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
[ 16, 80, 32, 57 ]
26
[ "16*57=912", "912-80=832", "832/32=26" ]
Current State: 26:[16, 80, 32, 57], Operations: [] Exploring Operation: 16*57=912, Resulting Numbers: [80, 32, 912] Generated Node #2: [80, 32, 912] from Operation: 16*57=912 Current State: 26:[80, 32, 912], Operations: ['16*57=912'] Exploring Operation: 912-80=832, Resulting Numbers: [32, 832] Generated Node #3: [32, 832] from Operation: 912-80=832 Current State: 26:[32, 832], Operations: ['16*57=912', '912-80=832'] Exploring Operation: 832/32=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[16, 80, 32, 57], Operations: [] Exploring Operation: 80/16=5, Resulting Numbers: [32, 57, 5] Generated Node #0,0: 26:[32, 57, 5] Operation: 80/16=5 Exploring Operation: 80-57=23, Resulting Numbers: [16, 32, 23] Generated Node #0,1: 26:[16, 32, 23] Operation: 80-57=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[16, 32, 23], Operations: ['80-57=23'] Exploring Operation: 32/16=2, Resulting Numbers: [23, 2] Generated Node #0,1,0: 26:[23, 2] Operation: 32/16=2 Exploring Operation: 32-16=16, Resulting Numbers: [23, 16] Generated Node #0,1,1: 26:[23, 16] Operation: 32-16=16 Moving to Node #0,1,0 Current State: 26:[23, 2], Operations: ['80-57=23', '32/16=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[23, 16], Operations: ['80-57=23', '32-16=16'] Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[32, 57, 5], Operations: ['80/16=5'] Exploring Operation: 32-5=27, Resulting Numbers: [57, 27] Generated Node #0,0,0: 26:[57, 27] Operation: 32-5=27 Exploring Operation: 57-32=25, Resulting Numbers: [5, 25] Generated Node #0,0,1: 26:[5, 25] Operation: 57-32=25 Moving to Node #0,0,1 Current State: 26:[5, 25], Operations: ['80/16=5', '57-32=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,26 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[57, 27], Operations: ['80/16=5', '32-5=27'] Exploring Operation: 57-27=30, Resulting Numbers: [30] 30,26 unequal: No Solution Exploring Operation: 57+27=84, Resulting Numbers: [84] 84,26 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
[ 53, 83, 19, 4 ]
80
[ "53+4=57", "57/19=3", "83-3=80" ]
Current State: 80:[53, 83, 19, 4], Operations: [] Exploring Operation: 53+4=57, Resulting Numbers: [83, 19, 57] Generated Node #2: [83, 19, 57] from Operation: 53+4=57 Current State: 80:[83, 19, 57], Operations: ['53+4=57'] Exploring Operation: 57/19=3, Resulting Numbers: [83, 3] Generated Node #3: [83, 3] from Operation: 57/19=3 Current State: 80:[83, 3], Operations: ['53+4=57', '57/19=3'] Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[53, 83, 19, 4], Operations: [] Exploring Operation: 53-19=34, Resulting Numbers: [83, 4, 34] Generated Node #0,0: 80:[83, 4, 34] Operation: 53-19=34 Moving to Node #0,0 Current State: 80:[83, 4, 34], Operations: ['53-19=34'] Exploring Operation: 4+34=38, Resulting Numbers: [83, 38] Generated Node #0,0,0: 80:[83, 38] Operation: 4+34=38 Moving to Node #0,0,0 Current State: 80:[83, 38], Operations: ['53-19=34', '4+34=38'] Exploring Operation: 83-38=45, Resulting Numbers: [45] 45,80 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 58, 24, 21, 92 ]
82
[ "24-21=3", "58*3=174", "174-92=82" ]
Current State: 82:[58, 24, 21, 92], Operations: [] Exploring Operation: 24-21=3, Resulting Numbers: [58, 92, 3] Generated Node #2: [58, 92, 3] from Operation: 24-21=3 Current State: 82:[58, 92, 3], Operations: ['24-21=3'] Exploring Operation: 58*3=174, Resulting Numbers: [92, 174] Generated Node #3: [92, 174] from Operation: 58*3=174 Current State: 82:[92, 174], Operations: ['24-21=3', '58*3=174'] Exploring Operation: 174-92=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[58, 24, 21, 92], Operations: [] Exploring Operation: 24-21=3, Resulting Numbers: [58, 92, 3] Generated Node #0,0: 82:[58, 92, 3] Operation: 24-21=3 Exploring Operation: 58-21=37, Resulting Numbers: [24, 92, 37] Generated Node #0,1: 82:[24, 92, 37] Operation: 58-21=37 Exploring Operation: 58+24=82, Resulting Numbers: [21, 92, 82] Generated Node #0,2: 82:[21, 92, 82] Operation: 58+24=82 Exploring Operation: 24+21=45, Resulting Numbers: [58, 92, 45] Generated Node #0,3: 82:[58, 92, 45] Operation: 24+21=45 Exploring Operation: 58+21=79, Resulting Numbers: [24, 92, 79] Generated Node #0,4: 82:[24, 92, 79] Operation: 58+21=79 Moving to Node #0,0 Current State: 82:[58, 92, 3], Operations: ['24-21=3'] Exploring Operation: 58+3=61, Resulting Numbers: [92, 61] Generated Node #0,0,0: 82:[92, 61] Operation: 58+3=61 Exploring Operation: 58-3=55, Resulting Numbers: [92, 55] Generated Node #0,0,1: 82:[92, 55] Operation: 58-3=55 Exploring Operation: 92-58=34, Resulting Numbers: [3, 34] Generated Node #0,0,2: 82:[3, 34] Operation: 92-58=34 Exploring Operation: 92-3=89, Resulting Numbers: [58, 89] Generated Node #0,0,3: 82:[58, 89] Operation: 92-3=89 Exploring Operation: 92+3=95, Resulting Numbers: [58, 95] Generated Node #0,0,4: 82:[58, 95] Operation: 92+3=95 Moving to Node #0,2 Current State: 82:[21, 92, 82], Operations: ['58+24=82'] Exploring Operation: 92-21=71, Resulting Numbers: [82, 71] Generated Node #0,2,0: 82:[82, 71] Operation: 92-21=71 Exploring Operation: 92-82=10, Resulting Numbers: [21, 10] Generated Node #0,2,1: 82:[21, 10] Operation: 92-82=10 Exploring Operation: 21+92=113, Resulting Numbers: [82, 113] Generated Node #0,2,2: 82:[82, 113] Operation: 21+92=113 Exploring Operation: 21+82=103, Resulting Numbers: [92, 103] Generated Node #0,2,3: 82:[92, 103] Operation: 21+82=103 Exploring Operation: 82-21=61, Resulting Numbers: [92, 61] Generated Node #0,2,4: 82:[92, 61] Operation: 82-21=61 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 82:[82, 71], Operations: ['58+24=82', '92-21=71'] Exploring Operation: 82+71=153, Resulting Numbers: [153] 153,82 unequal: No Solution Exploring Operation: 82*71=5822, Resulting Numbers: [5822] 5822,82 unequal: No Solution Exploring Operation: 82-71=11, Resulting Numbers: [11] 11,82 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:[21, 10], Operations: ['58+24=82', '92-82=10'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,82 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 #0,2,4 Current State: 82:[92, 61], Operations: ['58+24=82', '82-21=61'] Exploring Operation: 92-61=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 92*61=5612, Resulting Numbers: [5612] 5612,82 unequal: No Solution Exploring Operation: 92+61=153, Resulting Numbers: [153] 153,82 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:[82, 113], Operations: ['58+24=82', '21+92=113'] Exploring Operation: 82+113=195, Resulting Numbers: [195] 195,82 unequal: No Solution Exploring Operation: 82*113=9266, Resulting Numbers: [9266] 9266,82 unequal: No Solution Exploring Operation: 113-82=31, Resulting Numbers: [31] 31,82 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 #0,2,3 Current State: 82:[92, 103], Operations: ['58+24=82', '21+82=103'] Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,82 unequal: No Solution Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,82 unequal: No Solution Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,82 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: 82:[24, 92, 79], Operations: ['58+21=79'] Exploring Operation: 92-79=13, Resulting Numbers: [24, 13] Generated Node #0,4,0: 82:[24, 13] Operation: 92-79=13 Exploring Operation: 24+79=103, Resulting Numbers: [92, 103] Generated Node #0,4,1: 82:[92, 103] Operation: 24+79=103 Exploring Operation: 92-24=68, Resulting Numbers: [79, 68] Generated Node #0,4,2: 82:[79, 68] Operation: 92-24=68 Exploring Operation: 24+92=116, Resulting Numbers: [79, 116] Generated Node #0,4,3: 82:[79, 116] Operation: 24+92=116 Exploring Operation: 79-24=55, Resulting Numbers: [92, 55] Generated Node #0,4,4: 82:[92, 55] Operation: 79-24=55 Moving to Node #0,1 Current State: 82:[24, 92, 37], Operations: ['58-21=37'] Exploring Operation: 24+92=116, Resulting Numbers: [37, 116] Generated Node #0,1,0: 82:[37, 116] Operation: 24+92=116 Exploring Operation: 92-37=55, Resulting Numbers: [24, 55] Generated Node #0,1,1: 82:[24, 55] Operation: 92-37=55 Exploring Operation: 92-24=68, Resulting Numbers: [37, 68] Generated Node #0,1,2: 82:[37, 68] Operation: 92-24=68 Exploring Operation: 24+37=61, Resulting Numbers: [92, 61] Generated Node #0,1,3: 82:[92, 61] Operation: 24+37=61 Exploring Operation: 37-24=13, Resulting Numbers: [92, 13] Generated Node #0,1,4: 82:[92, 13] Operation: 37-24=13 Moving to Node #0,3 Current State: 82:[58, 92, 45], Operations: ['24+21=45'] Exploring Operation: 58+92=150, Resulting Numbers: [45, 150] Generated Node #0,3,0: 82:[45, 150] Operation: 58+92=150 Exploring Operation: 58+45=103, Resulting Numbers: [92, 103] Generated Node #0,3,1: 82:[92, 103] Operation: 58+45=103 Exploring Operation: 92-58=34, Resulting Numbers: [45, 34] Generated Node #0,3,2: 82:[45, 34] Operation: 92-58=34 Exploring Operation: 92-45=47, Resulting Numbers: [58, 47] Generated Node #0,3,3: 82:[58, 47] Operation: 92-45=47 Exploring Operation: 58-45=13, Resulting Numbers: [92, 13] Generated Node #0,3,4: 82:[92, 13] Operation: 58-45=13 Moving to Node #0,0,2 Current State: 82:[3, 34], Operations: ['24-21=3', '92-58=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,82 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[45, 34], Operations: ['24+21=45', '92-58=34'] Exploring Operation: 45*34=1530, Resulting Numbers: [1530] 1530,82 unequal: No Solution Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,82 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,82 unequal: No Solution Moving to Node #0,4,2 Current State: 82:[79, 68], Operations: ['58+21=79', '92-24=68'] Exploring Operation: 79+68=147, Resulting Numbers: [147] 147,82 unequal: No Solution Exploring Operation: 79-68=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 79*68=5372, Resulting Numbers: [5372] 5372,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[37, 68], Operations: ['58-21=37', '92-24=68'] Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 37*68=2516, Resulting Numbers: [2516] 2516,82 unequal: No Solution Exploring Operation: 37+68=105, Resulting Numbers: [105] 105,82 unequal: No Solution Moving to Node #0,1,4 Current State: 82:[92, 13], Operations: ['58-21=37', '37-24=13'] Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,82 unequal: No Solution Exploring Operation: 92+13=105, Resulting Numbers: [105] 105,82 unequal: No Solution Exploring Operation: 92*13=1196, Resulting Numbers: [1196] 1196,82 unequal: No Solution Moving to Node #0,3,4 Current State: 82:[92, 13], Operations: ['24+21=45', '58-45=13'] Exploring Operation: 92+13=105, Resulting Numbers: [105] 105,82 unequal: No Solution Exploring Operation: 92*13=1196, Resulting Numbers: [1196] 1196,82 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[58, 47], Operations: ['24+21=45', '92-45=47'] Exploring Operation: 58*47=2726, Resulting Numbers: [2726] 2726,82 unequal: No Solution Exploring Operation: 58+47=105, Resulting Numbers: [105] 105,82 unequal: No Solution Exploring Operation: 58-47=11, Resulting Numbers: [11] 11,82 unequal: No Solution Moving to Node #0,4,4 Current State: 82:[92, 55], Operations: ['58+21=79', '79-24=55'] Exploring Operation: 92*55=5060, Resulting Numbers: [5060] 5060,82 unequal: No Solution Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 92+55=147, Resulting Numbers: [147] 147,82 unequal: No Solution Moving to Node #0,0,3 Current State: 82:[58, 89], Operations: ['24-21=3', '92-3=89'] Exploring Operation: 89-58=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 58*89=5162, Resulting Numbers: [5162] 5162,82 unequal: No Solution Exploring Operation: 58+89=147, Resulting Numbers: [147] 147,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[92, 55], Operations: ['24-21=3', '58-3=55'] Exploring Operation: 92*55=5060, Resulting Numbers: [5060] 5060,82 unequal: No Solution Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 92+55=147, Resulting Numbers: [147] 147,82 unequal: No Solution Moving to Node #0,4,0 Current State: 82:[24, 13], Operations: ['58+21=79', '92-79=13'] Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[92, 61], Operations: ['58-21=37', '24+37=61'] Exploring Operation: 92-61=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 92*61=5612, Resulting Numbers: [5612] 5612,82 unequal: No Solution Exploring Operation: 92+61=153, Resulting Numbers: [153] 153,82 unequal: No Solution Moving to Node #0,0,4 Current State: 82:[58, 95], Operations: ['24-21=3', '92+3=95'] Exploring Operation: 58+95=153, Resulting Numbers: [153] 153,82 unequal: No Solution Exploring Operation: 95-58=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 58*95=5510, Resulting Numbers: [5510] 5510,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[92, 61], Operations: ['24-21=3', '58+3=61'] Exploring Operation: 92+61=153, Resulting Numbers: [153] 153,82 unequal: No Solution Exploring Operation: 92-61=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 92*61=5612, Resulting Numbers: [5612] 5612,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[24, 55], Operations: ['58-21=37', '92-37=55'] Exploring Operation: 24*55=1320, Resulting Numbers: [1320] 1320,82 unequal: No Solution Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 24+55=79, Resulting Numbers: [79] 79,82 unequal: No Solution Moving to Node #0,3,1 Current State: 82:[92, 103], Operations: ['24+21=45', '58+45=103'] Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,82 unequal: No Solution Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,82 unequal: No Solution Moving to Node #0,4,1 Current State: 82:[92, 103], Operations: ['58+21=79', '24+79=103'] Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,82 unequal: No Solution Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,82 unequal: No Solution Moving to Node #0,4,3 Current State: 82:[79, 116], Operations: ['58+21=79', '24+92=116'] Exploring Operation: 116-79=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 79*116=9164, Resulting Numbers: [9164] 9164,82 unequal: No Solution Exploring Operation: 79+116=195, Resulting Numbers: [195] 195,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[37, 116], Operations: ['58-21=37', '24+92=116'] Exploring Operation: 116-37=79, Resulting Numbers: [79] 79,82 unequal: No Solution Exploring Operation: 37*116=4292, Resulting Numbers: [4292] 4292,82 unequal: No Solution Exploring Operation: 37+116=153, Resulting Numbers: [153] 153,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[45, 150], Operations: ['24+21=45', '58+92=150'] Exploring Operation: 45*150=6750, Resulting Numbers: [6750] 6750,82 unequal: No Solution Exploring Operation: 150-45=105, Resulting Numbers: [105] 105,82 unequal: No Solution Exploring Operation: 45+150=195, Resulting Numbers: [195] 195,82 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 74, 98, 17, 78 ]
30
[ "78-74=4", "17*4=68", "98-68=30" ]
Current State: 30:[74, 98, 17, 78], Operations: [] Exploring Operation: 78-74=4, Resulting Numbers: [98, 17, 4] Generated Node #2: [98, 17, 4] from Operation: 78-74=4 Current State: 30:[98, 17, 4], Operations: ['78-74=4'] Exploring Operation: 17*4=68, Resulting Numbers: [98, 68] Generated Node #3: [98, 68] from Operation: 17*4=68 Current State: 30:[98, 68], Operations: ['78-74=4', '17*4=68'] Exploring Operation: 98-68=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[74, 98, 17, 78], Operations: [] Exploring Operation: 98-74=24, Resulting Numbers: [17, 78, 24] Generated Node #0,0: 30:[17, 78, 24] Operation: 98-74=24 Exploring Operation: 98-78=20, Resulting Numbers: [74, 17, 20] Generated Node #0,1: 30:[74, 17, 20] Operation: 98-78=20 Exploring Operation: 78-74=4, Resulting Numbers: [98, 17, 4] Generated Node #0,2: 30:[98, 17, 4] Operation: 78-74=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[74, 17, 20], Operations: ['98-78=20'] Exploring Operation: 20-17=3, Resulting Numbers: [74, 3] Generated Node #0,1,0: 30:[74, 3] Operation: 20-17=3 Exploring Operation: 74-20=54, Resulting Numbers: [17, 54] Generated Node #0,1,1: 30:[17, 54] Operation: 74-20=54 Exploring Operation: 74-17=57, Resulting Numbers: [20, 57] Generated Node #0,1,2: 30:[20, 57] Operation: 74-17=57 Moving to Node #0,1,1 Current State: 30:[17, 54], Operations: ['98-78=20', '74-20=54'] Exploring Operation: 17+54=71, Resulting Numbers: [71] 71,30 unequal: No Solution Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 17*54=918, Resulting Numbers: [918] 918,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[20, 57], Operations: ['98-78=20', '74-17=57'] Exploring Operation: 20*57=1140, Resulting Numbers: [1140] 1140,30 unequal: No Solution Exploring Operation: 20+57=77, Resulting Numbers: [77] 77,30 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[74, 3], Operations: ['98-78=20', '20-17=3'] Exploring Operation: 74*3=222, Resulting Numbers: [222] 222,30 unequal: No Solution Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,30 unequal: No Solution Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[17, 78, 24], Operations: ['98-74=24'] Exploring Operation: 78-17=61, Resulting Numbers: [24, 61] Generated Node #0,0,0: 30:[24, 61] Operation: 78-17=61 Exploring Operation: 24-17=7, Resulting Numbers: [78, 7] Generated Node #0,0,1: 30:[78, 7] Operation: 24-17=7 Exploring Operation: 78-24=54, Resulting Numbers: [17, 54] Generated Node #0,0,2: 30:[17, 54] Operation: 78-24=54 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 30:[17, 54], Operations: ['98-74=24', '78-24=54'] Exploring Operation: 17*54=918, Resulting Numbers: [918] 918,30 unequal: No Solution Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 17+54=71, Resulting Numbers: [71] 71,30 unequal: No Solution No 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: 30:[24, 61], Operations: ['98-74=24', '78-17=61'] Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,30 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,30 unequal: No Solution No 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: 30:[78, 7], Operations: ['98-74=24', '24-17=7'] Exploring Operation: 78+7=85, Resulting Numbers: [85] 85,30 unequal: No Solution Exploring Operation: 78*7=546, Resulting Numbers: [546] 546,30 unequal: No Solution Exploring Operation: 78-7=71, Resulting Numbers: [71] 71,30 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[98, 17, 4], Operations: ['78-74=4'] Exploring Operation: 98-4=94, Resulting Numbers: [17, 94] Generated Node #0,2,0: 30:[17, 94] Operation: 98-4=94 Exploring Operation: 17-4=13, Resulting Numbers: [98, 13] Generated Node #0,2,1: 30:[98, 13] Operation: 17-4=13 Exploring Operation: 98-17=81, Resulting Numbers: [4, 81] Generated Node #0,2,2: 30:[4, 81] Operation: 98-17=81 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[4, 81], Operations: ['78-74=4', '98-17=81'] Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,30 unequal: No Solution Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,30 unequal: No Solution Exploring Operation: 4*81=324, Resulting Numbers: [324] 324,30 unequal: No Solution No 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: 30:[17, 94], Operations: ['78-74=4', '98-4=94'] Exploring Operation: 17*94=1598, Resulting Numbers: [1598] 1598,30 unequal: No Solution Exploring Operation: 17+94=111, Resulting Numbers: [111] 111,30 unequal: No Solution Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,30 unequal: No Solution No 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: 30:[98, 13], Operations: ['78-74=4', '17-4=13'] Exploring Operation: 98-13=85, Resulting Numbers: [85] 85,30 unequal: No Solution Exploring Operation: 98+13=111, Resulting Numbers: [111] 111,30 unequal: No Solution Exploring Operation: 98*13=1274, Resulting Numbers: [1274] 1274,30 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_3
mult_heuristic
[ 11, 92, 64, 7 ]
49
[ "11*7=77", "92-64=28", "77-28=49" ]
Current State: 49:[11, 92, 64, 7], Operations: [] Exploring Operation: 11*7=77, Resulting Numbers: [92, 64, 77] Generated Node #2: [92, 64, 77] from Operation: 11*7=77 Current State: 49:[92, 64, 77], Operations: ['11*7=77'] Exploring Operation: 92-64=28, Resulting Numbers: [77, 28] Generated Node #3: [77, 28] from Operation: 92-64=28 Current State: 49:[77, 28], Operations: ['11*7=77', '92-64=28'] Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[11, 92, 64, 7], Operations: [] Exploring Operation: 92-64=28, Resulting Numbers: [11, 7, 28] Generated Node #0,0: 49:[11, 7, 28] Operation: 92-64=28 Exploring Operation: 92-11=81, Resulting Numbers: [64, 7, 81] Generated Node #0,1: 49:[64, 7, 81] Operation: 92-11=81 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[11, 7, 28], Operations: ['92-64=28'] Exploring Operation: 11+28=39, Resulting Numbers: [7, 39] Generated Node #0,0,0: 49:[7, 39] Operation: 11+28=39 Exploring Operation: 28/7=4, Resulting Numbers: [11, 4] Generated Node #0,0,1: 49:[11, 4] Operation: 28/7=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[11, 4], Operations: ['92-64=28', '28/7=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[7, 39], Operations: ['92-64=28', '11+28=39'] Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,49 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,49 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:[64, 7, 81], Operations: ['92-11=81'] Exploring Operation: 81-64=17, Resulting Numbers: [7, 17] Generated Node #0,1,0: 49:[7, 17] Operation: 81-64=17 Exploring Operation: 64-7=57, Resulting Numbers: [81, 57] Generated Node #0,1,1: 49:[81, 57] Operation: 64-7=57 Moving to Node #0,1,0 Current State: 49:[7, 17], Operations: ['92-11=81', '81-64=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[81, 57], Operations: ['92-11=81', '64-7=57'] Exploring Operation: 81+57=138, Resulting Numbers: [138] 138,49 unequal: No Solution Exploring Operation: 81-57=24, Resulting Numbers: [24] 24,49 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
[ 94, 83, 47, 46 ]
74
[ "94/47=2", "83-46=37", "2*37=74" ]
Current State: 74:[94, 83, 47, 46], Operations: [] Exploring Operation: 94/47=2, Resulting Numbers: [83, 46, 2] Generated Node #2: [83, 46, 2] from Operation: 94/47=2 Current State: 74:[83, 46, 2], Operations: ['94/47=2'] Exploring Operation: 83-46=37, Resulting Numbers: [2, 37] Generated Node #3: [2, 37] from Operation: 83-46=37 Current State: 74:[2, 37], Operations: ['94/47=2', '83-46=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[94, 83, 47, 46], Operations: [] Exploring Operation: 94/47=2, Resulting Numbers: [83, 46, 2] Generated Node #0,0: 74:[83, 46, 2] Operation: 94/47=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[83, 46, 2], Operations: ['94/47=2'] Exploring Operation: 83-46=37, Resulting Numbers: [2, 37] Generated Node #0,0,0: 74:[2, 37] Operation: 83-46=37 Moving to Node #0,0,0 Current State: 74:[2, 37], Operations: ['94/47=2', '83-46=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[94, 83, 47, 46], Operations: [] Exploring Operation: 94/47=2, Resulting Numbers: [83, 46, 2] Generated Node #0,0: 74:[83, 46, 2] Operation: 94/47=2 Moving to Node #0,0 Current State: 74:[83, 46, 2], Operations: ['94/47=2'] Exploring Operation: 83-46=37, Resulting Numbers: [2, 37] Generated Node #0,0,0: 74:[2, 37] Operation: 83-46=37 Moving to Node #0,0,0 Current State: 74:[2, 37], Operations: ['94/47=2', '83-46=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 98, 5, 79, 5 ]
19
[ "98+5=103", "79+5=84", "103-84=19" ]
Current State: 19:[98, 5, 79, 5], Operations: [] Exploring Operation: 98+5=103, Resulting Numbers: [79, 103] Generated Node #2: [79, 103] from Operation: 98+5=103 Current State: 19:[79, 103], Operations: ['98+5=103'] Exploring Operation: 79+5=84, Resulting Numbers: [103, 84] Generated Node #3: [103, 84] from Operation: 79+5=84 Current State: 19:[103, 84], Operations: ['98+5=103', '79+5=84'] Exploring Operation: 103-84=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[98, 5, 79, 5], Operations: [] Exploring Operation: 98-79=19, Resulting Numbers: [5, 5, 19] Generated Node #0,0: 19:[5, 5, 19] Operation: 98-79=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[5, 5, 19], Operations: ['98-79=19'] Exploring Operation: 5*5=25, Resulting Numbers: [19, 25] Generated Node #0,0,0: 19:[19, 25] Operation: 5*5=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[19, 25], Operations: ['98-79=19', '5*5=25'] Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 6, 11, 16 ]
34
[ "35*6=210", "11*16=176", "210-176=34" ]
Current State: 34:[35, 6, 11, 16], Operations: [] Exploring Operation: 35*6=210, Resulting Numbers: [11, 16, 210] Generated Node #2: [11, 16, 210] from Operation: 35*6=210 Current State: 34:[11, 16, 210], Operations: ['35*6=210'] Exploring Operation: 11*16=176, Resulting Numbers: [210, 176] Generated Node #3: [210, 176] from Operation: 11*16=176 Current State: 34:[210, 176], Operations: ['35*6=210', '11*16=176'] Exploring Operation: 210-176=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[35, 6, 11, 16], Operations: [] Exploring Operation: 16-11=5, Resulting Numbers: [35, 6, 5] Generated Node #0,0: 34:[35, 6, 5] Operation: 16-11=5 Exploring Operation: 11-6=5, Resulting Numbers: [35, 16, 5] Generated Node #0,1: 34:[35, 16, 5] Operation: 11-6=5 Exploring Operation: 35-6=29, Resulting Numbers: [11, 16, 29] Generated Node #0,2: 34:[11, 16, 29] Operation: 35-6=29 Exploring Operation: 6+11=17, Resulting Numbers: [35, 16, 17] Generated Node #0,3: 34:[35, 16, 17] Operation: 6+11=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[35, 16, 17], Operations: ['6+11=17'] Exploring Operation: 16+17=33, Resulting Numbers: [35, 33] Generated Node #0,3,0: 34:[35, 33] Operation: 16+17=33 Exploring Operation: 35-16=19, Resulting Numbers: [17, 19] Generated Node #0,3,1: 34:[17, 19] Operation: 35-16=19 Exploring Operation: 35-17=18, Resulting Numbers: [16, 18] Generated Node #0,3,2: 34:[16, 18] Operation: 35-17=18 Exploring Operation: 17-16=1, Resulting Numbers: [35, 1] Generated Node #0,3,3: 34:[35, 1] Operation: 17-16=1 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 34:[35, 33], Operations: ['6+11=17', '16+17=33'] Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,34 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,34 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 #0,3,1 Current State: 34:[17, 19], Operations: ['6+11=17', '35-16=19'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 17+19=36, Resulting Numbers: [36] 36,34 unequal: No Solution Exploring Operation: 17*19=323, Resulting Numbers: [323] 323,34 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 #0,3,2 Current State: 34:[16, 18], Operations: ['6+11=17', '35-17=18'] Exploring Operation: 16*18=288, Resulting Numbers: [288] 288,34 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[35, 6, 11, 16], Operations: [] Exploring Operation: 6+11=17, Resulting Numbers: [35, 16, 17] Generated Node #0,3: 34:[35, 16, 17] Operation: 6+11=17 Moving to Node #0,3 Current State: 34:[35, 16, 17], Operations: ['6+11=17'] Exploring Operation: 35-17=18, Resulting Numbers: [16, 18] Generated Node #0,3,2: 34:[16, 18] Operation: 35-17=18 Moving to Node #0,3,2 Current State: 34:[16, 18], Operations: ['6+11=17', '35-17=18'] Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 16, 25, 54, 35 ]
29
[ "25-16=9", "54/9=6", "35-6=29" ]
Current State: 29:[16, 25, 54, 35], Operations: [] Exploring Operation: 25-16=9, Resulting Numbers: [54, 35, 9] Generated Node #2: [54, 35, 9] from Operation: 25-16=9 Current State: 29:[54, 35, 9], Operations: ['25-16=9'] Exploring Operation: 54/9=6, Resulting Numbers: [35, 6] Generated Node #3: [35, 6] from Operation: 54/9=6 Current State: 29:[35, 6], Operations: ['25-16=9', '54/9=6'] Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[16, 25, 54, 35], Operations: [] Exploring Operation: 54-16=38, Resulting Numbers: [25, 35, 38] Generated Node #0,0: 29:[25, 35, 38] Operation: 54-16=38 Exploring Operation: 35-16=19, Resulting Numbers: [25, 54, 19] Generated Node #0,1: 29:[25, 54, 19] Operation: 35-16=19 Exploring Operation: 54-35=19, Resulting Numbers: [16, 25, 19] Generated Node #0,2: 29:[16, 25, 19] Operation: 54-35=19 Exploring Operation: 54-25=29, Resulting Numbers: [16, 35, 29] Generated Node #0,3: 29:[16, 35, 29] Operation: 54-25=29 Moving to Node #0,0 Current State: 29:[25, 35, 38], Operations: ['54-16=38'] Exploring Operation: 38-25=13, Resulting Numbers: [35, 13] Generated Node #0,0,0: 29:[35, 13] Operation: 38-25=13 Exploring Operation: 25+35=60, Resulting Numbers: [38, 60] Generated Node #0,0,1: 29:[38, 60] Operation: 25+35=60 Exploring Operation: 35-25=10, Resulting Numbers: [38, 10] Generated Node #0,0,2: 29:[38, 10] Operation: 35-25=10 Exploring Operation: 38-35=3, Resulting Numbers: [25, 3] Generated Node #0,0,3: 29:[25, 3] Operation: 38-35=3 Moving to Node #0,3 Current State: 29:[16, 35, 29], Operations: ['54-25=29'] Exploring Operation: 29-16=13, Resulting Numbers: [35, 13] Generated Node #0,3,0: 29:[35, 13] Operation: 29-16=13 Exploring Operation: 35-16=19, Resulting Numbers: [29, 19] Generated Node #0,3,1: 29:[29, 19] Operation: 35-16=19 Exploring Operation: 16+29=45, Resulting Numbers: [35, 45] Generated Node #0,3,2: 29:[35, 45] Operation: 16+29=45 Exploring Operation: 16+35=51, Resulting Numbers: [29, 51] Generated Node #0,3,3: 29:[29, 51] Operation: 16+35=51 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 29:[29, 19], Operations: ['54-25=29', '35-16=19'] Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 29*19=551, Resulting Numbers: [551] 551,29 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 #0,3,0 Current State: 29:[35, 13], Operations: ['54-25=29', '29-16=13'] Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,29 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,29 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 #0,3,2 Current State: 29:[35, 45], Operations: ['54-25=29', '16+29=45'] Exploring Operation: 35*45=1575, Resulting Numbers: [1575] 1575,29 unequal: No Solution Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,29 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 #0,3,3 Current State: 29:[29, 51], Operations: ['54-25=29', '16+35=51'] Exploring Operation: 29*51=1479, Resulting Numbers: [1479] 1479,29 unequal: No Solution Exploring Operation: 29+51=80, Resulting Numbers: [80] 80,29 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,29 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: 29:[16, 25, 19], Operations: ['54-35=19'] Exploring Operation: 25-16=9, Resulting Numbers: [19, 9] Generated Node #0,2,0: 29:[19, 9] Operation: 25-16=9 Exploring Operation: 25+19=44, Resulting Numbers: [16, 44] Generated Node #0,2,1: 29:[16, 44] Operation: 25+19=44 Exploring Operation: 16+19=35, Resulting Numbers: [25, 35] Generated Node #0,2,2: 29:[25, 35] Operation: 16+19=35 Exploring Operation: 16+25=41, Resulting Numbers: [19, 41] Generated Node #0,2,3: 29:[19, 41] Operation: 16+25=41 Moving to Node #0,1 Current State: 29:[25, 54, 19], Operations: ['35-16=19'] Exploring Operation: 54-19=35, Resulting Numbers: [25, 35] Generated Node #0,1,0: 29:[25, 35] Operation: 54-19=35 Exploring Operation: 25-19=6, Resulting Numbers: [54, 6] Generated Node #0,1,1: 29:[54, 6] Operation: 25-19=6 Exploring Operation: 25+19=44, Resulting Numbers: [54, 44] Generated Node #0,1,2: 29:[54, 44] Operation: 25+19=44 Exploring Operation: 54-25=29, Resulting Numbers: [19, 29] Generated Node #0,1,3: 29:[19, 29] Operation: 54-25=29 Moving to Node #0,2,2 Current State: 29:[25, 35], Operations: ['54-35=19', '16+19=35'] Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,29 unequal: No Solution Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[25, 35], Operations: ['35-16=19', '54-19=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,29 unequal: No Solution Moving to Node #0,1,3 Current State: 29:[19, 29], Operations: ['35-16=19', '54-25=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 19*29=551, Resulting Numbers: [551] 551,29 unequal: No Solution Moving to Node #0,2,3 Current State: 29:[19, 41], Operations: ['54-35=19', '16+25=41'] Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 19+41=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 19*41=779, Resulting Numbers: [779] 779,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[35, 13], Operations: ['54-16=38', '38-25=13'] Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,29 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[16, 44], Operations: ['54-35=19', '25+19=44'] Exploring Operation: 16*44=704, Resulting Numbers: [704] 704,29 unequal: No Solution Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 16+44=60, Resulting Numbers: [60] 60,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[38, 10], Operations: ['54-16=38', '35-25=10'] Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 38+10=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 38*10=380, Resulting Numbers: [380] 380,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[25, 3], Operations: ['54-16=38', '38-35=3'] Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[19, 9], Operations: ['54-35=19', '25-16=9'] Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,29 unequal: No Solution Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[38, 60], Operations: ['54-16=38', '25+35=60'] Exploring Operation: 38+60=98, Resulting Numbers: [98] 98,29 unequal: No Solution Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 38*60=2280, Resulting Numbers: [2280] 2280,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[54, 44], Operations: ['35-16=19', '25+19=44'] Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,29 unequal: No Solution Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[54, 6], Operations: ['35-16=19', '25-19=6'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,29 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 48, 30, 83, 98 ]
50
[ "98-83=15", "30/15=2", "48+2=50" ]
Current State: 50:[48, 30, 83, 98], Operations: [] Exploring Operation: 98-83=15, Resulting Numbers: [48, 30, 15] Generated Node #2: [48, 30, 15] from Operation: 98-83=15 Current State: 50:[48, 30, 15], Operations: ['98-83=15'] Exploring Operation: 30/15=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 30/15=2 Current State: 50:[48, 2], Operations: ['98-83=15', '30/15=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[48, 30, 83, 98], Operations: [] Exploring Operation: 98-83=15, Resulting Numbers: [48, 30, 15] Generated Node #0,0: 50:[48, 30, 15] Operation: 98-83=15 Moving to Node #0,0 Current State: 50:[48, 30, 15], Operations: ['98-83=15'] Exploring Operation: 30/15=2, Resulting Numbers: [48, 2] Generated Node #0,0,0: 50:[48, 2] Operation: 30/15=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[48, 2], Operations: ['98-83=15', '30/15=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[48, 30, 83, 98], Operations: [] Exploring Operation: 98-83=15, Resulting Numbers: [48, 30, 15] Generated Node #0,0: 50:[48, 30, 15] Operation: 98-83=15 Moving to Node #0,0 Current State: 50:[48, 30, 15], Operations: ['98-83=15'] Exploring Operation: 30/15=2, Resulting Numbers: [48, 2] Generated Node #0,0,0: 50:[48, 2] Operation: 30/15=2 Moving to Node #0,0,0 Current State: 50:[48, 2], Operations: ['98-83=15', '30/15=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 95, 35, 6, 14 ]
68
[ "95-35=60", "14-6=8", "60+8=68" ]
Current State: 68:[95, 35, 6, 14], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [6, 14, 60] Generated Node #2: [6, 14, 60] from Operation: 95-35=60 Current State: 68:[6, 14, 60], Operations: ['95-35=60'] Exploring Operation: 14-6=8, Resulting Numbers: [60, 8] Generated Node #3: [60, 8] from Operation: 14-6=8 Current State: 68:[60, 8], Operations: ['95-35=60', '14-6=8'] Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[95, 35, 6, 14], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [6, 14, 60] Generated Node #0,0: 68:[6, 14, 60] Operation: 95-35=60 Exploring Operation: 95-14=81, Resulting Numbers: [35, 6, 81] Generated Node #0,1: 68:[35, 6, 81] Operation: 95-14=81 Moving to Node #0,0 Current State: 68:[6, 14, 60], Operations: ['95-35=60'] Exploring Operation: 6+60=66, Resulting Numbers: [14, 66] Generated Node #0,0,0: 68:[14, 66] Operation: 6+60=66 Exploring Operation: 14+60=74, Resulting Numbers: [6, 74] Generated Node #0,0,1: 68:[6, 74] Operation: 14+60=74 Moving to Node #0,1 Current State: 68:[35, 6, 81], Operations: ['95-14=81'] Exploring Operation: 81-6=75, Resulting Numbers: [35, 75] Generated Node #0,1,0: 68:[35, 75] Operation: 81-6=75 Exploring Operation: 81-35=46, Resulting Numbers: [6, 46] Generated Node #0,1,1: 68:[6, 46] Operation: 81-35=46 Moving to Node #0,0,0 Current State: 68:[14, 66], Operations: ['95-35=60', '6+60=66'] Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 14+66=80, Resulting Numbers: [80] 80,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[35, 75], Operations: ['95-14=81', '81-6=75'] Exploring Operation: 35+75=110, Resulting Numbers: [110] 110,68 unequal: No Solution Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[6, 74], Operations: ['95-35=60', '14+60=74'] Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[95, 35, 6, 14], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [6, 14, 60] Generated Node #0,0: 68:[6, 14, 60] Operation: 95-35=60 Moving to Node #0,0 Current State: 68:[6, 14, 60], Operations: ['95-35=60'] Exploring Operation: 14+60=74, Resulting Numbers: [6, 74] Generated Node #0,0,1: 68:[6, 74] Operation: 14+60=74 Moving to Node #0,0,1 Current State: 68:[6, 74], Operations: ['95-35=60', '14+60=74'] Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 47, 1, 33, 66 ]
96
[ "47+1=48", "66/33=2", "48*2=96" ]
