated Node #0,3: 46:[22, 92, 1] Operation: 8-7=1 Exploring Operation: 92-22=70, Resulting Numbers: [8, 7, 70] Generated Node #0,4: 46:[8, 7, 70] Operation: 92-22=70 Moving to Node #0,4 Current State: 46:[8, 7, 70], Operations: ['92-22=70'] Exploring Operation: 70-8=62, Resulting Numbers: [7, 62] Generated Node #0,4,0: 46:[7, 62] Operation: 70-8=62 Exploring Operation: 70/7=10, Resulting Numbers: [8, 10] Generated Node #0,4,1: 46:[8, 10] Operation: 70/7=10 Exploring Operation: 8+7=15, Resulting Numbers: [70, 15] Generated Node #0,4,2: 46:[70, 15] Operation: 8+7=15 Exploring Operation: 8-7=1, Resulting Numbers: [70, 1] Generated Node #0,4,3: 46:[70, 1] Operation: 8-7=1 Exploring Operation: 70-7=63, Resulting Numbers: [8, 63] Generated Node #0,4,4: 46:[8, 63] Operation: 70-7=63 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 46:[8, 10], Operations: ['92-22=70', '70/7=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,46 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 46:[7, 62], Operations: ['92-22=70', '70-8=62'] Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,46 unequal: No Solution Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 7*62=434, Resulting Numbers: [434] 434,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 46:[8, 63], Operations: ['92-22=70', '70-7=63'] Exploring Operation: 8+63=71, Resulting Numbers: [71] 71,46 unequal: No Solution Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 8*63=504, Resulting Numbers: [504] 504,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 46:[70, 1], Operations: ['92-22=70', '8-7=1'] Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,46 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 46:[70, 15], Operations: ['92-22=70', '8+7=15'] Exploring Operation: 70+15=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 70*15=1050, Resulting Numbers: [1050] 1050,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 46:[7, 22, 84], Operations: ['92-8=84'] Exploring Operation: 22-7=15, Resulting Numbers: [84, 15] Generated Node #0,2,0: 46:[84, 15] Operation: 22-7=15 Exploring Operation: 84-7=77, Resulting Numbers: [22, 77] Generated Node #0,2,1: 46:[22, 77] Operation: 84-7=77 Exploring Operation: 84-22=62, Resulting Numbers: [7, 62] Generated Node #0,2,2: 46:[7, 62] Operation: 84-22=62 Exploring Operation: 7+22=29, Resulting Numbers: [84, 29] Generated Node #0,2,3: 46:[84, 29] Operation: 7+22=29 Exploring Operation: 84/7=12, Resulting Numbers: [22, 12] Generated Node #0,2,4: 46:[22, 12] Operation: 84/7=12 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 46:[22, 12], Operations: ['92-8=84', '84/7=12'] Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,46 unequal: No Solution Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,46 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 46:[7, 62], Operations: ['92-8=84', '84-22=62'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 7*62=434, Resulting Numbers: [434] 434,46 unequal: No Solution Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 46:[22, 77], Operations: ['92-8=84', '84-7=77'] Exploring Operation: 22*77=1694, Resulting Numbers: [1694] 1694,46 unequal: No Solution Exploring Operation: 77-22=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 22+77=99, Resulting Numbers: [99] 99,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 46:[84, 29], Operations: ['92-8=84', '7+22=29'] Exploring Operation: 84+29=113, Resulting Numbers: [113] 113,46 unequal: No Solution Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 84*29=2436, Resulting Numbers: [2436] 2436,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 46:[84, 15], Operations: ['92-8=84', '22-7=15'] Exploring Operation: 84*15=1260, Resulting Numbers: [1260] 1260,46 unequal: No Solution Exploring Operation: 84-15=69, Resulting Numbers: [69] 69,46 unequal: No Solution Exploring Operation: 84+15=99, Resulting Numbers: [99] 99,46 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: 46:[8, 22, 85], Operations: ['92-7=85'] Exploring Operation: 8+85=93, Resulting Numbers: [22, 93] Generated Node #0,0,0: 46:[22, 93] Operation: 8+85=93 Exploring Operation: 8+22=30, Resulting Numbers: [85, 30] Generated Node #0,0,1: 