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
[ 2, 31, 65, 25 ]
49
[ "65-25=40", "2*40=80", "80-31=49" ]
Current State: 49:[2, 31, 65, 25], Operations: [] Exploring Operation: 65-25=40, Resulting Numbers: [2, 31, 40] Generated Node #2: [2, 31, 40] from Operation: 65-25=40 Current State: 49:[2, 31, 40], Operations: ['65-25=40'] Exploring Operation: 2*40=80, Resulting Numbers: [31, 80] Generated Node #3: [31, 80] from Operation: 2*40=80 Current State: 49:[31, 80], Operations: ['65-25=40', '2*40=80'] Exploring Operation: 80-31=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[2, 31, 65, 25], Operations: [] Exploring Operation: 31+25=56, Resulting Numbers: [2, 65, 56] Generated Node #0,0: 49:[2, 65, 56] Operation: 31+25=56 Exploring Operation: 65-25=40, Resulting Numbers: [2, 31, 40] Generated Node #0,1: 49:[2, 31, 40] Operation: 65-25=40 Exploring Operation: 31-25=6, Resulting Numbers: [2, 65, 6] Generated Node #0,2: 49:[2, 65, 6] Operation: 31-25=6 Exploring Operation: 2*25=50, Resulting Numbers: [31, 65, 50] Generated Node #0,3: 49:[31, 65, 50] Operation: 2*25=50 Moving to Node #0,2 Current State: 49:[2, 65, 6], Operations: ['31-25=6'] Exploring Operation: 2+6=8, Resulting Numbers: [65, 8] Generated Node #0,2,0: 49:[65, 8] Operation: 2+6=8 Exploring Operation: 65-6=59, Resulting Numbers: [2, 59] Generated Node #0,2,1: 49:[2, 59] Operation: 65-6=59 Exploring Operation: 2+65=67, Resulting Numbers: [6, 67] Generated Node #0,2,2: 49:[6, 67] Operation: 2+65=67 Exploring Operation: 65-2=63, Resulting Numbers: [6, 63] Generated Node #0,2,3: 49:[6, 63] Operation: 65-2=63 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 49:[2, 59], Operations: ['31-25=6', '65-6=59'] Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,49 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,49 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 49:[6, 63], Operations: ['31-25=6', '65-2=63'] Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 6*63=378, Resulting Numbers: [378] 378,49 unequal: No Solution Exploring Operation: 6+63=69, Resulting Numbers: [69] 69,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 49:[65, 8], Operations: ['31-25=6', '2+6=8'] Exploring Operation: 65+8=73, Resulting Numbers: [73] 73,49 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 65*8=520, Resulting Numbers: [520] 520,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 49:[6, 67], Operations: ['31-25=6', '2+65=67'] Exploring Operation: 6+67=73, Resulting Numbers: [73] 73,49 unequal: No Solution Exploring Operation: 6*67=402, Resulting Numbers: [402] 402,49 unequal: No Solution Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,49 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: 49:[2, 65, 56], Operations: ['31+25=56'] Exploring Operation: 2+65=67, Resulting Numbers: [56, 67] Generated Node #0,0,0: 49:[56, 67] Operation: 2+65=67 Exploring Operation: 65-56=9, Resulting Numbers: [2, 9] Generated Node #0,0,1: 49:[2, 9] Operation: 65-56=9 Exploring Operation: 56-2=54, Resulting Numbers: [65, 54] Generated Node #0,0,2: 49:[65, 54] Operation: 56-2=54 Exploring Operation: 65-2=63, Resulting Numbers: [56, 63] Generated Node #0,0,3: 49:[56, 63] Operation: 65-2=63 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 49:[2, 9], Operations: ['31+25=56', '65-56=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 49:[65, 54], Operations: ['31+25=56', '56-2=54'] Exploring Operation: 65*54=3510, Resulting Numbers: [3510] 3510,49 unequal: No Solution Exploring Operation: 65+54=119, Resulting Numbers: [119] 119,49 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 49:[56, 63], Operations: ['31+25=56', '65-2=63'] Exploring Operation: 56+63=119, Resulting Numbers: [119] 119,49 unequal: No Solution Exploring Operation: 56*63=3528, Resulting Numbers: [3528] 3528,49 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[56, 67], Operations: ['31+25=56', '2+65=67'] Exploring Operation: 56*67=3752, Resulting Numbers: [3752] 3752,49 unequal: No Solution Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 56+67=123, Resulting Numbers: [123] 123,49 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: 49:[2, 31, 40], Operations: ['65-25=40'] Exploring Operation: 2+31=33, Resulting Numbers: [40, 33] Generated Node #0,1,0: 49:[40, 33] Operation: 2+31=33 Exploring Operation: 2+40=42, Resulting Numbers: [31, 42] Generated Node #0,1,1: 49:[31, 42] Operation: 2+40=42 Exploring Operation: 2*31=62, Resulting Numbers: [40, 62] Generated Node #0,1,2: 49:[40, 62] Operation: 2*31=62 Exploring Operation: 40-31=9, Resulting Numbers: [2, 9] Generated Node #0,1,3: 49:[2, 9] Operation: 40-31=9 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 49:[2, 9], Operations: ['65-25=40', '40-31=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 49:[40, 62], Operations: ['65-25=40', '2*31=62'] Exploring Operation: 40*62=2480, Resulting Numbers: [2480] 2480,49 unequal: No Solution Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,49 unequal: No Solution Exploring Operation: 40+62=102, Resulting Numbers: [102] 102,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[40, 33], Operations: ['65-25=40', '2+31=33'] Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 40*33=1320, Resulting Numbers: [1320] 1320,49 unequal: No Solution Exploring Operation: 40+33=73, Resulting Numbers: [73] 73,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 49:[31, 42], Operations: ['65-25=40', '2+40=42'] Exploring Operation: 31*42=1302, Resulting Numbers: [1302] 1302,49 unequal: No Solution Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 31+42=73, Resulting Numbers: [73] 73,49 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: 49:[31, 65, 50], Operations: ['2*25=50'] Exploring Operation: 65-31=34, Resulting Numbers: [50, 34] Generated Node #0,3,0: 49:[50, 34] Operation: 65-31=34 Exploring Operation: 50-31=19, Resulting Numbers: [65, 19] Generated Node #0,3,1: 49:[65, 19] Operation: 50-31=19 Exploring Operation: 31+65=96, Resulting Numbers: [50, 96] Generated Node #0,3,2: 49:[50, 96] Operation: 31+65=96 Exploring Operation: 65-50=15, Resulting Numbers: [31, 15] Generated Node #0,3,3: 49:[31, 15] Operation: 65-50=15 Moving to Node #0,3,0 Current State: 49:[50, 34], Operations: ['2*25=50', '65-31=34'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 50*34=1700, Resulting Numbers: [1700] 1700,49 unequal: No Solution Moving to Node #0,3,3 Current State: 49:[31, 15], Operations: ['2*25=50', '65-50=15'] Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,49 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[65, 19], Operations: ['2*25=50', '50-31=19'] Exploring Operation: 65+19=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 65*19=1235, Resulting Numbers: [1235] 1235,49 unequal: No Solution Moving to Node #0,3,2 Current State: 49:[50, 96], Operations: ['2*25=50', '31+65=96'] Exploring Operation: 96-50=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 50*96=4800, Resulting Numbers: [4800] 4800,49 unequal: No Solution Exploring Operation: 50+96=146, Resulting Numbers: [146] 146,49 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 26, 55, 16, 18 ]
63
[ "55-26=29", "16+18=34", "29+34=63" ]
Current State: 63:[26, 55, 16, 18], Operations: [] Exploring Operation: 55-26=29, Resulting Numbers: [16, 18, 29] Generated Node #2: [16, 18, 29] from Operation: 55-26=29 Current State: 63:[16, 18, 29], Operations: ['55-26=29'] Exploring Operation: 16+18=34, Resulting Numbers: [29, 34] Generated Node #3: [29, 34] from Operation: 16+18=34 Current State: 63:[29, 34], Operations: ['55-26=29', '16+18=34'] Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[26, 55, 16, 18], Operations: [] Exploring Operation: 26-16=10, Resulting Numbers: [55, 18, 10] Generated Node #0,0: 63:[55, 18, 10] Operation: 26-16=10 Exploring Operation: 26-18=8, Resulting Numbers: [55, 16, 8] Generated Node #0,1: 63:[55, 16, 8] Operation: 26-18=8 Exploring Operation: 18-16=2, Resulting Numbers: [26, 55, 2] Generated Node #0,2: 63:[26, 55, 2] Operation: 18-16=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[55, 18, 10], Operations: ['26-16=10'] Exploring Operation: 55+18=73, Resulting Numbers: [10, 73] Generated Node #0,0,0: 63:[10, 73] Operation: 55+18=73 Exploring Operation: 55+10=65, Resulting Numbers: [18, 65] Generated Node #0,0,1: 63:[18, 65] Operation: 55+10=65 Exploring Operation: 18-10=8, Resulting Numbers: [55, 8] Generated Node #0,0,2: 63:[55, 8] Operation: 18-10=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[18, 65], Operations: ['26-16=10', '55+10=65'] Exploring Operation: 18+65=83, Resulting Numbers: [83] 83,63 unequal: No Solution Exploring Operation: 18*65=1170, Resulting Numbers: [1170] 1170,63 unequal: No Solution Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 63:[55, 8], Operations: ['26-16=10', '18-10=8'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,63 unequal: No Solution Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[26, 55, 16, 18], Operations: [] Exploring Operation: 26-16=10, Resulting Numbers: [55, 18, 10] Generated Node #0,0: 63:[55, 18, 10] Operation: 26-16=10 Moving to Node #0,0 Current State: 63:[55, 18, 10], Operations: ['26-16=10'] Exploring Operation: 18-10=8, Resulting Numbers: [55, 8] Generated Node #0,0,2: 63:[55, 8] Operation: 18-10=8 Moving to Node #0,0,2 Current State: 63:[55, 8], Operations: ['26-16=10', '18-10=8'] Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 60, 27, 12, 15 ]
96
[ "60*27=1620", "1620/15=108", "108-12=96" ]
Current State: 96:[60, 27, 12, 15], Operations: [] Exploring Operation: 60*27=1620, Resulting Numbers: [12, 15, 1620] Generated Node #2: [12, 15, 1620] from Operation: 60*27=1620 Current State: 96:[12, 15, 1620], Operations: ['60*27=1620'] Exploring Operation: 1620/15=108, Resulting Numbers: [12, 108] Generated Node #3: [12, 108] from Operation: 1620/15=108 Current State: 96:[12, 108], Operations: ['60*27=1620', '1620/15=108'] Exploring Operation: 108-12=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[60, 27, 12, 15], Operations: [] Exploring Operation: 60-27=33, Resulting Numbers: [12, 15, 33] Generated Node #0,0: 96:[12, 15, 33] Operation: 60-27=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[12, 15, 33], Operations: ['60-27=33'] Exploring Operation: 15+33=48, Resulting Numbers: [12, 48] Generated Node #0,0,0: 96:[12, 48] Operation: 15+33=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[12, 48], Operations: ['60-27=33', '15+33=48'] Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 20, 48, 22, 70 ]
55
[ "48-20=28", "22*70=1540", "1540/28=55" ]
Current State: 55:[20, 48, 22, 70], Operations: [] Exploring Operation: 48-20=28, Resulting Numbers: [22, 70, 28] Generated Node #2: [22, 70, 28] from Operation: 48-20=28 Current State: 55:[22, 70, 28], Operations: ['48-20=28'] Exploring Operation: 22*70=1540, Resulting Numbers: [28, 1540] Generated Node #3: [28, 1540] from Operation: 22*70=1540 Current State: 55:[28, 1540], Operations: ['48-20=28', '22*70=1540'] Exploring Operation: 1540/28=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[20, 48, 22, 70], Operations: [] Exploring Operation: 70-20=50, Resulting Numbers: [48, 22, 50] Generated Node #0,0: 55:[48, 22, 50] Operation: 70-20=50 Moving to Node #0,0 Current State: 55:[48, 22, 50], Operations: ['70-20=50'] Exploring Operation: 50-48=2, Resulting Numbers: [22, 2] Generated Node #0,0,0: 55:[22, 2] Operation: 50-48=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[22, 2], Operations: ['70-20=50', '50-48=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 58, 69, 84, 9 ]
82
[ "69-58=11", "84+9=93", "93-11=82" ]
Current State: 82:[58, 69, 84, 9], Operations: [] Exploring Operation: 69-58=11, Resulting Numbers: [84, 9, 11] Generated Node #2: [84, 9, 11] from Operation: 69-58=11 Current State: 82:[84, 9, 11], Operations: ['69-58=11'] Exploring Operation: 84+9=93, Resulting Numbers: [11, 93] Generated Node #3: [11, 93] from Operation: 84+9=93 Current State: 82:[11, 93], Operations: ['69-58=11', '84+9=93'] Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[58, 69, 84, 9], Operations: [] Exploring Operation: 69-58=11, Resulting Numbers: [84, 9, 11] Generated Node #0,0: 82:[84, 9, 11] Operation: 69-58=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[84, 9, 11], Operations: ['69-58=11'] Exploring Operation: 11-9=2, Resulting Numbers: [84, 2] Generated Node #0,0,0: 82:[84, 2] Operation: 11-9=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[84, 2], Operations: ['69-58=11', '11-9=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[58, 69, 84, 9], Operations: [] Exploring Operation: 69-58=11, Resulting Numbers: [84, 9, 11] Generated Node #0,0: 82:[84, 9, 11] Operation: 69-58=11 Moving to Node #0,0 Current State: 82:[84, 9, 11], Operations: ['69-58=11'] Exploring Operation: 11-9=2, Resulting Numbers: [84, 2] Generated Node #0,0,0: 82:[84, 2] Operation: 11-9=2 Moving to Node #0,0,0 Current State: 82:[84, 2], Operations: ['69-58=11', '11-9=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 48, 87, 46, 16 ]
75
[ "48/16=3", "87/3=29", "46+29=75" ]
Current State: 75:[48, 87, 46, 16], Operations: [] Exploring Operation: 48/16=3, Resulting Numbers: [87, 46, 3] Generated Node #2: [87, 46, 3] from Operation: 48/16=3 Current State: 75:[87, 46, 3], Operations: ['48/16=3'] Exploring Operation: 87/3=29, Resulting Numbers: [46, 29] Generated Node #3: [46, 29] from Operation: 87/3=29 Current State: 75:[46, 29], Operations: ['48/16=3', '87/3=29'] Exploring Operation: 46+29=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[48, 87, 46, 16], Operations: [] Exploring Operation: 48/16=3, Resulting Numbers: [87, 46, 3] Generated Node #0,0: 75:[87, 46, 3] Operation: 48/16=3 Exploring Operation: 48+46=94, Resulting Numbers: [87, 16, 94] Generated Node #0,1: 75:[87, 16, 94] Operation: 48+46=94 Exploring Operation: 48-46=2, Resulting Numbers: [87, 16, 2] Generated Node #0,2: 75:[87, 16, 2] Operation: 48-46=2 Exploring Operation: 87-48=39, Resulting Numbers: [46, 16, 39] Generated Node #0,3: 75:[46, 16, 39] Operation: 87-48=39 Exploring Operation: 48-16=32, Resulting Numbers: [87, 46, 32] Generated Node #0,4: 75:[87, 46, 32] Operation: 48-16=32 Moving to Node #0,2 Current State: 75:[87, 16, 2], Operations: ['48-46=2'] Exploring Operation: 87+2=89, Resulting Numbers: [16, 89] Generated Node #0,2,0: 75:[16, 89] Operation: 87+2=89 Exploring Operation: 87-2=85, Resulting Numbers: [16, 85] Generated Node #0,2,1: 75:[16, 85] Operation: 87-2=85 Exploring Operation: 87-16=71, Resulting Numbers: [2, 71] Generated Node #0,2,2: 75:[2, 71] Operation: 87-16=71 Exploring Operation: 16-2=14, Resulting Numbers: [87, 14] Generated Node #0,2,3: 75:[87, 14] Operation: 16-2=14 Exploring Operation: 16+2=18, Resulting Numbers: [87, 18] Generated Node #0,2,4: 75:[87, 18] Operation: 16+2=18 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 75:[2, 71], Operations: ['48-46=2', '87-16=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,75 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,75 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,75 unequal: No Solution No 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: 75:[16, 85], Operations: ['48-46=2', '87-2=85'] Exploring Operation: 16+85=101, Resulting Numbers: [101] 101,75 unequal: No Solution Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,75 unequal: No Solution Exploring Operation: 16*85=1360, Resulting Numbers: [1360] 1360,75 unequal: No Solution No 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: 75:[87, 14], Operations: ['48-46=2', '16-2=14'] Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,75 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,75 unequal: No Solution Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,75 unequal: No Solution No 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: 75:[16, 89], Operations: ['48-46=2', '87+2=89'] Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,75 unequal: No Solution Exploring Operation: 16+89=105, Resulting Numbers: [105] 105,75 unequal: No Solution Exploring Operation: 16*89=1424, Resulting Numbers: [1424] 1424,75 unequal: No Solution No 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: 75:[87, 18], Operations: ['48-46=2', '16+2=18'] Exploring Operation: 87*18=1566, Resulting Numbers: [1566] 1566,75 unequal: No Solution Exploring Operation: 87-18=69, Resulting Numbers: [69] 69,75 unequal: No Solution Exploring Operation: 87+18=105, Resulting Numbers: [105] 105,75 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: 75:[87, 16, 94], Operations: ['48+46=94'] Exploring Operation: 94-16=78, Resulting Numbers: [87, 78] Generated Node #0,1,0: 75:[87, 78] Operation: 94-16=78 Exploring Operation: 94-87=7, Resulting Numbers: [16, 7] Generated Node #0,1,1: 75:[16, 7] Operation: 94-87=7 Exploring Operation: 87-16=71, Resulting Numbers: [94, 71] Generated Node #0,1,2: 75:[94, 71] Operation: 87-16=71 Exploring Operation: 87+16=103, Resulting Numbers: [94, 103] Generated Node #0,1,3: 75:[94, 103] Operation: 87+16=103 Exploring Operation: 16+94=110, Resulting Numbers: [87, 110] Generated Node #0,1,4: 75:[87, 110] Operation: 16+94=110 Moving to Node #0,0 Current State: 75:[87, 46, 3], Operations: ['48/16=3'] Exploring Operation: 87+3=90, Resulting Numbers: [46, 90] Generated Node #0,0,0: 75:[46, 90] Operation: 87+3=90 Exploring Operation: 87/3=29, Resulting Numbers: [46, 29] Generated Node #0,0,1: 75:[46, 29] Operation: 87/3=29 Exploring Operation: 87-46=41, Resulting Numbers: [3, 41] Generated Node #0,0,2: 75:[3, 41] Operation: 87-46=41 Exploring Operation: 87-3=84, Resulting Numbers: [46, 84] Generated Node #0,0,3: 75:[46, 84] Operation: 87-3=84 Exploring Operation: 46-3=43, Resulting Numbers: [87, 43] Generated Node #0,0,4: 75:[87, 43] Operation: 46-3=43 Moving to Node #0,3 Current State: 75:[46, 16, 39], Operations: ['87-48=39'] Exploring Operation: 46+16=62, Resulting Numbers: [39, 62] Generated Node #0,3,0: 75:[39, 62] Operation: 46+16=62 Exploring Operation: 46-39=7, Resulting Numbers: [16, 7] Generated Node #0,3,1: 75:[16, 7] Operation: 46-39=7 Exploring Operation: 39-16=23, Resulting Numbers: [46, 23] Generated Node #0,3,2: 75:[46, 23] Operation: 39-16=23 