Current State: 96:[47, 1, 33, 66], Operations: [] Exploring Operation: 47+1=48, Resulting Numbers: [33, 66, 48] Generated Node #2: [33, 66, 48] from Operation: 47+1=48 Current State: 96:[33, 66, 48], Operations: ['47+1=48'] Exploring Operation: 66/33=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 66/33=2 Current State: 96:[48, 2], Operations: ['47+1=48', '66/33=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[47, 1, 33, 66], Operations: [] Exploring Operation: 66/33=2, Resulting Numbers: [47, 1, 2] Generated Node #0,0: 96:[47, 1, 2] Operation: 66/33=2 Exploring Operation: 66-33=33, Resulting Numbers: [47, 1, 33] Generated Node #0,1: 96:[47, 1, 33] Operation: 66-33=33 Moving to Node #0,0 Current State: 96:[47, 1, 2], Operations: ['66/33=2'] Exploring Operation: 47+1=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 96:[2, 48] Operation: 47+1=48 Exploring Operation: 47*1=47, Resulting Numbers: [2, 47] Generated Node #0,0,1: 96:[2, 47] Operation: 47*1=47 Moving to Node #0,1 Current State: 96:[47, 1, 33], Operations: ['66-33=33'] Exploring Operation: 33-1=32, Resulting Numbers: [47, 32] Generated Node #0,1,0: 96:[47, 32] Operation: 33-1=32 Exploring Operation: 47+1=48, Resulting Numbers: [33, 48] Generated Node #0,1,1: 96:[33, 48] Operation: 47+1=48 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[47, 32], Operations: ['66-33=33', '33-1=32'] Exploring Operation: 47+32=79, Resulting Numbers: [79] 79,96 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[33, 48], Operations: ['66-33=33', '47+1=48'] Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,96 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,96 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: 96:[2, 48], Operations: ['66/33=2', '47+1=48'] Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[47, 1, 33, 66], Operations: [] Exploring Operation: 66/33=2, Resulting Numbers: [47, 1, 2] Generated Node #0,0: 96:[47, 1, 2] Operation: 66/33=2 Moving to Node #0,0 Current State: 96:[47, 1, 2], Operations: ['66/33=2'] Exploring Operation: 47+1=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 96:[2, 48] Operation: 47+1=48 Moving to Node #0,0,0 Current State: 96:[2, 48], Operations: ['66/33=2', '47+1=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 24, 79, 25, 64 ]
14
[ "24+79=103", "25+64=89", "103-89=14" ]
Current State: 14:[24, 79, 25, 64], Operations: [] Exploring Operation: 24+79=103, Resulting Numbers: [25, 64, 103] Generated Node #2: [25, 64, 103] from Operation: 24+79=103 Current State: 14:[25, 64, 103], Operations: ['24+79=103'] Exploring Operation: 25+64=89, Resulting Numbers: [103, 89] Generated Node #3: [103, 89] from Operation: 25+64=89 Current State: 14:[103, 89], Operations: ['24+79=103', '25+64=89'] Exploring Operation: 103-89=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[24, 79, 25, 64], Operations: [] Exploring Operation: 79-64=15, Resulting Numbers: [24, 25, 15] Generated Node #0,0: 14:[24, 25, 15] Operation: 79-64=15 Moving to Node #0,0 Current State: 14:[24, 25, 15], Operations: ['79-64=15'] Exploring Operation: 25-24=1, Resulting Numbers: [15, 1] Generated Node #0,0,0: 14:[15, 1] Operation: 25-24=1 Moving to Node #0,0,0 Current State: 14:[15, 1], Operations: ['79-64=15', '25-24=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[24, 79, 25, 64], Operations: [] Exploring Operation: 79-64=15, Resulting Numbers: [24, 25, 15] Generated Node #0,0: 14:[24, 25, 15] Operation: 79-64=15 Moving to Node #0,0 Current State: 14:[24, 25, 15], Operations: ['79-64=15'] Exploring Operation: 25-24=1, Resulting Numbers: [15, 1] Generated Node #0,0,0: 14:[15, 1] Operation: 25-24=1 Moving to Node #0,0,0 Current State: 14:[15, 1], Operations: ['79-64=15', '25-24=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 62, 59, 94, 12 ]
15
[ "62+59=121", "94+12=106", "121-106=15" ]
Current State: 15:[62, 59, 94, 12], Operations: [] Exploring Operation: 62+59=121, Resulting Numbers: [94, 12, 121] Generated Node #2: [94, 12, 121] from Operation: 62+59=121 Current State: 15:[94, 12, 121], Operations: ['62+59=121'] Exploring Operation: 94+12=106, Resulting Numbers: [121, 106] Generated Node #3: [121, 106] from Operation: 94+12=106 Current State: 15:[121, 106], Operations: ['62+59=121', '94+12=106'] Exploring Operation: 121-106=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[62, 59, 94, 12], Operations: [] Exploring Operation: 94-59=35, Resulting Numbers: [62, 12, 35] Generated Node #0,0: 15:[62, 12, 35] Operation: 94-59=35 Exploring Operation: 62-59=3, Resulting Numbers: [94, 12, 3] Generated Node #0,1: 15:[94, 12, 3] Operation: 62-59=3 Exploring Operation: 62-12=50, Resulting Numbers: [59, 94, 50] Generated Node #0,2: 15:[59, 94, 50] Operation: 62-12=50 Exploring Operation: 94-62=32, Resulting Numbers: [59, 12, 32] Generated Node #0,3: 15:[59, 12, 32] Operation: 94-62=32 Start Sub Search at level 1: Moving to Node #0,3 Current State: 15:[59, 12, 32], Operations: ['94-62=32'] Exploring Operation: 59+12=71, Resulting Numbers: [32, 71] Generated Node #0,3,0: 15:[32, 71] Operation: 59+12=71 Exploring Operation: 59-32=27, Resulting Numbers: [12, 27] Generated Node #0,3,1: 15:[12, 27] Operation: 59-32=27 Exploring Operation: 32-12=20, Resulting Numbers: [59, 20] Generated Node #0,3,2: 15:[59, 20] Operation: 32-12=20 Exploring Operation: 59-12=47, Resulting Numbers: [32, 47] Generated Node #0,3,3: 15:[32, 47] Operation: 59-12=47 Moving to Node #0,3,1 Current State: 15:[12, 27], Operations: ['94-62=32', '59-32=27'] Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,15 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,15 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[62, 59, 94, 12], Operations: [] Exploring Operation: 94-62=32, Resulting Numbers: [59, 12, 32] Generated Node #0,3: 15:[59, 12, 32] Operation: 94-62=32 Moving to Node #0,3 Current State: 15:[59, 12, 32], Operations: ['94-62=32'] Exploring Operation: 59-32=27, Resulting Numbers: [12, 27] Generated Node #0,3,1: 15:[12, 27] Operation: 59-32=27 Moving to Node #0,3,1 Current State: 15:[12, 27], Operations: ['94-62=32', '59-32=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 40, 65, 95, 49 ]
38
[ "65-49=16", "95*16=1520", "1520/40=38" ]
Current State: 38:[40, 65, 95, 49], Operations: [] Exploring Operation: 65-49=16, Resulting Numbers: [40, 95, 16] Generated Node #2: [40, 95, 16] from Operation: 65-49=16 Current State: 38:[40, 95, 16], Operations: ['65-49=16'] Exploring Operation: 95*16=1520, Resulting Numbers: [40, 1520] Generated Node #3: [40, 1520] from Operation: 95*16=1520 Current State: 38:[40, 1520], Operations: ['65-49=16', '95*16=1520'] Exploring Operation: 1520/40=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[40, 65, 95, 49], Operations: [] Exploring Operation: 95-40=55, Resulting Numbers: [65, 49, 55] Generated Node #0,0: 38:[65, 49, 55] Operation: 95-40=55 Exploring Operation: 95-65=30, Resulting Numbers: [40, 49, 30] Generated Node #0,1: 38:[40, 49, 30] Operation: 95-65=30 Exploring Operation: 95-49=46, Resulting Numbers: [40, 65, 46] Generated Node #0,2: 38:[40, 65, 46] Operation: 95-49=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[40, 49, 30], Operations: ['95-65=30'] Exploring Operation: 40-30=10, Resulting Numbers: [49, 10] Generated Node #0,1,0: 38:[49, 10] Operation: 40-30=10 Exploring Operation: 49-40=9, Resulting Numbers: [30, 9] Generated Node #0,1,1: 38:[30, 9] Operation: 49-40=9 Exploring Operation: 49-30=19, Resulting Numbers: [40, 19] Generated Node #0,1,2: 38:[40, 19] Operation: 49-30=19 Moving to Node #0,1,2 Current State: 38:[40, 19], Operations: ['95-65=30', '49-30=19'] Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 40+19=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 40*19=760, Resulting Numbers: [760] 760,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[30, 9], Operations: ['95-65=30', '49-40=9'] Exploring Operation: 30*9=270, Resulting Numbers: [270] 270,38 unequal: No Solution Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[49, 10], Operations: ['95-65=30', '40-30=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,38 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,38 unequal: No Solution No 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: 38:[40, 65, 46], Operations: ['95-49=46'] Exploring Operation: 65-46=19, Resulting Numbers: [40, 19] Generated Node #0,2,0: 38:[40, 19] Operation: 65-46=19 Exploring Operation: 46-40=6, Resulting Numbers: [65, 6] Generated Node #0,2,1: 38:[65, 6] Operation: 46-40=6 Exploring Operation: 65-40=25, Resulting Numbers: [46, 25] Generated Node #0,2,2: 38:[46, 25] Operation: 65-40=25 Moving to Node #0,2,0 Current State: 38:[40, 19], Operations: ['95-49=46', '65-46=19'] Exploring Operation: 40*19=760, Resulting Numbers: [760] 760,38 unequal: No Solution Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 40+19=59, Resulting Numbers: [59] 59,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[46, 25], Operations: ['95-49=46', '65-40=25'] Exploring Operation: 46*25=1150, Resulting Numbers: [1150] 1150,38 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 46+25=71, Resulting Numbers: [71] 71,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[65, 6], Operations: ['95-49=46', '46-40=6'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 65*6=390, Resulting Numbers: [390] 390,38 unequal: No Solution No 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: 38:[65, 49, 55], Operations: ['95-40=55'] Exploring Operation: 65-49=16, Resulting Numbers: [55, 16] Generated Node #0,0,0: 38:[55, 16] Operation: 65-49=16 Exploring Operation: 65-55=10, Resulting Numbers: [49, 10] Generated Node #0,0,1: 38:[49, 10] Operation: 65-55=10 Exploring Operation: 55-49=6, Resulting Numbers: [65, 6] Generated Node #0,0,2: 38:[65, 6] Operation: 55-49=6 Moving to Node #0,0,1 Current State: 38:[49, 10], Operations: ['95-40=55', '65-55=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,38 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[55, 16], Operations: ['95-40=55', '65-49=16'] Exploring Operation: 55*16=880, Resulting Numbers: [880] 880,38 unequal: No Solution Exploring Operation: 55-16=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 55+16=71, Resulting Numbers: [71] 71,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[65, 6], Operations: ['95-40=55', '55-49=6'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 65*6=390, Resulting Numbers: [390] 390,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 7, 68, 49, 59 ]
16
[ "49/7=7", "68-59=9", "7+9=16" ]
Current State: 16:[7, 68, 49, 59], Operations: [] Exploring Operation: 49/7=7, Resulting Numbers: [68, 59, 7] Generated Node #2: [68, 59, 7] from Operation: 49/7=7 Current State: 16:[68, 59, 7], Operations: ['49/7=7'] Exploring Operation: 68-59=9, Resulting Numbers: [7, 9] Generated Node #3: [7, 9] from Operation: 68-59=9 Current State: 16:[7, 9], Operations: ['49/7=7', '68-59=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[7, 68, 49, 59], Operations: [] Exploring Operation: 68-49=19, Resulting Numbers: [7, 59, 19] Generated Node #0,0: 16:[7, 59, 19] Operation: 68-49=19 Exploring Operation: 59-49=10, Resulting Numbers: [7, 68, 10] Generated Node #0,1: 16:[7, 68, 10] Operation: 59-49=10 Exploring Operation: 68-59=9, Resulting Numbers: [7, 49, 9] Generated Node #0,2: 16:[7, 49, 9] Operation: 68-59=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[7, 49, 9], Operations: ['68-59=9'] Exploring Operation: 49-7=42, Resulting Numbers: [9, 42] Generated Node #0,2,0: 16:[9, 42] Operation: 49-7=42 Exploring Operation: 49/7=7, Resulting Numbers: [9, 7] Generated Node #0,2,1: 16:[9, 7] Operation: 49/7=7 Exploring Operation: 49-9=40, Resulting Numbers: [7, 40] Generated Node #0,2,2: 16:[7, 40] Operation: 49-9=40 Moving to Node #0,2,1 Current State: 16:[9, 7], Operations: ['68-59=9', '49/7=7'] Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,16 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[7, 68, 49, 59], Operations: [] Exploring Operation: 68-59=9, Resulting Numbers: [7, 49, 9] Generated Node #0,2: 16:[7, 49, 9] Operation: 68-59=9 Moving to Node #0,2 Current State: 16:[7, 49, 9], Operations: ['68-59=9'] Exploring Operation: 49/7=7, Resulting Numbers: [9, 7] Generated Node #0,2,1: 16:[9, 7] Operation: 49/7=7 Moving to Node #0,2,1 Current State: 16:[9, 7], Operations: ['68-59=9', '49/7=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 73, 55, 96, 37 ]
98
[ "73+37=110", "110/55=2", "96+2=98" ]
Current State: 98:[73, 55, 96, 37], Operations: [] Exploring Operation: 73+37=110, Resulting Numbers: [55, 96, 110] Generated Node #2: [55, 96, 110] from Operation: 73+37=110 Current State: 98:[55, 96, 110], Operations: ['73+37=110'] Exploring Operation: 110/55=2, Resulting Numbers: [96, 2] Generated Node #3: [96, 2] from Operation: 110/55=2 Current State: 98:[96, 2], Operations: ['73+37=110', '110/55=2'] Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[73, 55, 96, 37], Operations: [] Exploring Operation: 73-37=36, Resulting Numbers: [55, 96, 36] Generated Node #0,0: 98:[55, 96, 36] Operation: 73-37=36 Exploring Operation: 73+37=110, Resulting Numbers: [55, 96, 110] Generated Node #0,1: 98:[55, 96, 110] Operation: 73+37=110 Exploring Operation: 73-55=18, Resulting Numbers: [96, 37, 18] Generated Node #0,2: 98:[96, 37, 18] Operation: 73-55=18 Moving to Node #0,2 Current State: 98:[96, 37, 18], Operations: ['73-55=18'] Exploring Operation: 37+18=55, Resulting Numbers: [96, 55] Generated Node #0,2,0: 98:[96, 55] Operation: 37+18=55 Exploring Operation: 37-18=19, Resulting Numbers: [96, 19] Generated Node #0,2,1: 98:[96, 19] Operation: 37-18=19 Exploring Operation: 96-37=59, Resulting Numbers: [18, 59] Generated Node #0,2,2: 98:[18, 59] Operation: 96-37=59 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 98:[96, 19], Operations: ['73-55=18', '37-18=19'] Exploring Operation: 96-19=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 96*19=1824, Resulting Numbers: [1824] 1824,98 unequal: No Solution Exploring Operation: 96+19=115, Resulting Numbers: [115] 115,98 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 #0,2,0 Current State: 98:[96, 55], Operations: ['73-55=18', '37+18=55'] Exploring Operation: 96+55=151, Resulting Numbers: [151] 151,98 unequal: No Solution Exploring Operation: 96*55=5280, Resulting Numbers: [5280] 5280,98 unequal: No Solution Exploring Operation: 96-55=41, Resulting Numbers: [41] 41,98 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 #0,2,2 Current State: 98:[18, 59], Operations: ['73-55=18', '96-37=59'] Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 18*59=1062, Resulting Numbers: [1062] 1062,98 unequal: No Solution Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,98 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: 98:[55, 96, 110], Operations: ['73+37=110'] Exploring Operation: 110-55=55, Resulting Numbers: [96, 55] Generated Node #0,1,0: 98:[96, 55] Operation: 110-55=55 Exploring Operation: 110/55=2, Resulting Numbers: [96, 2] Generated Node #0,1,1: 98:[96, 2] Operation: 110/55=2 Exploring Operation: 110-96=14, Resulting Numbers: [55, 14] Generated Node #0,1,2: 98:[55, 14] Operation: 110-96=14 Moving to Node #0,0 Current State: 98:[55, 96, 36], Operations: ['73-37=36'] Exploring Operation: 55-36=19, Resulting Numbers: [96, 19] Generated Node #0,0,0: 98:[96, 19] Operation: 55-36=19 Exploring Operation: 96-36=60, Resulting Numbers: [55, 60] Generated Node #0,0,1: 98:[55, 60] Operation: 96-36=60 Exploring Operation: 55+36=91, Resulting Numbers: [96, 91] Generated Node #0,0,2: 98:[96, 91] Operation: 55+36=91 Moving to Node #0,1,1 Current State: 98:[96, 2], Operations: ['73+37=110', '110/55=2'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[73, 55, 96, 37], Operations: [] Exploring Operation: 73+37=110, Resulting Numbers: [55, 96, 110] Generated Node #0,1: 98:[55, 96, 110] Operation: 73+37=110 Moving to Node #0,1 Current State: 98:[55, 96, 110], Operations: ['73+37=110'] Exploring Operation: 110/55=2, Resulting Numbers: [96, 2] Generated Node #0,1,1: 98:[96, 2] Operation: 110/55=2 Moving to Node #0,1,1 Current State: 98:[96, 2], Operations: ['73+37=110', '110/55=2'] Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 18, 98, 17, 92 ]
41
[ "18+98=116", "92-17=75", "116-75=41" ]
Current State: 41:[18, 98, 17, 92], Operations: [] Exploring Operation: 18+98=116, Resulting Numbers: [17, 92, 116] Generated Node #2: [17, 92, 116] from Operation: 18+98=116 Current State: 41:[17, 92, 116], Operations: ['18+98=116'] Exploring Operation: 92-17=75, Resulting Numbers: [116, 75] Generated Node #3: [116, 75] from Operation: 92-17=75 Current State: 41:[116, 75], Operations: ['18+98=116', '92-17=75'] Exploring Operation: 116-75=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[18, 98, 17, 92], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [18, 17, 6] Generated Node #0,0: 41:[18, 17, 6] Operation: 98-92=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[18, 17, 6], Operations: ['98-92=6'] Exploring Operation: 18+17=35, Resulting Numbers: [6, 35] Generated Node #0,0,0: 41:[6, 35] Operation: 18+17=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[6, 35], Operations: ['98-92=6', '18+17=35'] Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[18, 98, 17, 92], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [18, 17, 6] Generated Node #0,0: 41:[18, 17, 6] Operation: 98-92=6 Moving to Node #0,0 Current State: 41:[18, 17, 6], Operations: ['98-92=6'] Exploring Operation: 18+17=35, Resulting Numbers: [6, 35] Generated Node #0,0,0: 41:[6, 35] Operation: 18+17=35 Moving to Node #0,0,0 Current State: 41:[6, 35], Operations: ['98-92=6', '18+17=35'] Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 4, 29, 5, 77 ]
97
[ "29-4=25", "77-5=72", "25+72=97" ]
Current State: 97:[4, 29, 5, 77], Operations: [] Exploring Operation: 29-4=25, Resulting Numbers: [5, 77, 25] Generated Node #2: [5, 77, 25] from Operation: 29-4=25 Current State: 97:[5, 77, 25], Operations: ['29-4=25'] Exploring Operation: 77-5=72, Resulting Numbers: [25, 72] Generated Node #3: [25, 72] from Operation: 77-5=72 Current State: 97:[25, 72], Operations: ['29-4=25', '77-5=72'] Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[4, 29, 5, 77], Operations: [] Exploring Operation: 4*29=116, Resulting Numbers: [5, 77, 116] Generated Node #0,0: 97:[5, 77, 116] Operation: 4*29=116 Exploring Operation: 29*5=145, Resulting Numbers: [4, 77, 145] Generated Node #0,1: 97:[4, 77, 145] Operation: 29*5=145 Exploring Operation: 4*5=20, Resulting Numbers: [29, 77, 20] Generated Node #0,2: 97:[29, 77, 20] Operation: 4*5=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[5, 77, 116], Operations: ['4*29=116'] Exploring Operation: 5+77=82, Resulting Numbers: [116, 82] Generated Node #0,0,0: 97:[116, 82] Operation: 5+77=82 Exploring Operation: 77-5=72, Resulting Numbers: [116, 72] Generated Node #0,0,1: 97:[116, 72] Operation: 77-5=72 Exploring Operation: 116-5=111, Resulting Numbers: [77, 111] Generated Node #0,0,2: 97:[77, 111] Operation: 116-5=111 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[116, 82], Operations: ['4*29=116', '5+77=82'] Exploring Operation: 116-82=34, Resulting Numbers: [34] 34,97 unequal: No Solution Exploring Operation: 116+82=198, Resulting Numbers: [198] 198,97 unequal: No Solution Exploring Operation: 116*82=9512, Resulting Numbers: [9512] 9512,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 97:[77, 111], Operations: ['4*29=116', '116-5=111'] Exploring Operation: 77*111=8547, Resulting Numbers: [8547] 8547,97 unequal: No Solution Exploring Operation: 77+111=188, Resulting Numbers: [188] 188,97 unequal: No Solution Exploring Operation: 111-77=34, Resulting Numbers: [34] 34,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 97:[116, 72], Operations: ['4*29=116', '77-5=72'] Exploring Operation: 116*72=8352, Resulting Numbers: [8352] 8352,97 unequal: No Solution Exploring Operation: 116-72=44, Resulting Numbers: [44] 44,97 unequal: No Solution Exploring Operation: 116+72=188, Resulting Numbers: [188] 188,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[4, 77, 145], Operations: ['29*5=145'] Exploring Operation: 145-4=141, Resulting Numbers: [77, 141] Generated Node #0,1,0: 97:[77, 141] Operation: 145-4=141 Exploring Operation: 77-4=73, Resulting Numbers: [145, 73] Generated Node #0,1,1: 97:[145, 73] Operation: 77-4=73 Exploring Operation: 4+77=81, Resulting Numbers: [145, 81] Generated Node #0,1,2: 97:[145, 81] Operation: 4+77=81 Moving to Node #0,1,0 Current State: 97:[77, 141], Operations: ['29*5=145', '145-4=141'] Exploring Operation: 77*141=10857, Resulting Numbers: [10857] 10857,97 unequal: No Solution Exploring Operation: 77+141=218, Resulting Numbers: [218] 218,97 unequal: No Solution Exploring Operation: 141-77=64, Resulting Numbers: [64] 64,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[145, 81], Operations: ['29*5=145', '4+77=81'] Exploring Operation: 145-81=64, Resulting Numbers: [64] 64,97 unequal: No Solution Exploring Operation: 145*81=11745, Resulting Numbers: [11745] 11745,97 unequal: No Solution Exploring Operation: 145+81=226, Resulting Numbers: [226] 226,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[145, 73], Operations: ['29*5=145', '77-4=73'] Exploring Operation: 145+73=218, Resulting Numbers: [218] 218,97 unequal: No Solution Exploring Operation: 145*73=10585, Resulting Numbers: [10585] 10585,97 unequal: No Solution Exploring Operation: 145-73=72, Resulting Numbers: [72] 72,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[29, 77, 20], Operations: ['4*5=20'] Exploring Operation: 29+77=106, Resulting Numbers: [20, 106] Generated Node #0,2,0: 97:[20, 106] Operation: 29+77=106 Exploring Operation: 29+20=49, Resulting Numbers: [77, 49] Generated Node #0,2,1: 97:[77, 49] Operation: 29+20=49 Exploring Operation: 77+20=97, Resulting Numbers: [29, 97] Generated Node #0,2,2: 97:[29, 97] Operation: 77+20=97 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[77, 49], Operations: ['4*5=20', '29+20=49'] Exploring Operation: 77*49=3773, Resulting Numbers: [3773] 3773,97 unequal: No Solution Exploring Operation: 77+49=126, Resulting Numbers: [126] 126,97 unequal: No Solution Exploring Operation: 77-49=28, Resulting Numbers: [28] 28,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[29, 97], Operations: ['4*5=20', '77+20=97'] Exploring Operation: 29+97=126, Resulting Numbers: [126] 126,97 unequal: No Solution Exploring Operation: 29*97=2813, Resulting Numbers: [2813] 2813,97 unequal: No Solution Exploring Operation: 97-29=68, Resulting Numbers: [68] 68,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[20, 106], Operations: ['4*5=20', '29+77=106'] Exploring Operation: 106-20=86, Resulting Numbers: [86] 86,97 unequal: No Solution Exploring Operation: 20+106=126, Resulting Numbers: [126] 126,97 unequal: No Solution Exploring Operation: 20*106=2120, Resulting Numbers: [2120] 2120,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 49, 62, 5, 33 ]
68
[ "62+33=95", "95/5=19", "49+19=68" ]
Current State: 68:[49, 62, 5, 33], Operations: [] Exploring Operation: 62+33=95, Resulting Numbers: [49, 5, 95] Generated Node #2: [49, 5, 95] from Operation: 62+33=95 Current State: 68:[49, 5, 95], Operations: ['62+33=95'] Exploring Operation: 95/5=19, Resulting Numbers: [49, 19] Generated Node #3: [49, 19] from Operation: 95/5=19 Current State: 68:[49, 19], Operations: ['62+33=95', '95/5=19'] Exploring Operation: 49+19=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[49, 62, 5, 33], Operations: [] Exploring Operation: 49-33=16, Resulting Numbers: [62, 5, 16] Generated Node #0,0: 68:[62, 5, 16] Operation: 49-33=16 Exploring Operation: 62-49=13, Resulting Numbers: [5, 33, 13] Generated Node #0,1: 68:[5, 33, 13] Operation: 62-49=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[5, 33, 13], Operations: ['62-49=13'] Exploring Operation: 5*13=65, Resulting Numbers: [33, 65] Generated Node #0,1,0: 68:[33, 65] Operation: 5*13=65 Exploring Operation: 5+13=18, Resulting Numbers: [33, 18] Generated Node #0,1,1: 68:[33, 18] Operation: 5+13=18 Moving to Node #0,1,1 Current State: 68:[33, 18], Operations: ['62-49=13', '5+13=18'] Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,68 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[33, 65], Operations: ['62-49=13', '5*13=65'] Exploring Operation: 33+65=98, Resulting Numbers: [98] 98,68 unequal: No Solution Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[62, 5, 16], Operations: ['49-33=16'] Exploring Operation: 62+5=67, Resulting Numbers: [16, 67] Generated Node #0,0,0: 68:[16, 67] Operation: 62+5=67 Exploring Operation: 5+16=21, Resulting Numbers: [62, 21] Generated Node #0,0,1: 68:[62, 21] Operation: 5+16=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[16, 67], Operations: ['49-33=16', '62+5=67'] Exploring Operation: 67-16=51, Resulting Numbers: [51] 51,68 unequal: No Solution Exploring Operation: 16+67=83, Resulting Numbers: [83] 83,68 unequal: No Solution No 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: 68:[62, 21], Operations: ['49-33=16', '5+16=21'] Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 62+21=83, Resulting Numbers: [83] 83,68 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
[ 25, 45, 75, 91 ]
86
[ "25+45=70", "91-75=16", "70+16=86" ]
Current State: 86:[25, 45, 75, 91], Operations: [] Exploring Operation: 25+45=70, Resulting Numbers: [75, 91, 70] Generated Node #2: [75, 91, 70] from Operation: 25+45=70 Current State: 86:[75, 91, 70], Operations: ['25+45=70'] Exploring Operation: 91-75=16, Resulting Numbers: [70, 16] Generated Node #3: [70, 16] from Operation: 91-75=16 Current State: 86:[70, 16], Operations: ['25+45=70', '91-75=16'] Exploring Operation: 70+16=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[25, 45, 75, 91], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [45, 91, 3] Generated Node #0,0: 86:[45, 91, 3] Operation: 75/25=3 Exploring Operation: 75-25=50, Resulting Numbers: [45, 91, 50] Generated Node #0,1: 86:[45, 91, 50] Operation: 75-25=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[45, 91, 3], Operations: ['75/25=3'] Exploring Operation: 91-3=88, Resulting Numbers: [45, 88] Generated Node #0,0,0: 86:[45, 88] Operation: 91-3=88 Exploring Operation: 91-45=46, Resulting Numbers: [3, 46] Generated Node #0,0,1: 86:[3, 46] Operation: 91-45=46 Moving to Node #0,0,0 Current State: 86:[45, 88], Operations: ['75/25=3', '91-3=88'] Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[3, 46], Operations: ['75/25=3', '91-45=46'] Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[45, 91, 50], Operations: ['75-25=50'] Exploring Operation: 50-45=5, Resulting Numbers: [91, 5] Generated Node #0,1,0: 86:[91, 5] Operation: 50-45=5 Exploring Operation: 91-50=41, Resulting Numbers: [45, 41] Generated Node #0,1,1: 86:[45, 41] Operation: 91-50=41 Moving to Node #0,1,1 Current State: 86:[45, 41], Operations: ['75-25=50', '91-50=41'] Exploring Operation: 45-41=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 45+41=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[25, 45, 75, 91], Operations: [] Exploring Operation: 75-25=50, Resulting Numbers: [45, 91, 50] Generated Node #0,1: 86:[45, 91, 50] Operation: 75-25=50 Moving to Node #0,1 Current State: 86:[45, 91, 50], Operations: ['75-25=50'] Exploring Operation: 91-50=41, Resulting Numbers: [45, 41] Generated Node #0,1,1: 86:[45, 41] Operation: 91-50=41 Moving to Node #0,1,1 Current State: 86:[45, 41], Operations: ['75-25=50', '91-50=41'] Exploring Operation: 45+41=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 30, 3, 18, 15 ]
43
[ "30/3=10", "18+15=33", "10+33=43" ]
Current State: 43:[30, 3, 18, 15], Operations: [] Exploring Operation: 30/3=10, Resulting Numbers: [18, 15, 10] Generated Node #2: [18, 15, 10] from Operation: 30/3=10 Current State: 43:[18, 15, 10], Operations: ['30/3=10'] Exploring Operation: 18+15=33, Resulting Numbers: [10, 33] Generated Node #3: [10, 33] from Operation: 18+15=33 Current State: 43:[10, 33], Operations: ['30/3=10', '18+15=33'] Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[30, 3, 18, 15], Operations: [] Exploring Operation: 3*18=54, Resulting Numbers: [30, 15, 54] Generated Node #0,0: 43:[30, 15, 54] Operation: 3*18=54 Exploring Operation: 3+18=21, Resulting Numbers: [30, 15, 21] Generated Node #0,1: 43:[30, 15, 21] Operation: 3+18=21 Exploring Operation: 3*15=45, Resulting Numbers: [30, 18, 45] Generated Node #0,2: 43:[30, 18, 45] Operation: 3*15=45 Exploring Operation: 30+3=33, Resulting Numbers: [18, 15, 33] Generated Node #0,3: 43:[18, 15, 33] Operation: 30+3=33 Exploring Operation: 3+15=18, Resulting Numbers: [30, 18, 18] Generated Node #0,4: 43:[30, 18, 18] Operation: 3+15=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[30, 18, 45], Operations: ['3*15=45'] Exploring Operation: 45-30=15, Resulting Numbers: [18, 15] Generated Node #0,2,0: 43:[18, 15] Operation: 45-30=15 Exploring Operation: 30+18=48, Resulting Numbers: [45, 48] Generated Node #0,2,1: 43:[45, 48] Operation: 30+18=48 Exploring Operation: 30-18=12, Resulting Numbers: [45, 12] Generated Node #0,2,2: 43:[45, 12] Operation: 30-18=12 Exploring Operation: 18+45=63, Resulting Numbers: [30, 63] Generated Node #0,2,3: 43:[30, 63] Operation: 18+45=63 Exploring Operation: 45-18=27, Resulting Numbers: [30, 27] Generated Node #0,2,4: 43:[30, 27] Operation: 45-18=27 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 43:[45, 48], Operations: ['3*15=45', '30+18=48'] 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 Exploring Operation: 45*48=2160, Resulting Numbers: [2160] 2160,43 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 #0,2,4 Current State: 43:[30, 27], Operations: ['3*15=45', '45-18=27'] Exploring Operation: 30+27=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 30*27=810, Resulting Numbers: [810] 810,43 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 #0,2,2 Current State: 43:[45, 12], Operations: ['3*15=45', '30-18=12'] Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,43 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 #0,2,3 Current State: 43:[30, 63], Operations: ['3*15=45', '18+45=63'] Exploring Operation: 30*63=1890, Resulting Numbers: [1890] 1890,43 unequal: No Solution Exploring Operation: 30+63=93, Resulting Numbers: [93] 93,43 unequal: No Solution Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,43 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 #0,2,0 Current State: 43:[18, 15], Operations: ['3*15=45', '45-30=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,43 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,43 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 #0,0 Current State: 43:[30, 15, 54], Operations: ['3*18=54'] Exploring Operation: 30+15=45, Resulting Numbers: [54, 45] Generated Node #0,0,0: 43:[54, 45] Operation: 30+15=45 Exploring Operation: 30-15=15, Resulting Numbers: [54, 15] Generated Node #0,0,1: 43:[54, 15] Operation: 30-15=15 Exploring Operation: 15+54=69, Resulting Numbers: [30, 69] Generated Node #0,0,2: 43:[30, 69] Operation: 15+54=69 Exploring Operation: 54-15=39, Resulting Numbers: [30, 39] Generated Node #0,0,3: 43:[30, 39] Operation: 54-15=39 Exploring Operation: 54-30=24, Resulting Numbers: [15, 24] Generated Node #0,0,4: 43:[15, 24] Operation: 54-30=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[54, 45], Operations: ['3*18=54', '30+15=45'] Exploring Operation: 54+45=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 54*45=2430, Resulting Numbers: [2430] 2430,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 43:[30, 39], Operations: ['3*18=54', '54-15=39'] Exploring Operation: 30*39=1170, Resulting Numbers: [1170] 1170,43 unequal: No Solution Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 30+39=69, Resulting Numbers: [69] 69,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[54, 15], Operations: ['3*18=54', '30-15=15'] Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,43 unequal: No Solution Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 43:[30, 69], Operations: ['3*18=54', '15+54=69'] Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 30*69=2070, Resulting Numbers: [2070] 2070,43 unequal: No Solution Exploring Operation: 30+69=99, Resulting Numbers: [99] 99,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 43:[15, 24], Operations: ['3*18=54', '54-30=24'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[30, 15, 21], Operations: ['3+18=21'] Exploring Operation: 21-15=6, Resulting Numbers: [30, 6] Generated Node #0,1,0: 43:[30, 6] Operation: 21-15=6 Exploring Operation: 30+21=51, Resulting Numbers: [15, 51] Generated Node #0,1,1: 43:[15, 51] Operation: 30+21=51 Exploring Operation: 30+15=45, Resulting Numbers: [21, 45] Generated Node #0,1,2: 43:[21, 45] Operation: 30+15=45 Exploring Operation: 30-15=15, Resulting Numbers: [21, 15] Generated Node #0,1,3: 43:[21, 15] Operation: 30-15=15 Exploring Operation: 15+21=36, Resulting Numbers: [30, 36] Generated Node #0,1,4: 43:[30, 36] Operation: 15+21=36 Moving to Node #0,1,4 Current State: 43:[30, 36], Operations: ['3+18=21', '15+21=36'] Exploring Operation: 30+36=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 30*36=1080, Resulting Numbers: [1080] 1080,43 unequal: No Solution Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[21, 45], Operations: ['3+18=21', '30+15=45'] Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,43 unequal: No Solution Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[15, 51], Operations: ['3+18=21', '30+21=51'] Exploring Operation: 15+51=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 15*51=765, Resulting Numbers: [765] 765,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[30, 6], Operations: ['3+18=21', '21-15=6'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,43 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,43 unequal: No Solution Exploring Operation: 30*6=180, Resulting Numbers: [180] 180,43 unequal: No Solution Exploring Operation: 30+6=36, Resulting Numbers: [36] 36,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[21, 15], Operations: ['3+18=21', '30-15=15'] Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,43 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 43:[18, 15, 33], Operations: ['30+3=33'] Exploring Operation: 15+33=48, Resulting Numbers: [18, 48] Generated Node #0,3,0: 43:[18, 48] Operation: 15+33=48 Exploring Operation: 33-15=18, Resulting Numbers: [18, 18] Generated Node #0,3,1: 43:[18, 18] Operation: 33-15=18 Exploring Operation: 18+33=51, Resulting Numbers: [15, 51] Generated Node #0,3,2: 43:[15, 51] Operation: 18+33=51 Exploring Operation: 18+15=33, Resulting Numbers: [33, 33] Generated Node #0,3,3: 43:[33, 33] Operation: 18+15=33 Exploring Operation: 18-15=3, Resulting Numbers: [33, 3] Generated Node #0,3,4: 43:[33, 3] Operation: 18-15=3 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 43:[33, 33], Operations: ['30+3=33', '18+15=33'] Exploring Operation: 33+33=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 33/33=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 33*33=1089, Resulting Numbers: [1089] 1089,43 unequal: No Solution Exploring Operation: 33-33=0, Resulting Numbers: [0] 0,43 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 #0,3,0 Current State: 43:[18, 48], Operations: ['30+3=33', '15+33=48'] Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,43 unequal: No Solution 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 No 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: 43:[15, 51], Operations: ['30+3=33', '18+33=51'] Exploring Operation: 15*51=765, Resulting Numbers: [765] 765,43 unequal: No Solution Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 15+51=66, Resulting Numbers: [66] 66,43 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 #0,3,1 Current State: 43:[18, 18], Operations: ['30+3=33', '33-15=18'] Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,43 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,43 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 #0,3,4 Current State: 43:[33, 3], Operations: ['30+3=33', '18-15=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,43 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,43 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 #0,4 Current State: 43:[30, 18, 18], Operations: ['3+15=18'] Exploring Operation: 30+18=48, Resulting Numbers: [18, 48] Generated Node #0,4,0: 43:[18, 48] Operation: 30+18=48 Exploring Operation: 18+18=36, Resulting Numbers: [30, 36] Generated Node #0,4,1: 43:[30, 36] Operation: 18+18=36 Exploring Operation: 30+18=48, Resulting Numbers: [18, 48] Generated Node #0,4,2: 43:[18, 48] Operation: 30+18=48 Exploring Operation: 30-18=12, Resulting Numbers: [18, 12] Generated Node #0,4,3: 43:[18, 12] Operation: 30-18=12 Exploring Operation: 18/18=1, Resulting Numbers: [30, 1] Generated Node #0,4,4: 43:[30, 1] Operation: 18/18=1 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 43:[30, 36], Operations: ['3+15=18', '18+18=36'] Exploring Operation: 30*36=1080, Resulting Numbers: [1080] 1080,43 unequal: No Solution Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 30+36=66, Resulting Numbers: [66] 66,43 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 #0,4,0 Current State: 43:[18, 48], Operations: ['3+15=18', '30+18=48'] Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,43 unequal: No Solution 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 No 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: 43:[18, 48], Operations: ['3+15=18', '30+18=48'] Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,43 unequal: No Solution 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 No 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: 43:[30, 1], Operations: ['3+15=18', '18/18=1'] Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,43 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,43 unequal: No Solution Exploring Operation: 30*1=30, Resulting Numbers: [30] 30,43 unequal: No Solution Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,43 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 #0,4,3 Current State: 43:[18, 12], Operations: ['3+15=18', '30-18=12'] Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,43 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,43 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 No solution found.