46:[85, 30] Operation: 8+22=30 Exploring Operation: 85-8=77, Resulting Numbers: [22, 77] Generated Node #0,0,2: 46:[22, 77] Operation: 85-8=77 Exploring Operation: 85-22=63, Resulting Numbers: [8, 63] Generated Node #0,0,3: 46:[8, 63] Operation: 85-22=63 Exploring Operation: 22-8=14, Resulting Numbers: [85, 14] Generated Node #0,0,4: 46:[85, 14] Operation: 22-8=14 Moving to Node #0,3 Current State: 46:[22, 92, 1], Operations: ['8-7=1'] Exploring Operation: 22/1=22, Resulting Numbers: [92, 22] Generated Node #0,3,0: 46:[92, 22] Operation: 22/1=22 Exploring Operation: 22+1=23, Resulting Numbers: [92, 23] Generated Node #0,3,1: 46:[92, 23] Operation: 22+1=23 Exploring Operation: 22*1=22, Resulting Numbers: [92, 22] Generated Node #0,3,2: 46:[92, 22] Operation: 22*1=22 Exploring Operation: 92-1=91, Resulting Numbers: [22, 91] Generated Node #0,3,3: 46:[22, 91] Operation: 92-1=91 Exploring Operation: 92-22=70, Resulting Numbers: [1, 70] Generated Node #0,3,4: 46:[1, 70] Operation: 92-22=70 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 46:[1, 70], Operations: ['8-7=1', '92-22=70'] Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 1*70=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 1+70=71, Resulting Numbers: [71] 71,46 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 46:[92, 23], Operations: ['8-7=1', '22+1=23'] Exploring Operation: 92-23=69, Resulting Numbers: [69] 69,46 unequal: No Solution Exploring Operation: 92+23=115, Resulting Numbers: [115] 115,46 unequal: No Solution Exploring Operation: 92*23=2116, Resulting Numbers: [2116] 2116,46 unequal: No Solution Exploring Operation: 92/23=4, Resulting Numbers: [4] 4,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 46:[22, 91], Operations: ['8-7=1', '92-1=91'] Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,46 unequal: No Solution Exploring Operation: 22+91=113, Resulting Numbers: [113] 113,46 unequal: No Solution Exploring Operation: 22*91=2002, Resulting Numbers: [2002] 2002,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 46:[92, 22], Operations: ['8-7=1', '22/1=22'] Exploring Operation: 92-22=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 92+22=114, Resulting Numbers: [114] 114,46 unequal: No Solution Exploring Operation: 92*22=2024, Resulting Numbers: [2024] 2024,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 46:[92, 22], Operations: ['8-7=1', '22*1=22'] Exploring Operation: 92+22=114, Resulting Numbers: [114] 114,46 unequal: No Solution Exploring Operation: 92*22=2024, Resulting Numbers: [2024] 2024,46 unequal: No Solution Exploring Operation: 92-22=70, Resulting Numbers: [70] 70,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 46:[22, 92, 15], Operations: ['8+7=15'] Exploring Operation: 92+15=107, Resulting Numbers: [22, 107] Generated Node #0,1,0: 46:[22, 107] Operation: 92+15=107 Exploring Operation: 22-15=7, Resulting Numbers: [92, 7] Generated Node #0,1,1: 46:[92, 7] Operation: 22-15=7 Exploring Operation: 92-15=77, Resulting Numbers: [22, 77] Generated Node #0,1,2: 46:[22, 77] Operation: 92-15=77 Exploring Operation: 22+15=37, Resulting Numbers: [92, 37] Generated Node #0,1,3: 46:[92, 37] Operation: 22+15=37 Exploring Operation: 92-22=70, Resulting Numbers: [15, 70] Generated Node #0,1,4: 46:[15, 70] Operation: 92-22=70 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[22, 77], Operations: ['8+7=15', '92-15=77'] Exploring Operation: 77-22=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 22*77=1694, Resulting Numbers: [1694] 1694,46 unequal: No Solution Exploring Operation: 22+77=99, Resulting Numbers: [99] 99,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 46:[15, 70], Operations: ['8+7=15', '92-22=70'] Exploring Operation: 15+70=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 15*70=1050, Resulting Numbers: [1050] 1050,46 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 46:[92, 7], Operations: ['8+7=15', '22-15=7'] Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 92*7=644, Resulting Numbers: [644] 644,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 46:[92, 37], Operations: ['8+7=15', '22+15=37'] Exploring Operation: 92+37=129, Resulting Numbers: [129] 129,46 unequal: No Solution Exploring Operation: 92*37=3404, Resulting Numbers: [3404] 3404,46 unequal: No Solution Exploring Operation: 92-37=55, Resulting Numbers: [55] 55,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[22, 107], Operations: ['8+7=15', '92+15=107'] Exploring Operation: 107-22=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 22*107=2354, Resulting Numbers: [2354] 2354,46 unequal: No Solution Exploring Operation: 22+107=129, Resulting Numbers: [129] 129,46 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: 46:[8, 63], Operations: ['92-7=85', '85-22=63'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 8+63=71, Resulting Numbers: [71] 71,46 unequal: No Solution Exploring Operation: 8*63=504, Resulting Numbers: [504] 504,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[22, 77], Operations: ['92-7=85', '85-8=77'] Exploring Operation: 22*77=1694, Resulting Numbers: [1694] 1694,46 unequal: No Solution Exploring Operation: 22+77=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 77-22=55, Resulting Numbers: [55] 55,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[85, 30], Operations: ['92-7=85', '8+22=30'] Exploring Operation: 85-30=55, Resulting Numbers: [55] 55,46 unequal: No Solution Exploring Operation: 85+30=115, Resulting Numbers: [115] 115,46 unequal: No Solution Exploring Operation: 85*30=2550, Resulting Numbers: [2550] 2550,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[22, 93], Operations: ['92-7=85', '8+85=93'] Exploring Operation: 93-22=71, Resulting Numbers: [71] 71,46 unequal: No Solution Exploring Operation: 22+93=115, Resulting Numbers: [115] 115,46 unequal: No Solution Exploring Operation: 22*93=2046, Resulting Numbers: [2046] 2046,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[85, 14], Operations: ['92-7=85', '22-8=14'] Exploring Operation: 85*14=1190, Resulting Numbers: [1190] 1190,46 unequal: No Solution Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,46 unequal: No Solution Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,46 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 24, 7, 96, 30 ]
35
[ "24+7=31", "96-30=66", "66-31=35" ]
Current State: 35:[24, 7, 96, 30], Operations: [] Exploring Operation: 24+7=31, Resulting Numbers: [96, 30, 31] Generated Node #2: [96, 30, 31] from Operation: 24+7=31 Current State: 35:[96, 30, 31], Operations: ['24+7=31'] Exploring Operation: 96-30=66, Resulting Numbers: [31, 66] Generated Node #3: [31, 66] from Operation: 96-30=66 Current State: 35:[31, 66], Operations: ['24+7=31', '96-30=66'] Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[24, 7, 96, 30], Operations: [] Exploring Operation: 96-24=72, Resulting Numbers: [7, 30, 72] Generated Node #0,0: 35:[7, 30, 72] Operation: 96-24=72 Exploring Operation: 96/24=4, Resulting Numbers: [7, 30, 4] Generated Node #0,1: 35:[7, 30, 4] Operation: 96/24=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[7, 30, 4], Operations: ['96/24=4'] Exploring Operation: 30+4=34, Resulting Numbers: [7, 34] Generated Node #0,1,0: 35:[7, 34] Operation: 30+4=34 Exploring Operation: 7+30=37, Resulting Numbers: [4, 37] Generated Node #0,1,1: 35:[4, 37] Operation: 7+30=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[7, 34], Operations: ['96/24=4', '30+4=34'] Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,35 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:[4, 37], Operations: ['96/24=4', '7+30=37'] Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,35 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 #0,0 Current State: 35:[7, 30, 72], Operations: ['96-24=72'] Exploring Operation: 72-7=65, Resulting Numbers: [30, 65] Generated Node #0,0,0: 35:[30, 65] Operation: 72-7=65 Exploring Operation: 72-30=42, Resulting Numbers: [7, 42] Generated Node #0,0,1: 35:[7, 42] Operation: 72-30=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[7, 42], Operations: ['96-24=72', '72-30=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[24, 7, 96, 30], Operations: [] Exploring Operation: 96-24=72, Resulting Numbers: [7, 30, 72] Generated Node #0,0: 35:[7, 30, 72] Operation: 96-24=72 Moving to Node #0,0 Current State: 35:[7, 30, 72], Operations: ['96-24=72'] Exploring Operation: 72-30=42, Resulting Numbers: [7, 42] Generated Node #0,0,1: 35:[7, 42] Operation: 72-30=42 Moving to Node #0,0,1 Current State: 35:[7, 42], Operations: ['96-24=72', '72-30=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 22, 33, 35, 40 ]