Exploring Operation: 46+39=85, Resulting Numbers: [16, 85] Generated Node #0,3,3: 75:[16, 85] Operation: 46+39=85 Exploring Operation: 46-16=30, Resulting Numbers: [39, 30] Generated Node #0,3,4: 75:[39, 30] Operation: 46-16=30 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 75:[16, 7], Operations: ['87-48=39', '46-39=7'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,75 unequal: No Solution Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,75 unequal: No Solution No 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: 75:[16, 85], Operations: ['87-48=39', '46+39=85'] Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,75 unequal: No Solution Exploring Operation: 16*85=1360, Resulting Numbers: [1360] 1360,75 unequal: No Solution Exploring Operation: 16+85=101, Resulting Numbers: [101] 101,75 unequal: No Solution No 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: 75:[39, 30], Operations: ['87-48=39', '46-16=30'] Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,75 unequal: No Solution Exploring Operation: 39*30=1170, Resulting Numbers: [1170] 1170,75 unequal: No Solution Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,75 unequal: No Solution No 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: 75:[46, 23], Operations: ['87-48=39', '39-16=23'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,75 unequal: No Solution Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 46+23=69, Resulting Numbers: [69] 69,75 unequal: No Solution Exploring Operation: 46*23=1058, Resulting Numbers: [1058] 1058,75 unequal: No Solution No 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: 75:[39, 62], Operations: ['87-48=39', '46+16=62'] Exploring Operation: 39+62=101, Resulting Numbers: [101] 101,75 unequal: No Solution Exploring Operation: 62-39=23, Resulting Numbers: [23] 23,75 unequal: No Solution Exploring Operation: 39*62=2418, Resulting Numbers: [2418] 2418,75 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: 75:[87, 46, 32], Operations: ['48-16=32'] Exploring Operation: 87-32=55, Resulting Numbers: [46, 55] Generated Node #0,4,0: 75:[46, 55] Operation: 87-32=55 Exploring Operation: 87+46=133, Resulting Numbers: [32, 133] Generated Node #0,4,1: 75:[32, 133] Operation: 87+46=133 Exploring Operation: 87-46=41, Resulting Numbers: [32, 41] Generated Node #0,4,2: 75:[32, 41] Operation: 87-46=41 Exploring Operation: 46+32=78, Resulting Numbers: [87, 78] Generated Node #0,4,3: 75:[87, 78] Operation: 46+32=78 Exploring Operation: 46-32=14, Resulting Numbers: [87, 14] Generated Node #0,4,4: 75:[87, 14] Operation: 46-32=14 Moving to Node #0,1,1 Current State: 75:[16, 7], Operations: ['48+46=94', '94-87=7'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,75 unequal: No Solution Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,75 unequal: No Solution Moving to Node #0,4,4 Current State: 75:[87, 14], Operations: ['48-16=32', '46-32=14'] Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,75 unequal: No Solution Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,75 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,75 unequal: No Solution Moving to Node #0,4,3 Current State: 75:[87, 78], Operations: ['48-16=32', '46+32=78'] Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,75 unequal: No Solution Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,75 unequal: No Solution Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[87, 78], Operations: ['48+46=94', '94-16=78'] Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,75 unequal: No Solution Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[3, 41], Operations: ['48/16=3', '87-46=41'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,75 unequal: No Solution Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,75 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,75 unequal: No Solution Moving to Node #0,4,2 Current State: 75:[32, 41], Operations: ['48-16=32', '87-46=41'] Exploring Operation: 32*41=1312, Resulting Numbers: [1312] 1312,75 unequal: No Solution Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 32+41=73, Resulting Numbers: [73] 73,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[94, 71], Operations: ['48+46=94', '87-16=71'] Exploring Operation: 94+71=165, Resulting Numbers: [165] 165,75 unequal: No Solution Exploring Operation: 94-71=23, Resulting Numbers: [23] 23,75 unequal: No Solution Exploring Operation: 94*71=6674, Resulting Numbers: [6674] 6674,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[46, 29], Operations: ['48/16=3', '87/3=29'] Exploring Operation: 46+29=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[48, 87, 46, 16], Operations: [] Exploring Operation: 48/16=3, Resulting Numbers: [87, 46, 3] Generated Node #0,0: 75:[87, 46, 3] Operation: 48/16=3 Moving to Node #0,0 Current State: 75:[87, 46, 3], Operations: ['48/16=3'] Exploring Operation: 87/3=29, Resulting Numbers: [46, 29] Generated Node #0,0,1: 75:[46, 29] Operation: 87/3=29 Moving to Node #0,0,1 Current State: 75:[46, 29], Operations: ['48/16=3', '87/3=29'] Exploring Operation: 46+29=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.924479
hs_5
mult_heuristic
[ 91, 49, 94, 43 ]
18
[ "94-91=3", "49-43=6", "3*6=18" ]
Current State: 18:[91, 49, 94, 43], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [49, 43, 3] Generated Node #2: [49, 43, 3] from Operation: 94-91=3 Current State: 18:[49, 43, 3], Operations: ['94-91=3'] Exploring Operation: 49-43=6, Resulting Numbers: [3, 6] Generated Node #3: [3, 6] from Operation: 49-43=6 Current State: 18:[3, 6], Operations: ['94-91=3', '49-43=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[91, 49, 94, 43], Operations: [] Exploring Operation: 94-43=51, Resulting Numbers: [91, 49, 51] Generated Node #0,0: 18:[91, 49, 51] Operation: 94-43=51 Exploring Operation: 94-49=45, Resulting Numbers: [91, 43, 45] Generated Node #0,1: 18:[91, 43, 45] Operation: 94-49=45 Exploring Operation: 91-49=42, Resulting Numbers: [94, 43, 42] Generated Node #0,2: 18:[94, 43, 42] Operation: 91-49=42 Exploring Operation: 94-91=3, Resulting Numbers: [49, 43, 3] Generated Node #0,3: 18:[49, 43, 3] Operation: 94-91=3 Exploring Operation: 91-43=48, Resulting Numbers: [49, 94, 48] Generated Node #0,4: 18:[49, 94, 48] Operation: 91-43=48 Moving to Node #0,3 Current State: 18:[49, 43, 3], Operations: ['94-91=3'] Exploring Operation: 43-3=40, Resulting Numbers: [49, 40] Generated Node #0,3,0: 18:[49, 40] Operation: 43-3=40 Exploring Operation: 49-3=46, Resulting Numbers: [43, 46] Generated Node #0,3,1: 18:[43, 46] Operation: 49-3=46 Exploring Operation: 49+3=52, Resulting Numbers: [43, 52] Generated Node #0,3,2: 18:[43, 52] Operation: 49+3=52 Exploring Operation: 43+3=46, Resulting Numbers: [49, 46] Generated Node #0,3,3: 18:[49, 46] Operation: 43+3=46 Exploring Operation: 49-43=6, Resulting Numbers: [3, 6] Generated Node #0,3,4: 18:[3, 6] Operation: 49-43=6 Moving to Node #0,2 Current State: 18:[94, 43, 42], Operations: ['91-49=42'] Exploring Operation: 94+43=137, Resulting Numbers: [42, 137] Generated Node #0,2,0: 18:[42, 137] Operation: 94+43=137 Exploring Operation: 94-42=52, Resulting Numbers: [43, 52] Generated Node #0,2,1: 18:[43, 52] Operation: 94-42=52 Exploring Operation: 94-43=51, Resulting Numbers: [42, 51] Generated Node #0,2,2: 18:[42, 51] Operation: 94-43=51 Exploring Operation: 94+42=136, Resulting Numbers: [43, 136] Generated Node #0,2,3: 18:[43, 136] Operation: 94+42=136 Exploring Operation: 43-42=1, Resulting Numbers: [94, 1] Generated Node #0,2,4: 18:[94, 1] Operation: 43-42=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[42, 51], Operations: ['91-49=42', '94-43=51'] Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 42+51=93, Resulting Numbers: [93] 93,18 unequal: No Solution Exploring Operation: 42*51=2142, Resulting Numbers: [2142] 2142,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[43, 52], Operations: ['91-49=42', '94-42=52'] Exploring Operation: 43*52=2236, Resulting Numbers: [2236] 2236,18 unequal: No Solution Exploring Operation: 43+52=95, Resulting Numbers: [95] 95,18 unequal: No Solution Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[94, 1], Operations: ['91-49=42', '43-42=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,18 unequal: No Solution Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,18 unequal: No Solution Exploring Operation: 94*1=94, Resulting Numbers: [94] 94,18 unequal: No Solution Exploring Operation: 94+1=95, Resulting Numbers: [95] 95,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[42, 137], Operations: ['91-49=42', '94+43=137'] Exploring Operation: 42*137=5754, Resulting Numbers: [5754] 5754,18 unequal: No Solution Exploring Operation: 137-42=95, Resulting Numbers: [95] 95,18 unequal: No Solution Exploring Operation: 42+137=179, Resulting Numbers: [179] 179,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[43, 136], Operations: ['91-49=42', '94+42=136'] Exploring Operation: 43+136=179, Resulting Numbers: [179] 179,18 unequal: No Solution Exploring Operation: 136-43=93, Resulting Numbers: [93] 93,18 unequal: No Solution Exploring Operation: 43*136=5848, Resulting Numbers: [5848] 5848,18 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: 18:[91, 43, 45], Operations: ['94-49=45'] Exploring Operation: 45-43=2, Resulting Numbers: [91, 2] Generated Node #0,1,0: 18:[91, 2] Operation: 45-43=2 Exploring Operation: 91-43=48, Resulting Numbers: [45, 48] Generated Node #0,1,1: 18:[45, 48] Operation: 91-43=48 Exploring Operation: 91-45=46, Resulting Numbers: [43, 46] Generated Node #0,1,2: 18:[43, 46] Operation: 91-45=46 Exploring Operation: 91+45=136, Resulting Numbers: [43, 136] Generated Node #0,1,3: 18:[43, 136] Operation: 91+45=136 Exploring Operation: 91+43=134, Resulting Numbers: [45, 134] Generated Node #0,1,4: 18:[45, 134] Operation: 91+43=134 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[43, 46], Operations: ['94-49=45', '91-45=46'] Exploring Operation: 43*46=1978, Resulting Numbers: [1978] 1978,18 unequal: No Solution Exploring Operation: 43+46=89, Resulting Numbers: [89] 89,18 unequal: No Solution Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[45, 48], Operations: ['94-49=45', '91-43=48'] Exploring Operation: 45*48=2160, Resulting Numbers: [2160] 2160,18 unequal: No Solution Exploring Operation: 45+48=93, Resulting Numbers: [93] 93,18 unequal: No Solution Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[91, 2], Operations: ['94-49=45', '45-43=2'] Exploring Operation: 91*2=182, Resulting Numbers: [182] 182,18 unequal: No Solution Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,18 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[43, 136], Operations: ['94-49=45', '91+45=136'] Exploring Operation: 43+136=179, Resulting Numbers: [179] 179,18 unequal: No Solution Exploring Operation: 136-43=93, Resulting Numbers: [93] 93,18 unequal: No Solution Exploring Operation: 43*136=5848, Resulting Numbers: [5848] 5848,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[45, 134], Operations: ['94-49=45', '91+43=134'] Exploring Operation: 45+134=179, Resulting Numbers: [179] 179,18 unequal: No Solution Exploring Operation: 45*134=6030, Resulting Numbers: [6030] 6030,18 unequal: No Solution Exploring Operation: 134-45=89, Resulting Numbers: [89] 89,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 18:[91, 49, 51], Operations: ['94-43=51'] Exploring Operation: 91+51=142, Resulting Numbers: [49, 142] Generated Node #0,0,0: 18:[49, 142] Operation: 91+51=142 Exploring Operation: 91+49=140, Resulting Numbers: [51, 140] Generated Node #0,0,1: 18:[51, 140] Operation: 91+49=140 Exploring Operation: 91-51=40, Resulting Numbers: [49, 40] Generated Node #0,0,2: 18:[49, 40] Operation: 91-51=40 Exploring Operation: 51-49=2, Resulting Numbers: [91, 2] Generated Node #0,0,3: 18:[91, 2] Operation: 51-49=2 Exploring Operation: 91-49=42, Resulting Numbers: [51, 42] Generated Node #0,0,4: 18:[51, 42] Operation: 91-49=42 Moving to Node #0,4 Current State: 18:[49, 94, 48], Operations: ['91-43=48'] Exploring Operation: 49+94=143, Resulting Numbers: [48, 143] Generated Node #0,4,0: 18:[48, 143] Operation: 49+94=143 Exploring Operation: 49+48=97, Resulting Numbers: [94, 97] Generated Node #0,4,1: 18:[94, 97] Operation: 49+48=97 Exploring Operation: 49-48=1, Resulting Numbers: [94, 1] Generated Node #0,4,2: 18:[94, 1] Operation: 49-48=1 Exploring Operation: 94-48=46, Resulting Numbers: [49, 46] Generated Node #0,4,3: 18:[49, 46] Operation: 94-48=46 Exploring Operation: 94-49=45, Resulting Numbers: [48, 45] Generated Node #0,4,4: 18:[48, 45] Operation: 94-49=45 Moving to Node #0,3,4 Current State: 18:[3, 6], Operations: ['94-91=3', '49-43=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[91, 49, 94, 43], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [49, 43, 3] Generated Node #0,3: 18:[49, 43, 3] Operation: 94-91=3 Moving to Node #0,3 Current State: 18:[49, 43, 3], Operations: ['94-91=3'] Exploring Operation: 49-43=6, Resulting Numbers: [3, 6] Generated Node #0,3,4: 18:[3, 6] Operation: 49-43=6 Moving to Node #0,3,4 Current State: 18:[3, 6], Operations: ['94-91=3', '49-43=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.940104
hs_5
sum_heuristic
[ 80, 81, 76, 78 ]
83
[ "80+76=156", "156/78=2", "81+2=83" ]
Current State: 83:[80, 81, 76, 78], Operations: [] Exploring Operation: 80+76=156, Resulting Numbers: [81, 78, 156] Generated Node #2: [81, 78, 156] from Operation: 80+76=156 Current State: 83:[81, 78, 156], Operations: ['80+76=156'] Exploring Operation: 156/78=2, Resulting Numbers: [81, 2] Generated Node #3: [81, 2] from Operation: 156/78=2 Current State: 83:[81, 2], Operations: ['80+76=156', '156/78=2'] Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[80, 81, 76, 78], Operations: [] Exploring Operation: 80+78=158, Resulting Numbers: [81, 76, 158] Generated Node #0,0: 83:[81, 76, 158] Operation: 80+78=158 Exploring Operation: 80+76=156, Resulting Numbers: [81, 78, 156] Generated Node #0,1: 83:[81, 78, 156] Operation: 80+76=156 Exploring Operation: 76+78=154, Resulting Numbers: [80, 81, 154] Generated Node #0,2: 83:[80, 81, 154] Operation: 76+78=154 Exploring Operation: 81+76=157, Resulting Numbers: [80, 78, 157] Generated Node #0,3: 83:[80, 78, 157] Operation: 81+76=157 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[80, 81, 154], Operations: ['76+78=154'] Exploring Operation: 81-80=1, Resulting Numbers: [154, 1] Generated Node #0,2,0: 83:[154, 1] Operation: 81-80=1 Exploring Operation: 154-81=73, Resulting Numbers: [80, 73] Generated Node #0,2,1: 83:[80, 73] Operation: 154-81=73 Exploring Operation: 154-80=74, Resulting Numbers: [81, 74] Generated Node #0,2,2: 83:[81, 74] Operation: 154-80=74 Exploring Operation: 80+81=161, Resulting Numbers: [154, 161] Generated Node #0,2,3: 83:[154, 161] Operation: 80+81=161 Moving to Node #0,2,2 Current State: 83:[81, 74], Operations: ['76+78=154', '154-80=74'] Exploring Operation: 81-74=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 81*74=5994, Resulting Numbers: [5994] 5994,83 unequal: No Solution Exploring Operation: 81+74=155, Resulting Numbers: [155] 155,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[80, 73], Operations: ['76+78=154', '154-81=73'] Exploring Operation: 80+73=153, Resulting Numbers: [153] 153,83 unequal: No Solution Exploring Operation: 80-73=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 80*73=5840, Resulting Numbers: [5840] 5840,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[154, 161], Operations: ['76+78=154', '80+81=161'] Exploring Operation: 161-154=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 154+161=315, Resulting Numbers: [315] 315,83 unequal: No Solution Exploring Operation: 154*161=24794, Resulting Numbers: [24794] 24794,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[154, 1], Operations: ['76+78=154', '81-80=1'] Exploring Operation: 154*1=154, Resulting Numbers: [154] 154,83 unequal: No Solution Exploring Operation: 154-1=153, Resulting Numbers: [153] 153,83 unequal: No Solution Exploring Operation: 154+1=155, Resulting Numbers: [155] 155,83 unequal: No Solution Exploring Operation: 154/1=154, Resulting Numbers: [154] 154,83 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:[81, 78, 156], Operations: ['80+76=156'] Exploring Operation: 156-78=78, Resulting Numbers: [81, 78] Generated Node #0,1,0: 83:[81, 78] Operation: 156-78=78 Exploring Operation: 156-81=75, Resulting Numbers: [78, 75] Generated Node #0,1,1: 83:[78, 75] Operation: 156-81=75 Exploring Operation: 81+78=159, Resulting Numbers: [156, 159] Generated Node #0,1,2: 83:[156, 159] Operation: 81+78=159 Exploring Operation: 156/78=2, Resulting Numbers: [81, 2] Generated Node #0,1,3: 83:[81, 2] Operation: 156/78=2 Moving to Node #0,1,0 Current State: 83:[81, 78], Operations: ['80+76=156', '156-78=78'] Exploring Operation: 81*78=6318, Resulting Numbers: [6318] 6318,83 unequal: No Solution Exploring Operation: 81-78=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 81+78=159, Resulting Numbers: [159] 159,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[78, 75], Operations: ['80+76=156', '156-81=75'] Exploring Operation: 78+75=153, Resulting Numbers: [153] 153,83 unequal: No Solution Exploring Operation: 78-75=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 78*75=5850, Resulting Numbers: [5850] 5850,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[81, 2], Operations: ['80+76=156', '156/78=2'] Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[80, 81, 76, 78], Operations: [] Exploring Operation: 80+76=156, Resulting Numbers: [81, 78, 156] Generated Node #0,1: 83:[81, 78, 156] Operation: 80+76=156 Moving to Node #0,1 Current State: 83:[81, 78, 156], Operations: ['80+76=156'] Exploring Operation: 156/78=2, Resulting Numbers: [81, 2] Generated Node #0,1,3: 83:[81, 2] Operation: 156/78=2 Moving to Node #0,1,3 Current State: 83:[81, 2], Operations: ['80+76=156', '156/78=2'] Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
mult_heuristic
[ 69, 74, 10, 12 ]
50
[ "74-69=5", "12*5=60", "60-10=50" ]