0
hs_5
sum_heuristic
[ 15, 43, 8, 71 ]
36
[ "71-15=56", "56/8=7", "43-7=36" ]
Current State: 36:[15, 43, 8, 71], Operations: [] Exploring Operation: 71-15=56, Resulting Numbers: [43, 8, 56] Generated Node #2: [43, 8, 56] from Operation: 71-15=56 Current State: 36:[43, 8, 56], Operations: ['71-15=56'] Exploring Operation: 56/8=7, Resulting Numbers: [43, 7] Generated Node #3: [43, 7] from Operation: 56/8=7 Current State: 36:[43, 7], Operations: ['71-15=56', '56/8=7'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[15, 43, 8, 71], Operations: [] Exploring Operation: 71-8=63, Resulting Numbers: [15, 43, 63] Generated Node #0,0: 36:[15, 43, 63] Operation: 71-8=63 Exploring Operation: 15-8=7, Resulting Numbers: [43, 71, 7] Generated Node #0,1: 36:[43, 71, 7] Operation: 15-8=7 Exploring Operation: 71-15=56, Resulting Numbers: [43, 8, 56] Generated Node #0,2: 36:[43, 8, 56] Operation: 71-15=56 Exploring Operation: 43-8=35, Resulting Numbers: [15, 71, 35] Generated Node #0,3: 36:[15, 71, 35] Operation: 43-8=35 Exploring Operation: 71-43=28, Resulting Numbers: [15, 8, 28] Generated Node #0,4: 36:[15, 8, 28] Operation: 71-43=28 Start Sub Search at level 1: Moving to Node #0,4 Current State: 36:[15, 8, 28], Operations: ['71-43=28'] Exploring Operation: 28-8=20, Resulting Numbers: [15, 20] Generated Node #0,4,0: 36:[15, 20] Operation: 28-8=20 Exploring Operation: 15-8=7, Resulting Numbers: [28, 7] Generated Node #0,4,1: 36:[28, 7] Operation: 15-8=7 Exploring Operation: 8+28=36, Resulting Numbers: [15, 36] Generated Node #0,4,2: 36:[15, 36] Operation: 8+28=36 Exploring Operation: 15+28=43, Resulting Numbers: [8, 43] Generated Node #0,4,3: 36:[8, 43] Operation: 15+28=43 Exploring Operation: 28-15=13, Resulting Numbers: [8, 13] Generated Node #0,4,4: 36:[8, 13] Operation: 28-15=13 Moving to Node #0,4,4 Current State: 36:[8, 13], Operations: ['71-43=28', '28-15=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,36 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,36 unequal: No Solution Moving to Node #0,4,2 Current State: 36:[15, 36], Operations: ['71-43=28', '8+28=36'] Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 15+36=51, Resulting Numbers: [51] 51,36 unequal: No Solution Exploring Operation: 15*36=540, Resulting Numbers: [540] 540,36 unequal: No Solution Moving to Node #0,4,0 Current State: 36:[15, 20], Operations: ['71-43=28', '28-8=20'] Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 15*20=300, Resulting Numbers: [300] 300,36 unequal: No Solution Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,36 unequal: No Solution Moving to Node #0,4,3 Current State: 36:[8, 43], Operations: ['71-43=28', '15+28=43'] Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,36 unequal: No Solution Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,36 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,36 unequal: No Solution Moving to Node #0,4,1 Current State: 36:[28, 7], Operations: ['71-43=28', '15-8=7'] Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[43, 8, 56], Operations: ['71-15=56'] Exploring Operation: 56-8=48, Resulting Numbers: [43, 48] Generated Node #0,2,0: 36:[43, 48] Operation: 56-8=48 Exploring Operation: 56-43=13, Resulting Numbers: [8, 13] Generated Node #0,2,1: 36:[8, 13] Operation: 56-43=13 Exploring Operation: 43-8=35, Resulting Numbers: [56, 35] Generated Node #0,2,2: 36:[56, 35] Operation: 43-8=35 Exploring Operation: 43+8=51, Resulting Numbers: [56, 51] Generated Node #0,2,3: 36:[56, 51] Operation: 43+8=51 Exploring Operation: 56/8=7, Resulting Numbers: [43, 7] Generated Node #0,2,4: 36:[43, 7] Operation: 56/8=7 Moving to Node #0,2,1 Current State: 36:[8, 13], Operations: ['71-15=56', '56-43=13'] Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,36 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,36 unequal: No Solution Moving to Node #0,2,4 Current State: 36:[43, 7], Operations: ['71-15=56', '56/8=7'] Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,36 unequal: No Solution Exploring Operation: 43*7=301, Resulting Numbers: [301] 301,36 unequal: No Solution Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[15, 43, 8, 71], Operations: [] Exploring Operation: 71-15=56, Resulting Numbers: [43, 8, 56] Generated Node #0,2: 36:[43, 8, 56] Operation: 71-15=56 Moving to Node #0,2 Current State: 36:[43, 8, 56], Operations: ['71-15=56'] Exploring Operation: 56/8=7, Resulting Numbers: [43, 7] Generated Node #0,2,4: 36:[43, 7] Operation: 56/8=7 Moving to Node #0,2,4 Current State: 36:[43, 7], Operations: ['71-15=56', '56/8=7'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 71, 49, 8, 80 ]
49
[ "71+8=79", "80-79=1", "49*1=49" ]
Current State: 49:[71, 49, 8, 80], Operations: [] Exploring Operation: 71+8=79, Resulting Numbers: [49, 80, 79] Generated Node #2: [49, 80, 79] from Operation: 71+8=79 Current State: 49:[49, 80, 79], Operations: ['71+8=79'] Exploring Operation: 80-79=1, Resulting Numbers: [49, 1] Generated Node #3: [49, 1] from Operation: 80-79=1 Current State: 49:[49, 1], Operations: ['71+8=79', '80-79=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[71, 49, 8, 80], Operations: [] Exploring Operation: 80-49=31, Resulting Numbers: [71, 8, 31] Generated Node #0,0: 49:[71, 8, 31] Operation: 80-49=31 Exploring Operation: 80/8=10, Resulting Numbers: [71, 49, 10] Generated Node #0,1: 49:[71, 49, 10] Operation: 80/8=10 Exploring Operation: 71-8=63, Resulting Numbers: [49, 80, 63] Generated Node #0,2: 49:[49, 80, 63] Operation: 71-8=63 Exploring Operation: 80-71=9, Resulting Numbers: [49, 8, 9] Generated Node #0,3: 49:[49, 8, 9] Operation: 80-71=9 Moving to Node #0,3 Current State: 49:[49, 8, 9], Operations: ['80-71=9'] Exploring Operation: 49+8=57, Resulting Numbers: [9, 57] Generated Node #0,3,0: 49:[9, 57] Operation: 49+8=57 Exploring Operation: 9-8=1, Resulting Numbers: [49, 1] Generated Node #0,3,1: 49:[49, 1] Operation: 9-8=1 Exploring Operation: 49+9=58, Resulting Numbers: [8, 58] Generated Node #0,3,2: 49:[8, 58] Operation: 49+9=58 Exploring Operation: 49-8=41, Resulting Numbers: [9, 41] Generated Node #0,3,3: 49:[9, 41] Operation: 49-8=41 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 49:[49, 1], Operations: ['80-71=9', '9-8=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[71, 49, 8, 80], Operations: [] Exploring Operation: 80-71=9, Resulting Numbers: [49, 8, 9] Generated Node #0,3: 49:[49, 8, 9] Operation: 80-71=9 Moving to Node #0,3 Current State: 49:[49, 8, 9], Operations: ['80-71=9'] Exploring Operation: 9-8=1, Resulting Numbers: [49, 1] Generated Node #0,3,1: 49:[49, 1] Operation: 9-8=1 Moving to Node #0,3,1 Current State: 49:[49, 1], Operations: ['80-71=9', '9-8=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 27, 2, 52, 45 ]
72
[ "27-2=25", "52+45=97", "97-25=72" ]
Current State: 72:[27, 2, 52, 45], Operations: [] Exploring Operation: 27-2=25, Resulting Numbers: [52, 45, 25] Generated Node #2: [52, 45, 25] from Operation: 27-2=25 Current State: 72:[52, 45, 25], Operations: ['27-2=25'] Exploring Operation: 52+45=97, Resulting Numbers: [25, 97] Generated Node #3: [25, 97] from Operation: 52+45=97 Current State: 72:[25, 97], Operations: ['27-2=25', '52+45=97'] Exploring Operation: 97-25=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[27, 2, 52, 45], Operations: [] Exploring Operation: 52-45=7, Resulting Numbers: [27, 2, 7] Generated Node #0,0: 72:[27, 2, 7] Operation: 52-45=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[27, 2, 7], Operations: ['52-45=7'] Exploring Operation: 27-2=25, Resulting Numbers: [7, 25] Generated Node #0,0,0: 72:[7, 25] Operation: 27-2=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[7, 25], Operations: ['52-45=7', '27-2=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 54, 6, 55, 34 ]
98
[ "54/6=9", "55+34=89", "9+89=98" ]
Current State: 98:[54, 6, 55, 34], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [55, 34, 9] Generated Node #2: [55, 34, 9] from Operation: 54/6=9 Current State: 98:[55, 34, 9], Operations: ['54/6=9'] Exploring Operation: 55+34=89, Resulting Numbers: [9, 89] Generated Node #3: [9, 89] from Operation: 55+34=89 Current State: 98:[9, 89], Operations: ['54/6=9', '55+34=89'] Exploring Operation: 9+89=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[54, 6, 55, 34], Operations: [] Exploring Operation: 54-34=20, Resulting Numbers: [6, 55, 20] Generated Node #0,0: 98:[6, 55, 20] Operation: 54-34=20 Exploring Operation: 55-34=21, Resulting Numbers: [54, 6, 21] Generated Node #0,1: 98:[54, 6, 21] Operation: 55-34=21 Exploring Operation: 55+34=89, Resulting Numbers: [54, 6, 89] Generated Node #0,2: 98:[54, 6, 89] Operation: 55+34=89 Moving to Node #0,0 Current State: 98:[6, 55, 20], Operations: ['54-34=20'] Exploring Operation: 55-6=49, Resulting Numbers: [20, 49] Generated Node #0,0,0: 98:[20, 49] Operation: 55-6=49 Exploring Operation: 20-6=14, Resulting Numbers: [55, 14] Generated Node #0,0,1: 98:[55, 14] Operation: 20-6=14 Exploring Operation: 55-20=35, Resulting Numbers: [6, 35] Generated Node #0,0,2: 98:[6, 35] Operation: 55-20=35 Moving to Node #0,1 Current State: 98:[54, 6, 21], Operations: ['55-34=21'] Exploring Operation: 54/6=9, Resulting Numbers: [21, 9] Generated Node #0,1,0: 98:[21, 9] Operation: 54/6=9 Exploring Operation: 21-6=15, Resulting Numbers: [54, 15] Generated Node #0,1,1: 98:[54, 15] Operation: 21-6=15 Exploring Operation: 54-6=48, Resulting Numbers: [21, 48] Generated Node #0,1,2: 98:[21, 48] Operation: 54-6=48 Moving to Node #0,2 Current State: 98:[54, 6, 89], Operations: ['55+34=89'] Exploring Operation: 6+89=95, Resulting Numbers: [54, 95] Generated Node #0,2,0: 98:[54, 95] Operation: 6+89=95 Exploring Operation: 54/6=9, Resulting Numbers: [89, 9] Generated Node #0,2,1: 98:[89, 9] Operation: 54/6=9 Exploring Operation: 54-6=48, Resulting Numbers: [89, 48] Generated Node #0,2,2: 98:[89, 48] Operation: 54-6=48 Moving to Node #0,0,0 Current State: 98:[20, 49], Operations: ['54-34=20', '55-6=49'] Exploring Operation: 49-20=29, Resulting Numbers: [29] 29,98 unequal: No Solution Exploring Operation: 20*49=980, Resulting Numbers: [980] 980,98 unequal: No Solution Exploring Operation: 20+49=69, Resulting Numbers: [69] 69,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[55, 14], Operations: ['54-34=20', '20-6=14'] Exploring Operation: 55*14=770, Resulting Numbers: [770] 770,98 unequal: No Solution Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,98 unequal: No Solution Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[54, 15], Operations: ['55-34=21', '21-6=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,98 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,98 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[54, 95], Operations: ['55+34=89', '6+89=95'] Exploring Operation: 54*95=5130, Resulting Numbers: [5130] 5130,98 unequal: No Solution Exploring Operation: 95-54=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 54+95=149, Resulting Numbers: [149] 149,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[21, 48], Operations: ['55-34=21', '54-6=48'] Exploring Operation: 21+48=69, Resulting Numbers: [69] 69,98 unequal: No Solution Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,98 unequal: No Solution Exploring Operation: 21*48=1008, Resulting Numbers: [1008] 1008,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[21, 9], Operations: ['55-34=21', '54/6=9'] Exploring Operation: 21*9=189, Resulting Numbers: [189] 189,98 unequal: No Solution Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[89, 48], Operations: ['55+34=89', '54-6=48'] Exploring Operation: 89+48=137, Resulting Numbers: [137] 137,98 unequal: No Solution Exploring Operation: 89-48=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 89*48=4272, Resulting Numbers: [4272] 4272,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[89, 9], Operations: ['55+34=89', '54/6=9'] Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,98 unequal: No Solution Exploring Operation: 89+9=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[54, 6, 55, 34], Operations: [] Exploring Operation: 55+34=89, Resulting Numbers: [54, 6, 89] Generated Node #0,2: 98:[54, 6, 89] Operation: 55+34=89 Moving to Node #0,2 Current State: 98:[54, 6, 89], Operations: ['55+34=89'] Exploring Operation: 54/6=9, Resulting Numbers: [89, 9] Generated Node #0,2,1: 98:[89, 9] Operation: 54/6=9 Moving to Node #0,2,1 Current State: 98:[89, 9], Operations: ['55+34=89', '54/6=9'] Exploring Operation: 89+9=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
0.966146
hs_3
mult_heuristic
[ 26, 56, 4, 8 ]
26
[ "56-26=30", "8-4=4", "30-4=26" ]
Current State: 26:[26, 56, 4, 8], Operations: [] Exploring Operation: 56-26=30, Resulting Numbers: [4, 8, 30] Generated Node #2: [4, 8, 30] from Operation: 56-26=30 Current State: 26:[4, 8, 30], Operations: ['56-26=30'] Exploring Operation: 8-4=4, Resulting Numbers: [30, 4] Generated Node #3: [30, 4] from Operation: 8-4=4 Current State: 26:[30, 4], Operations: ['56-26=30', '8-4=4'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[26, 56, 4, 8], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [26, 4, 7] Generated Node #0,0: 26:[26, 4, 7] Operation: 56/8=7 Exploring Operation: 56/4=14, Resulting Numbers: [26, 8, 14] Generated Node #0,1: 26:[26, 8, 14] Operation: 56/4=14 Moving to Node #0,1 Current State: 26:[26, 8, 14], Operations: ['56/4=14'] Exploring Operation: 8+14=22, Resulting Numbers: [26, 22] Generated Node #0,1,0: 26:[26, 22] Operation: 8+14=22 Exploring Operation: 14-8=6, Resulting Numbers: [26, 6] Generated Node #0,1,1: 26:[26, 6] Operation: 14-8=6 Moving to Node #0,0 Current State: 26:[26, 4, 7], Operations: ['56/8=7'] Exploring Operation: 4+7=11, Resulting Numbers: [26, 11] Generated Node #0,0,0: 26:[26, 11] Operation: 4+7=11 Exploring Operation: 7-4=3, Resulting Numbers: [26, 3] Generated Node #0,0,1: 26:[26, 3] Operation: 7-4=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[26, 3], Operations: ['56/8=7', '7-4=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,26 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[26, 11], Operations: ['56/8=7', '4+7=11'] Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,26 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: 26:[26, 22], Operations: ['56/4=14', '8+14=22'] Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,26 unequal: No Solution Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[26, 6], Operations: ['56/4=14', '14-8=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,26 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 90, 19, 60, 99 ]
47
[ "60*99=5940", "5940/90=66", "66-19=47" ]
Current State: 47:[90, 19, 60, 99], Operations: [] Exploring Operation: 60*99=5940, Resulting Numbers: [90, 19, 5940] Generated Node #2: [90, 19, 5940] from Operation: 60*99=5940 Current State: 47:[90, 19, 5940], Operations: ['60*99=5940'] Exploring Operation: 5940/90=66, Resulting Numbers: [19, 66] Generated Node #3: [19, 66] from Operation: 5940/90=66 Current State: 47:[19, 66], Operations: ['60*99=5940', '5940/90=66'] Exploring Operation: 66-19=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[90, 19, 60, 99], Operations: [] Exploring Operation: 99-90=9, Resulting Numbers: [19, 60, 9] Generated Node #0,0: 47:[19, 60, 9] Operation: 99-90=9 Exploring Operation: 99-60=39, Resulting Numbers: [90, 19, 39] Generated Node #0,1: 47:[90, 19, 39] Operation: 99-60=39 Moving to Node #0,0 Current State: 47:[19, 60, 9], Operations: ['99-90=9'] Exploring Operation: 19+9=28, Resulting Numbers: [60, 28] Generated Node #0,0,0: 47:[60, 28] Operation: 19+9=28 Exploring Operation: 60-9=51, Resulting Numbers: [19, 51] Generated Node #0,0,1: 47:[19, 51] Operation: 60-9=51 Moving to Node #0,1 Current State: 47:[90, 19, 39], Operations: ['99-60=39'] Exploring Operation: 90-19=71, Resulting Numbers: [39, 71] Generated Node #0,1,0: 47:[39, 71] Operation: 90-19=71 Exploring Operation: 90-39=51, Resulting Numbers: [19, 51] Generated Node #0,1,1: 47:[19, 51] Operation: 90-39=51 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[39, 71], Operations: ['99-60=39', '90-19=71'] Exploring Operation: 71-39=32, Resulting Numbers: [32] 32,47 unequal: No Solution Exploring Operation: 39+71=110, Resulting Numbers: [110] 110,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[19, 51], Operations: ['99-60=39', '90-39=51'] Exploring Operation: 19+51=70, Resulting Numbers: [70] 70,47 unequal: No Solution Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,47 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: 47:[60, 28], Operations: ['99-90=9', '19+9=28'] Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,47 unequal: No Solution Exploring Operation: 60+28=88, Resulting Numbers: [88] 88,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[19, 51], Operations: ['99-90=9', '60-9=51'] Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,47 unequal: No Solution Exploring Operation: 19+51=70, Resulting Numbers: [70] 70,47 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 64, 89, 52, 44 ]
33
[ "89-64=25", "52-44=8", "25+8=33" ]
Current State: 33:[64, 89, 52, 44], Operations: [] Exploring Operation: 89-64=25, Resulting Numbers: [52, 44, 25] Generated Node #2: [52, 44, 25] from Operation: 89-64=25 Current State: 33:[52, 44, 25], Operations: ['89-64=25'] Exploring Operation: 52-44=8, Resulting Numbers: [25, 8] Generated Node #3: [25, 8] from Operation: 52-44=8 Current State: 33:[25, 8], Operations: ['89-64=25', '52-44=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[64, 89, 52, 44], Operations: [] Exploring Operation: 89-52=37, Resulting Numbers: [64, 44, 37] Generated Node #0,0: 33:[64, 44, 37] Operation: 89-52=37 Exploring Operation: 89-64=25, Resulting Numbers: [52, 44, 25] Generated Node #0,1: 33:[52, 44, 25] Operation: 89-64=25 Moving to Node #0,1 Current State: 33:[52, 44, 25], Operations: ['89-64=25'] Exploring Operation: 52-25=27, Resulting Numbers: [44, 27] Generated Node #0,1,0: 33:[44, 27] Operation: 52-25=27 Exploring Operation: 52-44=8, Resulting Numbers: [25, 8] Generated Node #0,1,1: 33:[25, 8] Operation: 52-44=8 Moving to Node #0,0 Current State: 33:[64, 44, 37], Operations: ['89-52=37'] Exploring Operation: 64-44=20, Resulting Numbers: [37, 20] Generated Node #0,0,0: 33:[37, 20] Operation: 64-44=20 Exploring Operation: 64-37=27, Resulting Numbers: [44, 27] Generated Node #0,0,1: 33:[44, 27] Operation: 64-37=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[37, 20], Operations: ['89-52=37', '64-44=20'] Exploring Operation: 37+20=57, Resulting Numbers: [57] 57,33 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[44, 27], Operations: ['89-52=37', '64-37=27'] Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,33 unequal: No Solution Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,33 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: 33:[25, 8], Operations: ['89-64=25', '52-44=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[64, 89, 52, 44], Operations: [] Exploring Operation: 89-64=25, Resulting Numbers: [52, 44, 25] Generated Node #0,1: 33:[52, 44, 25] Operation: 89-64=25 Moving to Node #0,1 Current State: 33:[52, 44, 25], Operations: ['89-64=25'] Exploring Operation: 52-44=8, Resulting Numbers: [25, 8] Generated Node #0,1,1: 33:[25, 8] Operation: 52-44=8 Moving to Node #0,1,1 Current State: 33:[25, 8], Operations: ['89-64=25', '52-44=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 15, 24, 57, 31 ]
49
[ "15+24=39", "57+31=88", "88-39=49" ]
Current State: 49:[15, 24, 57, 31], Operations: [] Exploring Operation: 15+24=39, Resulting Numbers: [57, 31, 39] Generated Node #2: [57, 31, 39] from Operation: 15+24=39 Current State: 49:[57, 31, 39], Operations: ['15+24=39'] Exploring Operation: 57+31=88, Resulting Numbers: [39, 88] Generated Node #3: [39, 88] from Operation: 57+31=88 Current State: 49:[39, 88], Operations: ['15+24=39', '57+31=88'] Exploring Operation: 88-39=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[15, 24, 57, 31], Operations: [] Exploring Operation: 31-24=7, Resulting Numbers: [15, 57, 7] Generated Node #0,0: 49:[15, 57, 7] Operation: 31-24=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[15, 57, 7], Operations: ['31-24=7'] Exploring Operation: 57-15=42, Resulting Numbers: [7, 42] Generated Node #0,0,0: 49:[7, 42] Operation: 57-15=42 Moving to Node #0,0,0 Current State: 49:[7, 42], Operations: ['31-24=7', '57-15=42'] Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[15, 24, 57, 31], Operations: [] Exploring Operation: 31-24=7, Resulting Numbers: [15, 57, 7] Generated Node #0,0: 49:[15, 57, 7] Operation: 31-24=7 Moving to Node #0,0 Current State: 49:[15, 57, 7], Operations: ['31-24=7'] Exploring Operation: 57-15=42, Resulting Numbers: [7, 42] Generated Node #0,0,0: 49:[7, 42] Operation: 57-15=42 Moving to Node #0,0,0 Current State: 49:[7, 42], Operations: ['31-24=7', '57-15=42'] Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 15, 92, 85, 91 ]
83
[ "92-15=77", "91-85=6", "77+6=83" ]
Current State: 83:[15, 92, 85, 91], Operations: [] Exploring Operation: 92-15=77, Resulting Numbers: [85, 91, 77] Generated Node #2: [85, 91, 77] from Operation: 92-15=77 Current State: 83:[85, 91, 77], Operations: ['92-15=77'] Exploring Operation: 91-85=6, Resulting Numbers: [77, 6] Generated Node #3: [77, 6] from Operation: 91-85=6 Current State: 83:[77, 6], Operations: ['92-15=77', '91-85=6'] Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[15, 92, 85, 91], Operations: [] Exploring Operation: 92-15=77, Resulting Numbers: [85, 91, 77] Generated Node #0,0: 83:[85, 91, 77] Operation: 92-15=77 Exploring Operation: 15+92=107, Resulting Numbers: [85, 91, 107] Generated Node #0,1: 83:[85, 91, 107] Operation: 15+92=107 Exploring Operation: 85-15=70, Resulting Numbers: [92, 91, 70] Generated Node #0,2: 83:[92, 91, 70] Operation: 85-15=70 Exploring Operation: 91-15=76, Resulting Numbers: [92, 85, 76] Generated Node #0,3: 83:[92, 85, 76] Operation: 91-15=76 Moving to Node #0,0 Current State: 83:[85, 91, 77], Operations: ['92-15=77'] Exploring Operation: 85+77=162, Resulting Numbers: [91, 162] Generated Node #0,0,0: 83:[91, 162] Operation: 85+77=162 Exploring Operation: 85-77=8, Resulting Numbers: [91, 8] Generated Node #0,0,1: 83:[91, 8] Operation: 85-77=8 Exploring Operation: 91-85=6, Resulting Numbers: [77, 6] Generated Node #0,0,2: 83:[77, 6] Operation: 91-85=6 Exploring Operation: 91-77=14, Resulting Numbers: [85, 14] Generated Node #0,0,3: 83:[85, 14] Operation: 91-77=14 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 83:[85, 14], Operations: ['92-15=77', '91-77=14'] Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 85*14=1190, Resulting Numbers: [1190] 1190,83 unequal: No Solution Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[91, 8], Operations: ['92-15=77', '85-77=8'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[15, 92, 85, 91], Operations: [] Exploring Operation: 92-15=77, Resulting Numbers: [85, 91, 77] Generated Node #0,0: 83:[85, 91, 77] Operation: 92-15=77 Moving to Node #0,0 Current State: 83:[85, 91, 77], Operations: ['92-15=77'] Exploring Operation: 85-77=8, Resulting Numbers: [91, 8] Generated Node #0,0,1: 83:[91, 8] Operation: 85-77=8 Moving to Node #0,0,1 Current State: 83:[91, 8], Operations: ['92-15=77', '85-77=8'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 65, 19, 89, 39 ]
82
[ "65-19=46", "89+39=128", "128-46=82" ]
Current State: 82:[65, 19, 89, 39], Operations: [] Exploring Operation: 65-19=46, Resulting Numbers: [89, 39, 46] Generated Node #2: [89, 39, 46] from Operation: 65-19=46 Current State: 82:[89, 39, 46], Operations: ['65-19=46'] Exploring Operation: 89+39=128, Resulting Numbers: [46, 128] Generated Node #3: [46, 128] from Operation: 89+39=128 Current State: 82:[46, 128], Operations: ['65-19=46', '89+39=128'] Exploring Operation: 128-46=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[65, 19, 89, 39], Operations: [] Exploring Operation: 65+19=84, Resulting Numbers: [89, 39, 84] Generated Node #0,0: 82:[89, 39, 84] Operation: 65+19=84 Exploring Operation: 65-19=46, Resulting Numbers: [89, 39, 46] Generated Node #0,1: 82:[89, 39, 46] Operation: 65-19=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[89, 39, 84], Operations: ['65+19=84'] Exploring Operation: 89-84=5, Resulting Numbers: [39, 5] Generated Node #0,0,0: 82:[39, 5] Operation: 89-84=5 Exploring Operation: 89-39=50, Resulting Numbers: [84, 50] Generated Node #0,0,1: 82:[84, 50] Operation: 89-39=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[39, 5], Operations: ['65+19=84', '89-84=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[84, 50], Operations: ['65+19=84', '89-39=50'] Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 84+50=134, Resulting Numbers: [134] 134,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[89, 39, 46], Operations: ['65-19=46'] Exploring Operation: 39+46=85, Resulting Numbers: [89, 85] Generated Node #0,1,0: 82:[89, 85] Operation: 39+46=85 Exploring Operation: 89-46=43, Resulting Numbers: [39, 43] Generated Node #0,1,1: 82:[39, 43] Operation: 89-46=43 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[39, 43], Operations: ['65-19=46', '89-46=43'] Exploring Operation: 43-39=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 39+43=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[65, 19, 89, 39], Operations: [] Exploring Operation: 65-19=46, Resulting Numbers: [89, 39, 46] Generated Node #0,1: 82:[89, 39, 46] Operation: 65-19=46 Moving to Node #0,1 Current State: 82:[89, 39, 46], Operations: ['65-19=46'] Exploring Operation: 89-46=43, Resulting Numbers: [39, 43] Generated Node #0,1,1: 82:[39, 43] Operation: 89-46=43 Moving to Node #0,1,1 Current State: 82:[39, 43], Operations: ['65-19=46', '89-46=43'] Exploring Operation: 39+43=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 71, 65, 12, 78 ]
80
[ "71-65=6", "12/6=2", "78+2=80" ]
Current State: 80:[71, 65, 12, 78], Operations: [] Exploring Operation: 71-65=6, Resulting Numbers: [12, 78, 6] Generated Node #2: [12, 78, 6] from Operation: 71-65=6 Current State: 80:[12, 78, 6], Operations: ['71-65=6'] Exploring Operation: 12/6=2, Resulting Numbers: [78, 2] Generated Node #3: [78, 2] from Operation: 12/6=2 Current State: 80:[78, 2], Operations: ['71-65=6', '12/6=2'] Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[71, 65, 12, 78], Operations: [] Exploring Operation: 65+12=77, Resulting Numbers: [71, 78, 77] Generated Node #0,0: 80:[71, 78, 77] Operation: 65+12=77 Exploring Operation: 78-65=13, Resulting Numbers: [71, 12, 13] Generated Node #0,1: 80:[71, 12, 13] Operation: 78-65=13 Exploring Operation: 71-65=6, Resulting Numbers: [12, 78, 6] Generated Node #0,2: 80:[12, 78, 6] Operation: 71-65=6 Exploring Operation: 78-71=7, Resulting Numbers: [65, 12, 7] Generated Node #0,3: 80:[65, 12, 7] Operation: 78-71=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[12, 78, 6], Operations: ['71-65=6'] Exploring Operation: 12-6=6, Resulting Numbers: [78, 6] Generated Node #0,2,0: 80:[78, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [78, 2] Generated Node #0,2,1: 80:[78, 2] Operation: 12/6=2 Exploring Operation: 78/6=13, Resulting Numbers: [12, 13] Generated Node #0,2,2: 80:[12, 13] Operation: 78/6=13 Exploring Operation: 12+6=18, Resulting Numbers: [78, 18] Generated Node #0,2,3: 80:[78, 18] Operation: 12+6=18 Moving to Node #0,2,1 Current State: 80:[78, 2], Operations: ['71-65=6', '12/6=2'] Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[71, 65, 12, 78], Operations: [] Exploring Operation: 71-65=6, Resulting Numbers: [12, 78, 6] Generated Node #0,2: 80:[12, 78, 6] Operation: 71-65=6 Moving to Node #0,2 Current State: 80:[12, 78, 6], Operations: ['71-65=6'] Exploring Operation: 12/6=2, Resulting Numbers: [78, 2] Generated Node #0,2,1: 80:[78, 2] Operation: 12/6=2 Moving to Node #0,2,1 Current State: 80:[78, 2], Operations: ['71-65=6', '12/6=2'] Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 36, 20, 5, 45 ]
35
[ "36-20=16", "5*16=80", "80-45=35" ]
Current State: 35:[36, 20, 5, 45], Operations: [] Exploring Operation: 36-20=16, Resulting Numbers: [5, 45, 16] Generated Node #2: [5, 45, 16] from Operation: 36-20=16 Current State: 35:[5, 45, 16], Operations: ['36-20=16'] Exploring Operation: 5*16=80, Resulting Numbers: [45, 80] Generated Node #3: [45, 80] from Operation: 5*16=80 Current State: 35:[45, 80], Operations: ['36-20=16', '5*16=80'] Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[36, 20, 5, 45], Operations: [] Exploring Operation: 20/5=4, Resulting Numbers: [36, 45, 4] Generated Node #0,0: 35:[36, 45, 4] Operation: 20/5=4 Exploring Operation: 45-20=25, Resulting Numbers: [36, 5, 25] Generated Node #0,1: 35:[36, 5, 25] Operation: 45-20=25 Moving to Node #0,1 Current State: 35:[36, 5, 25], Operations: ['45-20=25'] Exploring Operation: 36-25=11, Resulting Numbers: [5, 11] Generated Node #0,1,0: 35:[5, 11] Operation: 36-25=11 Exploring Operation: 25/5=5, Resulting Numbers: [36, 5] Generated Node #0,1,1: 35:[36, 5] Operation: 25/5=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[36, 5], Operations: ['45-20=25', '25/5=5'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,35 unequal: No Solution Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[5, 11], Operations: ['45-20=25', '36-25=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 35:[36, 45, 4], Operations: ['20/5=4'] Exploring Operation: 45-36=9, Resulting Numbers: [4, 9] Generated Node #0,0,0: 35:[4, 9] Operation: 45-36=9 Exploring Operation: 45-4=41, Resulting Numbers: [36, 41] Generated Node #0,0,1: 35:[36, 41] Operation: 45-4=41 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[4, 9], Operations: ['20/5=4', '45-36=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,35 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[36, 41], Operations: ['20/5=4', '45-4=41'] Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 36+41=77, Resulting Numbers: [77] 77,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 9, 94, 52, 22 ]
90
[ "22-9=13", "52/13=4", "94-4=90" ]
Current State: 90:[9, 94, 52, 22], Operations: [] Exploring Operation: 22-9=13, Resulting Numbers: [94, 52, 13] Generated Node #2: [94, 52, 13] from Operation: 22-9=13 Current State: 90:[94, 52, 13], Operations: ['22-9=13'] Exploring Operation: 52/13=4, Resulting Numbers: [94, 4] Generated Node #3: [94, 4] from Operation: 52/13=4 Current State: 90:[94, 4], Operations: ['22-9=13', '52/13=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[9, 94, 52, 22], Operations: [] Exploring Operation: 52-22=30, Resulting Numbers: [9, 94, 30] Generated Node #0,0: 90:[9, 94, 30] Operation: 52-22=30 Moving to Node #0,0 Current State: 90:[9, 94, 30], Operations: ['52-22=30'] Exploring Operation: 94-9=85, Resulting Numbers: [30, 85] Generated Node #0,0,0: 90:[30, 85] Operation: 94-9=85 Moving to Node #0,0,0 Current State: 90:[30, 85], Operations: ['52-22=30', '94-9=85'] Exploring Operation: 85-30=55, Resulting Numbers: [55] 55,90 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 23, 54, 99, 81 ]
89
[ "54*99=5346", "5346/81=66", "23+66=89" ]
Current State: 89:[23, 54, 99, 81], Operations: [] Exploring Operation: 54*99=5346, Resulting Numbers: [23, 81, 5346] Generated Node #2: [23, 81, 5346] from Operation: 54*99=5346 Current State: 89:[23, 81, 5346], Operations: ['54*99=5346'] Exploring Operation: 5346/81=66, Resulting Numbers: [23, 66] Generated Node #3: [23, 66] from Operation: 5346/81=66 Current State: 89:[23, 66], Operations: ['54*99=5346', '5346/81=66'] Exploring Operation: 23+66=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[23, 54, 99, 81], Operations: [] Exploring Operation: 23+54=77, Resulting Numbers: [99, 81, 77] Generated Node #0,0: 89:[99, 81, 77] Operation: 23+54=77 Exploring Operation: 99-23=76, Resulting Numbers: [54, 81, 76] Generated Node #0,1: 89:[54, 81, 76] Operation: 99-23=76 Moving to Node #0,0 Current State: 89:[99, 81, 77], Operations: ['23+54=77'] Exploring Operation: 99-77=22, Resulting Numbers: [81, 22] Generated Node #0,0,0: 89:[81, 22] Operation: 99-77=22 Exploring Operation: 81+77=158, Resulting Numbers: [99, 158] Generated Node #0,0,1: 89:[99, 158] Operation: 81+77=158 Moving to Node #0,1 Current State: 89:[54, 81, 76], Operations: ['99-23=76'] Exploring Operation: 54+76=130, Resulting Numbers: [81, 130] Generated Node #0,1,0: 89:[81, 130] Operation: 54+76=130 Exploring Operation: 54+81=135, Resulting Numbers: [76, 135] Generated Node #0,1,1: 89:[76, 135] Operation: 54+81=135 Moving to Node #0,1,0 Current State: 89:[81, 130], Operations: ['99-23=76', '54+76=130'] Exploring Operation: 81+130=211, Resulting Numbers: [211] 211,89 unequal: No Solution Exploring Operation: 130-81=49, Resulting Numbers: [49] 49,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[76, 135], Operations: ['99-23=76', '54+81=135'] Exploring Operation: 76+135=211, Resulting Numbers: [211] 211,89 unequal: No Solution Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[81, 22], Operations: ['23+54=77', '99-77=22'] Exploring Operation: 81+22=103, Resulting Numbers: [103] 103,89 unequal: No Solution Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[99, 158], Operations: ['23+54=77', '81+77=158'] Exploring Operation: 158-99=59, Resulting Numbers: [59] 59,89 unequal: No Solution Exploring Operation: 99+158=257, Resulting Numbers: [257] 257,89 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 56, 1, 8, 92 ]
100
[ "56/8=7", "1+92=93", "7+93=100" ]
Current State: 100:[56, 1, 8, 92], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [1, 92, 7] Generated Node #2: [1, 92, 7] from Operation: 56/8=7 Current State: 100:[1, 92, 7], Operations: ['56/8=7'] Exploring Operation: 1+92=93, Resulting Numbers: [7, 93] Generated Node #3: [7, 93] from Operation: 1+92=93 Current State: 100:[7, 93], Operations: ['56/8=7', '1+92=93'] Exploring Operation: 7+93=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[56, 1, 8, 92], Operations: [] Exploring Operation: 8+92=100, Resulting Numbers: [56, 1, 100] Generated Node #0,0: 100:[56, 1, 100] Operation: 8+92=100 Moving to Node #0,0 Current State: 100:[56, 1, 100], Operations: ['8+92=100'] Exploring Operation: 56-1=55, Resulting Numbers: [100, 55] Generated Node #0,0,0: 100:[100, 55] Operation: 56-1=55 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[100, 55], Operations: ['8+92=100', '56-1=55'] Exploring Operation: 100-55=45, Resulting Numbers: [45] 45,100 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
[ 32, 44, 49, 6 ]
55
[ "44-32=12", "49-6=43", "12+43=55" ]
Current State: 55:[32, 44, 49, 6], Operations: [] Exploring Operation: 44-32=12, Resulting Numbers: [49, 6, 12] Generated Node #2: [49, 6, 12] from Operation: 44-32=12 Current State: 55:[49, 6, 12], Operations: ['44-32=12'] Exploring Operation: 49-6=43, Resulting Numbers: [12, 43] Generated Node #3: [12, 43] from Operation: 49-6=43 Current State: 55:[12, 43], Operations: ['44-32=12', '49-6=43'] Exploring Operation: 12+43=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[32, 44, 49, 6], Operations: [] Exploring Operation: 49-32=17, Resulting Numbers: [44, 6, 17] Generated Node #0,0: 55:[44, 6, 17] Operation: 49-32=17 Exploring Operation: 32-6=26, Resulting Numbers: [44, 49, 26] Generated Node #0,1: 55:[44, 49, 26] Operation: 32-6=26 Exploring Operation: 32+44=76, Resulting Numbers: [49, 6, 76] Generated Node #0,2: 55:[49, 6, 76] Operation: 32+44=76 Exploring Operation: 44-32=12, Resulting Numbers: [49, 6, 12] Generated Node #0,3: 55:[49, 6, 12] Operation: 44-32=12 Exploring Operation: 49-44=5, Resulting Numbers: [32, 6, 5] Generated Node #0,4: 55:[32, 6, 5] Operation: 49-44=5 Moving to Node #0,3 Current State: 55:[49, 6, 12], Operations: ['44-32=12'] Exploring Operation: 12-6=6, Resulting Numbers: [49, 6] Generated Node #0,3,0: 55:[49, 6] Operation: 12-6=6 Exploring Operation: 49-6=43, Resulting Numbers: [12, 43] Generated Node #0,3,1: 55:[12, 43] Operation: 49-6=43 Exploring Operation: 49+12=61, Resulting Numbers: [6, 61] Generated Node #0,3,2: 55:[6, 61] Operation: 49+12=61 Exploring Operation: 12/6=2, Resulting Numbers: [49, 2] Generated Node #0,3,3: 55:[49, 2] Operation: 12/6=2 Exploring Operation: 49+6=55, Resulting Numbers: [12, 55] Generated Node #0,3,4: 55:[12, 55] Operation: 49+6=55 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 55:[12, 55], Operations: ['44-32=12', '49+6=55'] Exploring Operation: 12*55=660, Resulting Numbers: [660] 660,55 unequal: No Solution Exploring Operation: 12+55=67, Resulting Numbers: [67] 67,55 unequal: No Solution Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 55:[49, 6], Operations: ['44-32=12', '12-6=6'] Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[32, 44, 49, 6], Operations: [] Exploring Operation: 44-32=12, Resulting Numbers: [49, 6, 12] Generated Node #0,3: 55:[49, 6, 12] Operation: 44-32=12 Moving to Node #0,3 Current State: 55:[49, 6, 12], Operations: ['44-32=12'] Exploring Operation: 12-6=6, Resulting Numbers: [49, 6] Generated Node #0,3,0: 55:[49, 6] Operation: 12-6=6 Moving to Node #0,3,0 Current State: 55:[49, 6], Operations: ['44-32=12', '12-6=6'] Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 55, 88, 5, 4 ]
42
[ "88-55=33", "5+4=9", "33+9=42" ]