25
[ "33*40=1320", "1320/22=60", "60-35=25" ]
Current State: 25:[22, 33, 35, 40], Operations: [] Exploring Operation: 33*40=1320, Resulting Numbers: [22, 35, 1320] Generated Node #2: [22, 35, 1320] from Operation: 33*40=1320 Current State: 25:[22, 35, 1320], Operations: ['33*40=1320'] Exploring Operation: 1320/22=60, Resulting Numbers: [35, 60] Generated Node #3: [35, 60] from Operation: 1320/22=60 Current State: 25:[35, 60], Operations: ['33*40=1320', '1320/22=60'] Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[22, 33, 35, 40], Operations: [] Exploring Operation: 40-33=7, Resulting Numbers: [22, 35, 7] Generated Node #0,0: 25:[22, 35, 7] Operation: 40-33=7 Exploring Operation: 35-33=2, Resulting Numbers: [22, 40, 2] Generated Node #0,1: 25:[22, 40, 2] Operation: 35-33=2 Exploring Operation: 40-22=18, Resulting Numbers: [33, 35, 18] Generated Node #0,2: 25:[33, 35, 18] Operation: 40-22=18 Exploring Operation: 40-35=5, Resulting Numbers: [22, 33, 5] Generated Node #0,3: 25:[22, 33, 5] Operation: 40-35=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[22, 33, 5], Operations: ['40-35=5'] Exploring Operation: 33-22=11, Resulting Numbers: [5, 11] Generated Node #0,3,0: 25:[5, 11] Operation: 33-22=11 Exploring Operation: 33-5=28, Resulting Numbers: [22, 28] Generated Node #0,3,1: 25:[22, 28] Operation: 33-5=28 Exploring Operation: 22-5=17, Resulting Numbers: [33, 17] Generated Node #0,3,2: 25:[33, 17] Operation: 22-5=17 Exploring Operation: 22+5=27, Resulting Numbers: [33, 27] Generated Node #0,3,3: 25:[33, 27] Operation: 22+5=27 Moving to Node #0,3,0 Current State: 25:[5, 11], Operations: ['40-35=5', '33-22=11'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,25 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,25 unequal: No Solution Moving to Node #0,3,1 Current State: 25:[22, 28], Operations: ['40-35=5', '33-5=28'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 22*28=616, Resulting Numbers: [616] 616,25 unequal: No Solution Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,25 unequal: No Solution Moving to Node #0,3,3 Current State: 25:[33, 27], Operations: ['40-35=5', '22+5=27'] Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,25 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[33, 17], Operations: ['40-35=5', '22-5=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,25 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,25 unequal: No Solution No 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: 25:[22, 35, 7], Operations: ['40-33=7'] Exploring Operation: 35/7=5, Resulting Numbers: [22, 5] Generated Node #0,0,0: 25:[22, 5] Operation: 35/7=5 Exploring Operation: 35-7=28, Resulting Numbers: [22, 28] Generated Node #0,0,1: 25:[22, 28] Operation: 35-7=28 Exploring Operation: 22+7=29, Resulting Numbers: [35, 29] Generated Node #0,0,2: 25:[35, 29] Operation: 22+7=29 Exploring Operation: 35-22=13, Resulting Numbers: [7, 13] Generated Node #0,0,3: 25:[7, 13] Operation: 35-22=13 Moving to Node #0,0,0 Current State: 25:[22, 5], Operations: ['40-33=7', '35/7=5'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,25 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[22, 28], Operations: ['40-33=7', '35-7=28'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 22*28=616, Resulting Numbers: [616] 616,25 unequal: No Solution Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[7, 13], Operations: ['40-33=7', '35-22=13'] Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[35, 29], Operations: ['40-33=7', '22+7=29'] Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,25 unequal: No Solution Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,25 unequal: No Solution No 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: 25:[22, 40, 2], Operations: ['35-33=2'] Exploring Operation: 40-22=18, Resulting Numbers: [2, 18] Generated Node #0,1,0: 25:[2, 18] Operation: 40-22=18 Exploring Operation: 40-2=38, Resulting Numbers: [22, 