Current State: 50:[69, 74, 10, 12], Operations: [] Exploring Operation: 74-69=5, Resulting Numbers: [10, 12, 5] Generated Node #2: [10, 12, 5] from Operation: 74-69=5 Current State: 50:[10, 12, 5], Operations: ['74-69=5'] Exploring Operation: 12*5=60, Resulting Numbers: [10, 60] Generated Node #3: [10, 60] from Operation: 12*5=60 Current State: 50:[10, 60], Operations: ['74-69=5', '12*5=60'] Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[69, 74, 10, 12], Operations: [] Exploring Operation: 69-10=59, Resulting Numbers: [74, 12, 59] Generated Node #0,0: 50:[74, 12, 59] Operation: 69-10=59 Exploring Operation: 74-12=62, Resulting Numbers: [69, 10, 62] Generated Node #0,1: 50:[69, 10, 62] Operation: 74-12=62 Exploring Operation: 74-10=64, Resulting Numbers: [69, 12, 64] Generated Node #0,2: 50:[69, 12, 64] Operation: 74-10=64 Exploring Operation: 69-12=57, Resulting Numbers: [74, 10, 57] Generated Node #0,3: 50:[74, 10, 57] Operation: 69-12=57 Exploring Operation: 74-69=5, Resulting Numbers: [10, 12, 5] Generated Node #0,4: 50:[10, 12, 5] Operation: 74-69=5 Moving to Node #0,4 Current State: 50:[10, 12, 5], Operations: ['74-69=5'] Exploring Operation: 10-5=5, Resulting Numbers: [12, 5] Generated Node #0,4,0: 50:[12, 5] Operation: 10-5=5 Exploring Operation: 12-10=2, Resulting Numbers: [5, 2] Generated Node #0,4,1: 50:[5, 2] Operation: 12-10=2 Exploring Operation: 12-5=7, Resulting Numbers: [10, 7] Generated Node #0,4,2: 50:[10, 7] Operation: 12-5=7 Exploring Operation: 10/5=2, Resulting Numbers: [12, 2] Generated Node #0,4,3: 50:[12, 2] Operation: 10/5=2 Exploring Operation: 10*5=50, Resulting Numbers: [12, 50] Generated Node #0,4,4: 50:[12, 50] Operation: 10*5=50 Moving to Node #0,3 Current State: 50:[74, 10, 57], Operations: ['69-12=57'] Exploring Operation: 74-10=64, Resulting Numbers: [57, 64] Generated Node #0,3,0: 50:[57, 64] Operation: 74-10=64 Exploring Operation: 57-10=47, Resulting Numbers: [74, 47] Generated Node #0,3,1: 50:[74, 47] Operation: 57-10=47 Exploring Operation: 74-57=17, Resulting Numbers: [10, 17] Generated Node #0,3,2: 50:[10, 17] Operation: 74-57=17 Exploring Operation: 10+57=67, Resulting Numbers: [74, 67] Generated Node #0,3,3: 50:[74, 67] Operation: 10+57=67 Exploring Operation: 74+10=84, Resulting Numbers: [57, 84] Generated Node #0,3,4: 50:[57, 84] Operation: 74+10=84 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 50:[10, 17], Operations: ['69-12=57', '74-57=17'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,50 unequal: No Solution Exploring Operation: 10*17=170, Resulting Numbers: [170] 170,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 50:[57, 64], Operations: ['69-12=57', '74-10=64'] Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 57*64=3648, Resulting Numbers: [3648] 3648,50 unequal: No Solution Exploring Operation: 57+64=121, Resulting Numbers: [121] 121,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 50:[74, 47], Operations: ['69-12=57', '57-10=47'] Exploring Operation: 74*47=3478, Resulting Numbers: [3478] 3478,50 unequal: No Solution Exploring Operation: 74+47=121, Resulting Numbers: [121] 121,50 unequal: No Solution Exploring Operation: 74-47=27, Resulting Numbers: [27] 27,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 50:[74, 67], Operations: ['69-12=57', '10+57=67'] Exploring Operation: 74-67=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 74+67=141, Resulting Numbers: [141] 141,50 unequal: No Solution Exploring Operation: 74*67=4958, Resulting Numbers: [4958] 4958,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 50:[57, 84], Operations: ['69-12=57', '74+10=84'] Exploring Operation: 57+84=141, Resulting Numbers: [141] 141,50 unequal: No Solution Exploring Operation: 84-57=27, Resulting Numbers: [27] 27,50 unequal: No Solution Exploring Operation: 57*84=4788, Resulting Numbers: [4788] 4788,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 50:[69, 10, 62], Operations: ['74-12=62'] Exploring Operation: 10+62=72, Resulting Numbers: [69, 72] Generated Node #0,1,0: 50:[69, 72] Operation: 10+62=72 Exploring Operation: 69+10=79, Resulting Numbers: [62, 79] Generated Node #0,1,1: 50:[62, 79] Operation: 69+10=79 Exploring Operation: 62-10=52, Resulting Numbers: [69, 52] Generated Node #0,1,2: 50:[69, 52] Operation: 62-10=52 Exploring Operation: 69-62=7, Resulting Numbers: [10, 7] Generated Node #0,1,3: 50:[10, 7] Operation: 69-62=7 Exploring Operation: 69-10=59, Resulting Numbers: [62, 59] Generated Node #0,1,4: 50:[62, 59] Operation: 69-10=59 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 50:[10, 7], Operations: ['74-12=62', '69-62=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,50 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 50:[69, 52], Operations: ['74-12=62', '62-10=52'] Exploring Operation: 69+52=121, Resulting Numbers: [121] 121,50 unequal: No Solution Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 69*52=3588, Resulting Numbers: [3588] 3588,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 50:[62, 59], Operations: ['74-12=62', '69-10=59'] Exploring Operation: 62*59=3658, Resulting Numbers: [3658] 3658,50 unequal: No Solution Exploring Operation: 62+59=121, Resulting Numbers: [121] 121,50 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[69, 72], Operations: ['74-12=62', '10+62=72'] Exploring Operation: 72-69=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 69*72=4968, Resulting Numbers: [4968] 4968,50 unequal: No Solution Exploring Operation: 69+72=141, Resulting Numbers: [141] 141,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[62, 79], Operations: ['74-12=62', '69+10=79'] Exploring Operation: 79-62=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 62*79=4898, Resulting Numbers: [4898] 4898,50 unequal: No Solution Exploring Operation: 62+79=141, Resulting Numbers: [141] 141,50 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: 50:[74, 12, 59], Operations: ['69-10=59'] Exploring Operation: 74-59=15, Resulting Numbers: [12, 15] Generated Node #0,0,0: 50:[12, 15] Operation: 74-59=15 Exploring Operation: 12+59=71, Resulting Numbers: [74, 71] Generated Node #0,0,1: 50:[74, 71] Operation: 12+59=71 Exploring Operation: 74+12=86, Resulting Numbers: [59, 86] Generated Node #0,0,2: 50:[59, 86] Operation: 74+12=86 Exploring Operation: 74-12=62, Resulting Numbers: [59, 62] Generated Node #0,0,3: 50:[59, 62] Operation: 74-12=62 Exploring Operation: 59-12=47, Resulting Numbers: [74, 47] Generated Node #0,0,4: 50:[74, 47] Operation: 59-12=47 Moving to Node #0,2 Current State: 50:[69, 12, 64], Operations: ['74-10=64'] Exploring Operation: 64-12=52, Resulting Numbers: [69, 52] Generated Node #0,2,0: 50:[69, 52] Operation: 64-12=52 Exploring Operation: 69+12=81, Resulting Numbers: [64, 81] Generated Node #0,2,1: 50:[64, 81] Operation: 69+12=81 Exploring Operation: 69-12=57, Resulting Numbers: [64, 57] Generated Node #0,2,2: 50:[64, 57] Operation: 69-12=57 Exploring Operation: 69-64=5, Resulting Numbers: [12, 5] Generated Node #0,2,3: 50:[12, 5] Operation: 69-64=5 Exploring Operation: 12+64=76, Resulting Numbers: [69, 76] Generated Node #0,2,4: 50:[69, 76] Operation: 12+64=76 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 50:[12, 5], Operations: ['74-10=64', '69-64=5'] Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 50:[69, 52], Operations: ['74-10=64', '64-12=52'] Exploring Operation: 69*52=3588, Resulting Numbers: [3588] 3588,50 unequal: No Solution Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 69+52=121, Resulting Numbers: [121] 121,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 50:[64, 57], Operations: ['74-10=64', '69-12=57'] Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 64*57=3648, Resulting Numbers: [3648] 3648,50 unequal: No Solution Exploring Operation: 64+57=121, Resulting Numbers: [121] 121,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 50:[64, 81], Operations: ['74-10=64', '69+12=81'] Exploring Operation: 81-64=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 64*81=5184, Resulting Numbers: [5184] 5184,50 unequal: No Solution Exploring Operation: 64+81=145, Resulting Numbers: [145] 145,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 50:[69, 76], Operations: ['74-10=64', '12+64=76'] Exploring Operation: 76-69=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 69+76=145, Resulting Numbers: [145] 145,50 unequal: No Solution Exploring Operation: 69*76=5244, Resulting Numbers: [5244] 5244,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,1 Current State: 50:[5, 2], Operations: ['74-69=5', '12-10=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,50 unequal: No Solution Moving to Node #0,4,2 Current State: 50:[10, 7], Operations: ['74-69=5', '12-5=7'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,50 unequal: No Solution Moving to Node #0,4,0 Current State: 50:[12, 5], Operations: ['74-69=5', '10-5=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,50 unequal: No Solution Moving to Node #0,4,4 Current State: 50:[12, 50], Operations: ['74-69=5', '10*5=50'] Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,50 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,50 unequal: No Solution Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,50 unequal: No Solution Moving to Node #0,4,3 Current State: 50:[12, 2], Operations: ['74-69=5', '10/5=2'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,50 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[12, 15], Operations: ['69-10=59', '74-59=15'] Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,50 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,50 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,50 unequal: No Solution Moving to Node #0,0,3 Current State: 50:[59, 62], Operations: ['69-10=59', '74-12=62'] Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,50 unequal: No Solution Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,50 unequal: No Solution Moving to Node #0,0,4 Current State: 50:[74, 47], Operations: ['69-10=59', '59-12=47'] Exploring Operation: 74+47=121, Resulting Numbers: [121] 121,50 unequal: No Solution Exploring Operation: 74*47=3478, Resulting Numbers: [3478] 3478,50 unequal: No Solution Exploring Operation: 74-47=27, Resulting Numbers: [27] 27,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[74, 71], Operations: ['69-10=59', '12+59=71'] Exploring Operation: 74+71=145, Resulting Numbers: [145] 145,50 unequal: No Solution Exploring Operation: 74*71=5254, Resulting Numbers: [5254] 5254,50 unequal: No Solution Exploring Operation: 74-71=3, Resulting Numbers: [3] 3,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[59, 86], Operations: ['69-10=59', '74+12=86'] Exploring Operation: 59+86=145, Resulting Numbers: [145] 145,50 unequal: No Solution Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,50 unequal: No Solution Exploring Operation: 59*86=5074, Resulting Numbers: [5074] 5074,50 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 26, 74, 20, 23 ]
51
[ "74-26=48", "23-20=3", "48+3=51" ]
Current State: 51:[26, 74, 20, 23], Operations: [] Exploring Operation: 74-26=48, Resulting Numbers: [20, 23, 48] Generated Node #2: [20, 23, 48] from Operation: 74-26=48 Current State: 51:[20, 23, 48], Operations: ['74-26=48'] Exploring Operation: 23-20=3, Resulting Numbers: [48, 3] Generated Node #3: [48, 3] from Operation: 23-20=3 Current State: 51:[48, 3], Operations: ['74-26=48', '23-20=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[26, 74, 20, 23], Operations: [] Exploring Operation: 74-20=54, Resulting Numbers: [26, 23, 54] Generated Node #0,0: 51:[26, 23, 54] Operation: 74-20=54 Exploring Operation: 74-26=48, Resulting Numbers: [20, 23, 48] Generated Node #0,1: 51:[20, 23, 48] Operation: 74-26=48 Exploring Operation: 74-23=51, Resulting Numbers: [26, 20, 51] Generated Node #0,2: 51:[26, 20, 51] Operation: 74-23=51 Moving to Node #0,1 Current State: 51:[20, 23, 48], Operations: ['74-26=48'] Exploring Operation: 48-23=25, Resulting Numbers: [20, 25] Generated Node #0,1,0: 51:[20, 25] Operation: 48-23=25 Exploring Operation: 20+23=43, Resulting Numbers: [48, 43] Generated Node #0,1,1: 51:[48, 43] Operation: 20+23=43 Exploring Operation: 23-20=3, Resulting Numbers: [48, 3] Generated Node #0,1,2: 51:[48, 3] Operation: 23-20=3 Moving to Node #0,2 Current State: 51:[26, 20, 51], Operations: ['74-23=51'] Exploring Operation: 26+20=46, Resulting Numbers: [51, 46] Generated Node #0,2,0: 51:[51, 46] Operation: 26+20=46 Exploring Operation: 26-20=6, Resulting Numbers: [51, 6] Generated Node #0,2,1: 51:[51, 6] Operation: 26-20=6 Exploring Operation: 51-26=25, Resulting Numbers: [20, 25] Generated Node #0,2,2: 51:[20, 25] Operation: 51-26=25 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[51, 6], Operations: ['74-23=51', '26-20=6'] Exploring Operation: 51*6=306, Resulting Numbers: [306] 306,51 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 51:[51, 46], Operations: ['74-23=51', '26+20=46'] Exploring Operation: 51+46=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 51-46=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 51*46=2346, Resulting Numbers: [2346] 2346,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 51:[20, 25], Operations: ['74-23=51', '51-26=25'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,51 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 51:[26, 23, 54], Operations: ['74-20=54'] Exploring Operation: 54-26=28, Resulting Numbers: [23, 28] Generated Node #0,0,0: 51:[23, 28] Operation: 54-26=28 Exploring Operation: 26-23=3, Resulting Numbers: [54, 3] Generated Node #0,0,1: 51:[54, 3] Operation: 26-23=3 Exploring Operation: 26+23=49, Resulting Numbers: [54, 49] Generated Node #0,0,2: 51:[54, 49] Operation: 26+23=49 Moving to Node #0,1,2 Current State: 51:[48, 3], Operations: ['74-26=48', '23-20=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[26, 74, 20, 23], Operations: [] Exploring Operation: 74-26=48, Resulting Numbers: [20, 23, 48] Generated Node #0,1: 51:[20, 23, 48] Operation: 74-26=48 Moving to Node #0,1 Current State: 51:[20, 23, 48], Operations: ['74-26=48'] Exploring Operation: 23-20=3, Resulting Numbers: [48, 3] Generated Node #0,1,2: 51:[48, 3] Operation: 23-20=3 Moving to Node #0,1,2 Current State: 51:[48, 3], Operations: ['74-26=48', '23-20=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
0.977431
hs_3
mult_heuristic
[ 2, 61, 61, 57 ]
67
[ "2+61=63", "61-57=4", "63+4=67" ]
Current State: 67:[2, 61, 61, 57], Operations: [] Exploring Operation: 2+61=63, Resulting Numbers: [57, 63] Generated Node #2: [57, 63] from Operation: 2+61=63 Current State: 67:[57, 63], Operations: ['2+61=63'] Exploring Operation: 61-57=4, Resulting Numbers: [63, 4] Generated Node #3: [63, 4] from Operation: 61-57=4 Current State: 67:[63, 4], Operations: ['2+61=63', '61-57=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[2, 61, 61, 57], Operations: [] Exploring Operation: 2+61=63, Resulting Numbers: [61, 57, 63] Generated Node #0,0: 67:[61, 57, 63] Operation: 2+61=63 Exploring Operation: 2+61=63, Resulting Numbers: [61, 57, 63] Generated Node #0,1: 67:[61, 57, 63] Operation: 2+61=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[61, 57, 63], Operations: ['2+61=63'] Exploring Operation: 57+63=120, Resulting Numbers: [61, 120] Generated Node #0,0,0: 67:[61, 120] Operation: 57+63=120 Exploring Operation: 61+57=118, Resulting Numbers: [63, 118] Generated Node #0,0,1: 67:[63, 118] Operation: 61+57=118 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 67:[63, 118], Operations: ['2+61=63', '61+57=118'] Exploring Operation: 63+118=181, Resulting Numbers: [181] 181,67 unequal: No Solution Exploring Operation: 118-63=55, Resulting Numbers: [55] 55,67 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:[61, 120], Operations: ['2+61=63', '57+63=120'] Exploring Operation: 61+120=181, Resulting Numbers: [181] 181,67 unequal: No Solution Exploring Operation: 120-61=59, Resulting Numbers: [59] 59,67 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:[61, 57, 63], Operations: ['2+61=63'] Exploring Operation: 57+63=120, Resulting Numbers: [61, 120] Generated Node #0,1,0: 67:[61, 120] Operation: 57+63=120 Exploring Operation: 61+57=118, Resulting Numbers: [63, 118] Generated Node #0,1,1: 67:[63, 118] Operation: 61+57=118 Moving to Node #0,1,1 Current State: 67:[63, 118], Operations: ['2+61=63', '61+57=118'] Exploring Operation: 118-63=55, Resulting Numbers: [55] 55,67 unequal: No Solution Exploring Operation: 63+118=181, Resulting Numbers: [181] 181,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[61, 120], Operations: ['2+61=63', '57+63=120'] Exploring Operation: 61+120=181, Resulting Numbers: [181] 181,67 unequal: No Solution Exploring Operation: 120-61=59, Resulting Numbers: [59] 59,67 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
[ 66, 1, 13, 7 ]
33
[ "66*7=462", "1+13=14", "462/14=33" ]