Current State: 42:[55, 88, 5, 4], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [5, 4, 33] Generated Node #2: [5, 4, 33] from Operation: 88-55=33 Current State: 42:[5, 4, 33], Operations: ['88-55=33'] Exploring Operation: 5+4=9, Resulting Numbers: [33, 9] Generated Node #3: [33, 9] from Operation: 5+4=9 Current State: 42:[33, 9], Operations: ['88-55=33', '5+4=9'] Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[55, 88, 5, 4], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [55, 5, 22] Generated Node #0,0: 42:[55, 5, 22] Operation: 88/4=22 Exploring Operation: 88-55=33, Resulting Numbers: [5, 4, 33] Generated Node #0,1: 42:[5, 4, 33] Operation: 88-55=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[5, 4, 33], Operations: ['88-55=33'] Exploring Operation: 4+33=37, Resulting Numbers: [5, 37] Generated Node #0,1,0: 42:[5, 37] Operation: 4+33=37 Exploring Operation: 5+33=38, Resulting Numbers: [4, 38] Generated Node #0,1,1: 42:[4, 38] Operation: 5+33=38 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[4, 38], Operations: ['88-55=33', '5+33=38'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[55, 88, 5, 4], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [5, 4, 33] Generated Node #0,1: 42:[5, 4, 33] Operation: 88-55=33 Moving to Node #0,1 Current State: 42:[5, 4, 33], Operations: ['88-55=33'] Exploring Operation: 5+33=38, Resulting Numbers: [4, 38] Generated Node #0,1,1: 42:[4, 38] Operation: 5+33=38 Moving to Node #0,1,1 Current State: 42:[4, 38], Operations: ['88-55=33', '5+33=38'] Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 45, 81, 18, 32 ]
76
[ "45+81=126", "18+32=50", "126-50=76" ]
Current State: 76:[45, 81, 18, 32], Operations: [] Exploring Operation: 45+81=126, Resulting Numbers: [18, 32, 126] Generated Node #2: [18, 32, 126] from Operation: 45+81=126 Current State: 76:[18, 32, 126], Operations: ['45+81=126'] Exploring Operation: 18+32=50, Resulting Numbers: [126, 50] Generated Node #3: [126, 50] from Operation: 18+32=50 Current State: 76:[126, 50], Operations: ['45+81=126', '18+32=50'] Exploring Operation: 126-50=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[45, 81, 18, 32], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [81, 18, 13] Generated Node #0,0: 76:[81, 18, 13] Operation: 45-32=13 Exploring Operation: 32-18=14, Resulting Numbers: [45, 81, 14] Generated Node #0,1: 76:[45, 81, 14] Operation: 32-18=14 Exploring Operation: 81-45=36, Resulting Numbers: [18, 32, 36] Generated Node #0,2: 76:[18, 32, 36] Operation: 81-45=36 Exploring Operation: 45+32=77, Resulting Numbers: [81, 18, 77] Generated Node #0,3: 76:[81, 18, 77] Operation: 45+32=77 Moving to Node #0,3 Current State: 76:[81, 18, 77], Operations: ['45+32=77'] Exploring Operation: 81-77=4, Resulting Numbers: [18, 4] Generated Node #0,3,0: 76:[18, 4] Operation: 81-77=4 Exploring Operation: 77-18=59, Resulting Numbers: [81, 59] Generated Node #0,3,1: 76:[81, 59] Operation: 77-18=59 Exploring Operation: 81-18=63, Resulting Numbers: [77, 63] Generated Node #0,3,2: 76:[77, 63] Operation: 81-18=63 Exploring Operation: 81+18=99, Resulting Numbers: [77, 99] Generated Node #0,3,3: 76:[77, 99] Operation: 81+18=99 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 76:[18, 4], Operations: ['45+32=77', '81-77=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 76:[77, 63], Operations: ['45+32=77', '81-18=63'] Exploring Operation: 77+63=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 77-63=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 77*63=4851, Resulting Numbers: [4851] 4851,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 76:[81, 59], Operations: ['45+32=77', '77-18=59'] Exploring Operation: 81*59=4779, Resulting Numbers: [4779] 4779,76 unequal: No Solution Exploring Operation: 81+59=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 81-59=22, Resulting Numbers: [22] 22,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 76:[77, 99], Operations: ['45+32=77', '81+18=99'] Exploring Operation: 77*99=7623, Resulting Numbers: [7623] 7623,76 unequal: No Solution Exploring Operation: 77+99=176, Resulting Numbers: [176] 176,76 unequal: No Solution Exploring Operation: 99-77=22, Resulting Numbers: [22] 22,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 76:[18, 32, 36], Operations: ['81-45=36'] Exploring Operation: 36/18=2, Resulting Numbers: [32, 2] Generated Node #0,2,0: 76:[32, 2] Operation: 36/18=2 Exploring Operation: 32-18=14, Resulting Numbers: [36, 14] Generated Node #0,2,1: 76:[36, 14] Operation: 32-18=14 Exploring Operation: 36-18=18, Resulting Numbers: [32, 18] Generated Node #0,2,2: 76:[32, 18] Operation: 36-18=18 Exploring Operation: 36-32=4, Resulting Numbers: [18, 4] Generated Node #0,2,3: 76:[18, 4] Operation: 36-32=4 Moving to Node #0,0 Current State: 76:[81, 18, 13], Operations: ['45-32=13'] Exploring Operation: 81-13=68, Resulting Numbers: [18, 68] Generated Node #0,0,0: 76:[18, 68] Operation: 81-13=68 Exploring Operation: 18-13=5, Resulting Numbers: [81, 5] Generated Node #0,0,1: 76:[81, 5] Operation: 18-13=5 Exploring Operation: 81-18=63, Resulting Numbers: [13, 63] Generated Node #0,0,2: 76:[13, 63] Operation: 81-18=63 Exploring Operation: 18+13=31, Resulting Numbers: [81, 31] Generated Node #0,0,3: 76:[81, 31] Operation: 18+13=31 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[81, 5], Operations: ['45-32=13', '18-13=5'] Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[45, 81, 18, 32], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [81, 18, 13] Generated Node #0,0: 76:[81, 18, 13] Operation: 45-32=13 Moving to Node #0,0 Current State: 76:[81, 18, 13], Operations: ['45-32=13'] Exploring Operation: 18-13=5, Resulting Numbers: [81, 5] Generated Node #0,0,1: 76:[81, 5] Operation: 18-13=5 Moving to Node #0,0,1 Current State: 76:[81, 5], Operations: ['45-32=13', '18-13=5'] Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 12, 32, 42, 21 ]
91
[ "32*42=1344", "1344/12=112", "112-21=91" ]
Current State: 91:[12, 32, 42, 21], Operations: [] Exploring Operation: 32*42=1344, Resulting Numbers: [12, 21, 1344] Generated Node #2: [12, 21, 1344] from Operation: 32*42=1344 Current State: 91:[12, 21, 1344], Operations: ['32*42=1344'] Exploring Operation: 1344/12=112, Resulting Numbers: [21, 112] Generated Node #3: [21, 112] from Operation: 1344/12=112 Current State: 91:[21, 112], Operations: ['32*42=1344', '1344/12=112'] Exploring Operation: 112-21=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[12, 32, 42, 21], Operations: [] Exploring Operation: 42-32=10, Resulting Numbers: [12, 21, 10] Generated Node #0,0: 91:[12, 21, 10] Operation: 42-32=10 Moving to Node #0,0 Current State: 91:[12, 21, 10], Operations: ['42-32=10'] Exploring Operation: 21-10=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 91:[12, 11] Operation: 21-10=11 Moving to Node #0,0,0 Current State: 91:[12, 11], Operations: ['42-32=10', '21-10=11'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,91 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 53, 36, 11, 46 ]
18
[ "53-36=17", "46-11=35", "35-17=18" ]
Current State: 18:[53, 36, 11, 46], Operations: [] Exploring Operation: 53-36=17, Resulting Numbers: [11, 46, 17] Generated Node #2: [11, 46, 17] from Operation: 53-36=17 Current State: 18:[11, 46, 17], Operations: ['53-36=17'] Exploring Operation: 46-11=35, Resulting Numbers: [17, 35] Generated Node #3: [17, 35] from Operation: 46-11=35 Current State: 18:[17, 35], Operations: ['53-36=17', '46-11=35'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[53, 36, 11, 46], Operations: [] Exploring Operation: 46-36=10, Resulting Numbers: [53, 11, 10] Generated Node #0,0: 18:[53, 11, 10] Operation: 46-36=10 Exploring Operation: 53-36=17, Resulting Numbers: [11, 46, 17] Generated Node #0,1: 18:[11, 46, 17] Operation: 53-36=17 Exploring Operation: 53-46=7, Resulting Numbers: [36, 11, 7] Generated Node #0,2: 18:[36, 11, 7] Operation: 53-46=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[36, 11, 7], Operations: ['53-46=7'] Exploring Operation: 36-7=29, Resulting Numbers: [11, 29] Generated Node #0,2,0: 18:[11, 29] Operation: 36-7=29 Exploring Operation: 36-11=25, Resulting Numbers: [7, 25] Generated Node #0,2,1: 18:[7, 25] Operation: 36-11=25 Exploring Operation: 11+7=18, Resulting Numbers: [36, 18] Generated Node #0,2,2: 18:[36, 18] Operation: 11+7=18 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 18:[7, 25], Operations: ['53-46=7', '36-11=25'] Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,18 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[53, 36, 11, 46], Operations: [] Exploring Operation: 53-46=7, Resulting Numbers: [36, 11, 7] Generated Node #0,2: 18:[36, 11, 7] Operation: 53-46=7 Moving to Node #0,2 Current State: 18:[36, 11, 7], Operations: ['53-46=7'] Exploring Operation: 36-11=25, Resulting Numbers: [7, 25] Generated Node #0,2,1: 18:[7, 25] Operation: 36-11=25 Moving to Node #0,2,1 Current State: 18:[7, 25], Operations: ['53-46=7', '36-11=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 13, 70, 85, 10 ]
20
[ "13+70=83", "85-83=2", "10*2=20" ]
Current State: 20:[13, 70, 85, 10], Operations: [] Exploring Operation: 13+70=83, Resulting Numbers: [85, 10, 83] Generated Node #2: [85, 10, 83] from Operation: 13+70=83 Current State: 20:[85, 10, 83], Operations: ['13+70=83'] Exploring Operation: 85-83=2, Resulting Numbers: [10, 2] Generated Node #3: [10, 2] from Operation: 85-83=2 Current State: 20:[10, 2], Operations: ['13+70=83', '85-83=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[13, 70, 85, 10], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [13, 85, 7] Generated Node #0,0: 20:[13, 85, 7] Operation: 70/10=7 Exploring Operation: 70-13=57, Resulting Numbers: [85, 10, 57] Generated Node #0,1: 20:[85, 10, 57] Operation: 70-13=57 Exploring Operation: 85-70=15, Resulting Numbers: [13, 10, 15] Generated Node #0,2: 20:[13, 10, 15] Operation: 85-70=15 Exploring Operation: 85-13=72, Resulting Numbers: [70, 10, 72] Generated Node #0,3: 20:[70, 10, 72] Operation: 85-13=72 Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[13, 10, 15], Operations: ['85-70=15'] Exploring Operation: 13+10=23, Resulting Numbers: [15, 23] Generated Node #0,2,0: 20:[15, 23] Operation: 13+10=23 Exploring Operation: 13-10=3, Resulting Numbers: [15, 3] Generated Node #0,2,1: 20:[15, 3] Operation: 13-10=3 Exploring Operation: 15-10=5, Resulting Numbers: [13, 5] Generated Node #0,2,2: 20:[13, 5] Operation: 15-10=5 Exploring Operation: 15-13=2, Resulting Numbers: [10, 2] Generated Node #0,2,3: 20:[10, 2] Operation: 15-13=2 Moving to Node #0,2,3 Current State: 20:[10, 2], Operations: ['85-70=15', '15-13=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[13, 70, 85, 10], Operations: [] Exploring Operation: 85-70=15, Resulting Numbers: [13, 10, 15] Generated Node #0,2: 20:[13, 10, 15] Operation: 85-70=15 Moving to Node #0,2 Current State: 20:[13, 10, 15], Operations: ['85-70=15'] Exploring Operation: 15-13=2, Resulting Numbers: [10, 2] Generated Node #0,2,3: 20:[10, 2] Operation: 15-13=2 Moving to Node #0,2,3 Current State: 20:[10, 2], Operations: ['85-70=15', '15-13=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 90, 71, 95, 97 ]
17
[ "90-71=19", "97-95=2", "19-2=17" ]
Current State: 17:[90, 71, 95, 97], Operations: [] Exploring Operation: 90-71=19, Resulting Numbers: [95, 97, 19] Generated Node #2: [95, 97, 19] from Operation: 90-71=19 Current State: 17:[95, 97, 19], Operations: ['90-71=19'] Exploring Operation: 97-95=2, Resulting Numbers: [19, 2] Generated Node #3: [19, 2] from Operation: 97-95=2 Current State: 17:[19, 2], Operations: ['90-71=19', '97-95=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[90, 71, 95, 97], Operations: [] Exploring Operation: 90-71=19, Resulting Numbers: [95, 97, 19] Generated Node #0,0: 17:[95, 97, 19] Operation: 90-71=19 Exploring Operation: 97-90=7, Resulting Numbers: [71, 95, 7] Generated Node #0,1: 17:[71, 95, 7] Operation: 97-90=7 Exploring Operation: 97-95=2, Resulting Numbers: [90, 71, 2] Generated Node #0,2: 17:[90, 71, 2] Operation: 97-95=2 Exploring Operation: 95-90=5, Resulting Numbers: [71, 97, 5] Generated Node #0,3: 17:[71, 97, 5] Operation: 95-90=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[71, 95, 7], Operations: ['97-90=7'] Exploring Operation: 71-7=64, Resulting Numbers: [95, 64] Generated Node #0,1,0: 17:[95, 64] Operation: 71-7=64 Exploring Operation: 95-7=88, Resulting Numbers: [71, 88] Generated Node #0,1,1: 17:[71, 88] Operation: 95-7=88 Exploring Operation: 71+7=78, Resulting Numbers: [95, 78] Generated Node #0,1,2: 17:[95, 78] Operation: 71+7=78 Exploring Operation: 95-71=24, Resulting Numbers: [7, 24] Generated Node #0,1,3: 17:[7, 24] Operation: 95-71=24 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 17:[7, 24], Operations: ['97-90=7', '95-71=24'] Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,17 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[90, 71, 95, 97], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [71, 95, 7] Generated Node #0,1: 17:[71, 95, 7] Operation: 97-90=7 Moving to Node #0,1 Current State: 17:[71, 95, 7], Operations: ['97-90=7'] Exploring Operation: 95-71=24, Resulting Numbers: [7, 24] Generated Node #0,1,3: 17:[7, 24] Operation: 95-71=24 Moving to Node #0,1,3 Current State: 17:[7, 24], Operations: ['97-90=7', '95-71=24'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 23, 63, 74, 70 ]
10
[ "63-23=40", "74-70=4", "40/4=10" ]
Current State: 10:[23, 63, 74, 70], Operations: [] Exploring Operation: 63-23=40, Resulting Numbers: [74, 70, 40] Generated Node #2: [74, 70, 40] from Operation: 63-23=40 Current State: 10:[74, 70, 40], Operations: ['63-23=40'] Exploring Operation: 74-70=4, Resulting Numbers: [40, 4] Generated Node #3: [40, 4] from Operation: 74-70=4 Current State: 10:[40, 4], Operations: ['63-23=40', '74-70=4'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[23, 63, 74, 70], Operations: [] Exploring Operation: 74-63=11, Resulting Numbers: [23, 70, 11] Generated Node #0,0: 10:[23, 70, 11] Operation: 74-63=11 Exploring Operation: 74-70=4, Resulting Numbers: [23, 63, 4] Generated Node #0,1: 10:[23, 63, 4] Operation: 74-70=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[23, 63, 4], Operations: ['74-70=4'] Exploring Operation: 23-4=19, Resulting Numbers: [63, 19] Generated Node #0,1,0: 10:[63, 19] Operation: 23-4=19 Exploring Operation: 63-23=40, Resulting Numbers: [4, 40] Generated Node #0,1,1: 10:[4, 40] Operation: 63-23=40 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[4, 40], Operations: ['74-70=4', '63-23=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[23, 63, 74, 70], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [23, 63, 4] Generated Node #0,1: 10:[23, 63, 4] Operation: 74-70=4 Moving to Node #0,1 Current State: 10:[23, 63, 4], Operations: ['74-70=4'] Exploring Operation: 63-23=40, Resulting Numbers: [4, 40] Generated Node #0,1,1: 10:[4, 40] Operation: 63-23=40 Moving to Node #0,1,1 Current State: 10:[4, 40], Operations: ['74-70=4', '63-23=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 3, 15, 95, 41 ]
43
[ "3*41=123", "95-15=80", "123-80=43" ]
Current State: 43:[3, 15, 95, 41], Operations: [] Exploring Operation: 3*41=123, Resulting Numbers: [15, 95, 123] Generated Node #2: [15, 95, 123] from Operation: 3*41=123 Current State: 43:[15, 95, 123], Operations: ['3*41=123'] Exploring Operation: 95-15=80, Resulting Numbers: [123, 80] Generated Node #3: [123, 80] from Operation: 95-15=80 Current State: 43:[123, 80], Operations: ['3*41=123', '95-15=80'] Exploring Operation: 123-80=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[3, 15, 95, 41], Operations: [] Exploring Operation: 3*15=45, Resulting Numbers: [95, 41, 45] Generated Node #0,0: 43:[95, 41, 45] Operation: 3*15=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[95, 41, 45], Operations: ['3*15=45'] Exploring Operation: 95-45=50, Resulting Numbers: [41, 50] Generated Node #0,0,0: 43:[41, 50] Operation: 95-45=50 Moving to Node #0,0,0 Current State: 43:[41, 50], Operations: ['3*15=45', '95-45=50'] Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 74, 71, 59, 50 ]
27
[ "74-71=3", "59-50=9", "3*9=27" ]
Current State: 27:[74, 71, 59, 50], Operations: [] Exploring Operation: 74-71=3, Resulting Numbers: [59, 50, 3] Generated Node #2: [59, 50, 3] from Operation: 74-71=3 Current State: 27:[59, 50, 3], Operations: ['74-71=3'] Exploring Operation: 59-50=9, Resulting Numbers: [3, 9] Generated Node #3: [3, 9] from Operation: 59-50=9 Current State: 27:[3, 9], Operations: ['74-71=3', '59-50=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[74, 71, 59, 50], Operations: [] Exploring Operation: 74-59=15, Resulting Numbers: [71, 50, 15] Generated Node #0,0: 27:[71, 50, 15] Operation: 74-59=15 Exploring Operation: 74-71=3, Resulting Numbers: [59, 50, 3] Generated Node #0,1: 27:[59, 50, 3] Operation: 74-71=3 Exploring Operation: 71-59=12, Resulting Numbers: [74, 50, 12] Generated Node #0,2: 27:[74, 50, 12] Operation: 71-59=12 Moving to Node #0,1 Current State: 27:[59, 50, 3], Operations: ['74-71=3'] Exploring Operation: 50-3=47, Resulting Numbers: [59, 47] Generated Node #0,1,0: 27:[59, 47] Operation: 50-3=47 Exploring Operation: 59-50=9, Resulting Numbers: [3, 9] Generated Node #0,1,1: 27:[3, 9] Operation: 59-50=9 Exploring Operation: 59-3=56, Resulting Numbers: [50, 56] Generated Node #0,1,2: 27:[50, 56] Operation: 59-3=56 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 27:[3, 9], Operations: ['74-71=3', '59-50=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[74, 71, 59, 50], Operations: [] Exploring Operation: 74-71=3, Resulting Numbers: [59, 50, 3] Generated Node #0,1: 27:[59, 50, 3] Operation: 74-71=3 Moving to Node #0,1 Current State: 27:[59, 50, 3], Operations: ['74-71=3'] Exploring Operation: 59-50=9, Resulting Numbers: [3, 9] Generated Node #0,1,1: 27:[3, 9] Operation: 59-50=9 Moving to Node #0,1,1 Current State: 27:[3, 9], Operations: ['74-71=3', '59-50=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 40, 9, 46, 10 ]
33
[ "40/10=4", "46-9=37", "37-4=33" ]
Current State: 33:[40, 9, 46, 10], Operations: [] Exploring Operation: 40/10=4, Resulting Numbers: [9, 46, 4] Generated Node #2: [9, 46, 4] from Operation: 40/10=4 Current State: 33:[9, 46, 4], Operations: ['40/10=4'] Exploring Operation: 46-9=37, Resulting Numbers: [4, 37] Generated Node #3: [4, 37] from Operation: 46-9=37 Current State: 33:[4, 37], Operations: ['40/10=4', '46-9=37'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[40, 9, 46, 10], Operations: [] Exploring Operation: 46-40=6, Resulting Numbers: [9, 10, 6] Generated Node #0,0: 33:[9, 10, 6] Operation: 46-40=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[9, 10, 6], Operations: ['46-40=6'] Exploring Operation: 9-6=3, Resulting Numbers: [10, 3] Generated Node #0,0,0: 33:[10, 3] Operation: 9-6=3 Moving to Node #0,0,0 Current State: 33:[10, 3], Operations: ['46-40=6', '9-6=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,33 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
[ 42, 18, 31, 9 ]
81
[ "42-31=11", "9*11=99", "99-18=81" ]
Current State: 81:[42, 18, 31, 9], Operations: [] Exploring Operation: 42-31=11, Resulting Numbers: [18, 9, 11] Generated Node #2: [18, 9, 11] from Operation: 42-31=11 Current State: 81:[18, 9, 11], Operations: ['42-31=11'] Exploring Operation: 9*11=99, Resulting Numbers: [18, 99] Generated Node #3: [18, 99] from Operation: 9*11=99 Current State: 81:[18, 99], Operations: ['42-31=11', '9*11=99'] Exploring Operation: 99-18=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[42, 18, 31, 9], Operations: [] Exploring Operation: 42-18=24, Resulting Numbers: [31, 9, 24] Generated Node #0,0: 81:[31, 9, 24] Operation: 42-18=24 Exploring Operation: 42-31=11, Resulting Numbers: [18, 9, 11] Generated Node #0,1: 81:[18, 9, 11] Operation: 42-31=11 Moving to Node #0,0 Current State: 81:[31, 9, 24], Operations: ['42-18=24'] Exploring Operation: 31-9=22, Resulting Numbers: [24, 22] Generated Node #0,0,0: 81:[24, 22] Operation: 31-9=22 Exploring Operation: 31-24=7, Resulting Numbers: [9, 7] Generated Node #0,0,1: 81:[9, 7] Operation: 31-24=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[9, 7], Operations: ['42-18=24', '31-24=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[24, 22], Operations: ['42-18=24', '31-9=22'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,81 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 81:[18, 9, 11], Operations: ['42-31=11'] Exploring Operation: 18-9=9, Resulting Numbers: [11, 9] Generated Node #0,1,0: 81:[11, 9] Operation: 18-9=9 Exploring Operation: 18+9=27, Resulting Numbers: [11, 27] Generated Node #0,1,1: 81:[11, 27] Operation: 18+9=27 Moving to Node #0,1,0 Current State: 81:[11, 9], Operations: ['42-31=11', '18-9=9'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,81 unequal: No Solution Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[11, 27], Operations: ['42-31=11', '18+9=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,81 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,81 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 21, 36, 58, 6 ]
49
[ "36-21=15", "58+6=64", "64-15=49" ]
Current State: 49:[21, 36, 58, 6], Operations: [] Exploring Operation: 36-21=15, Resulting Numbers: [58, 6, 15] Generated Node #2: [58, 6, 15] from Operation: 36-21=15 Current State: 49:[58, 6, 15], Operations: ['36-21=15'] Exploring Operation: 58+6=64, Resulting Numbers: [15, 64] Generated Node #3: [15, 64] from Operation: 58+6=64 Current State: 49:[15, 64], Operations: ['36-21=15', '58+6=64'] Exploring Operation: 64-15=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[21, 36, 58, 6], Operations: [] Exploring Operation: 21+36=57, Resulting Numbers: [58, 6, 57] Generated Node #0,0: 49:[58, 6, 57] Operation: 21+36=57 Exploring Operation: 36-21=15, Resulting Numbers: [58, 6, 15] Generated Node #0,1: 49:[58, 6, 15] Operation: 36-21=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[58, 6, 57], Operations: ['21+36=57'] Exploring Operation: 58-57=1, Resulting Numbers: [6, 1] Generated Node #0,0,0: 49:[6, 1] Operation: 58-57=1 Exploring Operation: 58-6=52, Resulting Numbers: [57, 52] Generated Node #0,0,1: 49:[57, 52] Operation: 58-6=52 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[6, 1], Operations: ['21+36=57', '58-57=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,49 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:[57, 52], Operations: ['21+36=57', '58-6=52'] Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 57+52=109, Resulting Numbers: [109] 109,49 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:[58, 6, 15], Operations: ['36-21=15'] Exploring Operation: 58-15=43, Resulting Numbers: [6, 43] Generated Node #0,1,0: 49:[6, 43] Operation: 58-15=43 Exploring Operation: 58-6=52, Resulting Numbers: [15, 52] Generated Node #0,1,1: 49:[15, 52] Operation: 58-6=52 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[6, 43], Operations: ['36-21=15', '58-15=43'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[21, 36, 58, 6], Operations: [] Exploring Operation: 36-21=15, Resulting Numbers: [58, 6, 15] Generated Node #0,1: 49:[58, 6, 15] Operation: 36-21=15 Moving to Node #0,1 Current State: 49:[58, 6, 15], Operations: ['36-21=15'] Exploring Operation: 58-15=43, Resulting Numbers: [6, 43] Generated Node #0,1,0: 49:[6, 43] Operation: 58-15=43 Moving to Node #0,1,0 Current State: 49:[6, 43], Operations: ['36-21=15', '58-15=43'] Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 78, 33, 16, 34 ]
93
[ "78+33=111", "34-16=18", "111-18=93" ]
Current State: 93:[78, 33, 16, 34], Operations: [] Exploring Operation: 78+33=111, Resulting Numbers: [16, 34, 111] Generated Node #2: [16, 34, 111] from Operation: 78+33=111 Current State: 93:[16, 34, 111], Operations: ['78+33=111'] Exploring Operation: 34-16=18, Resulting Numbers: [111, 18] Generated Node #3: [111, 18] from Operation: 34-16=18 Current State: 93:[111, 18], Operations: ['78+33=111', '34-16=18'] Exploring Operation: 111-18=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[78, 33, 16, 34], Operations: [] Exploring Operation: 78+16=94, Resulting Numbers: [33, 34, 94] Generated Node #0,0: 93:[33, 34, 94] Operation: 78+16=94 Exploring Operation: 78-34=44, Resulting Numbers: [33, 16, 44] Generated Node #0,1: 93:[33, 16, 44] Operation: 78-34=44 Exploring Operation: 78-33=45, Resulting Numbers: [16, 34, 45] Generated Node #0,2: 93:[16, 34, 45] Operation: 78-33=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[33, 34, 94], Operations: ['78+16=94'] Exploring Operation: 94-34=60, Resulting Numbers: [33, 60] Generated Node #0,0,0: 93:[33, 60] Operation: 94-34=60 Exploring Operation: 34-33=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 34-33=1 Exploring Operation: 33+34=67, Resulting Numbers: [94, 67] Generated Node #0,0,2: 93:[94, 67] Operation: 33+34=67 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['78+16=94', '34-33=1'] Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,93 unequal: No Solution Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[78, 33, 16, 34], Operations: [] Exploring Operation: 78+16=94, Resulting Numbers: [33, 34, 94] Generated Node #0,0: 93:[33, 34, 94] Operation: 78+16=94 Moving to Node #0,0 Current State: 93:[33, 34, 94], Operations: ['78+16=94'] Exploring Operation: 34-33=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 34-33=1 Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['78+16=94', '34-33=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 93, 2, 21, 89 ]
23
[ "93-2=91", "89-21=68", "91-68=23" ]
Current State: 23:[93, 2, 21, 89], Operations: [] Exploring Operation: 93-2=91, Resulting Numbers: [21, 89, 91] Generated Node #2: [21, 89, 91] from Operation: 93-2=91 Current State: 23:[21, 89, 91], Operations: ['93-2=91'] Exploring Operation: 89-21=68, Resulting Numbers: [91, 68] Generated Node #3: [91, 68] from Operation: 89-21=68 Current State: 23:[91, 68], Operations: ['93-2=91', '89-21=68'] Exploring Operation: 91-68=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[93, 2, 21, 89], Operations: [] Exploring Operation: 93-89=4, Resulting Numbers: [2, 21, 4] Generated Node #0,0: 23:[2, 21, 4] Operation: 93-89=4 Exploring Operation: 93-2=91, Resulting Numbers: [21, 89, 91] Generated Node #0,1: 23:[21, 89, 91] Operation: 93-2=91 Exploring Operation: 93-21=72, Resulting Numbers: [2, 89, 72] Generated Node #0,2: 23:[2, 89, 72] Operation: 93-21=72 Moving to Node #0,0 Current State: 23:[2, 21, 4], Operations: ['93-89=4'] Exploring Operation: 2+21=23, Resulting Numbers: [4, 23] Generated Node #0,0,0: 23:[4, 23] Operation: 2+21=23 Exploring Operation: 2+4=6, Resulting Numbers: [21, 6] Generated Node #0,0,1: 23:[21, 6] Operation: 2+4=6 Exploring Operation: 2*4=8, Resulting Numbers: [21, 8] Generated Node #0,0,2: 23:[21, 8] Operation: 2*4=8 Moving to Node #0,1 Current State: 23:[21, 89, 91], Operations: ['93-2=91'] Exploring Operation: 89-21=68, Resulting Numbers: [91, 68] Generated Node #0,1,0: 23:[91, 68] Operation: 89-21=68 Exploring Operation: 91-21=70, Resulting Numbers: [89, 70] Generated Node #0,1,1: 23:[89, 70] Operation: 91-21=70 Exploring Operation: 91-89=2, Resulting Numbers: [21, 2] Generated Node #0,1,2: 23:[21, 2] Operation: 91-89=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[21, 2], Operations: ['93-2=91', '91-89=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[93, 2, 21, 89], Operations: [] Exploring Operation: 93-2=91, Resulting Numbers: [21, 89, 91] Generated Node #0,1: 23:[21, 89, 91] Operation: 93-2=91 Moving to Node #0,1 Current State: 23:[21, 89, 91], Operations: ['93-2=91'] Exploring Operation: 91-89=2, Resulting Numbers: [21, 2] Generated Node #0,1,2: 23:[21, 2] Operation: 91-89=2 Moving to Node #0,1,2 Current State: 23:[21, 2], Operations: ['93-2=91', '91-89=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 63, 47, 90, 81 ]
44
[ "90-63=27", "81/27=3", "47-3=44" ]
Current State: 44:[63, 47, 90, 81], Operations: [] Exploring Operation: 90-63=27, Resulting Numbers: [47, 81, 27] Generated Node #2: [47, 81, 27] from Operation: 90-63=27 Current State: 44:[47, 81, 27], Operations: ['90-63=27'] Exploring Operation: 81/27=3, Resulting Numbers: [47, 3] Generated Node #3: [47, 3] from Operation: 81/27=3 Current State: 44:[47, 3], Operations: ['90-63=27', '81/27=3'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[63, 47, 90, 81], Operations: [] Exploring Operation: 90-81=9, Resulting Numbers: [63, 47, 9] Generated Node #0,0: 44:[63, 47, 9] Operation: 90-81=9 Exploring Operation: 90-63=27, Resulting Numbers: [47, 81, 27] Generated Node #0,1: 44:[47, 81, 27] Operation: 90-63=27 Exploring Operation: 81-63=18, Resulting Numbers: [47, 90, 18] Generated Node #0,2: 44:[47, 90, 18] Operation: 81-63=18 Moving to Node #0,0 Current State: 44:[63, 47, 9], Operations: ['90-81=9'] Exploring Operation: 63-9=54, Resulting Numbers: [47, 54] Generated Node #0,0,0: 44:[47, 54] Operation: 63-9=54 Exploring Operation: 63/9=7, Resulting Numbers: [47, 7] Generated Node #0,0,1: 44:[47, 7] Operation: 63/9=7 Exploring Operation: 63-47=16, Resulting Numbers: [9, 16] Generated Node #0,0,2: 44:[9, 16] Operation: 63-47=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[47, 7], Operations: ['90-81=9', '63/9=7'] Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,44 unequal: No Solution Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,44 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,44 unequal: No Solution No 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: 44:[9, 16], Operations: ['90-81=9', '63-47=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,44 unequal: No Solution No 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: 44:[47, 54], Operations: ['90-81=9', '63-9=54'] Exploring Operation: 47+54=101, Resulting Numbers: [101] 101,44 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 47*54=2538, Resulting Numbers: [2538] 2538,44 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: 44:[47, 81, 27], Operations: ['90-63=27'] Exploring Operation: 81-27=54, Resulting Numbers: [47, 54] Generated Node #0,1,0: 44:[47, 54] Operation: 81-27=54 Exploring Operation: 81-47=34, Resulting Numbers: [27, 34] Generated Node #0,1,1: 44:[27, 34] Operation: 81-47=34 Exploring Operation: 81/27=3, Resulting Numbers: [47, 3] Generated Node #0,1,2: 44:[47, 3] Operation: 81/27=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 44:[47, 3], Operations: ['90-63=27', '81/27=3'] Exploring Operation: 47+3=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[63, 47, 90, 81], Operations: [] Exploring Operation: 90-63=27, Resulting Numbers: [47, 81, 27] Generated Node #0,1: 44:[47, 81, 27] Operation: 90-63=27 Moving to Node #0,1 Current State: 44:[47, 81, 27], Operations: ['90-63=27'] Exploring Operation: 81/27=3, Resulting Numbers: [47, 3] Generated Node #0,1,2: 44:[47, 3] Operation: 81/27=3 Moving to Node #0,1,2 Current State: 44:[47, 3], Operations: ['90-63=27', '81/27=3'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 67, 25, 95, 38 ]
41
[ "67+25=92", "95+38=133", "133-92=41" ]
Current State: 41:[67, 25, 95, 38], Operations: [] Exploring Operation: 67+25=92, Resulting Numbers: [95, 38, 92] Generated Node #2: [95, 38, 92] from Operation: 67+25=92 Current State: 41:[95, 38, 92], Operations: ['67+25=92'] Exploring Operation: 95+38=133, Resulting Numbers: [92, 133] Generated Node #3: [92, 133] from Operation: 95+38=133 Current State: 41:[92, 133], Operations: ['67+25=92', '95+38=133'] Exploring Operation: 133-92=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[67, 25, 95, 38], Operations: [] Exploring Operation: 67-25=42, Resulting Numbers: [95, 38, 42] Generated Node #0,0: 41:[95, 38, 42] Operation: 67-25=42 Exploring Operation: 95-67=28, Resulting Numbers: [25, 38, 28] Generated Node #0,1: 41:[25, 38, 28] Operation: 95-67=28 Moving to Node #0,1 Current State: 41:[25, 38, 28], Operations: ['95-67=28'] Exploring Operation: 25+28=53, Resulting Numbers: [38, 53] Generated Node #0,1,0: 41:[38, 53] Operation: 25+28=53 Exploring Operation: 25+38=63, Resulting Numbers: [28, 63] Generated Node #0,1,1: 41:[28, 63] Operation: 25+38=63 Moving to Node #0,0 Current State: 41:[95, 38, 42], Operations: ['67-25=42'] Exploring Operation: 95-38=57, Resulting Numbers: [42, 57] Generated Node #0,0,0: 41:[42, 57] Operation: 95-38=57 Exploring Operation: 95-42=53, Resulting Numbers: [38, 53] Generated Node #0,0,1: 41:[38, 53] Operation: 95-42=53 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[38, 53], Operations: ['67-25=42', '95-42=53'] Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[42, 57], Operations: ['67-25=42', '95-38=57'] Exploring Operation: 57-42=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 42+57=99, Resulting Numbers: [99] 99,41 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: 41:[38, 53], Operations: ['95-67=28', '25+28=53'] Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[28, 63], Operations: ['95-67=28', '25+38=63'] Exploring Operation: 63-28=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 28+63=91, Resulting Numbers: [91] 91,41 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 70, 27, 17, 15 ]
62
[ "17-15=2", "70/2=35", "27+35=62" ]
Current State: 62:[70, 27, 17, 15], Operations: [] Exploring Operation: 17-15=2, Resulting Numbers: [70, 27, 2] Generated Node #2: [70, 27, 2] from Operation: 17-15=2 Current State: 62:[70, 27, 2], Operations: ['17-15=2'] Exploring Operation: 70/2=35, Resulting Numbers: [27, 35] Generated Node #3: [27, 35] from Operation: 70/2=35 Current State: 62:[27, 35], Operations: ['17-15=2', '70/2=35'] Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[70, 27, 17, 15], Operations: [] Exploring Operation: 70-17=53, Resulting Numbers: [27, 15, 53] Generated Node #0,0: 62:[27, 15, 53] Operation: 70-17=53 Exploring Operation: 17-15=2, Resulting Numbers: [70, 27, 2] Generated Node #0,1: 62:[70, 27, 2] Operation: 17-15=2 Exploring Operation: 17+15=32, Resulting Numbers: [70, 27, 32] Generated Node #0,2: 62:[70, 27, 32] Operation: 17+15=32 Exploring Operation: 70-15=55, Resulting Numbers: [27, 17, 55] Generated Node #0,3: 62:[27, 17, 55] Operation: 70-15=55 Moving to Node #0,1 Current State: 62:[70, 27, 2], Operations: ['17-15=2'] Exploring Operation: 70/2=35, Resulting Numbers: [27, 35] Generated Node #0,1,0: 62:[27, 35] Operation: 70/2=35 Exploring Operation: 70-27=43, Resulting Numbers: [2, 43] Generated Node #0,1,1: 62:[2, 43] Operation: 70-27=43 Exploring Operation: 27+2=29, Resulting Numbers: [70, 29] Generated Node #0,1,2: 62:[70, 29] Operation: 27+2=29 Exploring Operation: 70-2=68, Resulting Numbers: [27, 68] Generated Node #0,1,3: 62:[27, 68] Operation: 70-2=68 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[27, 35], Operations: ['17-15=2', '70/2=35'] Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,62 unequal: No Solution Exploring Operation: 27*35=945, Resulting Numbers: [945] 945,62 unequal: No Solution Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[70, 27, 17, 15], Operations: [] Exploring Operation: 17-15=2, Resulting Numbers: [70, 27, 2] Generated Node #0,1: 62:[70, 27, 2] Operation: 17-15=2 Moving to Node #0,1 Current State: 62:[70, 27, 2], Operations: ['17-15=2'] Exploring Operation: 70/2=35, Resulting Numbers: [27, 35] Generated Node #0,1,0: 62:[27, 35] Operation: 70/2=35 Moving to Node #0,1,0 Current State: 62:[27, 35], Operations: ['17-15=2', '70/2=35'] Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 30, 71, 15, 1 ]
57
[ "71-30=41", "15+1=16", "41+16=57" ]
Current State: 57:[30, 71, 15, 1], Operations: [] Exploring Operation: 71-30=41, Resulting Numbers: [15, 1, 41] Generated Node #2: [15, 1, 41] from Operation: 71-30=41 Current State: 57:[15, 1, 41], Operations: ['71-30=41'] Exploring Operation: 15+1=16, Resulting Numbers: [41, 16] Generated Node #3: [41, 16] from Operation: 15+1=16 Current State: 57:[41, 16], Operations: ['71-30=41', '15+1=16'] Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[30, 71, 15, 1], Operations: [] Exploring Operation: 71-15=56, Resulting Numbers: [30, 1, 56] Generated Node #0,0: 57:[30, 1, 56] Operation: 71-15=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[30, 1, 56], Operations: ['71-15=56'] Exploring Operation: 56-30=26, Resulting Numbers: [1, 26] Generated Node #0,0,0: 57:[1, 26] Operation: 56-30=26 Moving to Node #0,0,0 Current State: 57:[1, 26], Operations: ['71-15=56', '56-30=26'] Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,57 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
[ 94, 19, 89, 33 ]
70
[ "94-89=5", "33-19=14", "5*14=70" ]
Current State: 70:[94, 19, 89, 33], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [19, 33, 5] Generated Node #2: [19, 33, 5] from Operation: 94-89=5 Current State: 70:[19, 33, 5], Operations: ['94-89=5'] Exploring Operation: 33-19=14, Resulting Numbers: [5, 14] Generated Node #3: [5, 14] from Operation: 33-19=14 Current State: 70:[5, 14], Operations: ['94-89=5', '33-19=14'] Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[94, 19, 89, 33], Operations: [] Exploring Operation: 94-19=75, Resulting Numbers: [89, 33, 75] Generated Node #0,0: 70:[89, 33, 75] Operation: 94-19=75 Exploring Operation: 89-19=70, Resulting Numbers: [94, 33, 70] Generated Node #0,1: 70:[94, 33, 70] Operation: 89-19=70 Exploring Operation: 94-89=5, Resulting Numbers: [19, 33, 5] Generated Node #0,2: 70:[19, 33, 5] Operation: 94-89=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[19, 33, 5], Operations: ['94-89=5'] Exploring Operation: 33-19=14, Resulting Numbers: [5, 14] Generated Node #0,2,0: 70:[5, 14] Operation: 33-19=14 Exploring Operation: 19-5=14, Resulting Numbers: [33, 14] Generated Node #0,2,1: 70:[33, 14] Operation: 19-5=14 Exploring Operation: 33+5=38, Resulting Numbers: [19, 38] Generated Node #0,2,2: 70:[19, 38] Operation: 33+5=38 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[5, 14], Operations: ['94-89=5', '33-19=14'] Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[94, 19, 89, 33], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [19, 33, 5] Generated Node #0,2: 70:[19, 33, 5] Operation: 94-89=5 Moving to Node #0,2 Current State: 70:[19, 33, 5], Operations: ['94-89=5'] Exploring Operation: 33-19=14, Resulting Numbers: [5, 14] Generated Node #0,2,0: 70:[5, 14] Operation: 33-19=14 Moving to Node #0,2,0 Current State: 70:[5, 14], Operations: ['94-89=5', '33-19=14'] Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 46, 11, 56, 42 ]