38] Generated Node #0,1,1: 25:[22, 38] Operation: 40-2=38 Exploring Operation: 22+2=24, Resulting Numbers: [40, 24] Generated Node #0,1,2: 25:[40, 24] Operation: 22+2=24 Exploring Operation: 40/2=20, Resulting Numbers: [22, 20] Generated Node #0,1,3: 25:[22, 20] Operation: 40/2=20 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 25:[22, 20], Operations: ['35-33=2', '40/2=20'] Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,25 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,25 unequal: No Solution No 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: 25:[2, 18], Operations: ['35-33=2', '40-22=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,25 unequal: No Solution No 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: 25:[22, 38], Operations: ['35-33=2', '40-2=38'] Exploring Operation: 22*38=836, Resulting Numbers: [836] 836,25 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,25 unequal: No Solution No 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: 25:[40, 24], Operations: ['35-33=2', '22+2=24'] Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 40*24=960, Resulting Numbers: [960] 960,25 unequal: No Solution Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[33, 35, 18], Operations: ['40-22=18'] Exploring Operation: 35-33=2, Resulting Numbers: [18, 2] Generated Node #0,2,0: 25:[18, 2] Operation: 35-33=2 Exploring Operation: 33-18=15, Resulting Numbers: [35, 15] Generated Node #0,2,1: 25:[35, 15] Operation: 33-18=15 Exploring Operation: 35-18=17, Resulting Numbers: [33, 17] Generated Node #0,2,2: 25:[33, 17] Operation: 35-18=17 Exploring Operation: 33+18=51, Resulting Numbers: [35, 51] Generated Node #0,2,3: 25:[35, 51] Operation: 33+18=51 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[18, 2], Operations: ['40-22=18', '35-33=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,25 unequal: No Solution No 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: 25:[33, 17], Operations: ['40-22=18', '35-18=17'] Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,25 unequal: No Solution No 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: 25:[35, 15], Operations: ['40-22=18', '33-18=15'] Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,25 unequal: No Solution No 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: 25:[35, 51], Operations: ['40-22=18', '33+18=51'] Exploring Operation: 35*51=1785, Resulting Numbers: [1785] 1785,25 unequal: No Solution Exploring Operation: 35+51=86, Resulting Numbers: [86] 86,25 unequal: No Solution Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 68, 65, 75, 66 ]
53
[ "68-65=3", "66/3=22", "75-22=53" ]
Current State: 53:[68, 65, 75, 66], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [75, 66, 3] Generated Node #2: [75, 66, 3] from Operation: 68-65=3 Current State: 53:[75, 66, 3], Operations: ['68-65=3'] Exploring Operation: 66/3=22, Resulting Numbers: [75, 22] Generated Node #3: [75, 22] from Operation: 66/3=22 Current State: 53:[75, 22], Operations: ['68-65=3', '66/3=22'] Exploring Operation: 75-22=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[68, 65, 75, 66], Operations: [] Exploring Operation: 75-68=7, Resulting Numbers: [65, 66, 7] Generated Node #0,0: 53:[65, 66, 7] Operation: 75-68=7 Moving to Node #0,0 Current State: 53:[65, 66, 7], Operations: ['75-68=7'] Exploring Operation: 65-7=58, Resulting Numbers: [66, 58] Generated Node #0,0,0: 53:[66, 58] Operation: 65-7=58 Moving to Node #0,0,0 Current State: 53:[66, 58], Operations: ['75-68=7', '65-7=58'] Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,53 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 50, 83, 42, 66 ]
34
[ "42*66=2772", "50+2772=2822", "2822/83=34" ]