Current State: 33:[66, 1, 13, 7], Operations: [] Exploring Operation: 66*7=462, Resulting Numbers: [1, 13, 462] Generated Node #2: [1, 13, 462] from Operation: 66*7=462 Current State: 33:[1, 13, 462], Operations: ['66*7=462'] Exploring Operation: 1+13=14, Resulting Numbers: [462, 14] Generated Node #3: [462, 14] from Operation: 1+13=14 Current State: 33:[462, 14], Operations: ['66*7=462', '1+13=14'] Exploring Operation: 462/14=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[66, 1, 13, 7], Operations: [] Exploring Operation: 66-13=53, Resulting Numbers: [1, 7, 53] Generated Node #0,0: 33:[1, 7, 53] Operation: 66-13=53 Exploring Operation: 66-7=59, Resulting Numbers: [1, 13, 59] Generated Node #0,1: 33:[1, 13, 59] Operation: 66-7=59 Exploring Operation: 66-1=65, Resulting Numbers: [13, 7, 65] Generated Node #0,2: 33:[13, 7, 65] Operation: 66-1=65 Moving to Node #0,0 Current State: 33:[1, 7, 53], Operations: ['66-13=53'] Exploring Operation: 53-7=46, Resulting Numbers: [1, 46] Generated Node #0,0,0: 33:[1, 46] Operation: 53-7=46 Exploring Operation: 7-1=6, Resulting Numbers: [53, 6] Generated Node #0,0,1: 33:[53, 6] Operation: 7-1=6 Exploring Operation: 1+7=8, Resulting Numbers: [53, 8] Generated Node #0,0,2: 33:[53, 8] Operation: 1+7=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[1, 46], Operations: ['66-13=53', '53-7=46'] Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 1*46=46, Resulting Numbers: [46] 46,33 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:[53, 6], Operations: ['66-13=53', '7-1=6'] Exploring Operation: 53+6=59, Resulting Numbers: [59] 59,33 unequal: No Solution Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,33 unequal: No Solution Exploring Operation: 53*6=318, Resulting Numbers: [318] 318,33 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 #0,0,2 Current State: 33:[53, 8], Operations: ['66-13=53', '1+7=8'] Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,33 unequal: No Solution Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,33 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,33 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: 33:[1, 13, 59], Operations: ['66-7=59'] Exploring Operation: 59-13=46, Resulting Numbers: [1, 46] Generated Node #0,1,0: 33:[1, 46] Operation: 59-13=46 Exploring Operation: 59-1=58, Resulting Numbers: [13, 58] Generated Node #0,1,1: 33:[13, 58] Operation: 59-1=58 Exploring Operation: 13-1=12, Resulting Numbers: [59, 12] Generated Node #0,1,2: 33:[59, 12] Operation: 13-1=12 Moving to Node #0,2 Current State: 33:[13, 7, 65], Operations: ['66-1=65'] Exploring Operation: 65-13=52, Resulting Numbers: [7, 52] Generated Node #0,2,0: 33:[7, 52] Operation: 65-13=52 Exploring Operation: 65/13=5, Resulting Numbers: [7, 5] Generated Node #0,2,1: 33:[7, 5] Operation: 65/13=5 Exploring Operation: 65-7=58, Resulting Numbers: [13, 58] Generated Node #0,2,2: 33:[13, 58] Operation: 65-7=58 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 33:[7, 5], Operations: ['66-1=65', '65/13=5'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,33 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 33:[7, 52], Operations: ['66-1=65', '65-13=52'] Exploring Operation: 7*52=364, Resulting Numbers: [364] 364,33 unequal: No Solution Exploring Operation: 7+52=59, Resulting Numbers: [59] 59,33 unequal: No Solution Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 33:[13, 58], Operations: ['66-1=65', '65-7=58'] Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,33 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,33 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: 33:[1, 46], Operations: ['66-7=59', '59-13=46'] Exploring Operation: 1*46=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[13, 58], Operations: ['66-7=59', '59-1=58'] Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,33 unequal: No Solution Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,33 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[59, 12], Operations: ['66-7=59', '13-1=12'] Exploring Operation: 59-12=47, Resulting Numbers: [47] 47,33 unequal: No Solution Exploring Operation: 59+12=71, Resulting Numbers: [71] 71,33 unequal: No Solution Exploring Operation: 59*12=708, Resulting Numbers: [708] 708,33 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 79, 4, 43, 47 ]
95
[ "47-43=4", "4*4=16", "79+16=95" ]
Current State: 95:[79, 4, 43, 47], Operations: [] Exploring Operation: 47-43=4, Resulting Numbers: [79, 4, 4] Generated Node #2: [79, 4, 4] from Operation: 47-43=4 Current State: 95:[79, 4, 4], Operations: ['47-43=4'] Exploring Operation: 4*4=16, Resulting Numbers: [79, 16] Generated Node #3: [79, 16] from Operation: 4*4=16 Current State: 95:[79, 16], Operations: ['47-43=4', '4*4=16'] Exploring Operation: 79+16=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[79, 4, 43, 47], Operations: [] Exploring Operation: 43+47=90, Resulting Numbers: [79, 4, 90] Generated Node #0,0: 95:[79, 4, 90] Operation: 43+47=90 Exploring Operation: 47-43=4, Resulting Numbers: [79, 4, 4] Generated Node #0,1: 95:[79, 4, 4] Operation: 47-43=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[79, 4, 4], Operations: ['47-43=4'] Exploring Operation: 79+4=83, Resulting Numbers: [4, 83] Generated Node #0,1,0: 95:[4, 83] Operation: 79+4=83 Exploring Operation: 79+4=83, Resulting Numbers: [4, 83] Generated Node #0,1,1: 95:[4, 83] Operation: 79+4=83 Moving to Node #0,1,0 Current State: 95:[4, 83], Operations: ['47-43=4', '79+4=83'] Exploring Operation: 4+83=87, Resulting Numbers: [87] 87,95 unequal: No Solution Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[4, 83], Operations: ['47-43=4', '79+4=83'] Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 4+83=87, Resulting Numbers: [87] 87,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[79, 4, 90], Operations: ['43+47=90'] Exploring Operation: 90-79=11, Resulting Numbers: [4, 11] Generated Node #0,0,0: 95:[4, 11] Operation: 90-79=11 Exploring Operation: 79+4=83, Resulting Numbers: [90, 83] Generated Node #0,0,1: 95:[90, 83] Operation: 79+4=83 Moving to Node #0,0,0 Current State: 95:[4, 11], Operations: ['43+47=90', '90-79=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[90, 83], Operations: ['43+47=90', '79+4=83'] Exploring Operation: 90+83=173, Resulting Numbers: [173] 173,95 unequal: No Solution Exploring Operation: 90-83=7, Resulting Numbers: [7] 7,95 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
[ 37, 28, 3, 10 ]
24
[ "37+3=40", "40/10=4", "28-4=24" ]
Current State: 24:[37, 28, 3, 10], Operations: [] Exploring Operation: 37+3=40, Resulting Numbers: [28, 10, 40] Generated Node #2: [28, 10, 40] from Operation: 37+3=40 Current State: 24:[28, 10, 40], Operations: ['37+3=40'] Exploring Operation: 40/10=4, Resulting Numbers: [28, 4] Generated Node #3: [28, 4] from Operation: 40/10=4 Current State: 24:[28, 4], Operations: ['37+3=40', '40/10=4'] Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[37, 28, 3, 10], Operations: [] Exploring Operation: 37-28=9, Resulting Numbers: [3, 10, 9] Generated Node #0,0: 24:[3, 10, 9] Operation: 37-28=9 Exploring Operation: 37-10=27, Resulting Numbers: [28, 3, 27] Generated Node #0,1: 24:[28, 3, 27] Operation: 37-10=27 Exploring Operation: 37-3=34, Resulting Numbers: [28, 10, 34] Generated Node #0,2: 24:[28, 10, 34] Operation: 37-3=34 Moving to Node #0,0 Current State: 24:[3, 10, 9], Operations: ['37-28=9'] Exploring Operation: 10-3=7, Resulting Numbers: [9, 7] Generated Node #0,0,0: 24:[9, 7] Operation: 10-3=7 Exploring Operation: 10-9=1, Resulting Numbers: [3, 1] Generated Node #0,0,1: 24:[3, 1] Operation: 10-9=1 Exploring Operation: 3+10=13, Resulting Numbers: [9, 13] Generated Node #0,0,2: 24:[9, 13] Operation: 3+10=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[3, 1], Operations: ['37-28=9', '10-9=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[9, 7], Operations: ['37-28=9', '10-3=7'] Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[9, 13], Operations: ['37-28=9', '3+10=13'] Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,24 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 24:[28, 3, 27], Operations: ['37-10=27'] Exploring Operation: 28-27=1, Resulting Numbers: [3, 1] Generated Node #0,1,0: 24:[3, 1] Operation: 28-27=1 Exploring Operation: 27-3=24, Resulting Numbers: [28, 24] Generated Node #0,1,1: 24:[28, 24] Operation: 27-3=24 Exploring Operation: 28-3=25, Resulting Numbers: [27, 25] Generated Node #0,1,2: 24:[27, 25] Operation: 28-3=25 Moving to Node #0,2 Current State: 24:[28, 10, 34], Operations: ['37-3=34'] Exploring Operation: 34-28=6, Resulting Numbers: [10, 6] Generated Node #0,2,0: 24:[10, 6] Operation: 34-28=6 Exploring Operation: 34-10=24, Resulting Numbers: [28, 24] Generated Node #0,2,1: 24:[28, 24] Operation: 34-10=24 Exploring Operation: 28-10=18, Resulting Numbers: [34, 18] Generated Node #0,2,2: 24:[34, 18] Operation: 28-10=18 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 24:[10, 6], Operations: ['37-3=34', '34-28=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,24 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 24:[28, 24], Operations: ['37-3=34', '34-10=24'] Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,24 unequal: No Solution Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 24:[34, 18], Operations: ['37-3=34', '28-10=18'] Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,24 unequal: No Solution Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 34*18=612, Resulting Numbers: [612] 612,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 24:[3, 1], Operations: ['37-10=27', '28-27=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[28, 24], Operations: ['37-10=27', '27-3=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,24 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[27, 25], Operations: ['37-10=27', '28-3=25'] Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,24 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 3, 47, 58, 7 ]
64
[ "58-7=51", "51/3=17", "47+17=64" ]
Current State: 64:[3, 47, 58, 7], Operations: [] Exploring Operation: 58-7=51, Resulting Numbers: [3, 47, 51] Generated Node #2: [3, 47, 51] from Operation: 58-7=51 Current State: 64:[3, 47, 51], Operations: ['58-7=51'] Exploring Operation: 51/3=17, Resulting Numbers: [47, 17] Generated Node #3: [47, 17] from Operation: 51/3=17 Current State: 64:[47, 17], Operations: ['58-7=51', '51/3=17'] Exploring Operation: 47+17=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[3, 47, 58, 7], Operations: [] Exploring Operation: 58-47=11, Resulting Numbers: [3, 7, 11] Generated Node #0,0: 64:[3, 7, 11] Operation: 58-47=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[3, 7, 11], Operations: ['58-47=11'] Exploring Operation: 11-3=8, Resulting Numbers: [7, 8] Generated Node #0,0,0: 64:[7, 8] Operation: 11-3=8 Moving to Node #0,0,0 Current State: 64:[7, 8], Operations: ['58-47=11', '11-3=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,64 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
[ 33, 15, 91, 13 ]
86
[ "33-15=18", "91+13=104", "104-18=86" ]
Current State: 86:[33, 15, 91, 13], Operations: [] Exploring Operation: 33-15=18, Resulting Numbers: [91, 13, 18] Generated Node #2: [91, 13, 18] from Operation: 33-15=18 Current State: 86:[91, 13, 18], Operations: ['33-15=18'] Exploring Operation: 91+13=104, Resulting Numbers: [18, 104] Generated Node #3: [18, 104] from Operation: 91+13=104 Current State: 86:[18, 104], Operations: ['33-15=18', '91+13=104'] Exploring Operation: 104-18=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[33, 15, 91, 13], Operations: [] Exploring Operation: 33+15=48, Resulting Numbers: [91, 13, 48] Generated Node #0,0: 86:[91, 13, 48] Operation: 33+15=48 Exploring Operation: 15-13=2, Resulting Numbers: [33, 91, 2] Generated Node #0,1: 86:[33, 91, 2] Operation: 15-13=2 Moving to Node #0,1 Current State: 86:[33, 91, 2], Operations: ['15-13=2'] Exploring Operation: 33+2=35, Resulting Numbers: [91, 35] Generated Node #0,1,0: 86:[91, 35] Operation: 33+2=35 Exploring Operation: 91-2=89, Resulting Numbers: [33, 89] Generated Node #0,1,1: 86:[33, 89] Operation: 91-2=89 Moving to Node #0,0 Current State: 86:[91, 13, 48], Operations: ['33+15=48'] Exploring Operation: 91-48=43, Resulting Numbers: [13, 43] Generated Node #0,0,0: 86:[13, 43] Operation: 91-48=43 Exploring Operation: 91/13=7, Resulting Numbers: [48, 7] Generated Node #0,0,1: 86:[48, 7] Operation: 91/13=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[48, 7], Operations: ['33+15=48', '91/13=7'] Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,86 unequal: No Solution Exploring Operation: 48+7=55, Resulting Numbers: [55] 55,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[13, 43], Operations: ['33+15=48', '91-48=43'] Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,86 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: 86:[91, 35], Operations: ['15-13=2', '33+2=35'] Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 91+35=126, Resulting Numbers: [126] 126,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[33, 89], Operations: ['15-13=2', '91-2=89'] Exploring Operation: 89-33=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 33+89=122, Resulting Numbers: [122] 122,86 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 92, 93, 93, 63 ]
30
[ "93-92=1", "93-63=30", "1*30=30" ]
Current State: 30:[92, 93, 93, 63], Operations: [] Exploring Operation: 93-92=1, Resulting Numbers: [63, 1] Generated Node #2: [63, 1] from Operation: 93-92=1 Current State: 30:[63, 1], Operations: ['93-92=1'] Exploring Operation: 93-63=30, Resulting Numbers: [1, 30] Generated Node #3: [1, 30] from Operation: 93-63=30 Current State: 30:[1, 30], Operations: ['93-92=1', '93-63=30'] Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[92, 93, 93, 63], Operations: [] Exploring Operation: 93-92=1, Resulting Numbers: [93, 63, 1] Generated Node #0,0: 30:[93, 63, 1] Operation: 93-92=1 Exploring Operation: 93/93=1, Resulting Numbers: [92, 63, 1] Generated Node #0,1: 30:[92, 63, 1] Operation: 93/93=1 Exploring Operation: 93-92=1, Resulting Numbers: [93, 63, 1] Generated Node #0,2: 30:[93, 63, 1] Operation: 93-92=1 Moving to Node #0,1 Current State: 30:[92, 63, 1], Operations: ['93/93=1'] Exploring Operation: 92-1=91, Resulting Numbers: [63, 91] Generated Node #0,1,0: 30:[63, 91] Operation: 92-1=91 Exploring Operation: 63-1=62, Resulting Numbers: [92, 62] Generated Node #0,1,1: 30:[92, 62] Operation: 63-1=62 Exploring Operation: 92-63=29, Resulting Numbers: [1, 29] Generated Node #0,1,2: 30:[1, 29] Operation: 92-63=29 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[1, 29], Operations: ['93/93=1', '92-63=29'] Exploring Operation: 1+29=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[92, 93, 93, 63], Operations: [] Exploring Operation: 93/93=1, Resulting Numbers: [92, 63, 1] Generated Node #0,1: 30:[92, 63, 1] Operation: 93/93=1 Moving to Node #0,1 Current State: 30:[92, 63, 1], Operations: ['93/93=1'] Exploring Operation: 92-63=29, Resulting Numbers: [1, 29] Generated Node #0,1,2: 30:[1, 29] Operation: 92-63=29 Moving to Node #0,1,2 Current State: 30:[1, 29], Operations: ['93/93=1', '92-63=29'] Exploring Operation: 1+29=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 80, 36, 87, 32 ]
67
[ "36-32=4", "80/4=20", "87-20=67" ]
Current State: 67:[80, 36, 87, 32], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [80, 87, 4] Generated Node #2: [80, 87, 4] from Operation: 36-32=4 Current State: 67:[80, 87, 4], Operations: ['36-32=4'] Exploring Operation: 80/4=20, Resulting Numbers: [87, 20] Generated Node #3: [87, 20] from Operation: 80/4=20 Current State: 67:[87, 20], Operations: ['36-32=4', '80/4=20'] Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[80, 36, 87, 32], Operations: [] Exploring Operation: 87-36=51, Resulting Numbers: [80, 32, 51] Generated Node #0,0: 67:[80, 32, 51] Operation: 87-36=51 Exploring Operation: 80-32=48, Resulting Numbers: [36, 87, 48] Generated Node #0,1: 67:[36, 87, 48] Operation: 80-32=48 Exploring Operation: 87-32=55, Resulting Numbers: [80, 36, 55] Generated Node #0,2: 67:[80, 36, 55] Operation: 87-32=55 Exploring Operation: 36+32=68, Resulting Numbers: [80, 87, 68] Generated Node #0,3: 67:[80, 87, 68] Operation: 36+32=68 Start Sub Search at level 1: Moving to Node #0,3 Current State: 67:[80, 87, 68], Operations: ['36+32=68'] Exploring Operation: 80-68=12, Resulting Numbers: [87, 12] Generated Node #0,3,0: 67:[87, 12] Operation: 80-68=12 Exploring Operation: 87-80=7, Resulting Numbers: [68, 7] Generated Node #0,3,1: 67:[68, 7] Operation: 87-80=7 Exploring Operation: 80+87=167, Resulting Numbers: [68, 167] Generated Node #0,3,2: 67:[68, 167] Operation: 80+87=167 Exploring Operation: 87-68=19, Resulting Numbers: [80, 19] Generated Node #0,3,3: 67:[80, 19] Operation: 87-68=19 Moving to Node #0,3,1 Current State: 67:[68, 7], Operations: ['36+32=68', '87-80=7'] Exploring Operation: 68+7=75, Resulting Numbers: [75] 75,67 unequal: No Solution Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 68*7=476, Resulting Numbers: [476] 476,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[80, 19], Operations: ['36+32=68', '87-68=19'] Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 80+19=99, Resulting Numbers: [99] 99,67 unequal: No Solution Exploring Operation: 80*19=1520, Resulting Numbers: [1520] 1520,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[87, 12], Operations: ['36+32=68', '80-68=12'] Exploring Operation: 87+12=99, Resulting Numbers: [99] 99,67 unequal: No Solution Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,67 unequal: No Solution Exploring Operation: 87*12=1044, Resulting Numbers: [1044] 1044,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[68, 167], Operations: ['36+32=68', '80+87=167'] Exploring Operation: 68+167=235, Resulting Numbers: [235] 235,67 unequal: No Solution Exploring Operation: 68*167=11356, Resulting Numbers: [11356] 11356,67 unequal: No Solution Exploring Operation: 167-68=99, Resulting Numbers: [99] 99,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 67:[80, 36, 55], Operations: ['87-32=55'] Exploring Operation: 55-36=19, Resulting Numbers: [80, 19] Generated Node #0,2,0: 67:[80, 19] Operation: 55-36=19 Exploring Operation: 36+55=91, Resulting Numbers: [80, 91] Generated Node #0,2,1: 67:[80, 91] Operation: 36+55=91 Exploring Operation: 80+36=116, Resulting Numbers: [55, 116] Generated Node #0,2,2: 67:[55, 116] Operation: 80+36=116 Exploring Operation: 80-36=44, Resulting Numbers: [55, 44] Generated Node #0,2,3: 67:[55, 44] Operation: 80-36=44 Moving to Node #0,2,3 Current State: 67:[55, 44], Operations: ['87-32=55', '80-36=44'] Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 55*44=2420, Resulting Numbers: [2420] 2420,67 unequal: No Solution Exploring Operation: 55+44=99, Resulting Numbers: [99] 99,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[80, 91], Operations: ['87-32=55', '36+55=91'] Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 80*91=7280, Resulting Numbers: [7280] 7280,67 unequal: No Solution Exploring Operation: 80+91=171, Resulting Numbers: [171] 171,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[55, 116], Operations: ['87-32=55', '80+36=116'] Exploring Operation: 55*116=6380, Resulting Numbers: [6380] 6380,67 unequal: No Solution Exploring Operation: 55+116=171, Resulting Numbers: [171] 171,67 unequal: No Solution Exploring Operation: 116-55=61, Resulting Numbers: [61] 61,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[80, 19], Operations: ['87-32=55', '55-36=19'] Exploring Operation: 80*19=1520, Resulting Numbers: [1520] 1520,67 unequal: No Solution Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 