42
[ "46+11=57", "57-56=1", "42*1=42" ]
Current State: 42:[46, 11, 56, 42], Operations: [] Exploring Operation: 46+11=57, Resulting Numbers: [56, 42, 57] Generated Node #2: [56, 42, 57] from Operation: 46+11=57 Current State: 42:[56, 42, 57], Operations: ['46+11=57'] Exploring Operation: 57-56=1, Resulting Numbers: [42, 1] Generated Node #3: [42, 1] from Operation: 57-56=1 Current State: 42:[42, 1], Operations: ['46+11=57', '57-56=1'] Exploring Operation: 42*1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[46, 11, 56, 42], Operations: [] Exploring Operation: 46-42=4, Resulting Numbers: [11, 56, 4] Generated Node #0,0: 42:[11, 56, 4] Operation: 46-42=4 Exploring Operation: 56-46=10, Resulting Numbers: [11, 42, 10] Generated Node #0,1: 42:[11, 42, 10] Operation: 56-46=10 Exploring Operation: 46-11=35, Resulting Numbers: [56, 42, 35] Generated Node #0,2: 42:[56, 42, 35] Operation: 46-11=35 Exploring Operation: 56-42=14, Resulting Numbers: [46, 11, 14] Generated Node #0,3: 42:[46, 11, 14] Operation: 56-42=14 Exploring Operation: 56-11=45, Resulting Numbers: [46, 42, 45] Generated Node #0,4: 42:[46, 42, 45] Operation: 56-11=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[11, 42, 10], Operations: ['56-46=10'] Exploring Operation: 42+10=52, Resulting Numbers: [11, 52] Generated Node #0,1,0: 42:[11, 52] Operation: 42+10=52 Exploring Operation: 42-11=31, Resulting Numbers: [10, 31] Generated Node #0,1,1: 42:[10, 31] Operation: 42-11=31 Exploring Operation: 11+10=21, Resulting Numbers: [42, 21] Generated Node #0,1,2: 42:[42, 21] Operation: 11+10=21 Exploring Operation: 42-10=32, Resulting Numbers: [11, 32] Generated Node #0,1,3: 42:[11, 32] Operation: 42-10=32 Exploring Operation: 11-10=1, Resulting Numbers: [42, 1] Generated Node #0,1,4: 42:[42, 1] Operation: 11-10=1 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 42:[42, 21], Operations: ['56-46=10', '11+10=21'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 42*21=882, Resulting Numbers: [882] 882,42 unequal: No Solution No 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: 42:[42, 1], Operations: ['56-46=10', '11-10=1'] Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[46, 11, 56, 42], Operations: [] Exploring Operation: 56-46=10, Resulting Numbers: [11, 42, 10] Generated Node #0,1: 42:[11, 42, 10] Operation: 56-46=10 Moving to Node #0,1 Current State: 42:[11, 42, 10], Operations: ['56-46=10'] Exploring Operation: 11-10=1, Resulting Numbers: [42, 1] Generated Node #0,1,4: 42:[42, 1] Operation: 11-10=1 Moving to Node #0,1,4 Current State: 42:[42, 1], Operations: ['56-46=10', '11-10=1'] Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 3, 10, 5, 92 ]
17
[ "10-3=7", "92-7=85", "85/5=17" ]
Current State: 17:[3, 10, 5, 92], Operations: [] Exploring Operation: 10-3=7, Resulting Numbers: [5, 92, 7] Generated Node #2: [5, 92, 7] from Operation: 10-3=7 Current State: 17:[5, 92, 7], Operations: ['10-3=7'] Exploring Operation: 92-7=85, Resulting Numbers: [5, 85] Generated Node #3: [5, 85] from Operation: 92-7=85 Current State: 17:[5, 85], Operations: ['10-3=7', '92-7=85'] Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[3, 10, 5, 92], Operations: [] Exploring Operation: 3*5=15, Resulting Numbers: [10, 92, 15] Generated Node #0,0: 17:[10, 92, 15] Operation: 3*5=15 Moving to Node #0,0 Current State: 17:[10, 92, 15], Operations: ['3*5=15'] Exploring Operation: 92-10=82, Resulting Numbers: [15, 82] Generated Node #0,0,0: 17:[15, 82] Operation: 92-10=82 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[15, 82], Operations: ['3*5=15', '92-10=82'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,17 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
[ 19, 47, 85, 38 ]
95
[ "47-19=28", "85+38=123", "123-28=95" ]
Current State: 95:[19, 47, 85, 38], Operations: [] Exploring Operation: 47-19=28, Resulting Numbers: [85, 38, 28] Generated Node #2: [85, 38, 28] from Operation: 47-19=28 Current State: 95:[85, 38, 28], Operations: ['47-19=28'] Exploring Operation: 85+38=123, Resulting Numbers: [28, 123] Generated Node #3: [28, 123] from Operation: 85+38=123 Current State: 95:[28, 123], Operations: ['47-19=28', '85+38=123'] Exploring Operation: 123-28=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[19, 47, 85, 38], Operations: [] Exploring Operation: 47-19=28, Resulting Numbers: [85, 38, 28] Generated Node #0,0: 95:[85, 38, 28] Operation: 47-19=28 Exploring Operation: 85-47=38, Resulting Numbers: [19, 38, 38] Generated Node #0,1: 95:[19, 38, 38] Operation: 85-47=38 Exploring Operation: 38-19=19, Resulting Numbers: [47, 85, 19] Generated Node #0,2: 95:[47, 85, 19] Operation: 38-19=19 Exploring Operation: 47+38=85, Resulting Numbers: [19, 85, 85] Generated Node #0,3: 95:[19, 85, 85] Operation: 47+38=85 Exploring Operation: 47-38=9, Resulting Numbers: [19, 85, 9] Generated Node #0,4: 95:[19, 85, 9] Operation: 47-38=9 Moving to Node #0,4 Current State: 95:[19, 85, 9], Operations: ['47-38=9'] Exploring Operation: 19-9=10, Resulting Numbers: [85, 10] Generated Node #0,4,0: 95:[85, 10] Operation: 19-9=10 Exploring Operation: 19+9=28, Resulting Numbers: [85, 28] Generated Node #0,4,1: 95:[85, 28] Operation: 19+9=28 Exploring Operation: 19+85=104, Resulting Numbers: [9, 104] Generated Node #0,4,2: 95:[9, 104] Operation: 19+85=104 Exploring Operation: 85-9=76, Resulting Numbers: [19, 76] Generated Node #0,4,3: 95:[19, 76] Operation: 85-9=76 Exploring Operation: 85+9=94, Resulting Numbers: [19, 94] Generated Node #0,4,4: 95:[19, 94] Operation: 85+9=94 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 95:[19, 94], Operations: ['47-38=9', '85+9=94'] Exploring Operation: 19+94=113, Resulting Numbers: [113] 113,95 unequal: No Solution Exploring Operation: 94-19=75, Resulting Numbers: [75] 75,95 unequal: No Solution Exploring Operation: 19*94=1786, Resulting Numbers: [1786] 1786,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 95:[9, 104], Operations: ['47-38=9', '19+85=104'] Exploring Operation: 9*104=936, Resulting Numbers: [936] 936,95 unequal: No Solution Exploring Operation: 9+104=113, Resulting Numbers: [113] 113,95 unequal: No Solution Exploring Operation: 104-9=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[19, 47, 85, 38], Operations: [] Exploring Operation: 47-38=9, Resulting Numbers: [19, 85, 9] Generated Node #0,4: 95:[19, 85, 9] Operation: 47-38=9 Moving to Node #0,4 Current State: 95:[19, 85, 9], Operations: ['47-38=9'] Exploring Operation: 19+85=104, Resulting Numbers: [9, 104] Generated Node #0,4,2: 95:[9, 104] Operation: 19+85=104 Moving to Node #0,4,2 Current State: 95:[9, 104], Operations: ['47-38=9', '19+85=104'] Exploring Operation: 104-9=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 96, 16, 35, 19 ]
96
[ "96+16=112", "35-19=16", "112-16=96" ]
Current State: 96:[96, 16, 35, 19], Operations: [] Exploring Operation: 96+16=112, Resulting Numbers: [35, 19, 112] Generated Node #2: [35, 19, 112] from Operation: 96+16=112 Current State: 96:[35, 19, 112], Operations: ['96+16=112'] Exploring Operation: 35-19=16, Resulting Numbers: [112, 16] Generated Node #3: [112, 16] from Operation: 35-19=16 Current State: 96:[112, 16], Operations: ['96+16=112', '35-19=16'] Exploring Operation: 112-16=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[96, 16, 35, 19], Operations: [] Exploring Operation: 16+35=51, Resulting Numbers: [96, 19, 51] Generated Node #0,0: 96:[96, 19, 51] Operation: 16+35=51 Exploring Operation: 19-16=3, Resulting Numbers: [96, 35, 3] Generated Node #0,1: 96:[96, 35, 3] Operation: 19-16=3 Exploring Operation: 96/16=6, Resulting Numbers: [35, 19, 6] Generated Node #0,2: 96:[35, 19, 6] Operation: 96/16=6 Exploring Operation: 35-19=16, Resulting Numbers: [96, 16, 16] Generated Node #0,3: 96:[96, 16, 16] Operation: 35-19=16 Moving to Node #0,3 Current State: 96:[96, 16, 16], Operations: ['35-19=16'] Exploring Operation: 96/16=6, Resulting Numbers: [16, 6] Generated Node #0,3,0: 96:[16, 6] Operation: 96/16=6 Exploring Operation: 16+16=32, Resulting Numbers: [96, 32] Generated Node #0,3,1: 96:[96, 32] Operation: 16+16=32 Exploring Operation: 96/16=6, Resulting Numbers: [16, 6] Generated Node #0,3,2: 96:[16, 6] Operation: 96/16=6 Exploring Operation: 16/16=1, Resulting Numbers: [96, 1] Generated Node #0,3,3: 96:[96, 1] Operation: 16/16=1 Moving to Node #0,1 Current State: 96:[96, 35, 3], Operations: ['19-16=3'] Exploring Operation: 35-3=32, Resulting Numbers: [96, 32] Generated Node #0,1,0: 96:[96, 32] Operation: 35-3=32 Exploring Operation: 96/3=32, Resulting Numbers: [35, 32] Generated Node #0,1,1: 96:[35, 32] Operation: 96/3=32 Exploring Operation: 96+3=99, Resulting Numbers: [35, 99] Generated Node #0,1,2: 96:[35, 99] Operation: 96+3=99 Exploring Operation: 96-3=93, Resulting Numbers: [35, 93] Generated Node #0,1,3: 96:[35, 93] Operation: 96-3=93 Moving to Node #0,2 Current State: 96:[35, 19, 6], Operations: ['96/16=6'] Exploring Operation: 35-19=16, Resulting Numbers: [6, 16] Generated Node #0,2,0: 96:[6, 16] Operation: 35-19=16 Exploring Operation: 19-6=13, Resulting Numbers: [35, 13] Generated Node #0,2,1: 96:[35, 13] Operation: 19-6=13 Exploring Operation: 35+19=54, Resulting Numbers: [6, 54] Generated Node #0,2,2: 96:[6, 54] Operation: 35+19=54 Exploring Operation: 19+6=25, Resulting Numbers: [35, 25] Generated Node #0,2,3: 96:[35, 25] Operation: 19+6=25 Moving to Node #0,0 Current State: 96:[96, 19, 51], Operations: ['16+35=51'] Exploring Operation: 96+19=115, Resulting Numbers: [51, 115] Generated Node #0,0,0: 96:[51, 115] Operation: 96+19=115 Exploring Operation: 96-51=45, Resulting Numbers: [19, 45] Generated Node #0,0,1: 96:[19, 45] Operation: 96-51=45 Exploring Operation: 51-19=32, Resulting Numbers: [96, 32] Generated Node #0,0,2: 96:[96, 32] Operation: 51-19=32 Exploring Operation: 96-19=77, Resulting Numbers: [51, 77] Generated Node #0,0,3: 96:[51, 77] Operation: 96-19=77 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 96:[96, 32], Operations: ['16+35=51', '51-19=32'] Exploring Operation: 96*32=3072, Resulting Numbers: [3072] 3072,96 unequal: No Solution Exploring Operation: 96+32=128, Resulting Numbers: [128] 128,96 unequal: No Solution Exploring Operation: 96/32=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 96-32=64, Resulting Numbers: [64] 64,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 96:[19, 45], Operations: ['16+35=51', '96-51=45'] Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,96 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 19*45=855, Resulting Numbers: [855] 855,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[51, 115], Operations: ['16+35=51', '96+19=115'] Exploring Operation: 115-51=64, Resulting Numbers: [64] 64,96 unequal: No Solution Exploring Operation: 51+115=166, Resulting Numbers: [166] 166,96 unequal: No Solution Exploring Operation: 51*115=5865, Resulting Numbers: [5865] 5865,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 96:[51, 77], Operations: ['16+35=51', '96-19=77'] Exploring Operation: 51+77=128, Resulting Numbers: [128] 128,96 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 51*77=3927, Resulting Numbers: [3927] 3927,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 96:[16, 6], Operations: ['35-19=16', '96/16=6'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,96 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[96, 16, 35, 19], Operations: [] Exploring Operation: 35-19=16, Resulting Numbers: [96, 16, 16] Generated Node #0,3: 96:[96, 16, 16] Operation: 35-19=16 Moving to Node #0,3 Current State: 96:[96, 16, 16], Operations: ['35-19=16'] Exploring Operation: 96/16=6, Resulting Numbers: [16, 6] Generated Node #0,3,0: 96:[16, 6] Operation: 96/16=6 Moving to Node #0,3,0 Current State: 96:[16, 6], Operations: ['35-19=16', '96/16=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 73, 55, 71, 24 ]
62
[ "73-71=2", "55-24=31", "2*31=62" ]
Current State: 62:[73, 55, 71, 24], Operations: [] Exploring Operation: 73-71=2, Resulting Numbers: [55, 24, 2] Generated Node #2: [55, 24, 2] from Operation: 73-71=2 Current State: 62:[55, 24, 2], Operations: ['73-71=2'] Exploring Operation: 55-24=31, Resulting Numbers: [2, 31] Generated Node #3: [2, 31] from Operation: 55-24=31 Current State: 62:[2, 31], Operations: ['73-71=2', '55-24=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[73, 55, 71, 24], Operations: [] Exploring Operation: 71-55=16, Resulting Numbers: [73, 24, 16] Generated Node #0,0: 62:[73, 24, 16] Operation: 71-55=16 Exploring Operation: 55-24=31, Resulting Numbers: [73, 71, 31] Generated Node #0,1: 62:[73, 71, 31] Operation: 55-24=31 Exploring Operation: 73-55=18, Resulting Numbers: [71, 24, 18] Generated Node #0,2: 62:[71, 24, 18] Operation: 73-55=18 Exploring Operation: 73-71=2, Resulting Numbers: [55, 24, 2] Generated Node #0,3: 62:[55, 24, 2] Operation: 73-71=2 Exploring Operation: 73-24=49, Resulting Numbers: [55, 71, 49] Generated Node #0,4: 62:[55, 71, 49] Operation: 73-24=49 Moving to Node #0,3 Current State: 62:[55, 24, 2], Operations: ['73-71=2'] Exploring Operation: 55-2=53, Resulting Numbers: [24, 53] Generated Node #0,3,0: 62:[24, 53] Operation: 55-2=53 Exploring Operation: 55+2=57, Resulting Numbers: [24, 57] Generated Node #0,3,1: 62:[24, 57] Operation: 55+2=57 Exploring Operation: 55-24=31, Resulting Numbers: [2, 31] Generated Node #0,3,2: 62:[2, 31] Operation: 55-24=31 Exploring Operation: 24+2=26, Resulting Numbers: [55, 26] Generated Node #0,3,3: 62:[55, 26] Operation: 24+2=26 Exploring Operation: 24-2=22, Resulting Numbers: [55, 22] Generated Node #0,3,4: 62:[55, 22] Operation: 24-2=22 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 62:[2, 31], Operations: ['73-71=2', '55-24=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[73, 55, 71, 24], Operations: [] Exploring Operation: 73-71=2, Resulting Numbers: [55, 24, 2] Generated Node #0,3: 62:[55, 24, 2] Operation: 73-71=2 Moving to Node #0,3 Current State: 62:[55, 24, 2], Operations: ['73-71=2'] Exploring Operation: 55-24=31, Resulting Numbers: [2, 31] Generated Node #0,3,2: 62:[2, 31] Operation: 55-24=31 Moving to Node #0,3,2 Current State: 62:[2, 31], Operations: ['73-71=2', '55-24=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 92, 54, 79, 88 ]
47
[ "92-54=38", "88-79=9", "38+9=47" ]
Current State: 47:[92, 54, 79, 88], Operations: [] Exploring Operation: 92-54=38, Resulting Numbers: [79, 88, 38] Generated Node #2: [79, 88, 38] from Operation: 92-54=38 Current State: 47:[79, 88, 38], Operations: ['92-54=38'] Exploring Operation: 88-79=9, Resulting Numbers: [38, 9] Generated Node #3: [38, 9] from Operation: 88-79=9 Current State: 47:[38, 9], Operations: ['92-54=38', '88-79=9'] Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[92, 54, 79, 88], Operations: [] Exploring Operation: 92-88=4, Resulting Numbers: [54, 79, 4] Generated Node #0,0: 47:[54, 79, 4] Operation: 92-88=4 Exploring Operation: 92-79=13, Resulting Numbers: [54, 88, 13] Generated Node #0,1: 47:[54, 88, 13] Operation: 92-79=13 Exploring Operation: 92-54=38, Resulting Numbers: [79, 88, 38] Generated Node #0,2: 47:[79, 88, 38] Operation: 92-54=38 Moving to Node #0,0 Current State: 47:[54, 79, 4], Operations: ['92-88=4'] Exploring Operation: 54+4=58, Resulting Numbers: [79, 58] Generated Node #0,0,0: 47:[79, 58] Operation: 54+4=58 Exploring Operation: 54-4=50, Resulting Numbers: [79, 50] Generated Node #0,0,1: 47:[79, 50] Operation: 54-4=50 Exploring Operation: 79-4=75, Resulting Numbers: [54, 75] Generated Node #0,0,2: 47:[54, 75] Operation: 79-4=75 Moving to Node #0,1 Current State: 47:[54, 88, 13], Operations: ['92-79=13'] Exploring Operation: 88-13=75, Resulting Numbers: [54, 75] Generated Node #0,1,0: 47:[54, 75] Operation: 88-13=75 Exploring Operation: 54-13=41, Resulting Numbers: [88, 41] Generated Node #0,1,1: 47:[88, 41] Operation: 54-13=41 Exploring Operation: 88-54=34, Resulting Numbers: [13, 34] Generated Node #0,1,2: 47:[13, 34] Operation: 88-54=34 Moving to Node #0,2 Current State: 47:[79, 88, 38], Operations: ['92-54=38'] Exploring Operation: 88-38=50, Resulting Numbers: [79, 50] Generated Node #0,2,0: 47:[79, 50] Operation: 88-38=50 Exploring Operation: 88-79=9, Resulting Numbers: [38, 9] Generated Node #0,2,1: 47:[38, 9] Operation: 88-79=9 Exploring Operation: 79-38=41, Resulting Numbers: [88, 41] Generated Node #0,2,2: 47:[88, 41] Operation: 79-38=41 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[79, 50], Operations: ['92-54=38', '88-38=50'] Exploring Operation: 79+50=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 79*50=3950, Resulting Numbers: [3950] 3950,47 unequal: No Solution Exploring Operation: 79-50=29, Resulting Numbers: [29] 29,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[38, 9], Operations: ['92-54=38', '88-79=9'] Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[92, 54, 79, 88], Operations: [] Exploring Operation: 92-54=38, Resulting Numbers: [79, 88, 38] Generated Node #0,2: 47:[79, 88, 38] Operation: 92-54=38 Moving to Node #0,2 Current State: 47:[79, 88, 38], Operations: ['92-54=38'] Exploring Operation: 88-79=9, Resulting Numbers: [38, 9] Generated Node #0,2,1: 47:[38, 9] Operation: 88-79=9 Moving to Node #0,2,1 Current State: 47:[38, 9], Operations: ['92-54=38', '88-79=9'] Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_3
sum_heuristic
[ 35, 46, 83, 23 ]
21
[ "35+46=81", "83-23=60", "81-60=21" ]
Current State: 21:[35, 46, 83, 23], Operations: [] Exploring Operation: 35+46=81, Resulting Numbers: [83, 23, 81] Generated Node #2: [83, 23, 81] from Operation: 35+46=81 Current State: 21:[83, 23, 81], Operations: ['35+46=81'] Exploring Operation: 83-23=60, Resulting Numbers: [81, 60] Generated Node #3: [81, 60] from Operation: 83-23=60 Current State: 21:[81, 60], Operations: ['35+46=81', '83-23=60'] Exploring Operation: 81-60=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[35, 46, 83, 23], Operations: [] Exploring Operation: 46-23=23, Resulting Numbers: [35, 83, 23] Generated Node #0,0: 21:[35, 83, 23] Operation: 46-23=23 Exploring Operation: 46-35=11, Resulting Numbers: [83, 23, 11] Generated Node #0,1: 21:[83, 23, 11] Operation: 46-35=11 Exploring Operation: 46/23=2, Resulting Numbers: [35, 83, 2] Generated Node #0,2: 21:[35, 83, 2] Operation: 46/23=2 Exploring Operation: 83-35=48, Resulting Numbers: [46, 23, 48] Generated Node #0,3: 21:[46, 23, 48] Operation: 83-35=48 Exploring Operation: 83-46=37, Resulting Numbers: [35, 23, 37] Generated Node #0,4: 21:[35, 23, 37] Operation: 83-46=37 Moving to Node #0,4 Current State: 21:[35, 23, 37], Operations: ['83-46=37'] Exploring Operation: 37-23=14, Resulting Numbers: [35, 14] Generated Node #0,4,0: 21:[35, 14] Operation: 37-23=14 Exploring Operation: 35-23=12, Resulting Numbers: [37, 12] Generated Node #0,4,1: 21:[37, 12] Operation: 35-23=12 Exploring Operation: 35+37=72, Resulting Numbers: [23, 72] Generated Node #0,4,2: 21:[23, 72] Operation: 35+37=72 Exploring Operation: 37-35=2, Resulting Numbers: [23, 2] Generated Node #0,4,3: 21:[23, 2] Operation: 37-35=2 Exploring Operation: 35+23=58, Resulting Numbers: [37, 58] Generated Node #0,4,4: 21:[37, 58] Operation: 35+23=58 Moving to Node #0,3 Current State: 21:[46, 23, 48], Operations: ['83-35=48'] Exploring Operation: 48-23=25, Resulting Numbers: [46, 25] Generated Node #0,3,0: 21:[46, 25] Operation: 48-23=25 Exploring Operation: 48-46=2, Resulting Numbers: [23, 2] Generated Node #0,3,1: 21:[23, 2] Operation: 48-46=2 Exploring Operation: 46/23=2, Resulting Numbers: [48, 2] Generated Node #0,3,2: 21:[48, 2] Operation: 46/23=2 Exploring Operation: 46+23=69, Resulting Numbers: [48, 69] Generated Node #0,3,3: 21:[48, 69] Operation: 46+23=69 Exploring Operation: 46-23=23, Resulting Numbers: [48, 23] Generated Node #0,3,4: 21:[48, 23] Operation: 46-23=23 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 21:[23, 2], Operations: ['83-35=48', '48-46=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[35, 46, 83, 23], Operations: [] Exploring Operation: 83-35=48, Resulting Numbers: [46, 23, 48] Generated Node #0,3: 21:[46, 23, 48] Operation: 83-35=48 Moving to Node #0,3 Current State: 21:[46, 23, 48], Operations: ['83-35=48'] Exploring Operation: 48-46=2, Resulting Numbers: [23, 2] Generated Node #0,3,1: 21:[23, 2] Operation: 48-46=2 Moving to Node #0,3,1 Current State: 21:[23, 2], Operations: ['83-35=48', '48-46=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 7, 62, 39, 3 ]
44
[ "7*3=21", "62-39=23", "21+23=44" ]
Current State: 44:[7, 62, 39, 3], Operations: [] Exploring Operation: 7*3=21, Resulting Numbers: [62, 39, 21] Generated Node #2: [62, 39, 21] from Operation: 7*3=21 Current State: 44:[62, 39, 21], Operations: ['7*3=21'] Exploring Operation: 62-39=23, Resulting Numbers: [21, 23] Generated Node #3: [21, 23] from Operation: 62-39=23 Current State: 44:[21, 23], Operations: ['7*3=21', '62-39=23'] Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[7, 62, 39, 3], Operations: [] Exploring Operation: 62-7=55, Resulting Numbers: [39, 3, 55] Generated Node #0,0: 44:[39, 3, 55] Operation: 62-7=55 Exploring Operation: 7+39=46, Resulting Numbers: [62, 3, 46] Generated Node #0,1: 44:[62, 3, 46] Operation: 7+39=46 Exploring Operation: 7-3=4, Resulting Numbers: [62, 39, 4] Generated Node #0,2: 44:[62, 39, 4] Operation: 7-3=4 Exploring Operation: 62-39=23, Resulting Numbers: [7, 3, 23] Generated Node #0,3: 44:[7, 3, 23] Operation: 62-39=23 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[7, 3, 23], Operations: ['62-39=23'] Exploring Operation: 23-3=20, Resulting Numbers: [7, 20] Generated Node #0,3,0: 44:[7, 20] Operation: 23-3=20 Exploring Operation: 7*3=21, Resulting Numbers: [23, 21] Generated Node #0,3,1: 44:[23, 21] Operation: 7*3=21 Exploring Operation: 7+3=10, Resulting Numbers: [23, 10] Generated Node #0,3,2: 44:[23, 10] Operation: 7+3=10 Exploring Operation: 7-3=4, Resulting Numbers: [23, 4] Generated Node #0,3,3: 44:[23, 4] Operation: 7-3=4 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 44:[23, 4], Operations: ['62-39=23', '7-3=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,44 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 44:[23, 21], Operations: ['62-39=23', '7*3=21'] Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[7, 62, 39, 3], Operations: [] Exploring Operation: 62-39=23, Resulting Numbers: [7, 3, 23] Generated Node #0,3: 44:[7, 3, 23] Operation: 62-39=23 Moving to Node #0,3 Current State: 44:[7, 3, 23], Operations: ['62-39=23'] Exploring Operation: 7*3=21, Resulting Numbers: [23, 21] Generated Node #0,3,1: 44:[23, 21] Operation: 7*3=21 Moving to Node #0,3,1 Current State: 44:[23, 21], Operations: ['62-39=23', '7*3=21'] Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 56, 2, 52, 20 ]
60
[ "56/2=28", "52-20=32", "28+32=60" ]
Current State: 60:[56, 2, 52, 20], Operations: [] Exploring Operation: 56/2=28, Resulting Numbers: [52, 20, 28] Generated Node #2: [52, 20, 28] from Operation: 56/2=28 Current State: 60:[52, 20, 28], Operations: ['56/2=28'] Exploring Operation: 52-20=32, Resulting Numbers: [28, 32] Generated Node #3: [28, 32] from Operation: 52-20=32 Current State: 60:[28, 32], Operations: ['56/2=28', '52-20=32'] Exploring Operation: 28+32=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[56, 2, 52, 20], Operations: [] Exploring Operation: 52-20=32, Resulting Numbers: [56, 2, 32] Generated Node #0,0: 60:[56, 2, 32] Operation: 52-20=32 Exploring Operation: 56-52=4, Resulting Numbers: [2, 20, 4] Generated Node #0,1: 60:[2, 20, 4] Operation: 56-52=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[2, 20, 4], Operations: ['56-52=4'] Exploring Operation: 20/2=10, Resulting Numbers: [4, 10] Generated Node #0,1,0: 60:[4, 10] Operation: 20/2=10 Exploring Operation: 2+4=6, Resulting Numbers: [20, 6] Generated Node #0,1,1: 60:[20, 6] Operation: 2+4=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 60:[4, 10], Operations: ['56-52=4', '20/2=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,60 unequal: No Solution No 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: 60:[20, 6], Operations: ['56-52=4', '2+4=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,60 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: 60:[56, 2, 32], Operations: ['52-20=32'] Exploring Operation: 56+2=58, Resulting Numbers: [32, 58] Generated Node #0,0,0: 60:[32, 58] Operation: 56+2=58 Exploring Operation: 56/2=28, Resulting Numbers: [32, 28] Generated Node #0,0,1: 60:[32, 28] Operation: 56/2=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[32, 58], Operations: ['52-20=32', '56+2=58'] Exploring Operation: 58-32=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 32+58=90, Resulting Numbers: [90] 90,60 unequal: No Solution No 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: 60:[32, 28], Operations: ['52-20=32', '56/2=28'] Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[56, 2, 52, 20], Operations: [] Exploring Operation: 52-20=32, Resulting Numbers: [56, 2, 32] Generated Node #0,0: 60:[56, 2, 32] Operation: 52-20=32 Moving to Node #0,0 Current State: 60:[56, 2, 32], Operations: ['52-20=32'] Exploring Operation: 56/2=28, Resulting Numbers: [32, 28] Generated Node #0,0,1: 60:[32, 28] Operation: 56/2=28 Moving to Node #0,0,1 Current State: 60:[32, 28], Operations: ['52-20=32', '56/2=28'] Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 89, 11, 17, 21 ]
45
[ "21-17=4", "11*4=44", "89-44=45" ]
Current State: 45:[89, 11, 17, 21], Operations: [] Exploring Operation: 21-17=4, Resulting Numbers: [89, 11, 4] Generated Node #2: [89, 11, 4] from Operation: 21-17=4 Current State: 45:[89, 11, 4], Operations: ['21-17=4'] Exploring Operation: 11*4=44, Resulting Numbers: [89, 44] Generated Node #3: [89, 44] from Operation: 11*4=44 Current State: 45:[89, 44], Operations: ['21-17=4', '11*4=44'] Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[89, 11, 17, 21], Operations: [] Exploring Operation: 89-17=72, Resulting Numbers: [11, 21, 72] Generated Node #0,0: 45:[11, 21, 72] Operation: 89-17=72 Exploring Operation: 89-11=78, Resulting Numbers: [17, 21, 78] Generated Node #0,1: 45:[17, 21, 78] Operation: 89-11=78 Exploring Operation: 89-21=68, Resulting Numbers: [11, 17, 68] Generated Node #0,2: 45:[11, 17, 68] Operation: 89-21=68 Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[11, 17, 68], Operations: ['89-21=68'] Exploring Operation: 68/17=4, Resulting Numbers: [11, 4] Generated Node #0,2,0: 45:[11, 4] Operation: 68/17=4 Exploring Operation: 68-11=57, Resulting Numbers: [17, 57] Generated Node #0,2,1: 45:[17, 57] Operation: 68-11=57 Exploring Operation: 68-17=51, Resulting Numbers: [11, 51] Generated Node #0,2,2: 45:[11, 51] Operation: 68-17=51 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 45:[11, 4], Operations: ['89-21=68', '68/17=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 45:[11, 51], Operations: ['89-21=68', '68-17=51'] Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,45 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 45:[17, 57], Operations: ['89-21=68', '68-11=57'] Exploring Operation: 17+57=74, Resulting Numbers: [74] 74,45 unequal: No Solution Exploring Operation: 57-17=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 17*57=969, Resulting Numbers: [969] 969,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[11, 21, 72], Operations: ['89-17=72'] Exploring Operation: 72-21=51, Resulting Numbers: [11, 51] Generated Node #0,0,0: 45:[11, 51] Operation: 72-21=51 Exploring Operation: 72-11=61, Resulting Numbers: [21, 61] Generated Node #0,0,1: 45:[21, 61] Operation: 72-11=61 Exploring Operation: 21-11=10, Resulting Numbers: [72, 10] Generated Node #0,0,2: 45:[72, 10] Operation: 21-11=10 Moving to Node #0,0,0 Current State: 45:[11, 51], Operations: ['89-17=72', '72-21=51'] Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[21, 61], Operations: ['89-17=72', '72-11=61'] Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 21*61=1281, Resulting Numbers: [1281] 1281,45 unequal: No Solution Exploring Operation: 21+61=82, Resulting Numbers: [82] 82,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[72, 10], Operations: ['89-17=72', '21-11=10'] Exploring Operation: 72*10=720, Resulting Numbers: [720] 720,45 unequal: No Solution Exploring Operation: 72-10=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 72+10=82, Resulting Numbers: [82] 82,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[17, 21, 78], Operations: ['89-11=78'] Exploring Operation: 78-17=61, Resulting Numbers: [21, 61] Generated Node #0,1,0: 45:[21, 61] Operation: 78-17=61 Exploring Operation: 78-21=57, Resulting Numbers: [17, 57] Generated Node #0,1,1: 45:[17, 57] Operation: 78-21=57 Exploring Operation: 21-17=4, Resulting Numbers: [78, 4] Generated Node #0,1,2: 45:[78, 4] Operation: 21-17=4 Moving to Node #0,1,1 Current State: 45:[17, 57], Operations: ['89-11=78', '78-21=57'] Exploring Operation: 57-17=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 17*57=969, Resulting Numbers: [969] 969,45 unequal: No Solution Exploring Operation: 17+57=74, Resulting Numbers: [74] 74,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[21, 61], Operations: ['89-11=78', '78-17=61'] Exploring Operation: 21*61=1281, Resulting Numbers: [1281] 1281,45 unequal: No Solution Exploring Operation: 21+61=82, Resulting Numbers: [82] 82,45 unequal: No Solution Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[78, 4], Operations: ['89-11=78', '21-17=4'] Exploring Operation: 78+4=82, Resulting Numbers: [82] 82,45 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,45 unequal: No Solution Exploring Operation: 78*4=312, Resulting Numbers: [312] 312,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 27, 89, 28, 97 ]
63
[ "89-27=62", "28+97=125", "125-62=63" ]
Current State: 63:[27, 89, 28, 97], Operations: [] Exploring Operation: 89-27=62, Resulting Numbers: [28, 97, 62] Generated Node #2: [28, 97, 62] from Operation: 89-27=62 Current State: 63:[28, 97, 62], Operations: ['89-27=62'] Exploring Operation: 28+97=125, Resulting Numbers: [62, 125] Generated Node #3: [62, 125] from Operation: 28+97=125 Current State: 63:[62, 125], Operations: ['89-27=62', '28+97=125'] Exploring Operation: 125-62=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[27, 89, 28, 97], Operations: [] Exploring Operation: 97-28=69, Resulting Numbers: [27, 89, 69] Generated Node #0,0: 63:[27, 89, 69] Operation: 97-28=69 Exploring Operation: 89-27=62, Resulting Numbers: [28, 97, 62] Generated Node #0,1: 63:[28, 97, 62] Operation: 89-27=62 Exploring Operation: 97-89=8, Resulting Numbers: [27, 28, 8] Generated Node #0,2: 63:[27, 28, 8] Operation: 97-89=8 Exploring Operation: 89-28=61, Resulting Numbers: [27, 97, 61] Generated Node #0,3: 63:[27, 97, 61] Operation: 89-28=61 Exploring Operation: 97-27=70, Resulting Numbers: [89, 28, 70] Generated Node #0,4: 63:[89, 28, 70] Operation: 97-27=70 Moving to Node #0,2 Current State: 63:[27, 28, 8], Operations: ['97-89=8'] Exploring Operation: 28-8=20, Resulting Numbers: [27, 20] Generated Node #0,2,0: 63:[27, 20] Operation: 28-8=20 Exploring Operation: 28-27=1, Resulting Numbers: [8, 1] Generated Node #0,2,1: 63:[8, 1] Operation: 28-27=1 Exploring Operation: 27+8=35, Resulting Numbers: [28, 35] Generated Node #0,2,2: 63:[28, 35] Operation: 27+8=35 Exploring Operation: 27+28=55, Resulting Numbers: [8, 55] Generated Node #0,2,3: 63:[8, 55] Operation: 27+28=55 Exploring Operation: 27-8=19, Resulting Numbers: [28, 19] Generated Node #0,2,4: 63:[28, 19] Operation: 27-8=19 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[8, 1], Operations: ['97-89=8', '28-27=1'] Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[27, 20], Operations: ['97-89=8', '28-8=20'] Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,63 unequal: No Solution Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 63:[8, 55], Operations: ['97-89=8', '27+28=55'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,63 unequal: No Solution Exploring Operation: 8+55=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[27, 89, 28, 97], Operations: [] Exploring Operation: 97-89=8, Resulting Numbers: [27, 28, 8] Generated Node #0,2: 63:[27, 28, 8] Operation: 97-89=8 Moving to Node #0,2 Current State: 63:[27, 28, 8], Operations: ['97-89=8'] Exploring Operation: 27+28=55, Resulting Numbers: [8, 55] Generated Node #0,2,3: 63:[8, 55] Operation: 27+28=55 Moving to Node #0,2,3 Current State: 63:[8, 55], Operations: ['97-89=8', '27+28=55'] Exploring Operation: 8+55=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 94, 89, 72, 96 ]
19
[ "94-89=5", "96-72=24", "24-5=19" ]
Current State: 19:[94, 89, 72, 96], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [72, 96, 5] Generated Node #2: [72, 96, 5] from Operation: 94-89=5 Current State: 19:[72, 96, 5], Operations: ['94-89=5'] Exploring Operation: 96-72=24, Resulting Numbers: [5, 24] Generated Node #3: [5, 24] from Operation: 96-72=24 Current State: 19:[5, 24], Operations: ['94-89=5', '96-72=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[94, 89, 72, 96], Operations: [] Exploring Operation: 96-94=2, Resulting Numbers: [89, 72, 2] Generated Node #0,0: 19:[89, 72, 2] Operation: 96-94=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[89, 72, 2], Operations: ['96-94=2'] Exploring Operation: 89-72=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 19:[2, 17] Operation: 89-72=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[2, 17], Operations: ['96-94=2', '89-72=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[94, 89, 72, 96], Operations: [] Exploring Operation: 96-94=2, Resulting Numbers: [89, 72, 2] Generated Node #0,0: 19:[89, 72, 2] Operation: 96-94=2 Moving to Node #0,0 Current State: 19:[89, 72, 2], Operations: ['96-94=2'] Exploring Operation: 89-72=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 19:[2, 17] Operation: 89-72=17 Moving to Node #0,0,0 Current State: 19:[2, 17], Operations: ['96-94=2', '89-72=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 17, 80, 70, 66 ]
39
[ "17+80=97", "70+66=136", "136-97=39" ]
Current State: 39:[17, 80, 70, 66], Operations: [] Exploring Operation: 17+80=97, Resulting Numbers: [70, 66, 97] Generated Node #2: [70, 66, 97] from Operation: 17+80=97 Current State: 39:[70, 66, 97], Operations: ['17+80=97'] Exploring Operation: 70+66=136, Resulting Numbers: [97, 136] Generated Node #3: [97, 136] from Operation: 70+66=136 Current State: 39:[97, 136], Operations: ['17+80=97', '70+66=136'] Exploring Operation: 136-97=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[17, 80, 70, 66], Operations: [] Exploring Operation: 80-70=10, Resulting Numbers: [17, 66, 10] Generated Node #0,0: 39:[17, 66, 10] Operation: 80-70=10 Exploring Operation: 70-66=4, Resulting Numbers: [17, 80, 4] Generated Node #0,1: 39:[17, 80, 4] Operation: 70-66=4 Exploring Operation: 80-66=14, Resulting Numbers: [17, 70, 14] Generated Node #0,2: 39:[17, 70, 14] Operation: 80-66=14 Moving to Node #0,0 Current State: 39:[17, 66, 10], Operations: ['80-70=10'] Exploring Operation: 66-10=56, Resulting Numbers: [17, 56] Generated Node #0,0,0: 39:[17, 56] Operation: 66-10=56 Exploring Operation: 17-10=7, Resulting Numbers: [66, 7] Generated Node #0,0,1: 39:[66, 7] Operation: 17-10=7 Exploring Operation: 66-17=49, Resulting Numbers: [10, 49] Generated Node #0,0,2: 39:[10, 49] Operation: 66-17=49 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[10, 49], Operations: ['80-70=10', '66-17=49'] Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,39 unequal: No Solution Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,39 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[17, 80, 70, 66], Operations: [] Exploring Operation: 80-70=10, Resulting Numbers: [17, 66, 10] Generated Node #0,0: 39:[17, 66, 10] Operation: 80-70=10 Moving to Node #0,0 Current State: 39:[17, 66, 10], Operations: ['80-70=10'] Exploring Operation: 66-17=49, Resulting Numbers: [10, 49] Generated Node #0,0,2: 39:[10, 49] Operation: 66-17=49 Moving to Node #0,0,2 Current State: 39:[10, 49], Operations: ['80-70=10', '66-17=49'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 80, 67, 54, 79 ]
38
[ "80-67=13", "79-54=25", "13+25=38" ]