Current State: 34:[50, 83, 42, 66], Operations: [] Exploring Operation: 42*66=2772, Resulting Numbers: [50, 83, 2772] Generated Node #2: [50, 83, 2772] from Operation: 42*66=2772 Current State: 34:[50, 83, 2772], Operations: ['42*66=2772'] Exploring Operation: 50+2772=2822, Resulting Numbers: [83, 2822] Generated Node #3: [83, 2822] from Operation: 50+2772=2822 Current State: 34:[83, 2822], Operations: ['42*66=2772', '50+2772=2822'] Exploring Operation: 2822/83=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[50, 83, 42, 66], Operations: [] Exploring Operation: 83-42=41, Resulting Numbers: [50, 66, 41] Generated Node #0,0: 34:[50, 66, 41] Operation: 83-42=41 Exploring Operation: 83-66=17, Resulting Numbers: [50, 42, 17] Generated Node #0,1: 34:[50, 42, 17] Operation: 83-66=17 Exploring Operation: 83-50=33, Resulting Numbers: [42, 66, 33] Generated Node #0,2: 34:[42, 66, 33] Operation: 83-50=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[50, 42, 17], Operations: ['83-66=17'] Exploring Operation: 50-17=33, Resulting Numbers: [42, 33] Generated Node #0,1,0: 34:[42, 33] Operation: 50-17=33 Exploring Operation: 50-42=8, Resulting Numbers: [17, 8] Generated Node #0,1,1: 34:[17, 8] Operation: 50-42=8 Exploring Operation: 42-17=25, Resulting Numbers: [50, 25] Generated Node #0,1,2: 34:[50, 25] Operation: 42-17=25 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[17, 8], Operations: ['83-66=17', '50-42=8'] Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,34 unequal: No Solution Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,34 unequal: No Solution No 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: 34:[42, 33], Operations: ['83-66=17', '50-17=33'] Exploring Operation: 42+33=75, Resulting Numbers: [75] 75,34 unequal: No Solution Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 42*33=1386, Resulting Numbers: [1386] 1386,34 unequal: No Solution No 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: 34:[50, 25], Operations: ['83-66=17', '42-17=25'] Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,34 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,34 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: 34:[42, 66, 33], Operations: ['83-50=33'] Exploring Operation: 66-33=33, Resulting Numbers: [42, 33] Generated Node #0,2,0: 34:[42, 33] Operation: 66-33=33 Exploring Operation: 66-42=24, Resulting Numbers: [33, 24] Generated Node #0,2,1: 34:[33, 24] Operation: 66-42=24 Exploring Operation: 66/33=2, Resulting Numbers: [42, 2] Generated Node #0,2,2: 34:[42, 2] Operation: 66/33=2 Moving to Node #0,2,1 Current State: 34:[33, 24], Operations: ['83-50=33', '66-42=24'] Exploring Operation: 33*24=792, Resulting Numbers: [792] 792,34 unequal: No Solution Exploring Operation: 33+24=57, Resulting Numbers: [57] 57,34 unequal: No Solution Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[42, 2], Operations: ['83-50=33', '66/33=2'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,34 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,34 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[42, 33], Operations: ['83-50=33', '66-33=33'] Exploring Operation: 42+33=75, Resulting Numbers: [75] 75,34 unequal: No Solution Exploring Operation: 42*33=1386, Resulting Numbers: [1386] 1386,34 unequal: No Solution Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[50, 66, 41], Operations: ['83-42=41'] Exploring Operation: 66-50=16, Resulting Numbers: [41, 16] Generated Node #0,0,0: 34:[41, 16] Operation: 66-50=16 Exploring Operation: 66-41=25, Resulting Numbers: [50, 25] Generated Node #0,0,1: 34:[50, 25] Operation: 66-41=25 Exploring Operation: 50-41=9, Resulting Numbers: [66, 9] Generated Node #0,0,2: 34:[66, 9] Operation: 50-41=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[41, 16], Operations: ['83-42=41', '66-50=16'] Exploring Operation: 41*16=656, Resulting Numbers: [656] 656,34 unequal: No Solution Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,34 unequal: No Solution Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,34 unequal: No Solution No 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: 34:[50, 25], Operations: ['83-42=41', '66-41=25'] Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,34 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,34 unequal: No Solution No 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: 34:[66, 9], Operations: ['83-42=41', '50-41=9'] Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,34 unequal: No Solution Exploring Operation: 66+9=75, Resulting Numbers: [75] 75,34 unequal: No Solution Exploring Operation: 66*9=594, Resulting Numbers: [594] 594,34 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