80+19=99, Resulting Numbers: [99] 99,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[80, 32, 51], Operations: ['87-36=51'] Exploring Operation: 80+32=112, Resulting Numbers: [51, 112] Generated Node #0,0,0: 67:[51, 112] Operation: 80+32=112 Exploring Operation: 32+51=83, Resulting Numbers: [80, 83] Generated Node #0,0,1: 67:[80, 83] Operation: 32+51=83 Exploring Operation: 51-32=19, Resulting Numbers: [80, 19] Generated Node #0,0,2: 67:[80, 19] Operation: 51-32=19 Exploring Operation: 80-32=48, Resulting Numbers: [51, 48] Generated Node #0,0,3: 67:[51, 48] Operation: 80-32=48 Moving to Node #0,0,1 Current State: 67:[80, 83], Operations: ['87-36=51', '32+51=83'] Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 80*83=6640, Resulting Numbers: [6640] 6640,67 unequal: No Solution Exploring Operation: 80+83=163, Resulting Numbers: [163] 163,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[51, 48], Operations: ['87-36=51', '80-32=48'] Exploring Operation: 51*48=2448, Resulting Numbers: [2448] 2448,67 unequal: No Solution Exploring Operation: 51+48=99, Resulting Numbers: [99] 99,67 unequal: No Solution Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[80, 19], Operations: ['87-36=51', '51-32=19'] Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 80*19=1520, Resulting Numbers: [1520] 1520,67 unequal: No Solution Exploring Operation: 80+19=99, Resulting Numbers: [99] 99,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[51, 112], Operations: ['87-36=51', '80+32=112'] Exploring Operation: 112-51=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 51*112=5712, Resulting Numbers: [5712] 5712,67 unequal: No Solution Exploring Operation: 51+112=163, Resulting Numbers: [163] 163,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[36, 87, 48], Operations: ['80-32=48'] Exploring Operation: 87-48=39, Resulting Numbers: [36, 39] Generated Node #0,1,0: 67:[36, 39] Operation: 87-48=39 Exploring Operation: 36+87=123, Resulting Numbers: [48, 123] Generated Node #0,1,1: 67:[48, 123] Operation: 36+87=123 Exploring Operation: 36+48=84, Resulting Numbers: [87, 84] Generated Node #0,1,2: 67:[87, 84] Operation: 36+48=84 Exploring Operation: 87-36=51, Resulting Numbers: [48, 51] Generated Node #0,1,3: 67:[48, 51] Operation: 87-36=51 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 67:[48, 51], Operations: ['80-32=48', '87-36=51'] Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 48*51=2448, Resulting Numbers: [2448] 2448,67 unequal: No Solution Exploring Operation: 48+51=99, Resulting Numbers: [99] 99,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 67:[87, 84], Operations: ['80-32=48', '36+48=84'] Exploring Operation: 87*84=7308, Resulting Numbers: [7308] 7308,67 unequal: No Solution Exploring Operation: 87+84=171, Resulting Numbers: [171] 171,67 unequal: No Solution Exploring Operation: 87-84=3, Resulting Numbers: [3] 3,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 67:[36, 39], Operations: ['80-32=48', '87-48=39'] Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 36+39=75, Resulting Numbers: [75] 75,67 unequal: No Solution Exploring Operation: 36*39=1404, Resulting Numbers: [1404] 1404,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 67:[48, 123], Operations: ['80-32=48', '36+87=123'] Exploring Operation: 48+123=171, Resulting Numbers: [171] 171,67 unequal: No Solution Exploring Operation: 48*123=5904, Resulting Numbers: [5904] 5904,67 unequal: No Solution Exploring Operation: 123-48=75, Resulting Numbers: [75] 75,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 84, 22, 69, 90 ]
18
[ "90-69=21", "84/21=4", "22-4=18" ]
Current State: 18:[84, 22, 69, 90], Operations: [] Exploring Operation: 90-69=21, Resulting Numbers: [84, 22, 21] Generated Node #2: [84, 22, 21] from Operation: 90-69=21 Current State: 18:[84, 22, 21], Operations: ['90-69=21'] Exploring Operation: 84/21=4, Resulting Numbers: [22, 4] Generated Node #3: [22, 4] from Operation: 84/21=4 Current State: 18:[22, 4], Operations: ['90-69=21', '84/21=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[84, 22, 69, 90], Operations: [] Exploring Operation: 90-84=6, Resulting Numbers: [22, 69, 6] Generated Node #0,0: 18:[22, 69, 6] Operation: 90-84=6 Exploring Operation: 90-69=21, Resulting Numbers: [84, 22, 21] Generated Node #0,1: 18:[84, 22, 21] Operation: 90-69=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[22, 69, 6], Operations: ['90-84=6'] Exploring Operation: 69-6=63, Resulting Numbers: [22, 63] Generated Node #0,0,0: 18:[22, 63] Operation: 69-6=63 Exploring Operation: 69-22=47, Resulting Numbers: [6, 47] Generated Node #0,0,1: 18:[6, 47] Operation: 69-22=47 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 18:[6, 47], Operations: ['90-84=6', '69-22=47'] Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[22, 63], Operations: ['90-84=6', '69-6=63'] Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,18 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[84, 22, 21], Operations: ['90-69=21'] Exploring Operation: 84/21=4, Resulting Numbers: [22, 4] Generated Node #0,1,0: 18:[22, 4] Operation: 84/21=4 Exploring Operation: 84-22=62, Resulting Numbers: [21, 62] Generated Node #0,1,1: 18:[21, 62] Operation: 84-22=62 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 18:[22, 4], Operations: ['90-69=21', '84/21=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[84, 22, 69, 90], Operations: [] Exploring Operation: 90-69=21, Resulting Numbers: [84, 22, 21] Generated Node #0,1: 18:[84, 22, 21] Operation: 90-69=21 Moving to Node #0,1 Current State: 18:[84, 22, 21], Operations: ['90-69=21'] Exploring Operation: 84/21=4, Resulting Numbers: [22, 4] Generated Node #0,1,0: 18:[22, 4] Operation: 84/21=4 Moving to Node #0,1,0 Current State: 18:[22, 4], Operations: ['90-69=21', '84/21=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 29, 51, 2, 15 ]
59
[ "51-29=22", "2*22=44", "15+44=59" ]
Current State: 59:[29, 51, 2, 15], Operations: [] Exploring Operation: 51-29=22, Resulting Numbers: [2, 15, 22] Generated Node #2: [2, 15, 22] from Operation: 51-29=22 Current State: 59:[2, 15, 22], Operations: ['51-29=22'] Exploring Operation: 2*22=44, Resulting Numbers: [15, 44] Generated Node #3: [15, 44] from Operation: 2*22=44 Current State: 59:[15, 44], Operations: ['51-29=22', '2*22=44'] Exploring Operation: 15+44=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[29, 51, 2, 15], Operations: [] Exploring Operation: 29*2=58, Resulting Numbers: [51, 15, 58] Generated Node #0,0: 59:[51, 15, 58] Operation: 29*2=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[51, 15, 58], Operations: ['29*2=58'] Exploring Operation: 51+15=66, Resulting Numbers: [58, 66] Generated Node #0,0,0: 59:[58, 66] Operation: 51+15=66 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[58, 66], Operations: ['29*2=58', '51+15=66'] Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 3, 50, 69, 26 ]
99
[ "69/3=23", "50+26=76", "23+76=99" ]
Current State: 99:[3, 50, 69, 26], Operations: [] Exploring Operation: 69/3=23, Resulting Numbers: [50, 26, 23] Generated Node #2: [50, 26, 23] from Operation: 69/3=23 Current State: 99:[50, 26, 23], Operations: ['69/3=23'] Exploring Operation: 50+26=76, Resulting Numbers: [23, 76] Generated Node #3: [23, 76] from Operation: 50+26=76 Current State: 99:[23, 76], Operations: ['69/3=23', '50+26=76'] Exploring Operation: 23+76=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[3, 50, 69, 26], Operations: [] Exploring Operation: 69+26=95, Resulting Numbers: [3, 50, 95] Generated Node #0,0: 99:[3, 50, 95] Operation: 69+26=95 Exploring Operation: 69-50=19, Resulting Numbers: [3, 26, 19] Generated Node #0,1: 99:[3, 26, 19] Operation: 69-50=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[3, 26, 19], Operations: ['69-50=19'] Exploring Operation: 26-19=7, Resulting Numbers: [3, 7] Generated Node #0,1,0: 99:[3, 7] Operation: 26-19=7 Exploring Operation: 3+26=29, Resulting Numbers: [19, 29] Generated Node #0,1,1: 99:[19, 29] Operation: 3+26=29 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 99:[3, 7], Operations: ['69-50=19', '26-19=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,99 unequal: No Solution No 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: 99:[19, 29], Operations: ['69-50=19', '3+26=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[3, 50, 95], Operations: ['69+26=95'] Exploring Operation: 95-50=45, Resulting Numbers: [3, 45] Generated Node #0,0,0: 99:[3, 45] Operation: 95-50=45 Exploring Operation: 50-3=47, Resulting Numbers: [95, 47] Generated Node #0,0,1: 99:[95, 47] Operation: 50-3=47 Moving to Node #0,0,0 Current State: 99:[3, 45], Operations: ['69+26=95', '95-50=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[95, 47], Operations: ['69+26=95', '50-3=47'] Exploring Operation: 95-47=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 95+47=142, Resulting Numbers: [142] 142,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 22, 61, 4, 78 ]
71
[ "22*4=88", "78-61=17", "88-17=71" ]
Current State: 71:[22, 61, 4, 78], Operations: [] Exploring Operation: 22*4=88, Resulting Numbers: [61, 78, 88] Generated Node #2: [61, 78, 88] from Operation: 22*4=88 Current State: 71:[61, 78, 88], Operations: ['22*4=88'] Exploring Operation: 78-61=17, Resulting Numbers: [88, 17] Generated Node #3: [88, 17] from Operation: 78-61=17 Current State: 71:[88, 17], Operations: ['22*4=88', '78-61=17'] Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[22, 61, 4, 78], Operations: [] Exploring Operation: 22*4=88, Resulting Numbers: [61, 78, 88] Generated Node #0,0: 71:[61, 78, 88] Operation: 22*4=88 Exploring Operation: 22+4=26, Resulting Numbers: [61, 78, 26] Generated Node #0,1: 71:[61, 78, 26] Operation: 22+4=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[61, 78, 88], Operations: ['22*4=88'] Exploring Operation: 88-61=27, Resulting Numbers: [78, 27] Generated Node #0,0,0: 71:[78, 27] Operation: 88-61=27 Exploring Operation: 78-61=17, Resulting Numbers: [88, 17] Generated Node #0,0,1: 71:[88, 17] Operation: 78-61=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[78, 27], Operations: ['22*4=88', '88-61=27'] Exploring Operation: 78+27=105, Resulting Numbers: [105] 105,71 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[88, 17], Operations: ['22*4=88', '78-61=17'] Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[22, 61, 4, 78], Operations: [] Exploring Operation: 22*4=88, Resulting Numbers: [61, 78, 88] Generated Node #0,0: 71:[61, 78, 88] Operation: 22*4=88 Moving to Node #0,0 Current State: 71:[61, 78, 88], Operations: ['22*4=88'] Exploring Operation: 78-61=17, Resulting Numbers: [88, 17] Generated Node #0,0,1: 71:[88, 17] Operation: 78-61=17 Moving to Node #0,0,1 Current State: 71:[88, 17], Operations: ['22*4=88', '78-61=17'] Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 47, 52, 40, 60 ]
100
[ "52-47=5", "60-40=20", "5*20=100" ]
Current State: 100:[47, 52, 40, 60], Operations: [] Exploring Operation: 52-47=5, Resulting Numbers: [40, 60, 5] Generated Node #2: [40, 60, 5] from Operation: 52-47=5 Current State: 100:[40, 60, 5], Operations: ['52-47=5'] Exploring Operation: 60-40=20, Resulting Numbers: [5, 20] Generated Node #3: [5, 20] from Operation: 60-40=20 Current State: 100:[5, 20], Operations: ['52-47=5', '60-40=20'] Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[47, 52, 40, 60], Operations: [] Exploring Operation: 47-40=7, Resulting Numbers: [52, 60, 7] Generated Node #0,0: 100:[52, 60, 7] Operation: 47-40=7 Exploring Operation: 40+60=100, Resulting Numbers: [47, 52, 100] Generated Node #0,1: 100:[47, 52, 100] Operation: 40+60=100 Exploring Operation: 60-40=20, Resulting Numbers: [47, 52, 20] Generated Node #0,2: 100:[47, 52, 20] Operation: 60-40=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[47, 52, 100], Operations: ['40+60=100'] Exploring Operation: 47+52=99, Resulting Numbers: [100, 99] Generated Node #0,1,0: 100:[100, 99] Operation: 47+52=99 Exploring Operation: 52-47=5, Resulting Numbers: [100, 5] Generated Node #0,1,1: 100:[100, 5] Operation: 52-47=5 Exploring Operation: 100-47=53, Resulting Numbers: [52, 53] Generated Node #0,1,2: 100:[52, 53] Operation: 100-47=53 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[100, 5], Operations: ['40+60=100', '52-47=5'] Exploring Operation: 100/5=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 100+5=105, Resulting Numbers: [105] 105,100 unequal: No Solution Exploring Operation: 100-5=95, Resulting Numbers: [95] 95,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[100, 99], Operations: ['40+60=100', '47+52=99'] Exploring Operation: 100+99=199, Resulting Numbers: [199] 199,100 unequal: No Solution Exploring Operation: 100*99=9900, Resulting Numbers: [9900] 9900,100 unequal: No Solution Exploring Operation: 100-99=1, Resulting Numbers: [1] 1,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 100:[52, 53], Operations: ['40+60=100', '100-47=53'] Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,100 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[47, 52, 20], Operations: ['60-40=20'] Exploring Operation: 47-20=27, Resulting Numbers: [52, 27] Generated Node #0,2,0: 100:[52, 27] Operation: 47-20=27 Exploring Operation: 47+52=99, Resulting Numbers: [20, 99] Generated Node #0,2,1: 100:[20, 99] Operation: 47+52=99 Exploring Operation: 52-47=5, Resulting Numbers: [20, 5] Generated Node #0,2,2: 100:[20, 5] Operation: 52-47=5 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 100:[20, 5], Operations: ['60-40=20', '52-47=5'] Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[47, 52, 40, 60], Operations: [] Exploring Operation: 60-40=20, Resulting Numbers: [47, 52, 20] Generated Node #0,2: 100:[47, 52, 20] Operation: 60-40=20 Moving to Node #0,2 Current State: 100:[47, 52, 20], Operations: ['60-40=20'] Exploring Operation: 52-47=5, Resulting Numbers: [20, 5] Generated Node #0,2,2: 100:[20, 5] Operation: 52-47=5 Moving to Node #0,2,2 Current State: 100:[20, 5], Operations: ['60-40=20', '52-47=5'] Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 52, 82, 65, 81 ]
14
[ "82-52=30", "81-65=16", "30-16=14" ]
Current State: 14:[52, 82, 65, 81], Operations: [] Exploring Operation: 82-52=30, Resulting Numbers: [65, 81, 30] Generated Node #2: [65, 81, 30] from Operation: 82-52=30 Current State: 14:[65, 81, 30], Operations: ['82-52=30'] Exploring Operation: 81-65=16, Resulting Numbers: [30, 16] Generated Node #3: [30, 16] from Operation: 81-65=16 Current State: 14:[30, 16], Operations: ['82-52=30', '81-65=16'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[52, 82, 65, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [52, 65, 1] Generated Node #0,0: 14:[52, 65, 1] Operation: 82-81=1 Exploring Operation: 81-65=16, Resulting Numbers: [52, 82, 16] Generated Node #0,1: 14:[52, 82, 16] Operation: 81-65=16 Exploring Operation: 82-65=17, Resulting Numbers: [52, 81, 17] Generated Node #0,2: 14:[52, 81, 17] Operation: 82-65=17 Moving to Node #0,0 Current State: 14:[52, 65, 1], Operations: ['82-81=1'] Exploring Operation: 65-1=64, Resulting Numbers: [52, 64] Generated Node #0,0,0: 14:[52, 64] Operation: 65-1=64 Exploring Operation: 52-1=51, Resulting Numbers: [65, 51] Generated Node #0,0,1: 14:[65, 51] Operation: 52-1=51 Exploring Operation: 65-52=13, Resulting Numbers: [1, 13] Generated Node #0,0,2: 14:[1, 13] Operation: 65-52=13 Moving to Node #0,1 Current State: 14:[52, 82, 16], Operations: ['81-65=16'] Exploring Operation: 82-52=30, Resulting Numbers: [16, 30] Generated Node #0,1,0: 14:[16, 30] Operation: 82-52=30 Exploring Operation: 52-16=36, Resulting Numbers: [82, 36] Generated Node #0,1,1: 14:[82, 36] Operation: 52-16=36 Exploring Operation: 82-16=66, Resulting Numbers: [52, 66] Generated Node #0,1,2: 14:[52, 66] Operation: 82-16=66 Moving to Node #0,2 Current State: 14:[52, 81, 17], Operations: ['82-65=17'] Exploring Operation: 52-17=35, Resulting Numbers: [81, 35] Generated Node #0,2,0: 14:[81, 35] Operation: 52-17=35 Exploring Operation: 81-17=64, Resulting Numbers: [52, 64] Generated Node #0,2,1: 14:[52, 64] Operation: 81-17=64 Exploring Operation: 81-52=29, Resulting Numbers: [17, 29] Generated Node #0,2,2: 14:[17, 29] Operation: 81-52=29 Moving to Node #0,0,2 Current State: 14:[1, 13], Operations: ['82-81=1', '65-52=13'] Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[52, 82, 65, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [52, 65, 1] Generated Node #0,0: 14:[52, 65, 1] Operation: 82-81=1 Moving to Node #0,0 Current State: 14:[52, 65, 1], Operations: ['82-81=1'] Exploring Operation: 65-52=13, Resulting Numbers: [1, 13] Generated Node #0,0,2: 14:[1, 13] Operation: 65-52=13 Moving to Node #0,0,2 Current State: 14:[1, 13], Operations: ['82-81=1', '65-52=13'] Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.985243
hs_3
mult_heuristic
[ 69, 18, 4, 40 ]
97
[ "69+18=87", "40/4=10", "87+10=97" ]
Current State: 97:[69, 18, 4, 40], Operations: [] Exploring Operation: 69+18=87, Resulting Numbers: [4, 40, 87] Generated Node #2: [4, 40, 87] from Operation: 69+18=87 Current State: 97:[4, 40, 87], Operations: ['69+18=87'] Exploring Operation: 40/4=10, Resulting Numbers: [87, 10] Generated Node #3: [87, 10] from Operation: 40/4=10 Current State: 97:[87, 10], Operations: ['69+18=87', '40/4=10'] Exploring Operation: 87+10=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[69, 18, 4, 40], Operations: [] Exploring Operation: 18*4=72, Resulting Numbers: [69, 40, 72] Generated Node #0,0: 97:[69, 40, 72] Operation: 18*4=72 Exploring Operation: 69+18=87, Resulting Numbers: [4, 40, 87] Generated Node #0,1: 97:[4, 40, 87] Operation: 69+18=87 Moving to Node #0,0 Current State: 97:[69, 40, 72], Operations: ['18*4=72'] Exploring Operation: 69+40=109, Resulting Numbers: [72, 109] Generated Node #0,0,0: 97:[72, 109] Operation: 69+40=109 Exploring Operation: 40+72=112, Resulting Numbers: [69, 112] Generated Node #0,0,1: 97:[69, 112] Operation: 40+72=112 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[72, 109], Operations: ['18*4=72', '69+40=109'] Exploring Operation: 72+109=181, Resulting Numbers: [181] 181,97 unequal: No Solution Exploring Operation: 109-72=37, Resulting Numbers: [37] 37,97 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:[69, 112], Operations: ['18*4=72', '40+72=112'] Exploring Operation: 69+112=181, Resulting Numbers: [181] 181,97 unequal: No Solution Exploring Operation: 112-69=43, Resulting Numbers: [43] 43,97 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: 97:[4, 40, 87], Operations: ['69+18=87'] Exploring Operation: 4+87=91, Resulting Numbers: [40, 91] Generated Node #0,1,0: 97:[40, 91] Operation: 4+87=91 Exploring Operation: 4+40=44, Resulting Numbers: [87, 44] Generated Node #0,1,1: 97:[87, 44] Operation: 4+40=44 Moving to Node #0,1,0 Current State: 97:[40, 91], Operations: ['69+18=87', '4+87=91'] Exploring Operation: 40+91=131, Resulting Numbers: [131] 131,97 unequal: No Solution Exploring Operation: 91-40=51, Resulting Numbers: [51] 51,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[87, 44], Operations: ['69+18=87', '4+40=44'] Exploring Operation: 87+44=131, Resulting Numbers: [131] 131,97 unequal: No Solution Exploring Operation: 87-44=43, Resulting Numbers: [43] 43,97 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 91, 68, 37, 7 ]