Current State: 38:[80, 67, 54, 79], Operations: [] Exploring Operation: 80-67=13, Resulting Numbers: [54, 79, 13] Generated Node #2: [54, 79, 13] from Operation: 80-67=13 Current State: 38:[54, 79, 13], Operations: ['80-67=13'] Exploring Operation: 79-54=25, Resulting Numbers: [13, 25] Generated Node #3: [13, 25] from Operation: 79-54=25 Current State: 38:[13, 25], Operations: ['80-67=13', '79-54=25'] Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[80, 67, 54, 79], Operations: [] Exploring Operation: 80-67=13, Resulting Numbers: [54, 79, 13] Generated Node #0,0: 38:[54, 79, 13] Operation: 80-67=13 Exploring Operation: 79-67=12, Resulting Numbers: [80, 54, 12] Generated Node #0,1: 38:[80, 54, 12] Operation: 79-67=12 Exploring Operation: 80-79=1, Resulting Numbers: [67, 54, 1] Generated Node #0,2: 38:[67, 54, 1] Operation: 80-79=1 Exploring Operation: 79-54=25, Resulting Numbers: [80, 67, 25] Generated Node #0,3: 38:[80, 67, 25] Operation: 79-54=25 Exploring Operation: 80-54=26, Resulting Numbers: [67, 79, 26] Generated Node #0,4: 38:[67, 79, 26] Operation: 80-54=26 Moving to Node #0,2 Current State: 38:[67, 54, 1], Operations: ['80-79=1'] Exploring Operation: 54-1=53, Resulting Numbers: [67, 53] Generated Node #0,2,0: 38:[67, 53] Operation: 54-1=53 Exploring Operation: 67*1=67, Resulting Numbers: [54, 67] Generated Node #0,2,1: 38:[54, 67] Operation: 67*1=67 Exploring Operation: 67-1=66, Resulting Numbers: [54, 66] Generated Node #0,2,2: 38:[54, 66] Operation: 67-1=66 Exploring Operation: 67-54=13, Resulting Numbers: [1, 13] Generated Node #0,2,3: 38:[1, 13] Operation: 67-54=13 Exploring Operation: 67/1=67, Resulting Numbers: [54, 67] Generated Node #0,2,4: 38:[54, 67] Operation: 67/1=67 Moving to Node #0,0 Current State: 38:[54, 79, 13], Operations: ['80-67=13'] Exploring Operation: 79-13=66, Resulting Numbers: [54, 66] Generated Node #0,0,0: 38:[54, 66] Operation: 79-13=66 Exploring Operation: 54+13=67, Resulting Numbers: [79, 67] Generated Node #0,0,1: 38:[79, 67] Operation: 54+13=67 Exploring Operation: 79-54=25, Resulting Numbers: [13, 25] Generated Node #0,0,2: 38:[13, 25] Operation: 79-54=25 Exploring Operation: 79+13=92, Resulting Numbers: [54, 92] Generated Node #0,0,3: 38:[54, 92] Operation: 79+13=92 Exploring Operation: 54-13=41, Resulting Numbers: [79, 41] Generated Node #0,0,4: 38:[79, 41] Operation: 54-13=41 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 38:[13, 25], Operations: ['80-67=13', '79-54=25'] Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 13*25=325, Resulting Numbers: [325] 325,38 unequal: No Solution Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[80, 67, 54, 79], Operations: [] Exploring Operation: 80-67=13, Resulting Numbers: [54, 79, 13] Generated Node #0,0: 38:[54, 79, 13] Operation: 80-67=13 Moving to Node #0,0 Current State: 38:[54, 79, 13], Operations: ['80-67=13'] Exploring Operation: 79-54=25, Resulting Numbers: [13, 25] Generated Node #0,0,2: 38:[13, 25] Operation: 79-54=25 Moving to Node #0,0,2 Current State: 38:[13, 25], Operations: ['80-67=13', '79-54=25'] Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 91, 95, 2, 93 ]
99
[ "95-91=4", "2+93=95", "4+95=99" ]
Current State: 99:[91, 95, 2, 93], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [2, 93, 4] Generated Node #2: [2, 93, 4] from Operation: 95-91=4 Current State: 99:[2, 93, 4], Operations: ['95-91=4'] Exploring Operation: 2+93=95, Resulting Numbers: [4, 95] Generated Node #3: [4, 95] from Operation: 2+93=95 Current State: 99:[4, 95], Operations: ['95-91=4', '2+93=95'] Exploring Operation: 4+95=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[91, 95, 2, 93], Operations: [] Exploring Operation: 91+2=93, Resulting Numbers: [95, 93, 93] Generated Node #0,0: 99:[95, 93, 93] Operation: 91+2=93 Exploring Operation: 95-91=4, Resulting Numbers: [2, 93, 4] Generated Node #0,1: 99:[2, 93, 4] Operation: 95-91=4 Exploring Operation: 93-91=2, Resulting Numbers: [95, 2, 2] Generated Node #0,2: 99:[95, 2, 2] Operation: 93-91=2 Exploring Operation: 95-93=2, Resulting Numbers: [91, 2, 2] Generated Node #0,3: 99:[91, 2, 2] Operation: 95-93=2 Moving to Node #0,2 Current State: 99:[95, 2, 2], Operations: ['93-91=2'] Exploring Operation: 95+2=97, Resulting Numbers: [2, 97] Generated Node #0,2,0: 99:[2, 97] Operation: 95+2=97 Exploring Operation: 2*2=4, Resulting Numbers: [95, 4] Generated Node #0,2,1: 99:[95, 4] Operation: 2*2=4 Exploring Operation: 95+2=97, Resulting Numbers: [2, 97] Generated Node #0,2,2: 99:[2, 97] Operation: 95+2=97 Exploring Operation: 2+2=4, Resulting Numbers: [95, 4] Generated Node #0,2,3: 99:[95, 4] Operation: 2+2=4 Moving to Node #0,1 Current State: 99:[2, 93, 4], Operations: ['95-91=4'] Exploring Operation: 93+4=97, Resulting Numbers: [2, 97] Generated Node #0,1,0: 99:[2, 97] Operation: 93+4=97 Exploring Operation: 2*4=8, Resulting Numbers: [93, 8] Generated Node #0,1,1: 99:[93, 8] Operation: 2*4=8 Exploring Operation: 2+93=95, Resulting Numbers: [4, 95] Generated Node #0,1,2: 99:[4, 95] Operation: 2+93=95 Exploring Operation: 4-2=2, Resulting Numbers: [93, 2] Generated Node #0,1,3: 99:[93, 2] Operation: 4-2=2 Moving to Node #0,3 Current State: 99:[91, 2, 2], Operations: ['95-93=2'] Exploring Operation: 2+2=4, Resulting Numbers: [91, 4] Generated Node #0,3,0: 99:[91, 4] Operation: 2+2=4 Exploring Operation: 91+2=93, Resulting Numbers: [2, 93] Generated Node #0,3,1: 99:[2, 93] Operation: 91+2=93 Exploring Operation: 2*2=4, Resulting Numbers: [91, 4] Generated Node #0,3,2: 99:[91, 4] Operation: 2*2=4 Exploring Operation: 91+2=93, Resulting Numbers: [2, 93] Generated Node #0,3,3: 99:[2, 93] Operation: 91+2=93 Moving to Node #0,0 Current State: 99:[95, 93, 93], Operations: ['91+2=93'] Exploring Operation: 93/93=1, Resulting Numbers: [95, 1] Generated Node #0,0,0: 99:[95, 1] Operation: 93/93=1 Exploring Operation: 93-93=0, Resulting Numbers: [95, 0] Generated Node #0,0,1: 99:[95, 0] Operation: 93-93=0 Exploring Operation: 95-93=2, Resulting Numbers: [93, 2] Generated Node #0,0,2: 99:[93, 2] Operation: 95-93=2 Exploring Operation: 95-93=2, Resulting Numbers: [93, 2] Generated Node #0,0,3: 99:[93, 2] Operation: 95-93=2 Moving to Node #0,2,0 Current State: 99:[2, 97], Operations: ['93-91=2', '95+2=97'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,99 unequal: No Solution Exploring Operation: 2*97=194, Resulting Numbers: [194] 194,99 unequal: No Solution Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[91, 95, 2, 93], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [95, 2, 2] Generated Node #0,2: 99:[95, 2, 2] Operation: 93-91=2 Moving to Node #0,2 Current State: 99:[95, 2, 2], Operations: ['93-91=2'] Exploring Operation: 95+2=97, Resulting Numbers: [2, 97] Generated Node #0,2,0: 99:[2, 97] Operation: 95+2=97 Moving to Node #0,2,0 Current State: 99:[2, 97], Operations: ['93-91=2', '95+2=97'] Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.976563
hs_4
sum_heuristic
[ 89, 87, 20, 4 ]
82
[ "89-87=2", "20*4=80", "2+80=82" ]
Current State: 82:[89, 87, 20, 4], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [20, 4, 2] Generated Node #2: [20, 4, 2] from Operation: 89-87=2 Current State: 82:[20, 4, 2], Operations: ['89-87=2'] Exploring Operation: 20*4=80, Resulting Numbers: [2, 80] Generated Node #3: [2, 80] from Operation: 20*4=80 Current State: 82:[2, 80], Operations: ['89-87=2', '20*4=80'] Exploring Operation: 2+80=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[89, 87, 20, 4], Operations: [] Exploring Operation: 89-20=69, Resulting Numbers: [87, 4, 69] Generated Node #0,0: 82:[87, 4, 69] Operation: 89-20=69 Exploring Operation: 89-87=2, Resulting Numbers: [20, 4, 2] Generated Node #0,1: 82:[20, 4, 2] Operation: 89-87=2 Exploring Operation: 20*4=80, Resulting Numbers: [89, 87, 80] Generated Node #0,2: 82:[89, 87, 80] Operation: 20*4=80 Exploring Operation: 20/4=5, Resulting Numbers: [89, 87, 5] Generated Node #0,3: 82:[89, 87, 5] Operation: 20/4=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[89, 87, 80], Operations: ['20*4=80'] Exploring Operation: 89-87=2, Resulting Numbers: [80, 2] Generated Node #0,2,0: 82:[80, 2] Operation: 89-87=2 Exploring Operation: 87-80=7, Resulting Numbers: [89, 7] Generated Node #0,2,1: 82:[89, 7] Operation: 87-80=7 Exploring Operation: 89+80=169, Resulting Numbers: [87, 169] Generated Node #0,2,2: 82:[87, 169] Operation: 89+80=169 Exploring Operation: 89-80=9, Resulting Numbers: [87, 9] Generated Node #0,2,3: 82:[87, 9] Operation: 89-80=9 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[80, 2], Operations: ['20*4=80', '89-87=2'] Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,82 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,82 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[89, 87, 20, 4], Operations: [] Exploring Operation: 20*4=80, Resulting Numbers: [89, 87, 80] Generated Node #0,2: 82:[89, 87, 80] Operation: 20*4=80 Moving to Node #0,2 Current State: 82:[89, 87, 80], Operations: ['20*4=80'] Exploring Operation: 89-87=2, Resulting Numbers: [80, 2] Generated Node #0,2,0: 82:[80, 2] Operation: 89-87=2 Moving to Node #0,2,0 Current State: 82:[80, 2], Operations: ['20*4=80', '89-87=2'] Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 55, 72, 59, 66 ]
84
[ "59-55=4", "72/4=18", "66+18=84" ]
Current State: 84:[55, 72, 59, 66], Operations: [] Exploring Operation: 59-55=4, Resulting Numbers: [72, 66, 4] Generated Node #2: [72, 66, 4] from Operation: 59-55=4 Current State: 84:[72, 66, 4], Operations: ['59-55=4'] Exploring Operation: 72/4=18, Resulting Numbers: [66, 18] Generated Node #3: [66, 18] from Operation: 72/4=18 Current State: 84:[66, 18], Operations: ['59-55=4', '72/4=18'] Exploring Operation: 66+18=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[55, 72, 59, 66], Operations: [] Exploring Operation: 66-59=7, Resulting Numbers: [55, 72, 7] Generated Node #0,0: 84:[55, 72, 7] Operation: 66-59=7 Moving to Node #0,0 Current State: 84:[55, 72, 7], Operations: ['66-59=7'] Exploring Operation: 72-55=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 84:[7, 17] Operation: 72-55=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[7, 17], Operations: ['66-59=7', '72-55=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,84 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
[ 22, 83, 84, 28 ]
69
[ "28-22=6", "84/6=14", "83-14=69" ]
Current State: 69:[22, 83, 84, 28], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [83, 84, 6] Generated Node #2: [83, 84, 6] from Operation: 28-22=6 Current State: 69:[83, 84, 6], Operations: ['28-22=6'] Exploring Operation: 84/6=14, Resulting Numbers: [83, 14] Generated Node #3: [83, 14] from Operation: 84/6=14 Current State: 69:[83, 14], Operations: ['28-22=6', '84/6=14'] Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[22, 83, 84, 28], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [22, 83, 3] Generated Node #0,0: 69:[22, 83, 3] Operation: 84/28=3 Exploring Operation: 84-83=1, Resulting Numbers: [22, 28, 1] Generated Node #0,1: 69:[22, 28, 1] Operation: 84-83=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[22, 28, 1], Operations: ['84-83=1'] Exploring Operation: 28-22=6, Resulting Numbers: [1, 6] Generated Node #0,1,0: 69:[1, 6] Operation: 28-22=6 Exploring Operation: 22+1=23, Resulting Numbers: [28, 23] Generated Node #0,1,1: 69:[28, 23] Operation: 22+1=23 Moving to Node #0,1,0 Current State: 69:[1, 6], Operations: ['84-83=1', '28-22=6'] Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,69 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[28, 23], Operations: ['84-83=1', '22+1=23'] Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,69 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 #0,0 Current State: 69:[22, 83, 3], Operations: ['84/28=3'] Exploring Operation: 83-22=61, Resulting Numbers: [3, 61] Generated Node #0,0,0: 69:[3, 61] Operation: 83-22=61 Exploring Operation: 83-3=80, Resulting Numbers: [22, 80] Generated Node #0,0,1: 69:[22, 80] Operation: 83-3=80 Moving to Node #0,0,0 Current State: 69:[3, 61], Operations: ['84/28=3', '83-22=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[22, 80], Operations: ['84/28=3', '83-3=80'] Exploring Operation: 80-22=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 22+80=102, Resulting Numbers: [102] 102,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 22, 8, 4, 28 ]
29
[ "8-4=4", "28/4=7", "22+7=29" ]
Current State: 29:[22, 8, 4, 28], Operations: [] Exploring Operation: 8-4=4, Resulting Numbers: [22, 28, 4] Generated Node #2: [22, 28, 4] from Operation: 8-4=4 Current State: 29:[22, 28, 4], Operations: ['8-4=4'] Exploring Operation: 28/4=7, Resulting Numbers: [22, 7] Generated Node #3: [22, 7] from Operation: 28/4=7 Current State: 29:[22, 7], Operations: ['8-4=4', '28/4=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[22, 8, 4, 28], Operations: [] Exploring Operation: 22+4=26, Resulting Numbers: [8, 28, 26] Generated Node #0,0: 29:[8, 28, 26] Operation: 22+4=26 Exploring Operation: 8*4=32, Resulting Numbers: [22, 28, 32] Generated Node #0,1: 29:[22, 28, 32] Operation: 8*4=32 Exploring Operation: 8+4=12, Resulting Numbers: [22, 28, 12] Generated Node #0,2: 29:[22, 28, 12] Operation: 8+4=12 Exploring Operation: 22+8=30, Resulting Numbers: [4, 28, 30] Generated Node #0,3: 29:[4, 28, 30] Operation: 22+8=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[22, 28, 32], Operations: ['8*4=32'] Exploring Operation: 22+32=54, Resulting Numbers: [28, 54] Generated Node #0,1,0: 29:[28, 54] Operation: 22+32=54 Exploring Operation: 32-22=10, Resulting Numbers: [28, 10] Generated Node #0,1,1: 29:[28, 10] Operation: 32-22=10 Exploring Operation: 28-22=6, Resulting Numbers: [32, 6] Generated Node #0,1,2: 29:[32, 6] Operation: 28-22=6 Exploring Operation: 22+28=50, Resulting Numbers: [32, 50] Generated Node #0,1,3: 29:[32, 50] Operation: 22+28=50 Moving to Node #0,1,1 Current State: 29:[28, 10], Operations: ['8*4=32', '32-22=10'] Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,29 unequal: No Solution Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,29 unequal: No Solution Moving to Node #0,1,3 Current State: 29:[32, 50], Operations: ['8*4=32', '22+28=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,29 unequal: No Solution Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,29 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[32, 6], Operations: ['8*4=32', '28-22=6'] Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,29 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[28, 54], Operations: ['8*4=32', '22+32=54'] Exploring Operation: 28*54=1512, Resulting Numbers: [1512] 1512,29 unequal: No Solution Exploring Operation: 54-28=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 28+54=82, Resulting Numbers: [82] 82,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[8, 28, 26], Operations: ['22+4=26'] Exploring Operation: 28-8=20, Resulting Numbers: [26, 20] Generated Node #0,0,0: 29:[26, 20] Operation: 28-8=20 Exploring Operation: 8+28=36, Resulting Numbers: [26, 36] Generated Node #0,0,1: 29:[26, 36] Operation: 8+28=36 Exploring Operation: 26-8=18, Resulting Numbers: [28, 18] Generated Node #0,0,2: 29:[28, 18] Operation: 26-8=18 Exploring Operation: 8+26=34, Resulting Numbers: [28, 34] Generated Node #0,0,3: 29:[28, 34] Operation: 8+26=34 Moving to Node #0,0,3 Current State: 29:[28, 34], Operations: ['22+4=26', '8+26=34'] Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,29 unequal: No Solution Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[26, 36], Operations: ['22+4=26', '8+28=36'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 26*36=936, Resulting Numbers: [936] 936,29 unequal: No Solution Exploring Operation: 26+36=62, Resulting Numbers: [62] 62,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[28, 18], Operations: ['22+4=26', '26-8=18'] Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,29 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[26, 20], Operations: ['22+4=26', '28-8=20'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,29 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,29 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 #0,2 Current State: 29:[22, 28, 12], Operations: ['8+4=12'] Exploring Operation: 22+12=34, Resulting Numbers: [28, 34] Generated Node #0,2,0: 29:[28, 34] Operation: 22+12=34 Exploring Operation: 28-12=16, Resulting Numbers: [22, 16] Generated Node #0,2,1: 29:[22, 16] Operation: 28-12=16 Exploring Operation: 22-12=10, Resulting Numbers: [28, 10] Generated Node #0,2,2: 29:[28, 10] Operation: 22-12=10 Exploring Operation: 28+12=40, Resulting Numbers: [22, 40] Generated Node #0,2,3: 29:[22, 40] Operation: 28+12=40 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 29:[28, 34], Operations: ['8+4=12', '22+12=34'] Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,29 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,29 unequal: No Solution No 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: 29:[22, 40], Operations: ['8+4=12', '28+12=40'] Exploring Operation: 22+40=62, Resulting Numbers: [62] 62,29 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 22*40=880, Resulting Numbers: [880] 880,29 unequal: No Solution No 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: 29:[22, 16], Operations: ['8+4=12', '28-12=16'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,29 unequal: No Solution No 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: 29:[28, 10], Operations: ['8+4=12', '22-12=10'] Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,29 unequal: No Solution Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,29 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: 29:[4, 28, 30], Operations: ['22+8=30'] Exploring Operation: 4+30=34, Resulting Numbers: [28, 34] Generated Node #0,3,0: 29:[28, 34] Operation: 4+30=34 Exploring Operation: 28-4=24, Resulting Numbers: [30, 24] Generated Node #0,3,1: 29:[30, 24] Operation: 28-4=24 Exploring Operation: 30-4=26, Resulting Numbers: [28, 26] Generated Node #0,3,2: 29:[28, 26] Operation: 30-4=26 Exploring Operation: 4+28=32, Resulting Numbers: [30, 32] Generated Node #0,3,3: 29:[30, 32] Operation: 4+28=32 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 29:[28, 26], Operations: ['22+8=30', '30-4=26'] Exploring Operation: 28+26=54, Resulting Numbers: [54] 54,29 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 28*26=728, Resulting Numbers: [728] 728,29 unequal: No Solution No 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: 29:[30, 32], Operations: ['22+8=30', '4+28=32'] Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,29 unequal: No Solution Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,29 unequal: No Solution No 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: 29:[28, 34], Operations: ['22+8=30', '4+30=34'] Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,29 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,29 unequal: No Solution No 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: 29:[30, 24], Operations: ['22+8=30', '28-4=24'] Exploring Operation: 30*24=720, Resulting Numbers: [720] 720,29 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 30+24=54, Resulting Numbers: [54] 54,29 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
[ 46, 32, 27, 29 ]
30
[ "29-27=2", "32/2=16", "46-16=30" ]
Current State: 30:[46, 32, 27, 29], Operations: [] Exploring Operation: 29-27=2, Resulting Numbers: [46, 32, 2] Generated Node #2: [46, 32, 2] from Operation: 29-27=2 Current State: 30:[46, 32, 2], Operations: ['29-27=2'] Exploring Operation: 32/2=16, Resulting Numbers: [46, 16] Generated Node #3: [46, 16] from Operation: 32/2=16 Current State: 30:[46, 16], Operations: ['29-27=2', '32/2=16'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[46, 32, 27, 29], Operations: [] Exploring Operation: 32-27=5, Resulting Numbers: [46, 29, 5] Generated Node #0,0: 30:[46, 29, 5] Operation: 32-27=5 Exploring Operation: 46-27=19, Resulting Numbers: [32, 29, 19] Generated Node #0,1: 30:[32, 29, 19] Operation: 46-27=19 Exploring Operation: 29-27=2, Resulting Numbers: [46, 32, 2] Generated Node #0,2: 30:[46, 32, 2] Operation: 29-27=2 Exploring Operation: 46-29=17, Resulting Numbers: [32, 27, 17] Generated Node #0,3: 30:[32, 27, 17] Operation: 46-29=17 Exploring Operation: 46-32=14, Resulting Numbers: [27, 29, 14] Generated Node #0,4: 30:[27, 29, 14] Operation: 46-32=14 Moving to Node #0,4 Current State: 30:[27, 29, 14], Operations: ['46-32=14'] Exploring Operation: 27+14=41, Resulting Numbers: [29, 41] Generated Node #0,4,0: 30:[29, 41] Operation: 27+14=41 Exploring Operation: 27-14=13, Resulting Numbers: [29, 13] Generated Node #0,4,1: 30:[29, 13] Operation: 27-14=13 Exploring Operation: 29-27=2, Resulting Numbers: [14, 2] Generated Node #0,4,2: 30:[14, 2] Operation: 29-27=2 Exploring Operation: 29+14=43, Resulting Numbers: [27, 43] Generated Node #0,4,3: 30:[27, 43] Operation: 29+14=43 Exploring Operation: 29-14=15, Resulting Numbers: [27, 15] Generated Node #0,4,4: 30:[27, 15] Operation: 29-14=15 Moving to Node #0,3 Current State: 30:[32, 27, 17], Operations: ['46-29=17'] Exploring Operation: 32-27=5, Resulting Numbers: [17, 5] Generated Node #0,3,0: 30:[17, 5] Operation: 32-27=5 Exploring Operation: 27-17=10, Resulting Numbers: [32, 10] Generated Node #0,3,1: 30:[32, 10] Operation: 27-17=10 Exploring Operation: 32+17=49, Resulting Numbers: [27, 49] Generated Node #0,3,2: 30:[27, 49] Operation: 32+17=49 Exploring Operation: 27+17=44, Resulting Numbers: [32, 44] Generated Node #0,3,3: 30:[32, 44] Operation: 27+17=44 Exploring Operation: 32-17=15, Resulting Numbers: [27, 15] Generated Node #0,3,4: 30:[27, 15] Operation: 32-17=15 Moving to Node #0,1 Current State: 30:[32, 29, 19], Operations: ['46-27=19'] Exploring Operation: 32+19=51, Resulting Numbers: [29, 51] Generated Node #0,1,0: 30:[29, 51] Operation: 32+19=51 Exploring Operation: 29+19=48, Resulting Numbers: [32, 48] Generated Node #0,1,1: 30:[32, 48] Operation: 29+19=48 Exploring Operation: 32-19=13, Resulting Numbers: [29, 13] Generated Node #0,1,2: 30:[29, 13] Operation: 32-19=13 Exploring Operation: 32-29=3, Resulting Numbers: [19, 3] Generated Node #0,1,3: 30:[19, 3] Operation: 32-29=3 Exploring Operation: 29-19=10, Resulting Numbers: [32, 10] Generated Node #0,1,4: 30:[32, 10] Operation: 29-19=10 Moving to Node #0,0 Current State: 30:[46, 29, 5], Operations: ['32-27=5'] Exploring Operation: 46-5=41, Resulting Numbers: [29, 41] Generated Node #0,0,0: 30:[29, 41] Operation: 46-5=41 Exploring Operation: 29+5=34, Resulting Numbers: [46, 34] Generated Node #0,0,1: 30:[46, 34] Operation: 29+5=34 Exploring Operation: 46-29=17, Resulting Numbers: [5, 17] Generated Node #0,0,2: 30:[5, 17] Operation: 46-29=17 Exploring Operation: 29-5=24, Resulting Numbers: [46, 24] Generated Node #0,0,3: 30:[46, 24] Operation: 29-5=24 Exploring Operation: 46+5=51, Resulting Numbers: [29, 51] Generated Node #0,0,4: 30:[29, 51] Operation: 46+5=51 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[5, 17], Operations: ['32-27=5', '46-29=17'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,30 unequal: No Solution Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[29, 41], Operations: ['32-27=5', '46-5=41'] Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,30 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[46, 34], Operations: ['32-27=5', '29+5=34'] Exploring Operation: 46*34=1564, Resulting Numbers: [1564] 1564,30 unequal: No Solution Exploring Operation: 46+34=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 30:[46, 24], Operations: ['32-27=5', '29-5=24'] Exploring Operation: 46-24=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 46*24=1104, Resulting Numbers: [1104] 1104,30 unequal: No Solution Exploring Operation: 46+24=70, Resulting Numbers: [70] 70,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 30:[29, 51], Operations: ['32-27=5', '46+5=51'] Exploring Operation: 29+51=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 29*51=1479, Resulting Numbers: [1479] 1479,30 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 30:[46, 32, 2], Operations: ['29-27=2'] Exploring Operation: 32/2=16, Resulting Numbers: [46, 16] Generated Node #0,2,0: 30:[46, 16] Operation: 32/2=16 Exploring Operation: 32-2=30, Resulting Numbers: [46, 30] Generated Node #0,2,1: 30:[46, 30] Operation: 32-2=30 Exploring Operation: 46/2=23, Resulting Numbers: [32, 23] Generated Node #0,2,2: 30:[32, 23] Operation: 46/2=23 Exploring Operation: 46-2=44, Resulting Numbers: [32, 44] Generated Node #0,2,3: 30:[32, 44] Operation: 46-2=44 Exploring Operation: 46-32=14, Resulting Numbers: [2, 14] Generated Node #0,2,4: 30:[2, 14] Operation: 46-32=14 Moving to Node #0,4,2 Current State: 30:[14, 2], Operations: ['46-32=14', '29-27=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,30 unequal: No Solution Moving to Node #0,2,4 Current State: 30:[2, 14], Operations: ['29-27=2', '46-32=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[17, 5], Operations: ['46-29=17', '32-27=5'] Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,30 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,30 unequal: No Solution Moving to Node #0,3,1 Current State: 30:[32, 10], Operations: ['46-29=17', '27-17=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,30 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,30 unequal: No Solution Moving to Node #0,1,4 Current State: 30:[32, 10], Operations: ['46-27=19', '29-19=10'] Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,30 unequal: No Solution Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,30 unequal: No Solution Moving to Node #0,4,4 Current State: 30:[27, 15], Operations: ['46-32=14', '29-14=15'] Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,30 unequal: No Solution Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[29, 13], Operations: ['46-27=19', '32-19=13'] Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,30 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,30 unequal: No Solution Moving to Node #0,4,1 Current State: 30:[29, 13], Operations: ['46-32=14', '27-14=13'] Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,30 unequal: No Solution Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,30 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,30 unequal: No Solution Moving to Node #0,3,4 Current State: 30:[27, 15], Operations: ['46-29=17', '32-17=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,30 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,30 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[19, 3], Operations: ['46-27=19', '32-29=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[32, 23], Operations: ['29-27=2', '46/2=23'] Exploring Operation: 32+23=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 32*23=736, Resulting Numbers: [736] 736,30 unequal: No Solution Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,30 unequal: No Solution Moving to Node #0,4,0 Current State: 30:[29, 41], Operations: ['46-32=14', '27+14=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,30 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[32, 44], Operations: ['29-27=2', '46-2=44'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[46, 30], Operations: ['29-27=2', '32-2=30'] Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,30 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,30 unequal: No Solution Moving to Node #0,4,3 Current State: 30:[27, 43], Operations: ['46-32=14', '29+14=43'] Exploring Operation: 27+43=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 27*43=1161, Resulting Numbers: [1161] 1161,30 unequal: No Solution Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[32, 44], Operations: ['46-29=17', '27+17=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[46, 16], Operations: ['29-27=2', '32/2=16'] Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,30 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[46, 32, 27, 29], Operations: [] Exploring Operation: 29-27=2, Resulting Numbers: [46, 32, 2] Generated Node #0,2: 30:[46, 32, 2] Operation: 29-27=2 Moving to Node #0,2 Current State: 30:[46, 32, 2], Operations: ['29-27=2'] Exploring Operation: 32/2=16, Resulting Numbers: [46, 16] Generated Node #0,2,0: 30:[46, 16] Operation: 32/2=16 Moving to Node #0,2,0 Current State: 30:[46, 16], Operations: ['29-27=2', '32/2=16'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.911458
hs_5
sum_heuristic
[ 5, 27, 78, 62 ]
83
[ "27+78=105", "105/5=21", "62+21=83" ]
Current State: 83:[5, 27, 78, 62], Operations: [] Exploring Operation: 27+78=105, Resulting Numbers: [5, 62, 105] Generated Node #2: [5, 62, 105] from Operation: 27+78=105 Current State: 83:[5, 62, 105], Operations: ['27+78=105'] Exploring Operation: 105/5=21, Resulting Numbers: [62, 21] Generated Node #3: [62, 21] from Operation: 105/5=21 Current State: 83:[62, 21], Operations: ['27+78=105', '105/5=21'] Exploring Operation: 62+21=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[5, 27, 78, 62], Operations: [] Exploring Operation: 5+27=32, Resulting Numbers: [78, 62, 32] Generated Node #0,0: 83:[78, 62, 32] Operation: 5+27=32 Exploring Operation: 5+78=83, Resulting Numbers: [27, 62, 83] Generated Node #0,1: 83:[27, 62, 83] Operation: 5+78=83 Exploring Operation: 5+62=67, Resulting Numbers: [27, 78, 67] Generated Node #0,2: 83:[27, 78, 67] Operation: 5+62=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[78, 62, 32], Operations: ['5+27=32'] Exploring Operation: 78+32=110, Resulting Numbers: [62, 110] Generated Node #0,0,0: 83:[62, 110] Operation: 78+32=110 Exploring Operation: 62+32=94, Resulting Numbers: [78, 94] Generated Node #0,0,1: 83:[78, 94] Operation: 62+32=94 Exploring Operation: 78-32=46, Resulting Numbers: [62, 46] Generated Node #0,0,2: 83:[62, 46] Operation: 78-32=46 Moving to Node #0,0,1 Current State: 83:[78, 94], Operations: ['5+27=32', '62+32=94'] Exploring Operation: 78*94=7332, Resulting Numbers: [7332] 7332,83 unequal: No Solution Exploring Operation: 94-78=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 78+94=172, Resulting Numbers: [172] 172,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[62, 110], Operations: ['5+27=32', '78+32=110'] Exploring Operation: 62*110=6820, Resulting Numbers: [6820] 6820,83 unequal: No Solution Exploring Operation: 62+110=172, Resulting Numbers: [172] 172,83 unequal: No Solution Exploring Operation: 110-62=48, Resulting Numbers: [48] 48,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[62, 46], Operations: ['5+27=32', '78-32=46'] Exploring Operation: 62+46=108, Resulting Numbers: [108] 108,83 unequal: No Solution Exploring Operation: 62*46=2852, Resulting Numbers: [2852] 2852,83 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[27, 62, 83], Operations: ['5+78=83'] Exploring Operation: 27+83=110, Resulting Numbers: [62, 110] Generated Node #0,1,0: 83:[62, 110] Operation: 27+83=110 Exploring Operation: 62-27=35, Resulting Numbers: [83, 35] Generated Node #0,1,1: 83:[83, 35] Operation: 62-27=35 Exploring Operation: 27+62=89, Resulting Numbers: [83, 89] Generated Node #0,1,2: 83:[83, 89] Operation: 27+62=89 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 83:[83, 89], Operations: ['5+78=83', '27+62=89'] Exploring Operation: 89-83=6, Resulting Numbers: [6] 6,83 unequal: No Solution Exploring Operation: 83+89=172, Resulting Numbers: [172] 172,83 unequal: No Solution Exploring Operation: 83*89=7387, Resulting Numbers: [7387] 7387,83 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:[62, 110], Operations: ['5+78=83', '27+83=110'] Exploring Operation: 62+110=172, Resulting Numbers: [172] 172,83 unequal: No Solution Exploring Operation: 110-62=48, Resulting Numbers: [48] 48,83 unequal: No Solution Exploring Operation: 62*110=6820, Resulting Numbers: [6820] 6820,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[83, 35], Operations: ['5+78=83', '62-27=35'] Exploring Operation: 83*35=2905, Resulting Numbers: [2905] 2905,83 unequal: No Solution Exploring Operation: 83+35=118, Resulting Numbers: [118] 118,83 unequal: No Solution Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,83 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 #0,2 Current State: 83:[27, 78, 67], Operations: ['5+62=67'] Exploring Operation: 27+78=105, Resulting Numbers: [67, 105] Generated Node #0,2,0: 83:[67, 105] Operation: 27+78=105 Exploring Operation: 27+67=94, Resulting Numbers: [78, 94] Generated Node #0,2,1: 83:[78, 94] Operation: 27+67=94 Exploring Operation: 78-27=51, Resulting Numbers: [67, 51] Generated Node #0,2,2: 83:[67, 51] Operation: 78-27=51 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[78, 94], Operations: ['5+62=67', '27+67=94'] Exploring Operation: 78+94=172, Resulting Numbers: [172] 172,83 unequal: No Solution Exploring Operation: 94-78=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 78*94=7332, Resulting Numbers: [7332] 7332,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[67, 105], Operations: ['5+62=67', '27+78=105'] Exploring Operation: 105-67=38, Resulting Numbers: [38] 38,83 unequal: No Solution Exploring Operation: 67*105=7035, Resulting Numbers: [7035] 7035,83 unequal: No Solution Exploring Operation: 67+105=172, Resulting Numbers: [172] 172,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[67, 51], Operations: ['5+62=67', '78-27=51'] Exploring Operation: 67*51=3417, Resulting Numbers: [3417] 3417,83 unequal: No Solution Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 67+51=118, Resulting Numbers: [118] 118,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 68, 6, 57, 19 ]
100
[ "68-6=62", "57-19=38", "62+38=100" ]
Current State: 100:[68, 6, 57, 19], Operations: [] Exploring Operation: 68-6=62, Resulting Numbers: [57, 19, 62] Generated Node #2: [57, 19, 62] from Operation: 68-6=62 Current State: 100:[57, 19, 62], Operations: ['68-6=62'] Exploring Operation: 57-19=38, Resulting Numbers: [62, 38] Generated Node #3: [62, 38] from Operation: 57-19=38 Current State: 100:[62, 38], Operations: ['68-6=62', '57-19=38'] Exploring Operation: 62+38=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[68, 6, 57, 19], Operations: [] Exploring Operation: 68-57=11, Resulting Numbers: [6, 19, 11] Generated Node #0,0: 100:[6, 19, 11] Operation: 68-57=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[6, 19, 11], Operations: ['68-57=11'] Exploring Operation: 6+19=25, Resulting Numbers: [11, 25] Generated Node #0,0,0: 100:[11, 25] Operation: 6+19=25 Moving to Node #0,0,0 Current State: 100:[11, 25], Operations: ['68-57=11', '6+19=25'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,100 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
[ 9, 71, 71, 97 ]
97
[ "71-71=0", "9*0=0", "97+0=97" ]
Current State: 97:[9, 71, 71, 97], Operations: [] Exploring Operation: 71-71=0, Resulting Numbers: [9, 97, 0] Generated Node #2: [9, 97, 0] from Operation: 71-71=0 Current State: 97:[9, 97, 0], Operations: ['71-71=0'] Exploring Operation: 9*0=0, Resulting Numbers: [97, 0] Generated Node #3: [97, 0] from Operation: 9*0=0 Current State: 97:[97, 0], Operations: ['71-71=0', '9*0=0'] Exploring Operation: 97+0=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[9, 71, 71, 97], Operations: [] Exploring Operation: 71-9=62, Resulting Numbers: [71, 97, 62] Generated Node #0,0: 97:[71, 97, 62] Operation: 71-9=62 Exploring Operation: 9+71=80, Resulting Numbers: [71, 97, 80] Generated Node #0,1: 97:[71, 97, 80] Operation: 9+71=80 Exploring Operation: 9+71=80, Resulting Numbers: [71, 97, 80] Generated Node #0,2: 97:[71, 97, 80] Operation: 9+71=80 Exploring Operation: 71-9=62, Resulting Numbers: [71, 97, 62] Generated Node #0,3: 97:[71, 97, 62] Operation: 71-9=62 Moving to Node #0,1 Current State: 97:[71, 97, 80], Operations: ['9+71=80'] Exploring Operation: 71+97=168, Resulting Numbers: [80, 168] Generated Node #0,1,0: 97:[80, 168] Operation: 71+97=168 Exploring Operation: 97-71=26, Resulting Numbers: [80, 26] Generated Node #0,1,1: 97:[80, 26] Operation: 97-71=26 Exploring Operation: 71+80=151, Resulting Numbers: [97, 151] Generated Node #0,1,2: 97:[97, 151] Operation: 71+80=151 Exploring Operation: 80-71=9, Resulting Numbers: [97, 9] Generated Node #0,1,3: 97:[97, 9] Operation: 80-71=9 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[97, 151], Operations: ['9+71=80', '71+80=151'] Exploring Operation: 97+151=248, Resulting Numbers: [248] 248,97 unequal: No Solution Exploring Operation: 151-97=54, Resulting Numbers: [54] 54,97 unequal: No Solution Exploring Operation: 97*151=14647, Resulting Numbers: [14647] 14647,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[80, 168], Operations: ['9+71=80', '71+97=168'] Exploring Operation: 80*168=13440, Resulting Numbers: [13440] 13440,97 unequal: No Solution Exploring Operation: 80+168=248, Resulting Numbers: [248] 248,97 unequal: No Solution Exploring Operation: 168-80=88, Resulting Numbers: [88] 88,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[80, 26], Operations: ['9+71=80', '97-71=26'] Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,97 unequal: No Solution Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,97 unequal: No Solution Exploring Operation: 80*26=2080, Resulting Numbers: [2080] 2080,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 97:[97, 9], Operations: ['9+71=80', '80-71=9'] Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,97 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,97 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: 97:[71, 97, 80], Operations: ['9+71=80'] Exploring Operation: 71+97=168, Resulting Numbers: [80, 168] Generated Node #0,2,0: 97:[80, 168] Operation: 71+97=168 Exploring Operation: 71+80=151, Resulting Numbers: [97, 151] Generated Node #0,2,1: 97:[97, 151] Operation: 71+80=151 Exploring Operation: 80-71=9, Resulting Numbers: [97, 9] Generated Node #0,2,2: 97:[97, 9] Operation: 80-71=9 Exploring Operation: 97-71=26, Resulting Numbers: [80, 26] Generated Node #0,2,3: 97:[80, 26] Operation: 97-71=26 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[97, 151], Operations: ['9+71=80', '71+80=151'] Exploring Operation: 97*151=14647, Resulting Numbers: [14647] 14647,97 unequal: No Solution Exploring Operation: 97+151=248, Resulting Numbers: [248] 248,97 unequal: No Solution Exploring Operation: 151-97=54, Resulting Numbers: [54] 54,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[80, 168], Operations: ['9+71=80', '71+97=168'] Exploring Operation: 80+168=248, Resulting Numbers: [248] 248,97 unequal: No Solution Exploring Operation: 80*168=13440, Resulting Numbers: [13440] 13440,97 unequal: No Solution Exploring Operation: 168-80=88, Resulting Numbers: [88] 88,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[97, 9], Operations: ['9+71=80', '80-71=9'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,97 unequal: No Solution Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[80, 26], Operations: ['9+71=80', '97-71=26'] Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,97 unequal: No Solution Exploring Operation: 80*26=2080, Resulting Numbers: [2080] 2080,97 unequal: No Solution Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,97 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: 97:[71, 97, 62], Operations: ['71-9=62'] Exploring Operation: 71+62=133, Resulting Numbers: [97, 133] Generated Node #0,3,0: 97:[97, 133] Operation: 71+62=133 Exploring Operation: 97+62=159, Resulting Numbers: [71, 159] Generated Node #0,3,1: 97:[71, 159] Operation: 97+62=159 Exploring Operation: 71-62=9, Resulting Numbers: [97, 9] Generated Node #0,3,2: 97:[97, 9] Operation: 71-62=9 Exploring Operation: 97-62=35, Resulting Numbers: [71, 35] Generated Node #0,3,3: 97:[71, 35] Operation: 97-62=35 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 97:[97, 133], Operations: ['71-9=62', '71+62=133'] Exploring Operation: 97+133=230, Resulting Numbers: [230] 230,97 unequal: No Solution Exploring Operation: 97*133=12901, Resulting Numbers: [12901] 12901,97 unequal: No Solution Exploring Operation: 133-97=36, Resulting Numbers: [36] 36,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 97:[71, 159], Operations: ['71-9=62', '97+62=159'] Exploring Operation: 159-71=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 71+159=230, Resulting Numbers: [230] 230,97 unequal: No Solution Exploring Operation: 71*159=11289, Resulting Numbers: [11289] 11289,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 97:[97, 9], Operations: ['71-9=62', '71-62=9'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,97 unequal: No Solution Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 97:[71, 35], Operations: ['71-9=62', '97-62=35'] Exploring Operation: 71+35=106, Resulting Numbers: [106] 106,97 unequal: No Solution Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,97 unequal: No Solution Exploring Operation: 71*35=2485, Resulting Numbers: [2485] 2485,97 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: 97:[71, 97, 62], Operations: ['71-9=62'] Exploring Operation: 71+62=133, Resulting Numbers: [97, 133] Generated Node #0,0,0: 97:[97, 133] Operation: 71+62=133 Exploring Operation: 97+62=159, Resulting Numbers: [71, 159] Generated Node #0,0,1: 97:[71, 159] Operation: 97+62=159 Exploring Operation: 97-62=35, Resulting Numbers: [71, 35] Generated Node #0,0,2: 97:[71, 35] Operation: 97-62=35 Exploring Operation: 71-62=9, Resulting Numbers: [97, 9] Generated Node #0,0,3: 97:[97, 9] Operation: 71-62=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[97, 133], Operations: ['71-9=62', '71+62=133'] Exploring Operation: 97+133=230, Resulting Numbers: [230] 230,97 unequal: No Solution Exploring Operation: 133-97=36, Resulting Numbers: [36] 36,97 unequal: No Solution Exploring Operation: 97*133=12901, Resulting Numbers: [12901] 12901,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[71, 159], Operations: ['71-9=62', '97+62=159'] Exploring Operation: 71+159=230, Resulting Numbers: [230] 230,97 unequal: No Solution Exploring Operation: 159-71=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 71*159=11289, Resulting Numbers: [11289] 11289,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[71, 35], Operations: ['71-9=62', '97-62=35'] Exploring Operation: 71*35=2485, Resulting Numbers: [2485] 2485,97 unequal: No Solution Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,97 unequal: No Solution Exploring Operation: 71+35=106, Resulting Numbers: [106] 106,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 97:[97, 9], Operations: ['71-9=62', '71-62=9'] Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,97 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,97 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