67
[ "91-68=23", "37+7=44", "23+44=67" ]
Current State: 67:[91, 68, 37, 7], Operations: [] Exploring Operation: 91-68=23, Resulting Numbers: [37, 7, 23] Generated Node #2: [37, 7, 23] from Operation: 91-68=23 Current State: 67:[37, 7, 23], Operations: ['91-68=23'] Exploring Operation: 37+7=44, Resulting Numbers: [23, 44] Generated Node #3: [23, 44] from Operation: 37+7=44 Current State: 67:[23, 44], Operations: ['91-68=23', '37+7=44'] Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[91, 68, 37, 7], Operations: [] Exploring Operation: 37+7=44, Resulting Numbers: [91, 68, 44] Generated Node #0,0: 67:[91, 68, 44] Operation: 37+7=44 Exploring Operation: 68-7=61, Resulting Numbers: [91, 37, 61] Generated Node #0,1: 67:[91, 37, 61] Operation: 68-7=61 Exploring Operation: 91-7=84, Resulting Numbers: [68, 37, 84] Generated Node #0,2: 67:[68, 37, 84] Operation: 91-7=84 Moving to Node #0,0 Current State: 67:[91, 68, 44], Operations: ['37+7=44'] Exploring Operation: 91-44=47, Resulting Numbers: [68, 47] Generated Node #0,0,0: 67:[68, 47] Operation: 91-44=47 Exploring Operation: 68-44=24, Resulting Numbers: [91, 24] Generated Node #0,0,1: 67:[91, 24] Operation: 68-44=24 Exploring Operation: 91-68=23, Resulting Numbers: [44, 23] Generated Node #0,0,2: 67:[44, 23] Operation: 91-68=23 Moving to Node #0,2 Current State: 67:[68, 37, 84], Operations: ['91-7=84'] Exploring Operation: 68-37=31, Resulting Numbers: [84, 31] Generated Node #0,2,0: 67:[84, 31] Operation: 68-37=31 Exploring Operation: 84-37=47, Resulting Numbers: [68, 47] Generated Node #0,2,1: 67:[68, 47] Operation: 84-37=47 Exploring Operation: 68+37=105, Resulting Numbers: [84, 105] Generated Node #0,2,2: 67:[84, 105] Operation: 68+37=105 Moving to Node #0,1 Current State: 67:[91, 37, 61], Operations: ['68-7=61'] Exploring Operation: 37+61=98, Resulting Numbers: [91, 98] Generated Node #0,1,0: 67:[91, 98] Operation: 37+61=98 Exploring Operation: 91+37=128, Resulting Numbers: [61, 128] Generated Node #0,1,1: 67:[61, 128] Operation: 91+37=128 Exploring Operation: 91-37=54, Resulting Numbers: [61, 54] Generated Node #0,1,2: 67:[61, 54] Operation: 91-37=54 Moving to Node #0,1,2 Current State: 67:[61, 54], Operations: ['68-7=61', '91-37=54'] Exploring Operation: 61*54=3294, Resulting Numbers: [3294] 3294,67 unequal: No Solution Exploring Operation: 61-54=7, Resulting Numbers: [7] 7,67 unequal: No Solution Exploring Operation: 61+54=115, Resulting Numbers: [115] 115,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[68, 47], Operations: ['37+7=44', '91-44=47'] Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 68+47=115, Resulting Numbers: [115] 115,67 unequal: No Solution Exploring Operation: 68*47=3196, Resulting Numbers: [3196] 3196,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[68, 47], Operations: ['91-7=84', '84-37=47'] Exploring Operation: 68*47=3196, Resulting Numbers: [3196] 3196,67 unequal: No Solution Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 68+47=115, Resulting Numbers: [115] 115,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[84, 31], Operations: ['91-7=84', '68-37=31'] Exploring Operation: 84-31=53, Resulting Numbers: [53] 53,67 unequal: No Solution Exploring Operation: 84+31=115, Resulting Numbers: [115] 115,67 unequal: No Solution Exploring Operation: 84*31=2604, Resulting Numbers: [2604] 2604,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[84, 105], Operations: ['91-7=84', '68+37=105'] Exploring Operation: 105-84=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 84+105=189, Resulting Numbers: [189] 189,67 unequal: No Solution Exploring Operation: 84*105=8820, Resulting Numbers: [8820] 8820,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[91, 98], Operations: ['68-7=61', '37+61=98'] Exploring Operation: 91+98=189, Resulting Numbers: [189] 189,67 unequal: No Solution Exploring Operation: 91*98=8918, Resulting Numbers: [8918] 8918,67 unequal: No Solution Exploring Operation: 98-91=7, Resulting Numbers: [7] 7,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[44, 23], Operations: ['37+7=44', '91-68=23'] Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,67 unequal: No Solution Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[91, 68, 37, 7], Operations: [] Exploring Operation: 37+7=44, Resulting Numbers: [91, 68, 44] Generated Node #0,0: 67:[91, 68, 44] Operation: 37+7=44 Moving to Node #0,0 Current State: 67:[91, 68, 44], Operations: ['37+7=44'] Exploring Operation: 91-68=23, Resulting Numbers: [44, 23] Generated Node #0,0,2: 67:[44, 23] Operation: 91-68=23 Moving to Node #0,0,2 Current State: 67:[44, 23], Operations: ['37+7=44', '91-68=23'] Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
0.967882
hs_3
sum_heuristic
[ 36, 69, 38, 37 ]
32
[ "69-36=33", "38-37=1", "33-1=32" ]
Current State: 32:[36, 69, 38, 37], Operations: [] Exploring Operation: 69-36=33, Resulting Numbers: [38, 37, 33] Generated Node #2: [38, 37, 33] from Operation: 69-36=33 Current State: 32:[38, 37, 33], Operations: ['69-36=33'] Exploring Operation: 38-37=1, Resulting Numbers: [33, 1] Generated Node #3: [33, 1] from Operation: 38-37=1 Current State: 32:[33, 1], Operations: ['69-36=33', '38-37=1'] Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[36, 69, 38, 37], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [36, 37, 31] Generated Node #0,0: 32:[36, 37, 31] Operation: 69-38=31 Exploring Operation: 69-37=32, Resulting Numbers: [36, 38, 32] Generated Node #0,1: 32:[36, 38, 32] Operation: 69-37=32 Exploring Operation: 69-36=33, Resulting Numbers: [38, 37, 33] Generated Node #0,2: 32:[38, 37, 33] Operation: 69-36=33 Moving to Node #0,0 Current State: 32:[36, 37, 31], Operations: ['69-38=31'] Exploring Operation: 36-31=5, Resulting Numbers: [37, 5] Generated Node #0,0,0: 32:[37, 5] Operation: 36-31=5 Exploring Operation: 37-36=1, Resulting Numbers: [31, 1] Generated Node #0,0,1: 32:[31, 1] Operation: 37-36=1 Exploring Operation: 37-31=6, Resulting Numbers: [36, 6] Generated Node #0,0,2: 32:[36, 6] Operation: 37-31=6 Moving to Node #0,1 Current State: 32:[36, 38, 32], Operations: ['69-37=32'] Exploring Operation: 38-32=6, Resulting Numbers: [36, 6] Generated Node #0,1,0: 32:[36, 6] Operation: 38-32=6 Exploring Operation: 38-36=2, Resulting Numbers: [32, 2] Generated Node #0,1,1: 32:[32, 2] Operation: 38-36=2 Exploring Operation: 36-32=4, Resulting Numbers: [38, 4] Generated Node #0,1,2: 32:[38, 4] Operation: 36-32=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[32, 2], Operations: ['69-37=32', '38-36=2'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,32 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:[36, 6], Operations: ['69-37=32', '38-32=6'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,32 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:[38, 4], Operations: ['69-37=32', '36-32=4'] Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,32 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,32 unequal: No Solution Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 32:[38, 37, 33], Operations: ['69-36=33'] Exploring Operation: 38-37=1, Resulting Numbers: [33, 1] Generated Node #0,2,0: 32:[33, 1] Operation: 38-37=1 Exploring Operation: 38-33=5, Resulting Numbers: [37, 5] Generated Node #0,2,1: 32:[37, 5] Operation: 38-33=5 Exploring Operation: 37-33=4, Resulting Numbers: [38, 4] Generated Node #0,2,2: 32:[38, 4] Operation: 37-33=4 Moving to Node #0,0,1 Current State: 32:[31, 1], Operations: ['69-38=31', '37-36=1'] Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[36, 69, 38, 37], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [36, 37, 31] Generated Node #0,0: 32:[36, 37, 31] Operation: 69-38=31 Moving to Node #0,0 Current State: 32:[36, 37, 31], Operations: ['69-38=31'] Exploring Operation: 37-36=1, Resulting Numbers: [31, 1] Generated Node #0,0,1: 32:[31, 1] Operation: 37-36=1 Moving to Node #0,0,1 Current State: 32:[31, 1], Operations: ['69-38=31', '37-36=1'] Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.977431
hs_3
mult_heuristic
[ 60, 26, 3, 4 ]
90
[ "60-26=34", "34-4=30", "3*30=90" ]
Current State: 90:[60, 26, 3, 4], Operations: [] Exploring Operation: 60-26=34, Resulting Numbers: [3, 4, 34] Generated Node #2: [3, 4, 34] from Operation: 60-26=34 Current State: 90:[3, 4, 34], Operations: ['60-26=34'] Exploring Operation: 34-4=30, Resulting Numbers: [3, 30] Generated Node #3: [3, 30] from Operation: 34-4=30 Current State: 90:[3, 30], Operations: ['60-26=34', '34-4=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[60, 26, 3, 4], Operations: [] Exploring Operation: 60/4=15, Resulting Numbers: [26, 3, 15] Generated Node #0,0: 90:[26, 3, 15] Operation: 60/4=15 Exploring Operation: 60-26=34, Resulting Numbers: [3, 4, 34] Generated Node #0,1: 90:[3, 4, 34] Operation: 60-26=34 Exploring Operation: 60-4=56, Resulting Numbers: [26, 3, 56] Generated Node #0,2: 90:[26, 3, 56] Operation: 60-4=56 Exploring Operation: 60/3=20, Resulting Numbers: [26, 4, 20] Generated Node #0,3: 90:[26, 4, 20] Operation: 60/3=20 Exploring Operation: 60+26=86, Resulting Numbers: [3, 4, 86] Generated Node #0,4: 90:[3, 4, 86] Operation: 60+26=86 Moving to Node #0,0 Current State: 90:[26, 3, 15], Operations: ['60/4=15'] Exploring Operation: 26-15=11, Resulting Numbers: [3, 11] Generated Node #0,0,0: 90:[3, 11] Operation: 26-15=11 Exploring Operation: 26+15=41, Resulting Numbers: [3, 41] Generated Node #0,0,1: 90:[3, 41] Operation: 26+15=41 Exploring Operation: 3+15=18, Resulting Numbers: [26, 18] Generated Node #0,0,2: 90:[26, 18] Operation: 3+15=18 Exploring Operation: 26+3=29, Resulting Numbers: [15, 29] Generated Node #0,0,3: 90:[15, 29] Operation: 26+3=29 Exploring Operation: 3*15=45, Resulting Numbers: [26, 45] Generated Node #0,0,4: 90:[26, 45] Operation: 3*15=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[3, 11], Operations: ['60/4=15', '26-15=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[15, 29], Operations: ['60/4=15', '26+3=29'] Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,90 unequal: No Solution Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[3, 41], Operations: ['60/4=15', '26+15=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,90 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,90 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[26, 18], Operations: ['60/4=15', '3+15=18'] Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 26*18=468, Resulting Numbers: [468] 468,90 unequal: No Solution Exploring Operation: 26+18=44, Resulting Numbers: [44] 44,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 90:[26, 45], Operations: ['60/4=15', '3*15=45'] Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,90 unequal: No Solution Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,90 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: 90:[3, 4, 86], Operations: ['60+26=86'] Exploring Operation: 3*4=12, Resulting Numbers: [86, 12] Generated Node #0,4,0: 90:[86, 12] Operation: 3*4=12 Exploring Operation: 4+86=90, Resulting Numbers: [3, 90] Generated Node #0,4,1: 90:[3, 90] Operation: 4+86=90 Exploring Operation: 3+86=89, Resulting Numbers: [4, 89] Generated Node #0,4,2: 90:[4, 89] Operation: 3+86=89 Exploring Operation: 3+4=7, Resulting Numbers: [86, 7] Generated Node #0,4,3: 90:[86, 7] Operation: 3+4=7 Exploring Operation: 4-3=1, Resulting Numbers: [86, 1] Generated Node #0,4,4: 90:[86, 1] Operation: 4-3=1 Moving to Node #0,1 Current State: 90:[3, 4, 34], Operations: ['60-26=34'] Exploring Operation: 4-3=1, Resulting Numbers: [34, 1] Generated Node #0,1,0: 90:[34, 1] Operation: 4-3=1 Exploring Operation: 34-3=31, Resulting Numbers: [4, 31] Generated Node #0,1,1: 90:[4, 31] Operation: 34-3=31 Exploring Operation: 34-4=30, Resulting Numbers: [3, 30] Generated Node #0,1,2: 90:[3, 30] Operation: 34-4=30 Exploring Operation: 3*4=12, Resulting Numbers: [34, 12] Generated Node #0,1,3: 90:[34, 12] Operation: 3*4=12 Exploring Operation: 3+4=7, Resulting Numbers: [34, 7] Generated Node #0,1,4: 90:[34, 7] Operation: 3+4=7 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[3, 30], Operations: ['60-26=34', '34-4=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[60, 26, 3, 4], Operations: [] Exploring Operation: 60-26=34, Resulting Numbers: [3, 4, 34] Generated Node #0,1: 90:[3, 4, 34] Operation: 60-26=34 Moving to Node #0,1 Current State: 90:[3, 4, 34], Operations: ['60-26=34'] Exploring Operation: 34-4=30, Resulting Numbers: [3, 30] Generated Node #0,1,2: 90:[3, 30] Operation: 34-4=30 Moving to Node #0,1,2 Current State: 90:[3, 30], Operations: ['60-26=34', '34-4=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
mult_heuristic
[ 56, 5, 15, 38 ]
58
[ "15/5=3", "38*3=114", "114-56=58" ]
Current State: 58:[56, 5, 15, 38], Operations: [] Exploring Operation: 15/5=3, Resulting Numbers: [56, 38, 3] Generated Node #2: [56, 38, 3] from Operation: 15/5=3 Current State: 58:[56, 38, 3], Operations: ['15/5=3'] Exploring Operation: 38*3=114, Resulting Numbers: [56, 114] Generated Node #3: [56, 114] from Operation: 38*3=114 Current State: 58:[56, 114], Operations: ['15/5=3', '38*3=114'] Exploring Operation: 114-56=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[56, 5, 15, 38], Operations: [] Exploring Operation: 15+38=53, Resulting Numbers: [56, 5, 53] Generated Node #0,0: 58:[56, 5, 53] Operation: 15+38=53 Moving to Node #0,0 Current State: 58:[56, 5, 53], Operations: ['15+38=53'] Exploring Operation: 5+53=58, Resulting Numbers: [56, 58] Generated Node #0,0,0: 58:[56, 58] Operation: 5+53=58 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[56, 58], Operations: ['15+38=53', '5+53=58'] Exploring Operation: 58-56=2, Resulting Numbers: [2] 2,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 53, 2, 61, 94 ]
12
[ "61-53=8", "2+94=96", "96/8=12" ]
Current State: 12:[53, 2, 61, 94], Operations: [] Exploring Operation: 61-53=8, Resulting Numbers: [2, 94, 8] Generated Node #2: [2, 94, 8] from Operation: 61-53=8 Current State: 12:[2, 94, 8], Operations: ['61-53=8'] Exploring Operation: 2+94=96, Resulting Numbers: [8, 96] Generated Node #3: [8, 96] from Operation: 2+94=96 Current State: 12:[8, 96], Operations: ['61-53=8', '2+94=96'] Exploring Operation: 96/8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[53, 2, 61, 94], Operations: [] Exploring Operation: 53-2=51, Resulting Numbers: [61, 94, 51] Generated Node #0,0: 12:[61, 94, 51] Operation: 53-2=51 Exploring Operation: 94-53=41, Resulting Numbers: [2, 61, 41] Generated Node #0,1: 12:[2, 61, 41] Operation: 94-53=41 Exploring Operation: 61-53=8, Resulting Numbers: [2, 94, 8] Generated Node #0,2: 12:[2, 94, 8] Operation: 61-53=8 Exploring Operation: 94-61=33, Resulting Numbers: [53, 2, 33] Generated Node #0,3: 12:[53, 2, 33] Operation: 94-61=33 Exploring Operation: 94/2=47, Resulting Numbers: [53, 61, 47] Generated Node #0,4: 12:[53, 61, 47] Operation: 94/2=47 Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[53, 2, 33], Operations: ['94-61=33'] Exploring Operation: 33-2=31, Resulting Numbers: [53, 31] Generated Node #0,3,0: 12:[53, 31] Operation: 33-2=31 Exploring Operation: 53-2=51, Resulting Numbers: [33, 51] Generated Node #0,3,1: 12:[33, 51] Operation: 53-2=51 Exploring Operation: 53-33=20, Resulting Numbers: [2, 20] Generated Node #0,3,2: 12:[2, 20] Operation: 53-33=20 Exploring Operation: 53+2=55, Resulting Numbers: [33, 55] Generated Node #0,3,3: 12:[33, 55] Operation: 53+2=55 Exploring Operation: 2+33=35, Resulting Numbers: [53, 35] Generated Node #0,3,4: 12:[53, 35] Operation: 2+33=35 Moving to Node #0,3,2 Current State: 12:[2, 20], Operations: ['94-61=33', '53-33=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[33, 51], Operations: ['94-61=33', '53-2=51'] Exploring Operation: 33+51=84, Resulting Numbers: [84] 84,12 unequal: No Solution Exploring Operation: 33*51=1683, Resulting Numbers: [1683] 1683,12 unequal: No Solution Exploring Operation: 51-33=18, Resulting Numbers: [18] 18,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[53, 31], Operations: ['94-61=33', '33-2=31'] Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,12 unequal: No Solution Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,12 unequal: No Solution Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[33, 55], Operations: ['94-61=33', '53+2=55'] Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,12 unequal: No Solution Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,12 unequal: No Solution Moving to Node #0,3,4 Current State: 12:[53, 35], Operations: ['94-61=33', '2+33=35'] Exploring Operation: 53*35=1855, Resulting Numbers: [1855] 1855,12 unequal: No Solution Exploring Operation: 53-35=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 53+35=88, Resulting Numbers: [88] 88,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[2, 61, 41], Operations: ['94-53=41'] Exploring Operation: 61-41=20, Resulting Numbers: [2, 20] Generated Node #0,1,0: 12:[2, 20] Operation: 61-41=20 Exploring Operation: 2+61=63, Resulting Numbers: [41, 63] Generated Node #0,1,1: 12:[41, 63] Operation: 2+61=63 Exploring Operation: 61-2=59, Resulting Numbers: [41, 59] Generated Node #0,1,2: 12:[41, 59] Operation: 61-2=59 Exploring Operation: 2+41=43, Resulting Numbers: [61, 43] Generated Node #0,1,3: 12:[61, 43] Operation: 2+41=43 Exploring Operation: 41-2=39, Resulting Numbers: [61, 39] Generated Node #0,1,4: 12:[61, 39] Operation: 41-2=39 Moving to Node #0,1,0 Current State: 12:[2, 20], Operations: ['94-53=41', '61-41=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,12 unequal: No Solution Moving to Node #0,1,4 Current State: 12:[61, 39], Operations: ['94-53=41', '41-2=39'] Exploring Operation: 61*39=2379, Resulting Numbers: [2379] 2379,12 unequal: No Solution Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 61+39=100, Resulting Numbers: [100] 100,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[41, 59], Operations: ['94-53=41', '61-2=59'] Exploring Operation: 59-41=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 41*59=2419, Resulting Numbers: [2419] 2419,12 unequal: No Solution Exploring Operation: 41+59=100, Resulting Numbers: [100] 100,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[41, 63], Operations: ['94-53=41', '2+61=63'] Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,12 unequal: No Solution Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[61, 43], Operations: ['94-53=41', '2+41=43'] Exploring Operation: 61*43=2623, Resulting Numbers: [2623] 2623,12 unequal: No Solution Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 61+43=104, Resulting Numbers: [104] 104,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[2, 94, 8], Operations: ['61-53=8'] Exploring Operation: 94/2=47, Resulting Numbers: [8, 47] Generated Node #0,2,0: 12:[8, 47] Operation: 94/2=47 Exploring Operation: 94-2=92, Resulting Numbers: [8, 92] Generated Node #0,2,1: 12:[8, 92] Operation: 94-2=92 Exploring Operation: 94-8=86, Resulting Numbers: [2, 86] Generated Node #0,2,2: 12:[2, 86] Operation: 94-8=86 Exploring Operation: 8/2=4, Resulting Numbers: [94, 4] Generated Node #0,2,3: 12:[94, 4] Operation: 8/2=4 Exploring Operation: 8-2=6, Resulting Numbers: [94, 6] Generated Node #0,2,4: 12:[94, 6] Operation: 8-2=6 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 12:[8, 47], Operations: ['61-53=8', '94/2=47'] Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,12 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 12:[2, 86], Operations: ['61-53=8', '94-8=86'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,12 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 2*86=172, Resulting Numbers: [172] 172,12 unequal: No Solution Exploring Operation: 2+86=88, Resulting Numbers: [88] 88,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 12:[8, 92], Operations: ['61-53=8', '94-2=92'] Exploring Operation: 8+92=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 8*92=736, Resulting Numbers: [736] 736,12 unequal: No Solution Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 12:[94, 4], Operations: ['61-53=8', '8/2=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,12 unequal: No Solution Exploring Operation: 94+4=98, Resulting Numbers: [98] 98,12 unequal: No Solution Exploring Operation: 94*4=376, Resulting Numbers: [376] 376,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 12:[94, 6], Operations: ['61-53=8', '8-2=6'] Exploring Operation: 94*6=564, Resulting Numbers: [564] 564,12 unequal: No Solution Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 12:[53, 61, 47], Operations: ['94/2=47'] Exploring Operation: 53+47=100, Resulting Numbers: [61, 100] Generated Node #0,4,0: 12:[61, 100] Operation: 53+47=100 Exploring Operation: 61-47=14, Resulting Numbers: [53, 14] Generated Node #0,4,1: 12:[53, 14] Operation: 61-47=14 Exploring Operation: 53+61=114, Resulting Numbers: [47, 114] Generated Node #0,4,2: 12:[47, 114] Operation: 53+61=114 Exploring Operation: 53-47=6, Resulting Numbers: [61, 6] Generated Node #0,4,3: 12:[61, 6] Operation: 53-47=6 Exploring Operation: 61-53=8, Resulting Numbers: [47, 8] Generated Node #0,4,4: 12:[47, 8] Operation: 61-53=8 Moving to Node #0,4,4 Current State: 12:[47, 8], Operations: ['94/2=47', '61-53=8'] Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 47*8=376, Resulting Numbers: [376] 376,12 unequal: No Solution Moving to Node #0,4,1 Current State: 12:[53, 14], Operations: ['94/2=47', '61-47=14'] Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,12 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 53*14=742, Resulting Numbers: [742] 742,12 unequal: No Solution Moving to Node #0,4,3 Current State: 12:[61, 6], Operations: ['94/2=47', '53-47=6'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,12 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,12 unequal: No Solution Moving to Node #0,4,0 Current State: 12:[61, 100], Operations: ['94/2=47', '53+47=100'] Exploring Operation: 61+100=161, Resulting Numbers: [161] 161,12 unequal: No Solution Exploring Operation: 100-61=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 61*100=6100, Resulting Numbers: [6100] 6100,12 unequal: No Solution Moving to Node #0,4,2 Current State: 12:[47, 114], Operations: ['94/2=47', '53+61=114'] Exploring Operation: 47+114=161, Resulting Numbers: [161] 161,12 unequal: No Solution Exploring Operation: 47*114=5358, Resulting Numbers: [5358] 5358,12 unequal: No Solution Exploring Operation: 114-47=67, Resulting Numbers: [67] 67,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[61, 94, 51], Operations: ['53-2=51'] Exploring Operation: 61+94=155, Resulting Numbers: [51, 155] Generated Node #0,0,0: 12:[51, 155] Operation: 61+94=155 Exploring Operation: 61-51=10, Resulting Numbers: [94, 10] Generated Node #0,0,1: 12:[94, 10] Operation: 61-51=10 Exploring Operation: 94-61=33, Resulting Numbers: [51, 33] Generated Node #0,0,2: 12:[51, 33] Operation: 94-61=33 Exploring Operation: 61+51=112, Resulting Numbers: [94, 112] Generated Node #0,0,3: 12:[94, 112] Operation: 61+51=112 Exploring Operation: 94-51=43, Resulting Numbers: [61, 43] Generated Node #0,0,4: 12:[61, 43] Operation: 94-51=43 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 12:[51, 33], Operations: ['53-2=51', '94-61=33'] Exploring Operation: 51-33=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 51*33=1683, Resulting Numbers: [1683] 1683,12 unequal: No Solution Exploring Operation: 51+33=84, Resulting Numbers: [84] 84,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 12:[61, 43], Operations: ['53-2=51', '94-51=43'] Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 61+43=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 61*43=2623, Resulting Numbers: [2623] 2623,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[94, 10], Operations: ['53-2=51', '61-51=10'] Exploring Operation: 94*10=940, Resulting Numbers: [940] 940,12 unequal: No Solution Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,12 unequal: No Solution Exploring Operation: 94+10=104, Resulting Numbers: [104] 104,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[51, 155], Operations: ['53-2=51', '61+94=155'] Exploring Operation: 155-51=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 51*155=7905, Resulting Numbers: [7905] 7905,12 unequal: No Solution Exploring Operation: 51+155=206, Resulting Numbers: [206] 206,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 12:[94, 112], Operations: ['53-2=51', '61+51=112'] Exploring Operation: 94*112=10528, Resulting Numbers: [10528] 10528,12 unequal: No Solution Exploring Operation: 112-94=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 94+112=206, Resulting Numbers: [206] 206,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 68, 5, 48, 84 ]
69
[ "68-5=63", "48+84=132", "132-63=69" ]
Current State: 69:[68, 5, 48, 84], Operations: [] Exploring Operation: 68-5=63, Resulting Numbers: [48, 84, 63] Generated Node #2: [48, 84, 63] from Operation: 68-5=63 Current State: 69:[48, 84, 63], Operations: ['68-5=63'] Exploring Operation: 48+84=132, Resulting Numbers: [63, 132] Generated Node #3: [63, 132] from Operation: 48+84=132 Current State: 69:[63, 132], Operations: ['68-5=63', '48+84=132'] Exploring Operation: 132-63=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[68, 5, 48, 84], Operations: [] Exploring Operation: 84-68=16, Resulting Numbers: [5, 48, 16] Generated Node #0,0: 69:[5, 48, 16] Operation: 84-68=16 Exploring Operation: 84-48=36, Resulting Numbers: [68, 5, 36] Generated Node #0,1: 69:[68, 5, 36] Operation: 84-48=36 Exploring Operation: 68-48=20, Resulting Numbers: [5, 84, 20] Generated Node #0,2: 69:[5, 84, 20] Operation: 68-48=20 Exploring Operation: 5+48=53, Resulting Numbers: [68, 84, 53] Generated Node #0,3: 69:[68, 84, 53] Operation: 5+48=53 Exploring Operation: 84-5=79, Resulting Numbers: [68, 48, 79] Generated Node #0,4: 69:[68, 48, 79] Operation: 84-5=79 Moving to Node #0,1 Current State: 69:[68, 5, 36], Operations: ['84-48=36'] Exploring Operation: 5+36=41, Resulting Numbers: [68, 41] Generated Node #0,1,0: 69:[68, 41] Operation: 5+36=41 Exploring Operation: 36-5=31, Resulting Numbers: [68, 31] Generated Node #0,1,1: 69:[68, 31] Operation: 36-5=31 Exploring Operation: 68-36=32, Resulting Numbers: [5, 32] Generated Node #0,1,2: 69:[5, 32] Operation: 68-36=32 Exploring Operation: 68-5=63, Resulting Numbers: [36, 63] Generated Node #0,1,3: 69:[36, 63] Operation: 68-5=63 Exploring Operation: 68+5=73, Resulting Numbers: [36, 73] Generated Node #0,1,4: 69:[36, 73] Operation: 68+5=73 Moving to Node #0,2 Current State: 69:[5, 84, 20], Operations: ['68-48=20'] Exploring Operation: 5+84=89, Resulting Numbers: [20, 89] Generated Node #0,2,0: 69:[20, 89] Operation: 5+84=89 Exploring Operation: 5+20=25, Resulting Numbers: [84, 25] Generated Node #0,2,1: 69:[84, 25] Operation: 5+20=25 Exploring Operation: 20/5=4, Resulting Numbers: [84, 4] Generated Node #0,2,2: 69:[84, 4] Operation: 20/5=4 Exploring Operation: 84-20=64, Resulting Numbers: [5, 64] Generated Node #0,2,3: 69:[5, 64] Operation: 84-20=64 Exploring Operation: 84-5=79, Resulting Numbers: [20, 79] Generated Node #0,2,4: 69:[20, 79] Operation: 84-5=79 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 69:[5, 64], Operations: ['68-48=20', '84-20=64'] Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,69 unequal: No Solution Exploring Operation: 5+64=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[68, 5, 48, 84], Operations: [] Exploring Operation: 68-48=20, Resulting Numbers: [5, 84, 20] Generated Node #0,2: 69:[5, 84, 20] Operation: 68-48=20 Moving to Node #0,2 Current State: 69:[5, 84, 20], Operations: ['68-48=20'] Exploring Operation: 84-20=64, Resulting Numbers: [5, 64] Generated Node #0,2,3: 69:[5, 64] Operation: 84-20=64 Moving to Node #0,2,3 Current State: 69:[5, 64], Operations: ['68-48=20', '84-20=64'] Exploring Operation: 5+64=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 37, 16, 11, 39 ]
100
[ "37+39=76", "16*11=176", "176-76=100" ]
Current State: 100:[37, 16, 11, 39], Operations: [] Exploring Operation: 37+39=76, Resulting Numbers: [16, 11, 76] Generated Node #2: [16, 11, 76] from Operation: 37+39=76 Current State: 100:[16, 11, 76], Operations: ['37+39=76'] Exploring Operation: 16*11=176, Resulting Numbers: [76, 176] Generated Node #3: [76, 176] from Operation: 16*11=176 Current State: 100:[76, 176], Operations: ['37+39=76', '16*11=176'] Exploring Operation: 176-76=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[37, 16, 11, 39], Operations: [] Exploring Operation: 37-16=21, Resulting Numbers: [11, 39, 21] Generated Node #0,0: 100:[11, 39, 21] Operation: 37-16=21 Exploring Operation: 37+16=53, Resulting Numbers: [11, 39, 53] Generated Node #0,1: 100:[11, 39, 53] Operation: 37+16=53 Exploring Operation: 39-37=2, Resulting Numbers: [16, 11, 2] Generated Node #0,2: 100:[16, 11, 2] Operation: 39-37=2 Exploring Operation: 39-16=23, Resulting Numbers: [37, 11, 23] Generated Node #0,3: 100:[37, 11, 23] Operation: 39-16=23 Moving to Node #0,2 Current State: 100:[16, 11, 2], Operations: ['39-37=2'] Exploring Operation: 16-11=5, Resulting Numbers: [2, 5] Generated Node #0,2,0: 100:[2, 5] Operation: 16-11=5 Exploring Operation: 16+11=27, Resulting Numbers: [2, 27] Generated Node #0,2,1: 100:[2, 27] Operation: 16+11=27 Exploring Operation: 16/2=8, Resulting Numbers: [11, 8] Generated Node #0,2,2: 100:[11, 8] Operation: 16/2=8 Exploring Operation: 16+2=18, Resulting Numbers: [11, 18] Generated Node #0,2,3: 100:[11, 18] Operation: 16+2=18 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[2, 5], Operations: ['39-37=2', '16-11=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[2, 27], Operations: ['39-37=2', '16+11=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,100 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[11, 8], Operations: ['39-37=2', '16/2=8'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 11*8=88, Resulting Numbers: [88] 88,100 unequal: No Solution Exploring Operation: 11+8=19, Resulting Numbers: [19] 19,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 100:[11, 18], Operations: ['39-37=2', '16+2=18'] Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 11*18=198, Resulting Numbers: [198] 198,100 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,100 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: 100:[11, 39, 21], Operations: ['37-16=21'] Exploring Operation: 11+39=50, Resulting Numbers: [21, 50] Generated Node #0,0,0: 100:[21, 50] Operation: 11+39=50 Exploring Operation: 39-11=28, Resulting Numbers: [21, 28] Generated Node #0,0,1: 100:[21, 28] Operation: 39-11=28 Exploring Operation: 21-11=10, Resulting Numbers: [39, 10] Generated Node #0,0,2: 100:[39, 10] Operation: 21-11=10 Exploring Operation: 39-21=18, Resulting Numbers: [11, 18] Generated Node #0,0,3: 100:[11, 18] Operation: 39-21=18 Moving to Node #0,3 Current State: 100:[37, 11, 23], Operations: ['39-16=23'] Exploring Operation: 37+23=60, Resulting Numbers: [11, 60] Generated Node #0,3,0: 100:[11, 60] Operation: 37+23=60 Exploring Operation: 37-23=14, Resulting Numbers: [11, 14] Generated Node #0,3,1: 100:[11, 14] Operation: 37-23=14 Exploring Operation: 37+11=48, Resulting Numbers: [23, 48] Generated Node #0,3,2: 100:[23, 48] Operation: 37+11=48 Exploring Operation: 37-11=26, Resulting Numbers: [23, 26] Generated Node #0,3,3: 100:[23, 26] Operation: 37-11=26 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 100:[23, 26], Operations: ['39-16=23', '37-11=26'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,100 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 100:[23, 48], Operations: ['39-16=23', '37+11=48'] Exploring Operation: 23+48=71, Resulting Numbers: [71] 71,100 unequal: No Solution Exploring Operation: 23*48=1104, Resulting Numbers: [1104] 1104,100 unequal: No Solution Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 100:[11, 14], Operations: ['39-16=23', '37-23=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 100:[11, 60], Operations: ['39-16=23', '37+23=60'] Exploring Operation: 11+60=71, Resulting Numbers: [71] 71,100 unequal: No Solution Exploring Operation: 11*60=660, Resulting Numbers: [660] 660,100 unequal: No Solution Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,100 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: 100:[11, 39, 53], Operations: ['37+16=53'] Exploring Operation: 53-39=14, Resulting Numbers: [11, 14] Generated Node #0,1,0: 100:[11, 14] Operation: 53-39=14 Exploring Operation: 11+39=50, Resulting Numbers: [53, 50] Generated Node #0,1,1: 100:[53, 50] Operation: 11+39=50 Exploring Operation: 39-11=28, Resulting Numbers: [53, 28] Generated Node #0,1,2: 100:[53, 28] Operation: 39-11=28 Exploring Operation: 39+53=92, Resulting Numbers: [11, 92] Generated Node #0,1,3: 100:[11, 92] Operation: 39+53=92 Moving to Node #0,0,0 Current State: 100:[21, 50], Operations: ['37-16=21', '11+39=50'] Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,100 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,100 unequal: No Solution Moving to Node #0,0,3 Current State: 100:[11, 18], Operations: ['37-16=21', '39-21=18'] Exploring Operation: 11*18=198, Resulting Numbers: [198] 198,100 unequal: No Solution Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[53, 50], Operations: ['37+16=53', '11+39=50'] Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,100 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[21, 28], Operations: ['37-16=21', '39-11=28'] Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,100 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[11, 14], Operations: ['37+16=53', '53-39=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[53, 28], Operations: ['37+16=53', '39-11=28'] Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,100 unequal: No Solution Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,100 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[11, 92], Operations: ['37+16=53', '39+53=92'] Exploring Operation: 11+92=103, Resulting Numbers: [103] 103,100 unequal: No Solution Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,100 unequal: No Solution Exploring Operation: 11*92=1012, Resulting Numbers: [1012] 1012,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[39, 10], Operations: ['37-16=21', '21-11=10'] Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,100 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,100 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 53, 37, 43, 10 ]
17
[ "53-37=16", "43-10=33", "33-16=17" ]