[ 70, 35, 24, 59 ]
94
[ "70/35=2", "59*2=118", "118-24=94" ]
Current State: 94:[70, 35, 24, 59], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [24, 59, 2] Generated Node #2: [24, 59, 2] from Operation: 70/35=2 Current State: 94:[24, 59, 2], Operations: ['70/35=2'] Exploring Operation: 59*2=118, Resulting Numbers: [24, 118] Generated Node #3: [24, 118] from Operation: 59*2=118 Current State: 94:[24, 118], Operations: ['70/35=2', '59*2=118'] Exploring Operation: 118-24=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[70, 35, 24, 59], Operations: [] Exploring Operation: 70-24=46, Resulting Numbers: [35, 59, 46] Generated Node #0,0: 94:[35, 59, 46] Operation: 70-24=46 Exploring Operation: 70+24=94, Resulting Numbers: [35, 59, 94] Generated Node #0,1: 94:[35, 59, 94] Operation: 70+24=94 Moving to Node #0,1 Current State: 94:[35, 59, 94], Operations: ['70+24=94'] Exploring Operation: 59-35=24, Resulting Numbers: [94, 24] Generated Node #0,1,0: 94:[94, 24] Operation: 59-35=24 Exploring Operation: 35+59=94, Resulting Numbers: [94, 94] Generated Node #0,1,1: 94:[94, 94] Operation: 35+59=94 Moving to Node #0,0 Current State: 94:[35, 59, 46], Operations: ['70-24=46'] Exploring Operation: 35+59=94, Resulting Numbers: [46, 94] Generated Node #0,0,0: 94:[46, 94] Operation: 35+59=94 Exploring Operation: 46-35=11, Resulting Numbers: [59, 11] Generated Node #0,0,1: 94:[59, 11] Operation: 46-35=11 Moving to Node #0,1,1 Current State: 94:[94, 94], Operations: ['70+24=94', '35+59=94'] Exploring Operation: 94/94=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 94-94=0, Resulting Numbers: [0] 0,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[46, 94], Operations: ['70-24=46', '35+59=94'] Exploring Operation: 94-46=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 46+94=140, Resulting Numbers: [140] 140,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[59, 11], Operations: ['70-24=46', '46-35=11'] Exploring Operation: 59+11=70, Resulting Numbers: [70] 70,94 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[94, 24], Operations: ['70+24=94', '59-35=24'] Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,94 unequal: No Solution Exploring Operation: 94+24=118, Resulting Numbers: [118] 118,94 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 85, 44, 42, 72 ]
15
[ "85+44=129", "42+72=114", "129-114=15" ]
Current State: 15:[85, 44, 42, 72], Operations: [] Exploring Operation: 85+44=129, Resulting Numbers: [42, 72, 129] Generated Node #2: [42, 72, 129] from Operation: 85+44=129 Current State: 15:[42, 72, 129], Operations: ['85+44=129'] Exploring Operation: 42+72=114, Resulting Numbers: [129, 114] Generated Node #3: [129, 114] from Operation: 42+72=114 Current State: 15:[129, 114], Operations: ['85+44=129', '42+72=114'] Exploring Operation: 129-114=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[85, 44, 42, 72], Operations: [] Exploring Operation: 85-44=41, Resulting Numbers: [42, 72, 41] Generated Node #0,0: 15:[42, 72, 41] Operation: 85-44=41 Exploring Operation: 85-72=13, Resulting Numbers: [44, 42, 13] Generated Node #0,1: 15:[44, 42, 13] Operation: 85-72=13 Exploring Operation: 72-44=28, Resulting Numbers: [85, 42, 28] Generated Node #0,2: 15:[85, 42, 28] Operation: 72-44=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[44, 42, 13], Operations: ['85-72=13'] Exploring Operation: 44-13=31, Resulting Numbers: [42, 31] Generated Node #0,1,0: 15:[42, 31] Operation: 44-13=31 Exploring Operation: 42-13=29, Resulting Numbers: [44, 29] Generated Node #0,1,1: 15:[44, 29] Operation: 42-13=29 Exploring Operation: 44-42=2, Resulting Numbers: [13, 2] Generated Node #0,1,2: 15:[13, 2] Operation: 44-42=2 Moving to Node #0,1,2 Current State: 15:[13, 2], Operations: ['85-72=13', '44-42=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,15 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[85, 44, 42, 72], Operations: [] Exploring Operation: 85-72=13, Resulting Numbers: [44, 42, 13] Generated Node #0,1: 15:[44, 42, 13] Operation: 85-72=13 Moving to Node #0,1 Current State: 15:[44, 42, 13], Operations: ['85-72=13'] Exploring Operation: 44-42=2, Resulting Numbers: [13, 2] Generated Node #0,1,2: 15:[13, 2] Operation: 44-42=2 Moving to Node #0,1,2 Current State: 15:[13, 2], Operations: ['85-72=13', '44-42=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 27, 33, 79, 6 ]
92
[ "27+79=106", "33*6=198", "198-106=92" ]
Current State: 92:[27, 33, 79, 6], Operations: [] Exploring Operation: 27+79=106, Resulting Numbers: [33, 6, 106] Generated Node #2: [33, 6, 106] from Operation: 27+79=106 Current State: 92:[33, 6, 106], Operations: ['27+79=106'] Exploring Operation: 33*6=198, Resulting Numbers: [106, 198] Generated Node #3: [106, 198] from Operation: 33*6=198 Current State: 92:[106, 198], Operations: ['27+79=106', '33*6=198'] Exploring Operation: 198-106=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[27, 33, 79, 6], Operations: [] Exploring Operation: 79-33=46, Resulting Numbers: [27, 6, 46] Generated Node #0,0: 92:[27, 6, 46] Operation: 79-33=46 Moving to Node #0,0 Current State: 92:[27, 6, 46], Operations: ['79-33=46'] Exploring Operation: 27-6=21, Resulting Numbers: [46, 21] Generated Node #0,0,0: 92:[46, 21] Operation: 27-6=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[46, 21], Operations: ['79-33=46', '27-6=21'] Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 88, 5, 4, 64 ]
67
[ "88-5=83", "64/4=16", "83-16=67" ]
Current State: 67:[88, 5, 4, 64], Operations: [] Exploring Operation: 88-5=83, Resulting Numbers: [4, 64, 83] Generated Node #2: [4, 64, 83] from Operation: 88-5=83 Current State: 67:[4, 64, 83], Operations: ['88-5=83'] Exploring Operation: 64/4=16, Resulting Numbers: [83, 16] Generated Node #3: [83, 16] from Operation: 64/4=16 Current State: 67:[83, 16], Operations: ['88-5=83', '64/4=16'] Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[88, 5, 4, 64], Operations: [] Exploring Operation: 5+4=9, Resulting Numbers: [88, 64, 9] Generated Node #0,0: 67:[88, 64, 9] Operation: 5+4=9 Exploring Operation: 88-5=83, Resulting Numbers: [4, 64, 83] Generated Node #0,1: 67:[4, 64, 83] Operation: 88-5=83 Exploring Operation: 88-4=84, Resulting Numbers: [5, 64, 84] Generated Node #0,2: 67:[5, 64, 84] Operation: 88-4=84 Exploring Operation: 4+64=68, Resulting Numbers: [88, 5, 68] Generated Node #0,3: 67:[88, 5, 68] Operation: 4+64=68 Exploring Operation: 5*4=20, Resulting Numbers: [88, 64, 20] Generated Node #0,4: 67:[88, 64, 20] Operation: 5*4=20 Start Sub Search at level 1: Moving to Node #0,4 Current State: 67:[88, 64, 20], Operations: ['5*4=20'] Exploring Operation: 64-20=44, Resulting Numbers: [88, 44] Generated Node #0,4,0: 67:[88, 44] Operation: 64-20=44 Exploring Operation: 64+20=84, Resulting Numbers: [88, 84] Generated Node #0,4,1: 67:[88, 84] Operation: 64+20=84 Exploring Operation: 88-20=68, Resulting Numbers: [64, 68] Generated Node #0,4,2: 67:[64, 68] Operation: 88-20=68 Exploring Operation: 88-64=24, Resulting Numbers: [20, 24] Generated Node #0,4,3: 67:[20, 24] Operation: 88-64=24 Exploring Operation: 88+20=108, Resulting Numbers: [64, 108] Generated Node #0,4,4: 67:[64, 108] Operation: 88+20=108 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 67:[64, 68], Operations: ['5*4=20', '88-20=68'] Exploring Operation: 68-64=4, Resulting Numbers: [4] 4,67 unequal: No Solution Exploring Operation: 64+68=132, Resulting Numbers: [132] 132,67 unequal: No Solution Exploring Operation: 64*68=4352, Resulting Numbers: [4352] 4352,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 67:[88, 84], Operations: ['5*4=20', '64+20=84'] Exploring Operation: 88-84=4, Resulting Numbers: [4] 4,67 unequal: No Solution Exploring Operation: 88*84=7392, Resulting Numbers: [7392] 7392,67 unequal: No Solution Exploring Operation: 88+84=172, Resulting Numbers: [172] 172,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 67:[88, 44], Operations: ['5*4=20', '64-20=44'] Exploring Operation: 88+44=132, Resulting Numbers: [132] 132,67 unequal: No Solution Exploring Operation: 88/44=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 88*44=3872, Resulting Numbers: [3872] 3872,67 unequal: No Solution Exploring Operation: 88-44=44, Resulting Numbers: [44] 44,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 67:[64, 108], Operations: ['5*4=20', '88+20=108'] Exploring Operation: 64+108=172, Resulting Numbers: [172] 172,67 unequal: No Solution Exploring Operation: 64*108=6912, Resulting Numbers: [6912] 6912,67 unequal: No Solution Exploring Operation: 108-64=44, Resulting Numbers: [44] 44,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 67:[20, 24], Operations: ['5*4=20', '88-64=24'] Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,67 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,67 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[88, 64, 9], Operations: ['5+4=9'] Exploring Operation: 64-9=55, Resulting Numbers: [88, 55] Generated Node #0,0,0: 67:[88, 55] Operation: 64-9=55 Exploring Operation: 88-64=24, Resulting Numbers: [9, 24] Generated Node #0,0,1: 67:[9, 24] Operation: 88-64=24 Exploring Operation: 88+9=97, Resulting Numbers: [64, 97] Generated Node #0,0,2: 67:[64, 97] Operation: 88+9=97 Exploring Operation: 88-9=79, Resulting Numbers: [64, 79] Generated Node #0,0,3: 67:[64, 79] Operation: 88-9=79 Exploring Operation: 64+9=73, Resulting Numbers: [88, 73] Generated Node #0,0,4: 67:[88, 73] Operation: 64+9=73 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 67:[64, 79], Operations: ['5+4=9', '88-9=79'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,67 unequal: No Solution Exploring Operation: 64*79=5056, Resulting Numbers: [5056] 5056,67 unequal: No Solution Exploring Operation: 64+79=143, Resulting Numbers: [143] 143,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 67:[88, 73], Operations: ['5+4=9', '64+9=73'] Exploring Operation: 88+73=161, Resulting Numbers: [161] 161,67 unequal: No Solution Exploring Operation: 88*73=6424, Resulting Numbers: [6424] 6424,67 unequal: No Solution Exploring Operation: 88-73=15, Resulting Numbers: [15] 15,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[88, 55], Operations: ['5+4=9', '64-9=55'] Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,67 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 67:[64, 97], Operations: ['5+4=9', '88+9=97'] Exploring Operation: 97-64=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 64*97=6208, Resulting Numbers: [6208] 6208,67 unequal: No Solution Exploring Operation: 64+97=161, Resulting Numbers: [161] 161,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 67:[9, 24], Operations: ['5+4=9', '88-64=24'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,67 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,67 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[4, 64, 83], Operations: ['88-5=83'] Exploring Operation: 64-4=60, Resulting Numbers: [83, 60] Generated Node #0,1,0: 67:[83, 60] Operation: 64-4=60 Exploring Operation: 4+83=87, Resulting Numbers: [64, 87] Generated Node #0,1,1: 67:[64, 87] Operation: 4+83=87 Exploring Operation: 83-4=79, Resulting Numbers: [64, 79] Generated Node #0,1,2: 67:[64, 79] Operation: 83-4=79 Exploring Operation: 64/4=16, Resulting Numbers: [83, 16] Generated Node #0,1,3: 67:[83, 16] Operation: 64/4=16 Exploring Operation: 4+64=68, Resulting Numbers: [83, 68] Generated Node #0,1,4: 67:[83, 68] Operation: 4+64=68 Moving to Node #0,1,2 Current State: 67:[64, 79], Operations: ['88-5=83', '83-4=79'] Exploring Operation: 64*79=5056, Resulting Numbers: [5056] 5056,67 unequal: No Solution Exploring Operation: 64+79=143, Resulting Numbers: [143] 143,67 unequal: No Solution Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,67 unequal: No Solution Moving to Node #0,1,4 Current State: 67:[83, 68], Operations: ['88-5=83', '4+64=68'] Exploring Operation: 83+68=151, Resulting Numbers: [151] 151,67 unequal: No Solution Exploring Operation: 83-68=15, Resulting Numbers: [15] 15,67 unequal: No Solution Exploring Operation: 83*68=5644, Resulting Numbers: [5644] 5644,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[83, 60], Operations: ['88-5=83', '64-4=60'] Exploring Operation: 83-60=23, Resulting Numbers: [23] 23,67 unequal: No Solution Exploring Operation: 83+60=143, Resulting Numbers: [143] 143,67 unequal: No Solution Exploring Operation: 83*60=4980, Resulting Numbers: [4980] 4980,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[64, 87], Operations: ['88-5=83', '4+83=87'] Exploring Operation: 87-64=23, Resulting Numbers: [23] 23,67 unequal: No Solution Exploring Operation: 64+87=151, Resulting Numbers: [151] 151,67 unequal: No Solution Exploring Operation: 64*87=5568, Resulting Numbers: [5568] 5568,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[83, 16], Operations: ['88-5=83', '64/4=16'] Exploring Operation: 83*16=1328, Resulting Numbers: [1328] 1328,67 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[88, 5, 4, 64], Operations: [] Exploring Operation: 88-5=83, Resulting Numbers: [4, 64, 83] Generated Node #0,1: 67:[4, 64, 83] Operation: 88-5=83 Moving to Node #0,1 Current State: 67:[4, 64, 83], Operations: ['88-5=83'] Exploring Operation: 64/4=16, Resulting Numbers: [83, 16] Generated Node #0,1,3: 67:[83, 16] Operation: 64/4=16 Moving to Node #0,1,3 Current State: 67:[83, 16], Operations: ['88-5=83', '64/4=16'] Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.940104
hs_5
mult_heuristic
[ 46, 8, 32, 88 ]
31
[ "32+88=120", "120/8=15", "46-15=31" ]
Current State: 31:[46, 8, 32, 88], Operations: [] Exploring Operation: 32+88=120, Resulting Numbers: [46, 8, 120] Generated Node #2: [46, 8, 120] from Operation: 32+88=120 Current State: 31:[46, 8, 120], Operations: ['32+88=120'] Exploring Operation: 120/8=15, Resulting Numbers: [46, 15] Generated Node #3: [46, 15] from Operation: 120/8=15 Current State: 31:[46, 15], Operations: ['32+88=120', '120/8=15'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[46, 8, 32, 88], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [46, 32, 11] Generated Node #0,0: 31:[46, 32, 11] Operation: 88/8=11 Exploring Operation: 88-46=42, Resulting Numbers: [8, 32, 42] Generated Node #0,1: 31:[8, 32, 42] Operation: 88-46=42 Exploring Operation: 88-32=56, Resulting Numbers: [46, 8, 56] Generated Node #0,2: 31:[46, 8, 56] Operation: 88-32=56 Exploring Operation: 46-8=38, Resulting Numbers: [32, 88, 38] Generated Node #0,3: 31:[32, 88, 38] Operation: 46-8=38 Moving to Node #0,1 Current State: 31:[8, 32, 42], Operations: ['88-46=42'] Exploring Operation: 8+32=40, Resulting Numbers: [42, 40] Generated Node #0,1,0: 31:[42, 40] Operation: 8+32=40 Exploring Operation: 42-8=34, Resulting Numbers: [32, 34] Generated Node #0,1,1: 31:[32, 34] Operation: 42-8=34 Exploring Operation: 8+42=50, Resulting Numbers: [32, 50] Generated Node #0,1,2: 31:[32, 50] Operation: 8+42=50 Exploring Operation: 32-8=24, Resulting Numbers: [42, 24] Generated Node #0,1,3: 31:[42, 24] Operation: 32-8=24 Moving to Node #0,0 Current State: 31:[46, 32, 11], Operations: ['88/8=11'] Exploring Operation: 46+11=57, Resulting Numbers: [32, 57] Generated Node #0,0,0: 31:[32, 57] Operation: 46+11=57 Exploring Operation: 32-11=21, Resulting Numbers: [46, 21] Generated Node #0,0,1: 31:[46, 21] Operation: 32-11=21 Exploring Operation: 46-11=35, Resulting Numbers: [32, 35] Generated Node #0,0,2: 31:[32, 35] Operation: 46-11=35 Exploring Operation: 32+11=43, Resulting Numbers: [46, 43] Generated Node #0,0,3: 31:[46, 43] Operation: 32+11=43 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[32, 35], Operations: ['88/8=11', '46-11=35'] Exploring Operation: 32*35=1120, Resulting Numbers: [1120] 1120,31 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 32+35=67, Resulting Numbers: [67] 67,31 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 #0,0,1 Current State: 31:[46, 21], Operations: ['88/8=11', '32-11=21'] Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,31 unequal: No Solution Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,31 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 #0,0,0 Current State: 31:[32, 57], Operations: ['88/8=11', '46+11=57'] Exploring Operation: 57-32=25, Resulting Numbers: [25] 25,31 unequal: No Solution Exploring Operation: 32*57=1824, Resulting Numbers: [1824] 1824,31 unequal: No Solution Exploring Operation: 32+57=89, Resulting Numbers: [89] 89,31 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 #0,0,3 Current State: 31:[46, 43], Operations: ['88/8=11', '32+11=43'] Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,31 unequal: No Solution Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,31 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: 31:[46, 8, 56], Operations: ['88-32=56'] Exploring Operation: 46-8=38, Resulting Numbers: [56, 38] Generated Node #0,2,0: 31:[56, 38] Operation: 46-8=38 Exploring Operation: 56-46=10, Resulting Numbers: [8, 10] Generated Node #0,2,1: 31:[8, 10] Operation: 56-46=10 Exploring Operation: 56/8=7, Resulting Numbers: [46, 7] Generated Node #0,2,2: 31:[46, 7] Operation: 56/8=7 Exploring Operation: 56-8=48, Resulting Numbers: [46, 48] Generated Node #0,2,3: 31:[46, 48] Operation: 56-8=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[56, 38], Operations: ['88-32=56', '46-8=38'] Exploring Operation: 56*38=2128, Resulting Numbers: [2128] 2128,31 unequal: No Solution Exploring Operation: 56+38=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,31 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 #0,2,3 Current State: 31:[46, 48], Operations: ['88-32=56', '56-8=48'] Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 46*48=2208, Resulting Numbers: [2208] 2208,31 unequal: No Solution Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[46, 7], Operations: ['88-32=56', '56/8=7'] Exploring Operation: 46*7=322, Resulting Numbers: [322] 322,31 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,31 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 #0,2,1 Current State: 31:[8, 10], Operations: ['88-32=56', '56-46=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,31 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: 31:[32, 88, 38], Operations: ['46-8=38'] Exploring Operation: 32+88=120, Resulting Numbers: [38, 120] Generated Node #0,3,0: 31:[38, 120] Operation: 32+88=120 Exploring Operation: 88-32=56, Resulting Numbers: [38, 56] Generated Node #0,3,1: 31:[38, 56] Operation: 88-32=56 Exploring Operation: 88-38=50, Resulting Numbers: [32, 50] Generated Node #0,3,2: 31:[32, 50] Operation: 88-38=50 Exploring Operation: 38-32=6, Resulting Numbers: [88, 6] Generated Node #0,3,3: 31:[88, 6] Operation: 38-32=6 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[32, 50], Operations: ['46-8=38', '88-38=50'] Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,31 unequal: No Solution Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,31 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 #0,3,1 Current State: 31:[38, 56], Operations: ['46-8=38', '88-32=56'] Exploring Operation: 38+56=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 38*56=2128, Resulting Numbers: [2128] 2128,31 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 #0,3,3 Current State: 31:[88, 6], Operations: ['46-8=38', '38-32=6'] Exploring Operation: 88*6=528, Resulting Numbers: [528] 528,31 unequal: No Solution Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,31 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 #0,3,0 Current State: 31:[38, 120], Operations: ['46-8=38', '32+88=120'] Exploring Operation: 120-38=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 38*120=4560, Resulting Numbers: [4560] 4560,31 unequal: No Solution Exploring Operation: 38+120=158, Resulting Numbers: [158] 158,31 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: 31:[32, 34], Operations: ['88-46=42', '42-8=34'] Exploring Operation: 32*34=1088, Resulting Numbers: [1088] 1088,31 unequal: No Solution Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[42, 24], Operations: ['88-46=42', '32-8=24'] Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,31 unequal: No Solution Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[32, 50], Operations: ['88-46=42', '8+42=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,31 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[42, 40], Operations: ['88-46=42', '8+32=40'] Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 42*40=1680, Resulting Numbers: [1680] 1680,31 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 38, 8, 10, 36 ]
52
[ "38*10=380", "36+380=416", "416/8=52" ]
Current State: 52:[38, 8, 10, 36], Operations: [] Exploring Operation: 38*10=380, Resulting Numbers: [8, 36, 380] Generated Node #2: [8, 36, 380] from Operation: 38*10=380 Current State: 52:[8, 36, 380], Operations: ['38*10=380'] Exploring Operation: 36+380=416, Resulting Numbers: [8, 416] Generated Node #3: [8, 416] from Operation: 36+380=416 Current State: 52:[8, 416], Operations: ['38*10=380', '36+380=416'] Exploring Operation: 416/8=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[38, 8, 10, 36], Operations: [] Exploring Operation: 36-10=26, Resulting Numbers: [38, 8, 26] Generated Node #0,0: 52:[38, 8, 26] Operation: 36-10=26 Exploring Operation: 38-36=2, Resulting Numbers: [8, 10, 2] Generated Node #0,1: 52:[8, 10, 2] Operation: 38-36=2 Exploring Operation: 38-10=28, Resulting Numbers: [8, 36, 28] Generated Node #0,2: 52:[8, 36, 28] Operation: 38-10=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[8, 10, 2], Operations: ['38-36=2'] Exploring Operation: 10-8=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 52:[2, 2] Operation: 10-8=2 Exploring Operation: 8/2=4, Resulting Numbers: [10, 4] Generated Node #0,1,1: 52:[10, 4] Operation: 8/2=4 Exploring Operation: 8+10=18, Resulting Numbers: [2, 18] Generated Node #0,1,2: 52:[2, 18] Operation: 8+10=18 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[2, 2], Operations: ['38-36=2', '10-8=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[10, 4], Operations: ['38-36=2', '8/2=4'] Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,52 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[2, 18], Operations: ['38-36=2', '8+10=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[38, 8, 26], Operations: ['36-10=26'] Exploring Operation: 38+8=46, Resulting Numbers: [26, 46] Generated Node #0,0,0: 52:[26, 46] Operation: 38+8=46 Exploring Operation: 38-26=12, Resulting Numbers: [8, 12] Generated Node #0,0,1: 52:[8, 12] Operation: 38-26=12 Exploring Operation: 38-8=30, Resulting Numbers: [26, 30] Generated Node #0,0,2: 52:[26, 30] Operation: 38-8=30 Moving to Node #0,0,2 Current State: 52:[26, 30], Operations: ['36-10=26', '38-8=30'] Exploring Operation: 26+30=56, Resulting Numbers: [56] 56,52 unequal: No Solution Exploring Operation: 30-26=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 26*30=780, Resulting Numbers: [780] 780,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[8, 12], Operations: ['36-10=26', '38-26=12'] Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,52 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[26, 46], Operations: ['36-10=26', '38+8=46'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,52 unequal: No Solution Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,52 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 Current State: 52:[8, 36, 28], Operations: ['38-10=28'] Exploring Operation: 36-8=28, Resulting Numbers: [28, 28] Generated Node #0,2,0: 52:[28, 28] Operation: 36-8=28 Exploring Operation: 8+36=44, Resulting Numbers: [28, 44] Generated Node #0,2,1: 52:[28, 44] Operation: 8+36=44 Exploring Operation: 36-28=8, Resulting Numbers: [8, 8] Generated Node #0,2,2: 52:[8, 8] Operation: 36-28=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[28, 28], Operations: ['38-10=28', '36-8=28'] Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,52 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,52 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[8, 8], Operations: ['38-10=28', '36-28=8'] Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,52 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[28, 44], Operations: ['38-10=28', '8+36=44'] Exploring Operation: 28*44=1232, Resulting Numbers: [1232] 1232,52 unequal: No Solution Exploring Operation: 28+44=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 99, 68, 89, 40 ]
80
[ "99-68=31", "89-40=49", "31+49=80" ]
Current State: 80:[99, 68, 89, 40], Operations: [] Exploring Operation: 99-68=31, Resulting Numbers: [89, 40, 31] Generated Node #2: [89, 40, 31] from Operation: 99-68=31 Current State: 80:[89, 40, 31], Operations: ['99-68=31'] Exploring Operation: 89-40=49, Resulting Numbers: [31, 49] Generated Node #3: [31, 49] from Operation: 89-40=49 Current State: 80:[31, 49], Operations: ['99-68=31', '89-40=49'] Exploring Operation: 31+49=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[99, 68, 89, 40], Operations: [] Exploring Operation: 99-68=31, Resulting Numbers: [89, 40, 31] Generated Node #0,0: 80:[89, 40, 31] Operation: 99-68=31 Exploring Operation: 99-89=10, Resulting Numbers: [68, 40, 10] Generated Node #0,1: 80:[68, 40, 10] Operation: 99-89=10 Exploring Operation: 68-40=28, Resulting Numbers: [99, 89, 28] Generated Node #0,2: 80:[99, 89, 28] Operation: 68-40=28 Exploring Operation: 89-68=21, Resulting Numbers: [99, 40, 21] Generated Node #0,3: 80:[99, 40, 21] Operation: 89-68=21 Moving to Node #0,1 Current State: 80:[68, 40, 10], Operations: ['99-89=10'] Exploring Operation: 68-10=58, Resulting Numbers: [40, 58] Generated Node #0,1,0: 80:[40, 58] Operation: 68-10=58 Exploring Operation: 68-40=28, Resulting Numbers: [10, 28] Generated Node #0,1,1: 80:[10, 28] Operation: 68-40=28 Exploring Operation: 40/10=4, Resulting Numbers: [68, 4] Generated Node #0,1,2: 80:[68, 4] Operation: 40/10=4 Exploring Operation: 68+10=78, Resulting Numbers: [40, 78] Generated Node #0,1,3: 80:[40, 78] Operation: 68+10=78 Moving to Node #0,0 Current State: 80:[89, 40, 31], Operations: ['99-68=31'] Exploring Operation: 40-31=9, Resulting Numbers: [89, 9] Generated Node #0,0,0: 80:[89, 9] Operation: 40-31=9 Exploring Operation: 89-31=58, Resulting Numbers: [40, 58] Generated Node #0,0,1: 80:[40, 58] Operation: 89-31=58 Exploring Operation: 89-40=49, Resulting Numbers: [31, 49] Generated Node #0,0,2: 80:[31, 49] Operation: 89-40=49 Exploring Operation: 40+31=71, Resulting Numbers: [89, 71] Generated Node #0,0,3: 80:[89, 71] Operation: 40+31=71 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[89, 9], Operations: ['99-68=31', '40-31=9'] Exploring Operation: 89*9=801, Resulting Numbers: [801] 801,80 unequal: No Solution Exploring Operation: 89+9=98, Resulting Numbers: [98] 98,80 unequal: No Solution Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[99, 68, 89, 40], Operations: [] Exploring Operation: 99-68=31, Resulting Numbers: [89, 40, 31] Generated Node #0,0: 80:[89, 40, 31] Operation: 99-68=31 Moving to Node #0,0 Current State: 80:[89, 40, 31], Operations: ['99-68=31'] Exploring Operation: 40-31=9, Resulting Numbers: [89, 9] Generated Node #0,0,0: 80:[89, 9] Operation: 40-31=9 Moving to Node #0,0,0 Current State: 80:[89, 9], Operations: ['99-68=31', '40-31=9'] Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 39, 52, 11, 3 ]
44
[ "39/3=13", "52*11=572", "572/13=44" ]
Current State: 44:[39, 52, 11, 3], Operations: [] Exploring Operation: 39/3=13, Resulting Numbers: [52, 11, 13] Generated Node #2: [52, 11, 13] from Operation: 39/3=13 Current State: 44:[52, 11, 13], Operations: ['39/3=13'] Exploring Operation: 52*11=572, Resulting Numbers: [13, 572] Generated Node #3: [13, 572] from Operation: 52*11=572 Current State: 44:[13, 572], Operations: ['39/3=13', '52*11=572'] Exploring Operation: 572/13=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[39, 52, 11, 3], Operations: [] Exploring Operation: 52-39=13, Resulting Numbers: [11, 3, 13] Generated Node #0,0: 44:[11, 3, 13] Operation: 52-39=13 Moving to Node #0,0 Current State: 44:[11, 3, 13], Operations: ['52-39=13'] Exploring Operation: 13-11=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 44:[3, 2] Operation: 13-11=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[3, 2], Operations: ['52-39=13', '13-11=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 54, 34, 58, 25 ]
36
[ "58-54=4", "34-25=9", "4*9=36" ]
Current State: 36:[54, 34, 58, 25], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [34, 25, 4] Generated Node #2: [34, 25, 4] from Operation: 58-54=4 Current State: 36:[34, 25, 4], Operations: ['58-54=4'] Exploring Operation: 34-25=9, Resulting Numbers: [4, 9] Generated Node #3: [4, 9] from Operation: 34-25=9 Current State: 36:[4, 9], Operations: ['58-54=4', '34-25=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[54, 34, 58, 25], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [34, 25, 4] Generated Node #0,0: 36:[34, 25, 4] Operation: 58-54=4 Exploring Operation: 54-25=29, Resulting Numbers: [34, 58, 29] Generated Node #0,1: 36:[34, 58, 29] Operation: 54-25=29 Exploring Operation: 54-34=20, Resulting Numbers: [58, 25, 20] Generated Node #0,2: 36:[58, 25, 20] Operation: 54-34=20 Exploring Operation: 58-25=33, Resulting Numbers: [54, 34, 33] Generated Node #0,3: 36:[54, 34, 33] Operation: 58-25=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[34, 25, 4], Operations: ['58-54=4'] Exploring Operation: 34-25=9, Resulting Numbers: [4, 9] Generated Node #0,0,0: 36:[4, 9] Operation: 34-25=9 Exploring Operation: 34+4=38, Resulting Numbers: [25, 38] Generated Node #0,0,1: 36:[25, 38] Operation: 34+4=38 Exploring Operation: 25-4=21, Resulting Numbers: [34, 21] Generated Node #0,0,2: 36:[34, 21] Operation: 25-4=21 Exploring Operation: 25+4=29, Resulting Numbers: [34, 29] Generated Node #0,0,3: 36:[34, 29] Operation: 25+4=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[4, 9], Operations: ['58-54=4', '34-25=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[54, 34, 58, 25], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [34, 25, 4] Generated Node #0,0: 36:[34, 25, 4] Operation: 58-54=4 Moving to Node #0,0 Current State: 36:[34, 25, 4], Operations: ['58-54=4'] Exploring Operation: 34-25=9, Resulting Numbers: [4, 9] Generated Node #0,0,0: 36:[4, 9] Operation: 34-25=9 Moving to Node #0,0,0 Current State: 36:[4, 9], Operations: ['58-54=4', '34-25=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 34, 38, 86, 88 ]
53
[ "88-86=2", "38/2=19", "34+19=53" ]
Current State: 53:[34, 38, 86, 88], Operations: [] Exploring Operation: 88-86=2, Resulting Numbers: [34, 38, 2] Generated Node #2: [34, 38, 2] from Operation: 88-86=2 Current State: 53:[34, 38, 2], Operations: ['88-86=2'] Exploring Operation: 38/2=19, Resulting Numbers: [34, 19] Generated Node #3: [34, 19] from Operation: 38/2=19 Current State: 53:[34, 19], Operations: ['88-86=2', '38/2=19'] Exploring Operation: 34+19=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[34, 38, 86, 88], Operations: [] Exploring Operation: 88-38=50, Resulting Numbers: [34, 86, 50] Generated Node #0,0: 53:[34, 86, 50] Operation: 88-38=50 Exploring Operation: 86-34=52, Resulting Numbers: [38, 88, 52] Generated Node #0,1: 53:[38, 88, 52] Operation: 86-34=52 Exploring Operation: 86-38=48, Resulting Numbers: [34, 88, 48] Generated Node #0,2: 53:[34, 88, 48] Operation: 86-38=48 Exploring Operation: 88-34=54, Resulting Numbers: [38, 86, 54] Generated Node #0,3: 53:[38, 86, 54] Operation: 88-34=54 Start Sub Search at level 1: Moving to Node #0,3 Current State: 53:[38, 86, 54], Operations: ['88-34=54'] Exploring Operation: 86-54=32, Resulting Numbers: [38, 32] Generated Node #0,3,0: 53:[38, 32] Operation: 86-54=32 Exploring Operation: 38+86=124, Resulting Numbers: [54, 124] Generated Node #0,3,1: 53:[54, 124] Operation: 38+86=124 Exploring Operation: 54-38=16, Resulting Numbers: [86, 16] Generated Node #0,3,2: 53:[86, 16] Operation: 54-38=16 Exploring Operation: 86-38=48, Resulting Numbers: [54, 48] Generated Node #0,3,3: 53:[54, 48] Operation: 86-38=48 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 53:[54, 48], Operations: ['88-34=54', '86-38=48'] Exploring Operation: 54+48=102, Resulting Numbers: [102] 102,53 unequal: No Solution Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 54*48=2592, Resulting Numbers: [2592] 2592,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 53:[38, 32], Operations: ['88-34=54', '86-54=32'] Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 53:[86, 16], Operations: ['88-34=54', '54-38=16'] Exploring Operation: 86*16=1376, Resulting Numbers: [1376] 1376,53 unequal: No Solution Exploring Operation: 86-16=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 86+16=102, Resulting Numbers: [102] 102,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 53:[54, 124], Operations: ['88-34=54', '38+86=124'] Exploring Operation: 54+124=178, Resulting Numbers: [178] 178,53 unequal: No Solution Exploring Operation: 124-54=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 54*124=6696, Resulting Numbers: [6696] 6696,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[38, 88, 52], Operations: ['86-34=52'] Exploring Operation: 88-38=50, Resulting Numbers: [52, 50] Generated Node #0,1,0: 53:[52, 50] Operation: 88-38=50 Exploring Operation: 88-52=36, Resulting Numbers: [38, 36] Generated Node #0,1,1: 53:[38, 36] Operation: 88-52=36 Exploring Operation: 38+52=90, Resulting Numbers: [88, 90] Generated Node #0,1,2: 53:[88, 90] Operation: 38+52=90 Exploring Operation: 38+88=126, Resulting Numbers: [52, 126] Generated Node #0,1,3: 53:[52, 126] Operation: 38+88=126 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[52, 50], Operations: ['86-34=52', '88-38=50'] Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,53 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 52*50=2600, Resulting Numbers: [2600] 2600,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[38, 36], Operations: ['86-34=52', '88-52=36'] Exploring Operation: 38*36=1368, Resulting Numbers: [1368] 1368,53 unequal: No Solution Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[88, 90], Operations: ['86-34=52', '38+52=90'] Exploring Operation: 88+90=178, Resulting Numbers: [178] 178,53 unequal: No Solution Exploring Operation: 88*90=7920, Resulting Numbers: [7920] 7920,53 unequal: No Solution Exploring Operation: 90-88=2, Resulting Numbers: [2] 2,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 53:[52, 126], Operations: ['86-34=52', '38+88=126'] Exploring Operation: 52+126=178, Resulting Numbers: [178] 178,53 unequal: No Solution Exploring Operation: 52*126=6552, Resulting Numbers: [6552] 6552,53 unequal: No Solution Exploring Operation: 126-52=74, Resulting Numbers: [74] 74,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[34, 86, 50], Operations: ['88-38=50'] Exploring Operation: 34+86=120, Resulting Numbers: [50, 120] Generated Node #0,0,0: 53:[50, 120] Operation: 34+86=120 Exploring Operation: 86-34=52, Resulting Numbers: [50, 52] Generated Node #0,0,1: 53:[50, 52] Operation: 86-34=52 Exploring Operation: 86-50=36, Resulting Numbers: [34, 36] Generated Node #0,0,2: 53:[34, 36] Operation: 86-50=36 Exploring Operation: 34+50=84, Resulting Numbers: [86, 84] Generated Node #0,0,3: 53:[86, 84] Operation: 34+50=84 Moving to Node #0,0,1 Current State: 53:[50, 52], Operations: ['88-38=50', '86-34=52'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,53 unequal: No Solution Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[34, 36], Operations: ['88-38=50', '86-50=36'] Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,53 unequal: No Solution Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[86, 84], Operations: ['88-38=50', '34+50=84'] Exploring Operation: 86*84=7224, Resulting Numbers: [7224] 7224,53 unequal: No Solution Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 86+84=170, Resulting Numbers: [170] 170,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[50, 120], Operations: ['88-38=50', '34+86=120'] Exploring Operation: 50+120=170, Resulting Numbers: [170] 170,53 unequal: No Solution Exploring Operation: 50*120=6000, Resulting Numbers: [6000] 6000,53 unequal: No Solution Exploring Operation: 120-50=70, Resulting Numbers: [70] 70,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[34, 88, 48], Operations: ['86-38=48'] Exploring Operation: 34+88=122, Resulting Numbers: [48, 122] Generated Node #0,2,0: 53:[48, 122] Operation: 34+88=122 Exploring Operation: 88-34=54, Resulting Numbers: [48, 54] Generated Node #0,2,1: 53:[48, 54] Operation: 88-34=54 Exploring Operation: 88-48=40, Resulting Numbers: [34, 40] Generated Node #0,2,2: 53:[34, 40] Operation: 88-48=40 Exploring Operation: 34+48=82, Resulting Numbers: [88, 82] Generated Node #0,2,3: 53:[88, 82] Operation: 34+48=82 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 53:[48, 54], Operations: ['86-38=48', '88-34=54'] Exploring Operation: 48*54=2592, Resulting Numbers: [2592] 2592,53 unequal: No Solution Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 48+54=102, Resulting Numbers: [102] 102,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[34, 40], Operations: ['86-38=48', '88-48=40'] Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 53:[88, 82], Operations: ['86-38=48', '34+48=82'] Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 88*82=7216, Resulting Numbers: [7216] 7216,53 unequal: No Solution Exploring Operation: 88+82=170, Resulting Numbers: [170] 170,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 53:[48, 122], Operations: ['86-38=48', '34+88=122'] Exploring Operation: 48*122=5856, Resulting Numbers: [5856] 5856,53 unequal: No Solution Exploring Operation: 48+122=170, Resulting Numbers: [170] 170,53 unequal: No Solution Exploring Operation: 122-48=74, Resulting Numbers: [74] 74,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 75, 21, 24, 16 ]
14
[ "75-21=54", "24+16=40", "54-40=14" ]
Current State: 14:[75, 21, 24, 16], Operations: [] Exploring Operation: 75-21=54, Resulting Numbers: [24, 16, 54] Generated Node #2: [24, 16, 54] from Operation: 75-21=54 Current State: 14:[24, 16, 54], Operations: ['75-21=54'] Exploring Operation: 24+16=40, Resulting Numbers: [54, 40] Generated Node #3: [54, 40] from Operation: 24+16=40 Current State: 14:[54, 40], Operations: ['75-21=54', '24+16=40'] Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[75, 21, 24, 16], Operations: [] Exploring Operation: 75-24=51, Resulting Numbers: [21, 16, 51] Generated Node #0,0: 14:[21, 16, 51] Operation: 75-24=51 Exploring Operation: 24-21=3, Resulting Numbers: [75, 16, 3] Generated Node #0,1: 14:[75, 16, 3] Operation: 24-21=3 Exploring Operation: 75-16=59, Resulting Numbers: [21, 24, 59] Generated Node #0,2: 14:[21, 24, 59] Operation: 75-16=59 Exploring Operation: 75-21=54, Resulting Numbers: [24, 16, 54] Generated Node #0,3: 14:[24, 16, 54] Operation: 75-21=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[21, 16, 51], Operations: ['75-24=51'] Exploring Operation: 21+16=37, Resulting Numbers: [51, 37] Generated Node #0,0,0: 14:[51, 37] Operation: 21+16=37 Exploring Operation: 51-16=35, Resulting Numbers: [21, 35] Generated Node #0,0,1: 14:[21, 35] Operation: 51-16=35 Exploring Operation: 51-21=30, Resulting Numbers: [16, 30] Generated Node #0,0,2: 14:[16, 30] Operation: 51-21=30 Exploring Operation: 21-16=5, Resulting Numbers: [51, 5] Generated Node #0,0,3: 14:[51, 5] Operation: 21-16=5 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 14:[16, 30], Operations: ['75-24=51', '51-21=30'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[75, 21, 24, 16], Operations: [] Exploring Operation: 75-24=51, Resulting Numbers: [21, 16, 51] Generated Node #0,0: 14:[21, 16, 51] Operation: 75-24=51 Moving to Node #0,0 Current State: 14:[21, 16, 51], Operations: ['75-24=51'] Exploring Operation: 51-21=30, Resulting Numbers: [16, 30] Generated Node #0,0,2: 14:[16, 30] Operation: 51-21=30 Moving to Node #0,0,2 Current State: 14:[16, 30], Operations: ['75-24=51', '51-21=30'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 48, 20, 67, 93 ]
40
[ "67+93=160", "160/20=8", "48-8=40" ]
Current State: 40:[48, 20, 67, 93], Operations: [] Exploring Operation: 67+93=160, Resulting Numbers: [48, 20, 160] Generated Node #2: [48, 20, 160] from Operation: 67+93=160 Current State: 40:[48, 20, 160], Operations: ['67+93=160'] Exploring Operation: 160/20=8, Resulting Numbers: [48, 8] Generated Node #3: [48, 8] from Operation: 160/20=8 Current State: 40:[48, 8], Operations: ['67+93=160', '160/20=8'] Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[48, 20, 67, 93], Operations: [] Exploring Operation: 67-48=19, Resulting Numbers: [20, 93, 19] Generated Node #0,0: 40:[20, 93, 19] Operation: 67-48=19 Exploring Operation: 93-48=45, Resulting Numbers: [20, 67, 45] Generated Node #0,1: 40:[20, 67, 45] Operation: 93-48=45 Exploring Operation: 93-20=73, Resulting Numbers: [48, 67, 73] Generated Node #0,2: 40:[48, 67, 73] Operation: 93-20=73 Exploring Operation: 93-67=26, Resulting Numbers: [48, 20, 26] Generated Node #0,3: 40:[48, 20, 26] Operation: 93-67=26 Exploring Operation: 67-20=47, Resulting Numbers: [48, 93, 47] Generated Node #0,4: 40:[48, 93, 47] Operation: 67-20=47 Moving to Node #0,3 Current State: 40:[48, 20, 26], Operations: ['93-67=26'] Exploring Operation: 48+20=68, Resulting Numbers: [26, 68] Generated Node #0,3,0: 40:[26, 68] Operation: 48+20=68 Exploring Operation: 20+26=46, Resulting Numbers: [48, 46] Generated Node #0,3,1: 40:[48, 46] Operation: 20+26=46 Exploring Operation: 48-20=28, Resulting Numbers: [26, 28] Generated Node #0,3,2: 40:[26, 28] Operation: 48-20=28 Exploring Operation: 48-26=22, Resulting Numbers: [20, 22] Generated Node #0,3,3: 40:[20, 22] Operation: 48-26=22 Exploring Operation: 26-20=6, Resulting Numbers: [48, 6] Generated Node #0,3,4: 40:[48, 6] Operation: 26-20=6 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 40:[20, 22], Operations: ['93-67=26', '48-26=22'] Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,40 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 40:[48, 6], Operations: ['93-67=26', '26-20=6'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,40 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,40 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 40:[48, 46], Operations: ['93-67=26', '20+26=46'] Exploring Operation: 48*46=2208, Resulting Numbers: [2208] 2208,40 unequal: No Solution Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,40 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 #0,3,2 Current State: 40:[26, 28], Operations: ['93-67=26', '48-20=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,40 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,40 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 #0,3,0 Current State: 40:[26, 68], Operations: ['93-67=26', '48+20=68'] Exploring Operation: 68-26=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 26+68=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 26*68=1768, Resulting Numbers: [1768] 1768,40 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: 40:[20, 67, 45], Operations: ['93-48=45'] Exploring Operation: 20+67=87, Resulting Numbers: [45, 87] Generated Node #0,1,0: 40:[45, 87] Operation: 20+67=87 Exploring Operation: 20+45=65, Resulting Numbers: [67, 65] Generated Node #0,1,1: 40:[67, 65] Operation: 20+45=65 Exploring Operation: 67-45=22, Resulting Numbers: [20, 22] Generated Node #0,1,2: 40:[20, 22] Operation: 67-45=22 Exploring Operation: 45-20=25, Resulting Numbers: [67, 25] Generated Node #0,1,3: 40:[67, 25] Operation: 45-20=25 Exploring Operation: 67-20=47, Resulting Numbers: [45, 47] Generated Node #0,1,4: 40:[45, 47] Operation: 67-20=47 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 40:[20, 22], Operations: ['93-48=45', '67-45=22'] Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,40 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 40:[45, 47], Operations: ['93-48=45', '67-20=47'] Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,40 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,40 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 #0,1,3 Current State: 40:[67, 25], Operations: ['93-48=45', '45-20=25'] Exploring Operation: 67+25=92, Resulting Numbers: [92] 92,40 unequal: No Solution Exploring Operation: 67*25=1675, Resulting Numbers: [1675] 1675,40 unequal: No Solution Exploring Operation: 67-25=42, Resulting Numbers: [42] 42,40 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 #0,1,0 Current State: 40:[45, 87], Operations: ['93-48=45', '20+67=87'] Exploring Operation: 87-45=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 45+87=132, Resulting Numbers: [132] 132,40 unequal: No Solution Exploring Operation: 45*87=3915, Resulting Numbers: [3915] 3915,40 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 #0,1,1 Current State: 40:[67, 65], Operations: ['93-48=45', '20+45=65'] Exploring Operation: 67-65=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 67+65=132, Resulting Numbers: [132] 132,40 unequal: No Solution Exploring Operation: 67*65=4355, Resulting Numbers: [4355] 4355,40 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: 40:[20, 93, 19], Operations: ['67-48=19'] Exploring Operation: 20-19=1, Resulting Numbers: [93, 1] Generated Node #0,0,0: 40:[93, 1] Operation: 20-19=1 Exploring Operation: 20+19=39, Resulting Numbers: [93, 39] Generated Node #0,0,1: 40:[93, 39] Operation: 20+19=39 Exploring Operation: 93+19=112, Resulting Numbers: [20, 112] Generated Node #0,0,2: 40:[20, 112] Operation: 93+19=112 Exploring Operation: 93-20=73, Resulting Numbers: [19, 73] Generated Node #0,0,3: 40:[19, 73] Operation: 93-20=73 Exploring Operation: 93-19=74, Resulting Numbers: [20, 74] Generated Node #0,0,4: 40:[20, 74] Operation: 93-19=74 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 40:[19, 73], Operations: ['67-48=19', '93-20=73'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,40 unequal: No Solution Exploring Operation: 19*73=1387, Resulting Numbers: [1387] 1387,40 unequal: No Solution Exploring Operation: 19+73=92, Resulting Numbers: [92] 92,40 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 #0,0,4 Current State: 40:[20, 74], Operations: ['67-48=19', '93-19=74'] Exploring Operation: 20+74=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 74-20=54, Resulting Numbers: [54] 54,40 unequal: No Solution Exploring Operation: 20*74=1480, Resulting Numbers: [1480] 1480,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[93, 1], Operations: ['67-48=19', '20-19=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,40 unequal: No Solution Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,40 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,40 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 #0,0,1 Current State: 40:[93, 39], Operations: ['67-48=19', '20+19=39'] Exploring Operation: 93*39=3627, Resulting Numbers: [3627] 3627,40 unequal: No Solution Exploring Operation: 93+39=132, Resulting Numbers: [132] 132,40 unequal: No Solution Exploring Operation: 93-39=54, Resulting Numbers: [54] 54,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 40:[20, 112], Operations: ['67-48=19', '93+19=112'] Exploring Operation: 20+112=132, Resulting Numbers: [132] 132,40 unequal: No Solution Exploring Operation: 112-20=92, Resulting Numbers: [92] 92,40 unequal: No Solution Exploring Operation: 20*112=2240, Resulting Numbers: [2240] 2240,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 40:[48, 67, 73], Operations: ['93-20=73'] Exploring Operation: 73-67=6, Resulting Numbers: [48, 6] Generated Node #0,2,0: 40:[48, 6] Operation: 73-67=6 Exploring Operation: 67-48=19, Resulting Numbers: [73, 19] Generated Node #0,2,1: 40:[73, 19] Operation: 67-48=19 Exploring Operation: 48+67=115, Resulting Numbers: [73, 115] Generated Node #0,2,2: 40:[73, 115] Operation: 48+67=115 Exploring Operation: 73-48=25, Resulting Numbers: [67, 25] Generated Node #0,2,3: 40:[67, 25] Operation: 73-48=25 Exploring Operation: 48+73=121, Resulting Numbers: [67, 121] Generated Node #0,2,4: 40:[67, 121] Operation: 48+73=121 Moving to Node #0,4 Current State: 40:[48, 93, 47], Operations: ['67-20=47'] Exploring Operation: 48+47=95, Resulting Numbers: [93, 95] Generated Node #0,4,0: 40:[93, 95] Operation: 48+47=95 Exploring Operation: 48-47=1, Resulting Numbers: [93, 1] Generated Node #0,4,1: 40:[93, 1] Operation: 48-47=1 Exploring Operation: 48+93=141, Resulting Numbers: [47, 141] Generated Node #0,4,2: 40:[47, 141] Operation: 48+93=141 Exploring Operation: 93-47=46, Resulting Numbers: [48, 46] Generated Node #0,4,3: 40:[48, 46] Operation: 93-47=46 Exploring Operation: 93-48=45, Resulting Numbers: [47, 45] Generated Node #0,4,4: 40:[47, 45] Operation: 93-48=45 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 40:[47, 45], Operations: ['67-20=47', '93-48=45'] Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 47*45=2115, Resulting Numbers: [2115] 2115,40 unequal: No Solution Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,40 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 #0,4,3 Current State: 40:[48, 46], Operations: ['67-20=47', '93-47=46'] Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 48*46=2208, Resulting Numbers: [2208] 2208,40 unequal: No Solution Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,40 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 #0,4,1 Current State: 40:[93, 1], Operations: ['67-20=47', '48-47=1'] Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,40 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,40 unequal: No Solution Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,40 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 #0,4,0 Current State: 40:[93, 95], Operations: ['67-20=47', '48+47=95'] Exploring Operation: 93+95=188, Resulting Numbers: [188] 188,40 unequal: No Solution Exploring Operation: 95-93=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 93*95=8835, Resulting Numbers: [8835] 8835,40 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 #0,4,2 Current State: 40:[47, 141], Operations: ['67-20=47', '48+93=141'] Exploring Operation: 47*141=6627, Resulting Numbers: [6627] 6627,40 unequal: No Solution Exploring Operation: 141/47=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 141-47=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 47+141=188, Resulting Numbers: [188] 188,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 40:[48, 6], Operations: ['93-20=73', '73-67=6'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,40 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,40 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,40 unequal: No Solution Moving to Node #0,2,3 Current State: 40:[67, 25], Operations: ['93-20=73', '73-48=25'] Exploring Operation: 67+25=92, Resulting Numbers: [92] 92,40 unequal: No Solution Exploring Operation: 67-25=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 67*25=1675, Resulting Numbers: [1675] 1675,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[73, 19], Operations: ['93-20=73', '67-48=19'] Exploring Operation: 73*19=1387, Resulting Numbers: [1387] 1387,40 unequal: No Solution Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,40 unequal: No Solution Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[73, 115], Operations: ['93-20=73', '48+67=115'] Exploring Operation: 73*115=8395, Resulting Numbers: [8395] 8395,40 unequal: No Solution Exploring Operation: 115-73=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 73+115=188, Resulting Numbers: [188] 188,40 unequal: No Solution Moving to Node #0,2,4 Current State: 40:[67, 121], Operations: ['93-20=73', '48+73=121'] Exploring Operation: 67+121=188, Resulting Numbers: [188] 188,40 unequal: No Solution Exploring Operation: 67*121=8107, Resulting Numbers: [8107] 8107,40 unequal: No Solution Exploring Operation: 121-67=54, Resulting Numbers: [54] 54,40 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 10, 40, 28, 40 ]
28
[ "40-40=0", "10*0=0", "28+0=28" ]
Current State: 28:[10, 40, 28, 40], Operations: [] Exploring Operation: 40-40=0, Resulting Numbers: [10, 28, 0] Generated Node #2: [10, 28, 0] from Operation: 40-40=0 Current State: 28:[10, 28, 0], Operations: ['40-40=0'] Exploring Operation: 10*0=0, Resulting Numbers: [28, 0] Generated Node #3: [28, 0] from Operation: 10*0=0 Current State: 28:[28, 0], Operations: ['40-40=0', '10*0=0'] Exploring Operation: 28+0=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[10, 40, 28, 40], Operations: [] Exploring Operation: 40/10=4, Resulting Numbers: [28, 40, 4] Generated Node #0,0: 28:[28, 40, 4] Operation: 40/10=4 Exploring Operation: 40-40=0, Resulting Numbers: [10, 28, 0] Generated Node #0,1: 28:[10, 28, 0] Operation: 40-40=0 Exploring Operation: 40/40=1, Resulting Numbers: [10, 28, 1] Generated Node #0,2: 28:[10, 28, 1] Operation: 40/40=1 Exploring Operation: 40/10=4, Resulting Numbers: [40, 28, 4] Generated Node #0,3: 28:[40, 28, 4] Operation: 40/10=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[10, 28, 1], Operations: ['40/40=1'] Exploring Operation: 10+1=11, Resulting Numbers: [28, 11] Generated Node #0,2,0: 28:[28, 11] Operation: 10+1=11 Exploring Operation: 10/1=10, Resulting Numbers: [28, 10] Generated Node #0,2,1: 28:[28, 10] Operation: 10/1=10 Exploring Operation: 10*1=10, Resulting Numbers: [28, 10] Generated Node #0,2,2: 28:[28, 10] Operation: 10*1=10 Exploring Operation: 10-1=9, Resulting Numbers: [28, 9] Generated Node #0,2,3: 28:[28, 9] Operation: 10-1=9 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 28:[28, 9], Operations: ['40/40=1', '10-1=9'] Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,28 unequal: No Solution Exploring Operation: 28*9=252, Resulting Numbers: [252] 252,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 28:[28, 11], Operations: ['40/40=1', '10+1=11'] Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,28 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 28:[28, 10], Operations: ['40/40=1', '10/1=10'] Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,28 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 28:[28, 10], Operations: ['40/40=1', '10*1=10'] Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,28 unequal: No Solution Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[10, 28, 0], Operations: ['40-40=0'] Exploring Operation: 10*0=0, Resulting Numbers: [28, 0] Generated Node #0,1,0: 28:[28, 0] Operation: 10*0=0 Exploring Operation: 10+0=10, Resulting Numbers: [28, 10] Generated Node #0,1,1: 28:[28, 10] Operation: 10+0=10 Exploring Operation: 28+0=28, Resulting Numbers: [10, 28] Generated Node #0,1,2: 28:[10, 28] Operation: 28+0=28 Exploring Operation: 10-0=10, Resulting Numbers: [28, 10] Generated Node #0,1,3: 28:[28, 10] Operation: 10-0=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[28, 0], Operations: ['40-40=0', '10*0=0'] Exploring Operation: 28+0=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[10, 40, 28, 40], Operations: [] Exploring Operation: 40-40=0, Resulting Numbers: [10, 28, 0] Generated Node #0,1: 28:[10, 28, 0] Operation: 40-40=0 Moving to Node #0,1 Current State: 28:[10, 28, 0], Operations: ['40-40=0'] Exploring Operation: 10*0=0, Resulting Numbers: [28, 0] Generated Node #0,1,0: 28:[28, 0] Operation: 10*0=0 Moving to Node #0,1,0 Current State: 28:[28, 0], Operations: ['40-40=0', '10*0=0'] Exploring Operation: 28+0=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 52, 9, 60, 27 ]
26
[ "52+9=61", "60+27=87", "87-61=26" ]
Current State: 26:[52, 9, 60, 27], Operations: [] Exploring Operation: 52+9=61, Resulting Numbers: [60, 27, 61] Generated Node #2: [60, 27, 61] from Operation: 52+9=61 Current State: 26:[60, 27, 61], Operations: ['52+9=61'] Exploring Operation: 60+27=87, Resulting Numbers: [61, 87] Generated Node #3: [61, 87] from Operation: 60+27=87 Current State: 26:[61, 87], Operations: ['52+9=61', '60+27=87'] Exploring Operation: 87-61=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[52, 9, 60, 27], Operations: [] Exploring Operation: 60-52=8, Resulting Numbers: [9, 27, 8] Generated Node #0,0: 26:[9, 27, 8] Operation: 60-52=8 Moving to Node #0,0 Current State: 26:[9, 27, 8], Operations: ['60-52=8'] Exploring Operation: 9-8=1, Resulting Numbers: [27, 1] Generated Node #0,0,0: 26:[27, 1] Operation: 9-8=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[27, 1], Operations: ['60-52=8', '9-8=1'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[52, 9, 60, 27], Operations: [] Exploring Operation: 60-52=8, Resulting Numbers: [9, 27, 8] Generated Node #0,0: 26:[9, 27, 8] Operation: 60-52=8 Moving to Node #0,0 Current State: 26:[9, 27, 8], Operations: ['60-52=8'] Exploring Operation: 9-8=1, Resulting Numbers: [27, 1] Generated Node #0,0,0: 26:[27, 1] Operation: 9-8=1 Moving to Node #0,0,0 Current State: 26:[27, 1], Operations: ['60-52=8', '9-8=1'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 78, 2, 97, 83 ]
32
[ "97-78=19", "83-19=64", "64/2=32" ]
Current State: 32:[78, 2, 97, 83], Operations: [] Exploring Operation: 97-78=19, Resulting Numbers: [2, 83, 19] Generated Node #2: [2, 83, 19] from Operation: 97-78=19 Current State: 32:[2, 83, 19], Operations: ['97-78=19'] Exploring Operation: 83-19=64, Resulting Numbers: [2, 64] Generated Node #3: [2, 64] from Operation: 83-19=64 Current State: 32:[2, 64], Operations: ['97-78=19', '83-19=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[78, 2, 97, 83], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [78, 2, 14] Generated Node #0,0: 32:[78, 2, 14] Operation: 97-83=14 Moving to Node #0,0 Current State: 32:[78, 2, 14], Operations: ['97-83=14'] Exploring Operation: 78/2=39, Resulting Numbers: [14, 39] Generated Node #0,0,0: 32:[14, 39] Operation: 78/2=39 Moving to Node #0,0,0 Current State: 32:[14, 39], Operations: ['97-83=14', '78/2=39'] Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,32 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 6, 15, 32, 53 ]
69
[ "6*15=90", "53-32=21", "90-21=69" ]
Current State: 69:[6, 15, 32, 53], Operations: [] Exploring Operation: 6*15=90, Resulting Numbers: [32, 53, 90] Generated Node #2: [32, 53, 90] from Operation: 6*15=90 Current State: 69:[32, 53, 90], Operations: ['6*15=90'] Exploring Operation: 53-32=21, Resulting Numbers: [90, 21] Generated Node #3: [90, 21] from Operation: 53-32=21 Current State: 69:[90, 21], Operations: ['6*15=90', '53-32=21'] Exploring Operation: 90-21=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[6, 15, 32, 53], Operations: [] Exploring Operation: 15+53=68, Resulting Numbers: [6, 32, 68] Generated Node #0,0: 69:[6, 32, 68] Operation: 15+53=68 Exploring Operation: 53-32=21, Resulting Numbers: [6, 15, 21] Generated Node #0,1: 69:[6, 15, 21] Operation: 53-32=21 Moving to Node #0,0 Current State: 69:[6, 32, 68], Operations: ['15+53=68'] Exploring Operation: 32-6=26, Resulting Numbers: [68, 26] Generated Node #0,0,0: 69:[68, 26] Operation: 32-6=26 Exploring Operation: 6+68=74, Resulting Numbers: [32, 74] Generated Node #0,0,1: 69:[32, 74] Operation: 6+68=74 Moving to Node #0,1 Current State: 69:[6, 15, 21], Operations: ['53-32=21'] Exploring Operation: 6+15=21, Resulting Numbers: [21, 21] Generated Node #0,1,0: 69:[21, 21] Operation: 6+15=21 Exploring Operation: 21-15=6, Resulting Numbers: [6, 6] Generated Node #0,1,1: 69:[6, 6] Operation: 21-15=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[21, 21], Operations: ['53-32=21', '6+15=21'] Exploring Operation: 21/21=1, Resulting Numbers: [1] 1,69 unequal: No Solution Exploring Operation: 21-21=0, Resulting Numbers: [0] 0,69 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:[6, 6], Operations: ['53-32=21', '21-15=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,69 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,69 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: 69:[68, 26], Operations: ['15+53=68', '32-6=26'] Exploring Operation: 68-26=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 68+26=94, Resulting Numbers: [94] 94,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[32, 74], Operations: ['15+53=68', '6+68=74'] Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 32+74=106, Resulting Numbers: [106] 106,69 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 98, 67, 95, 38 ]
32
[ "98+67=165", "95+38=133", "165-133=32" ]
Current State: 32:[98, 67, 95, 38], Operations: [] Exploring Operation: 98+67=165, Resulting Numbers: [95, 38, 165] Generated Node #2: [95, 38, 165] from Operation: 98+67=165 Current State: 32:[95, 38, 165], Operations: ['98+67=165'] Exploring Operation: 95+38=133, Resulting Numbers: [165, 133] Generated Node #3: [165, 133] from Operation: 95+38=133 Current State: 32:[165, 133], Operations: ['98+67=165', '95+38=133'] Exploring Operation: 165-133=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[98, 67, 95, 38], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [67, 38, 3] Generated Node #0,0: 32:[67, 38, 3] Operation: 98-95=3 Moving to Node #0,0 Current State: 32:[67, 38, 3], Operations: ['98-95=3'] Exploring Operation: 67-38=29, Resulting Numbers: [3, 29] Generated Node #0,0,0: 32:[3, 29] Operation: 67-38=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[3, 29], Operations: ['98-95=3', '67-38=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[98, 67, 95, 38], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [67, 38, 3] Generated Node #0,0: 32:[67, 38, 3] Operation: 98-95=3 Moving to Node #0,0 Current State: 32:[67, 38, 3], Operations: ['98-95=3'] Exploring Operation: 67-38=29, Resulting Numbers: [3, 29] Generated Node #0,0,0: 32:[3, 29] Operation: 67-38=29 Moving to Node #0,0,0 Current State: 32:[3, 29], Operations: ['98-95=3', '67-38=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 32, 3, 48, 4 ]
73
[ "32-3=29", "48-4=44", "29+44=73" ]
Current State: 73:[32, 3, 48, 4], Operations: [] Exploring Operation: 32-3=29, Resulting Numbers: [48, 4, 29] Generated Node #2: [48, 4, 29] from Operation: 32-3=29 Current State: 73:[48, 4, 29], Operations: ['32-3=29'] Exploring Operation: 48-4=44, Resulting Numbers: [29, 44] Generated Node #3: [29, 44] from Operation: 48-4=44 Current State: 73:[29, 44], Operations: ['32-3=29', '48-4=44'] Exploring Operation: 29+44=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[32, 3, 48, 4], Operations: [] Exploring Operation: 32*3=96, Resulting Numbers: [48, 4, 96] Generated Node #0,0: 73:[48, 4, 96] Operation: 32*3=96 Exploring Operation: 3*4=12, Resulting Numbers: [32, 48, 12] Generated Node #0,1: 73:[32, 48, 12] Operation: 3*4=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[48, 4, 96], Operations: ['32*3=96'] Exploring Operation: 48+4=52, Resulting Numbers: [96, 52] Generated Node #0,0,0: 73:[96, 52] Operation: 48+4=52 Exploring Operation: 96-4=92, Resulting Numbers: [48, 92] Generated Node #0,0,1: 73:[48, 92] Operation: 96-4=92 Moving to Node #0,0,0 Current State: 73:[96, 52], Operations: ['32*3=96', '48+4=52'] Exploring Operation: 96+52=148, Resulting Numbers: [148] 148,73 unequal: No Solution Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[48, 92], Operations: ['32*3=96', '96-4=92'] Exploring Operation: 92-48=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 48+92=140, Resulting Numbers: [140] 140,73 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:[32, 48, 12], Operations: ['3*4=12'] Exploring Operation: 48+12=60, Resulting Numbers: [32, 60] Generated Node #0,1,0: 73:[32, 60] Operation: 48+12=60 Exploring Operation: 32+12=44, Resulting Numbers: [48, 44] Generated Node #0,1,1: 73:[48, 44] Operation: 32+12=44 Moving to Node #0,1,0 Current State: 73:[32, 60], Operations: ['3*4=12', '48+12=60'] Exploring Operation: 60-32=28, Resulting Numbers: [28] 28,73 unequal: No Solution Exploring Operation: 32+60=92, Resulting Numbers: [92] 92,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[48, 44], Operations: ['3*4=12', '32+12=44'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,73 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 47, 7, 13, 53 ]
36
[ "53-47=6", "13-7=6", "6*6=36" ]
Current State: 36:[47, 7, 13, 53], Operations: [] Exploring Operation: 53-47=6, Resulting Numbers: [7, 13, 6] Generated Node #2: [7, 13, 6] from Operation: 53-47=6 Current State: 36:[7, 13, 6], Operations: ['53-47=6'] Exploring Operation: 13-7=6, Resulting Numbers: [6, 6] Generated Node #3: [6, 6] from Operation: 13-7=6 Current State: 36:[6, 6], Operations: ['53-47=6', '13-7=6'] Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[47, 7, 13, 53], Operations: [] Exploring Operation: 53-13=40, Resulting Numbers: [47, 7, 40] Generated Node #0,0: 36:[47, 7, 40] Operation: 53-13=40 Exploring Operation: 47-13=34, Resulting Numbers: [7, 53, 34] Generated Node #0,1: 36:[7, 53, 34] Operation: 47-13=34 Exploring Operation: 53-47=6, Resulting Numbers: [7, 13, 6] Generated Node #0,2: 36:[7, 13, 6] Operation: 53-47=6 Moving to Node #0,2 Current State: 36:[7, 13, 6], Operations: ['53-47=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13, 13] Generated Node #0,2,0: 36:[13, 13] Operation: 7+6=13 Exploring Operation: 7+13=20, Resulting Numbers: [6, 20] Generated Node #0,2,1: 36:[6, 20] Operation: 7+13=20 Exploring Operation: 13-7=6, Resulting Numbers: [6, 6] Generated Node #0,2,2: 36:[6, 6] Operation: 13-7=6 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 36:[6, 6], Operations: ['53-47=6', '13-7=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,36 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[47, 7, 13, 53], Operations: [] Exploring Operation: 53-47=6, Resulting Numbers: [7, 13, 6] Generated Node #0,2: 36:[7, 13, 6] Operation: 53-47=6 Moving to Node #0,2 Current State: 36:[7, 13, 6], Operations: ['53-47=6'] Exploring Operation: 13-7=6, Resulting Numbers: [6, 6] Generated Node #0,2,2: 36:[6, 6] Operation: 13-7=6 Moving to Node #0,2,2 Current State: 36:[6, 6], Operations: ['53-47=6', '13-7=6'] Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 2, 32, 43, 27 ]
32
[ "32/2=16", "43-27=16", "16+16=32" ]
Current State: 32:[2, 32, 43, 27], Operations: [] Exploring Operation: 32/2=16, Resulting Numbers: [43, 27, 16] Generated Node #2: [43, 27, 16] from Operation: 32/2=16 Current State: 32:[43, 27, 16], Operations: ['32/2=16'] Exploring Operation: 43-27=16, Resulting Numbers: [16, 16] Generated Node #3: [16, 16] from Operation: 43-27=16 Current State: 32:[16, 16], Operations: ['32/2=16', '43-27=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[2, 32, 43, 27], Operations: [] Exploring Operation: 43-32=11, Resulting Numbers: [2, 27, 11] Generated Node #0,0: 32:[2, 27, 11] Operation: 43-32=11 Exploring Operation: 43-2=41, Resulting Numbers: [32, 27, 41] Generated Node #0,1: 32:[32, 27, 41] Operation: 43-2=41 Exploring Operation: 32-27=5, Resulting Numbers: [2, 43, 5] Generated Node #0,2: 32:[2, 43, 5] Operation: 32-27=5 Exploring Operation: 2+27=29, Resulting Numbers: [32, 43, 29] Generated Node #0,3: 32:[32, 43, 29] Operation: 2+27=29 Exploring Operation: 43-27=16, Resulting Numbers: [2, 32, 16] Generated Node #0,4: 32:[2, 32, 16] Operation: 43-27=16 Moving to Node #0,4 Current State: 32:[2, 32, 16], Operations: ['43-27=16'] Exploring Operation: 32-16=16, Resulting Numbers: [2, 16] Generated Node #0,4,0: 32:[2, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [2, 2] Generated Node #0,4,1: 32:[2, 2] Operation: 32/16=2 Exploring Operation: 16/2=8, Resulting Numbers: [32, 8] Generated Node #0,4,2: 32:[32, 8] Operation: 16/2=8 Exploring Operation: 32/2=16, Resulting Numbers: [16, 16] Generated Node #0,4,3: 32:[16, 16] Operation: 32/2=16 Exploring Operation: 2*16=32, Resulting Numbers: [32, 32] Generated Node #0,4,4: 32:[32, 32] Operation: 2*16=32 Moving to Node #0,0 Current State: 32:[2, 27, 11], Operations: ['43-32=11'] Exploring Operation: 2+27=29, Resulting Numbers: [11, 29] Generated Node #0,0,0: 32:[11, 29] Operation: 2+27=29 Exploring Operation: 2+11=13, Resulting Numbers: [27, 13] Generated Node #0,0,1: 32:[27, 13] Operation: 2+11=13 Exploring Operation: 11-2=9, Resulting Numbers: [27, 9] Generated Node #0,0,2: 32:[27, 9] Operation: 11-2=9 Exploring Operation: 27+11=38, Resulting Numbers: [2, 38] Generated Node #0,0,3: 32:[2, 38] Operation: 27+11=38 Exploring Operation: 27-11=16, Resulting Numbers: [2, 16] Generated Node #0,0,4: 32:[2, 16] Operation: 27-11=16 Moving to Node #0,2 Current State: 32:[2, 43, 5], Operations: ['32-27=5'] Exploring Operation: 5-2=3, Resulting Numbers: [43, 3] Generated Node #0,2,0: 32:[43, 3] Operation: 5-2=3 Exploring Operation: 2*5=10, Resulting Numbers: [43, 10] Generated Node #0,2,1: 32:[43, 10] Operation: 2*5=10 Exploring Operation: 43-5=38, Resulting Numbers: [2, 38] Generated Node #0,2,2: 32:[2, 38] Operation: 43-5=38 Exploring Operation: 43-2=41, Resulting Numbers: [5, 41] Generated Node #0,2,3: 32:[5, 41] Operation: 43-2=41 Exploring Operation: 2+5=7, Resulting Numbers: [43, 7] Generated Node #0,2,4: 32:[43, 7] Operation: 2+5=7 Moving to Node #0,1 Current State: 32:[32, 27, 41], Operations: ['43-2=41'] Exploring Operation: 27+41=68, Resulting Numbers: [32, 68] Generated Node #0,1,0: 32:[32, 68] Operation: 27+41=68 Exploring Operation: 32-27=5, Resulting Numbers: [41, 5] Generated Node #0,1,1: 32:[41, 5] Operation: 32-27=5 Exploring Operation: 32+27=59, Resulting Numbers: [41, 59] Generated Node #0,1,2: 32:[41, 59] Operation: 32+27=59 Exploring Operation: 41-32=9, Resulting Numbers: [27, 9] Generated Node #0,1,3: 32:[27, 9] Operation: 41-32=9 Exploring Operation: 41-27=14, Resulting Numbers: [32, 14] Generated Node #0,1,4: 32:[32, 14] Operation: 41-27=14 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 32:[32, 14], Operations: ['43-2=41', '41-27=14'] Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,32 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[27, 9], Operations: ['43-2=41', '41-32=9'] Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 27*9=243, Resulting Numbers: [243] 243,32 unequal: No Solution Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[41, 5], Operations: ['43-2=41', '32-27=5'] Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,32 unequal: No Solution Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[32, 68], Operations: ['43-2=41', '27+41=68'] Exploring Operation: 32+68=100, Resulting Numbers: [100] 100,32 unequal: No Solution Exploring Operation: 32*68=2176, Resulting Numbers: [2176] 2176,32 unequal: No Solution Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[41, 59], Operations: ['43-2=41', '32+27=59'] Exploring Operation: 41*59=2419, Resulting Numbers: [2419] 2419,32 unequal: No Solution Exploring Operation: 59-41=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 41+59=100, Resulting Numbers: [100] 100,32 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: 32:[32, 43, 29], Operations: ['2+27=29'] Exploring Operation: 43+29=72, Resulting Numbers: [32, 72] Generated Node #0,3,0: 32:[32, 72] Operation: 43+29=72 Exploring Operation: 32+29=61, Resulting Numbers: [43, 61] Generated Node #0,3,1: 32:[43, 61] Operation: 32+29=61 Exploring Operation: 32-29=3, Resulting Numbers: [43, 3] Generated Node #0,3,2: 32:[43, 3] Operation: 32-29=3 Exploring Operation: 43-32=11, Resulting Numbers: [29, 11] Generated Node #0,3,3: 32:[29, 11] Operation: 43-32=11 Exploring Operation: 43-29=14, Resulting Numbers: [32, 14] Generated Node #0,3,4: 32:[32, 14] Operation: 43-29=14 Moving to Node #0,4,0 Current State: 32:[2, 16], Operations: ['43-27=16', '32-16=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[2, 32, 43, 27], Operations: [] Exploring Operation: 43-27=16, Resulting Numbers: [2, 32, 16] Generated Node #0,4: 32:[2, 32, 16] Operation: 43-27=16 Moving to Node #0,4 Current State: 32:[2, 32, 16], Operations: ['43-27=16'] Exploring Operation: 32-16=16, Resulting Numbers: [2, 16] Generated Node #0,4,0: 32:[2, 16] Operation: 32-16=16 Moving to Node #0,4,0 Current State: 32:[2, 16], Operations: ['43-27=16', '32-16=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.953993
hs_5
mult_heuristic