Current State: 17:[53, 37, 43, 10], Operations: [] Exploring Operation: 53-37=16, Resulting Numbers: [43, 10, 16] Generated Node #2: [43, 10, 16] from Operation: 53-37=16 Current State: 17:[43, 10, 16], Operations: ['53-37=16'] Exploring Operation: 43-10=33, Resulting Numbers: [16, 33] Generated Node #3: [16, 33] from Operation: 43-10=33 Current State: 17:[16, 33], Operations: ['53-37=16', '43-10=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[53, 37, 43, 10], Operations: [] Exploring Operation: 53-43=10, Resulting Numbers: [37, 10, 10] Generated Node #0,0: 17:[37, 10, 10] Operation: 53-43=10 Exploring Operation: 53-37=16, Resulting Numbers: [43, 10, 16] Generated Node #0,1: 17:[43, 10, 16] Operation: 53-37=16 Exploring Operation: 43-37=6, Resulting Numbers: [53, 10, 6] Generated Node #0,2: 17:[53, 10, 6] Operation: 43-37=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[37, 10, 10], Operations: ['53-43=10'] Exploring Operation: 37-10=27, Resulting Numbers: [10, 27] Generated Node #0,0,0: 17:[10, 27] Operation: 37-10=27 Exploring Operation: 10+10=20, Resulting Numbers: [37, 20] Generated Node #0,0,1: 17:[37, 20] Operation: 10+10=20 Exploring Operation: 37-10=27, Resulting Numbers: [10, 27] Generated Node #0,0,2: 17:[10, 27] Operation: 37-10=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[10, 27], Operations: ['53-43=10', '37-10=27'] Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,17 unequal: No Solution Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,17 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[53, 37, 43, 10], Operations: [] Exploring Operation: 53-43=10, Resulting Numbers: [37, 10, 10] Generated Node #0,0: 17:[37, 10, 10] Operation: 53-43=10 Moving to Node #0,0 Current State: 17:[37, 10, 10], Operations: ['53-43=10'] Exploring Operation: 37-10=27, Resulting Numbers: [10, 27] Generated Node #0,0,0: 17:[10, 27] Operation: 37-10=27 Moving to Node #0,0,0 Current State: 17:[10, 27], Operations: ['53-43=10', '37-10=27'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 30, 31, 75, 84 ]
70
[ "30+31=61", "84-75=9", "61+9=70" ]
Current State: 70:[30, 31, 75, 84], Operations: [] Exploring Operation: 30+31=61, Resulting Numbers: [75, 84, 61] Generated Node #2: [75, 84, 61] from Operation: 30+31=61 Current State: 70:[75, 84, 61], Operations: ['30+31=61'] Exploring Operation: 84-75=9, Resulting Numbers: [61, 9] Generated Node #3: [61, 9] from Operation: 84-75=9 Current State: 70:[61, 9], Operations: ['30+31=61', '84-75=9'] Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[30, 31, 75, 84], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [30, 31, 9] Generated Node #0,0: 70:[30, 31, 9] Operation: 84-75=9 Exploring Operation: 84-30=54, Resulting Numbers: [31, 75, 54] Generated Node #0,1: 70:[31, 75, 54] Operation: 84-30=54 Exploring Operation: 31-30=1, Resulting Numbers: [75, 84, 1] Generated Node #0,2: 70:[75, 84, 1] Operation: 31-30=1 Moving to Node #0,0 Current State: 70:[30, 31, 9], Operations: ['84-75=9'] Exploring Operation: 31-30=1, Resulting Numbers: [9, 1] Generated Node #0,0,0: 70:[9, 1] Operation: 31-30=1 Exploring Operation: 30+9=39, Resulting Numbers: [31, 39] Generated Node #0,0,1: 70:[31, 39] Operation: 30+9=39 Exploring Operation: 30+31=61, Resulting Numbers: [9, 61] Generated Node #0,0,2: 70:[9, 61] Operation: 30+31=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[9, 1], Operations: ['84-75=9', '31-30=1'] Exploring Operation: 9*1=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 9+1=10, Resulting Numbers: [10] 10,70 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[31, 39], Operations: ['84-75=9', '30+9=39'] Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 31*39=1209, Resulting Numbers: [1209] 1209,70 unequal: No Solution Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[30, 31, 75, 84], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [30, 31, 9] Generated Node #0,0: 70:[30, 31, 9] Operation: 84-75=9 Moving to Node #0,0 Current State: 70:[30, 31, 9], Operations: ['84-75=9'] Exploring Operation: 30+9=39, Resulting Numbers: [31, 39] Generated Node #0,0,1: 70:[31, 39] Operation: 30+9=39 Moving to Node #0,0,1 Current State: 70:[31, 39], Operations: ['84-75=9', '30+9=39'] Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 72, 6, 32, 99 ]
48
[ "72-6=66", "32*99=3168", "3168/66=48" ]
Current State: 48:[72, 6, 32, 99], Operations: [] Exploring Operation: 72-6=66, Resulting Numbers: [32, 99, 66] Generated Node #2: [32, 99, 66] from Operation: 72-6=66 Current State: 48:[32, 99, 66], Operations: ['72-6=66'] Exploring Operation: 32*99=3168, Resulting Numbers: [66, 3168] Generated Node #3: [66, 3168] from Operation: 32*99=3168 Current State: 48:[66, 3168], Operations: ['72-6=66', '32*99=3168'] Exploring Operation: 3168/66=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[72, 6, 32, 99], Operations: [] Exploring Operation: 99-72=27, Resulting Numbers: [6, 32, 27] Generated Node #0,0: 48:[6, 32, 27] Operation: 99-72=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[6, 32, 27], Operations: ['99-72=27'] Exploring Operation: 32-27=5, Resulting Numbers: [6, 5] Generated Node #0,0,0: 48:[6, 5] Operation: 32-27=5 Moving to Node #0,0,0 Current State: 48:[6, 5], Operations: ['99-72=27', '32-27=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,48 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
[ 1, 53, 76, 9 ]
13
[ "1+53=54", "76-9=67", "67-54=13" ]
Current State: 13:[1, 53, 76, 9], Operations: [] Exploring Operation: 1+53=54, Resulting Numbers: [76, 9, 54] Generated Node #2: [76, 9, 54] from Operation: 1+53=54 Current State: 13:[76, 9, 54], Operations: ['1+53=54'] Exploring Operation: 76-9=67, Resulting Numbers: [54, 67] Generated Node #3: [54, 67] from Operation: 76-9=67 Current State: 13:[54, 67], Operations: ['1+53=54', '76-9=67'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[1, 53, 76, 9], Operations: [] Exploring Operation: 76-1=75, Resulting Numbers: [53, 9, 75] Generated Node #0,0: 13:[53, 9, 75] Operation: 76-1=75 Exploring Operation: 76-53=23, Resulting Numbers: [1, 9, 23] Generated Node #0,1: 13:[1, 9, 23] Operation: 76-53=23 Exploring Operation: 53-9=44, Resulting Numbers: [1, 76, 44] Generated Node #0,2: 13:[1, 76, 44] Operation: 53-9=44 Exploring Operation: 1+9=10, Resulting Numbers: [53, 76, 10] Generated Node #0,3: 13:[53, 76, 10] Operation: 1+9=10 Exploring Operation: 53-1=52, Resulting Numbers: [76, 9, 52] Generated Node #0,4: 13:[76, 9, 52] Operation: 53-1=52 Moving to Node #0,1 Current State: 13:[1, 9, 23], Operations: ['76-53=23'] Exploring Operation: 23-1=22, Resulting Numbers: [9, 22] Generated Node #0,1,0: 13:[9, 22] Operation: 23-1=22 Exploring Operation: 1*9=9, Resulting Numbers: [23, 9] Generated Node #0,1,1: 13:[23, 9] Operation: 1*9=9 Exploring Operation: 1+9=10, Resulting Numbers: [23, 10] Generated Node #0,1,2: 13:[23, 10] Operation: 1+9=10 Exploring Operation: 9/1=9, Resulting Numbers: [23, 9] Generated Node #0,1,3: 13:[23, 9] Operation: 9/1=9 Exploring Operation: 23-9=14, Resulting Numbers: [1, 14] Generated Node #0,1,4: 13:[1, 14] Operation: 23-9=14 Moving to Node #0,2 Current State: 13:[1, 76, 44], Operations: ['53-9=44'] Exploring Operation: 44-1=43, Resulting Numbers: [76, 43] Generated Node #0,2,0: 13:[76, 43] Operation: 44-1=43 Exploring Operation: 76-44=32, Resulting Numbers: [1, 32] Generated Node #0,2,1: 13:[1, 32] Operation: 76-44=32 Exploring Operation: 76/1=76, Resulting Numbers: [44, 76] Generated Node #0,2,2: 13:[44, 76] Operation: 76/1=76 Exploring Operation: 1*76=76, Resulting Numbers: [44, 76] Generated Node #0,2,3: 13:[44, 76] Operation: 1*76=76 Exploring Operation: 76-1=75, Resulting Numbers: [44, 75] Generated Node #0,2,4: 13:[44, 75] Operation: 76-1=75 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 13:[1, 32], Operations: ['53-9=44', '76-44=32'] Exploring Operation: 1*32=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 13:[76, 43], Operations: ['53-9=44', '44-1=43'] Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,13 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 13:[44, 75], Operations: ['53-9=44', '76-1=75'] Exploring Operation: 44*75=3300, Resulting Numbers: [3300] 3300,13 unequal: No Solution Exploring Operation: 44+75=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 13:[44, 76], Operations: ['53-9=44', '76/1=76'] Exploring Operation: 44*76=3344, Resulting Numbers: [3344] 3344,13 unequal: No Solution Exploring Operation: 76-44=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 44+76=120, Resulting Numbers: [120] 120,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 13:[44, 76], Operations: ['53-9=44', '1*76=76'] Exploring Operation: 44+76=120, Resulting Numbers: [120] 120,13 unequal: No Solution Exploring Operation: 44*76=3344, Resulting Numbers: [3344] 3344,13 unequal: No Solution Exploring Operation: 76-44=32, Resulting Numbers: [32] 32,13 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: 13:[76, 9, 52], Operations: ['53-1=52'] Exploring Operation: 76-9=67, Resulting Numbers: [52, 67] Generated Node #0,4,0: 13:[52, 67] Operation: 76-9=67 Exploring Operation: 52-9=43, Resulting Numbers: [76, 43] Generated Node #0,4,1: 13:[76, 43] Operation: 52-9=43 Exploring Operation: 9+52=61, Resulting Numbers: [76, 61] Generated Node #0,4,2: 13:[76, 61] Operation: 9+52=61 Exploring Operation: 76+9=85, Resulting Numbers: [52, 85] Generated Node #0,4,3: 13:[52, 85] Operation: 76+9=85 Exploring Operation: 76-52=24, Resulting Numbers: [9, 24] Generated Node #0,4,4: 13:[9, 24] Operation: 76-52=24 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 13:[9, 24], Operations: ['53-1=52', '76-52=24'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,13 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 13:[52, 67], Operations: ['53-1=52', '76-9=67'] Exploring Operation: 52+67=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 52*67=3484, Resulting Numbers: [3484] 3484,13 unequal: No Solution Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 13:[76, 43], Operations: ['53-1=52', '52-9=43'] Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 13:[76, 61], Operations: ['53-1=52', '9+52=61'] Exploring Operation: 76-61=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 76*61=4636, Resulting Numbers: [4636] 4636,13 unequal: No Solution Exploring Operation: 76+61=137, Resulting Numbers: [137] 137,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 13:[52, 85], Operations: ['53-1=52', '76+9=85'] Exploring Operation: 52*85=4420, Resulting Numbers: [4420] 4420,13 unequal: No Solution Exploring Operation: 85-52=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 52+85=137, Resulting Numbers: [137] 137,13 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: 13:[53, 9, 75], Operations: ['76-1=75'] Exploring Operation: 75-53=22, Resulting Numbers: [9, 22] Generated Node #0,0,0: 13:[9, 22] Operation: 75-53=22 Exploring Operation: 75-9=66, Resulting Numbers: [53, 66] Generated Node #0,0,1: 13:[53, 66] Operation: 75-9=66 Exploring Operation: 53-9=44, Resulting Numbers: [75, 44] Generated Node #0,0,2: 13:[75, 44] Operation: 53-9=44 Exploring Operation: 53+9=62, Resulting Numbers: [75, 62] Generated Node #0,0,3: 13:[75, 62] Operation: 53+9=62 Exploring Operation: 9+75=84, Resulting Numbers: [53, 84] Generated Node #0,0,4: 13:[53, 84] Operation: 9+75=84 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[9, 22], Operations: ['76-1=75', '75-53=22'] Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[1, 53, 76, 9], Operations: [] Exploring Operation: 76-1=75, Resulting Numbers: [53, 9, 75] Generated Node #0,0: 13:[53, 9, 75] Operation: 76-1=75 Moving to Node #0,0 Current State: 13:[53, 9, 75], Operations: ['76-1=75'] Exploring Operation: 75-53=22, Resulting Numbers: [9, 22] Generated Node #0,0,0: 13:[9, 22] Operation: 75-53=22 Moving to Node #0,0,0 Current State: 13:[9, 22], Operations: ['76-1=75', '75-53=22'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_5
mult_heuristic
[ 70, 96, 70, 4 ]
59
[ "70+96=166", "70+166=236", "236/4=59" ]
Current State: 59:[70, 96, 70, 4], Operations: [] Exploring Operation: 70+96=166, Resulting Numbers: [4, 166] Generated Node #2: [4, 166] from Operation: 70+96=166 Current State: 59:[4, 166], Operations: ['70+96=166'] Exploring Operation: 70+166=236, Resulting Numbers: [4, 236] Generated Node #3: [4, 236] from Operation: 70+166=236 Current State: 59:[4, 236], Operations: ['70+96=166', '70+166=236'] Exploring Operation: 236/4=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[70, 96, 70, 4], Operations: [] Exploring Operation: 70-4=66, Resulting Numbers: [70, 96, 66] Generated Node #0,0: 59:[70, 96, 66] Operation: 70-4=66 Exploring Operation: 96/4=24, Resulting Numbers: [70, 70, 24] Generated Node #0,1: 59:[70, 70, 24] Operation: 96/4=24 Exploring Operation: 96-4=92, Resulting Numbers: [70, 70, 92] Generated Node #0,2: 59:[70, 70, 92] Operation: 96-4=92 Exploring Operation: 70-4=66, Resulting Numbers: [96, 70, 66] Generated Node #0,3: 59:[96, 70, 66] Operation: 70-4=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[70, 96, 66], Operations: ['70-4=66'] Exploring Operation: 96-70=26, Resulting Numbers: [66, 26] Generated Node #0,0,0: 59:[66, 26] Operation: 96-70=26 Exploring Operation: 96-66=30, Resulting Numbers: [70, 30] Generated Node #0,0,1: 59:[70, 30] Operation: 96-66=30 Exploring Operation: 70-66=4, Resulting Numbers: [96, 4] Generated Node #0,0,2: 59:[96, 4] Operation: 70-66=4 Exploring Operation: 70+96=166, Resulting Numbers: [66, 166] Generated Node #0,0,3: 59:[66, 166] Operation: 70+96=166 Moving to Node #0,0,0 Current State: 59:[66, 26], Operations: ['70-4=66', '96-70=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[70, 30], Operations: ['70-4=66', '96-66=30'] Exploring Operation: 70+30=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 70*30=2100, Resulting Numbers: [2100] 2100,59 unequal: No Solution Exploring Operation: 70-30=40, Resulting Numbers: [40] 40,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[96, 4], Operations: ['70-4=66', '70-66=4'] Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 96*4=384, Resulting Numbers: [384] 384,59 unequal: No Solution Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[66, 166], Operations: ['70-4=66', '70+96=166'] Exploring Operation: 166-66=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 66*166=10956, Resulting Numbers: [10956] 10956,59 unequal: No Solution Exploring Operation: 66+166=232, Resulting Numbers: [232] 232,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[70, 70, 92], Operations: ['96-4=92'] Exploring Operation: 92-70=22, Resulting Numbers: [70, 22] Generated Node #0,2,0: 59:[70, 22] Operation: 92-70=22 Exploring Operation: 70/70=1, Resulting Numbers: [92, 1] Generated Node #0,2,1: 59:[92, 1] Operation: 70/70=1 Exploring Operation: 70-70=0, Resulting Numbers: [92, 0] Generated Node #0,2,2: 59:[92, 0] Operation: 70-70=0 Exploring Operation: 92-70=22, Resulting Numbers: [70, 22] Generated Node #0,2,3: 59:[70, 22] Operation: 92-70=22 Moving to Node #0,2,0 Current State: 59:[70, 22], Operations: ['96-4=92', '92-70=22'] Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[70, 22], Operations: ['96-4=92', '92-70=22'] Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[92, 1], Operations: ['96-4=92', '70/70=1'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[92, 0], Operations: ['96-4=92', '70-70=0'] Exploring Operation: 92*0=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 92+0=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 92-0=92, Resulting Numbers: [92] 92,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[96, 70, 66], Operations: ['70-4=66'] Exploring Operation: 70-66=4, Resulting Numbers: [96, 4] Generated Node #0,3,0: 59:[96, 4] Operation: 70-66=4 Exploring Operation: 96+70=166, Resulting Numbers: [66, 166] Generated Node #0,3,1: 59:[66, 166] Operation: 96+70=166 Exploring Operation: 96-70=26, Resulting Numbers: [66, 26] Generated Node #0,3,2: 59:[66, 26] Operation: 96-70=26 Exploring Operation: 96-66=30, Resulting Numbers: [70, 30] Generated Node #0,3,3: 59:[70, 30] Operation: 96-66=30 Moving to Node #0,3,2 Current State: 59:[66, 26], Operations: ['70-4=66', '96-70=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[70, 30], Operations: ['70-4=66', '96-66=30'] Exploring Operation: 70+30=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 70-30=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 70*30=2100, Resulting Numbers: [2100] 2100,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[96, 4], Operations: ['70-4=66', '70-66=4'] Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 96*4=384, Resulting Numbers: [384] 384,59 unequal: No Solution Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[66, 166], Operations: ['70-4=66', '96+70=166'] Exploring Operation: 66*166=10956, Resulting Numbers: [10956] 10956,59 unequal: No Solution Exploring Operation: 166-66=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 66+166=232, Resulting Numbers: [232] 232,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[70, 70, 24], Operations: ['96/4=24'] Exploring Operation: 70+24=94, Resulting Numbers: [70, 94] Generated Node #0,1,0: 59:[70, 94] Operation: 70+24=94 Exploring Operation: 70-24=46, Resulting Numbers: [70, 46] Generated Node #0,1,1: 59:[70, 46] Operation: 70-24=46 Exploring Operation: 70+24=94, Resulting Numbers: [70, 94] Generated Node #0,1,2: 59:[70, 94] Operation: 70+24=94 Exploring Operation: 70-24=46, Resulting Numbers: [70, 46] Generated Node #0,1,3: 59:[70, 46] Operation: 70-24=46 Moving to Node #0,1,1 Current State: 59:[70, 46], Operations: ['96/4=24', '70-24=46'] Exploring Operation: 70+46=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 70*46=3220, Resulting Numbers: [3220] 3220,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[70, 46], Operations: ['96/4=24', '70-24=46'] Exploring Operation: 70*46=3220, Resulting Numbers: [3220] 3220,59 unequal: No Solution Exploring Operation: 70+46=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[70, 94], Operations: ['96/4=24', '70+24=94'] Exploring Operation: 94-70=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 70+94=164, Resulting Numbers: [164] 164,59 unequal: No Solution Exploring Operation: 70*94=6580, Resulting Numbers: [6580] 6580,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[70, 94], Operations: ['96/4=24', '70+24=94'] Exploring Operation: 70+94=164, Resulting Numbers: [164] 164,59 unequal: No Solution Exploring Operation: 94-70=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 70*94=6580, Resulting Numbers: [6580] 6580,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 85, 49, 52, 66 ]
57
[ "85-66=19", "52-49=3", "19*3=57" ]
Current State: 57:[85, 49, 52, 66], Operations: [] Exploring Operation: 85-66=19, Resulting Numbers: [49, 52, 19] Generated Node #2: [49, 52, 19] from Operation: 85-66=19 Current State: 57:[49, 52, 19], Operations: ['85-66=19'] Exploring Operation: 52-49=3, Resulting Numbers: [19, 3] Generated Node #3: [19, 3] from Operation: 52-49=3 Current State: 57:[19, 3], Operations: ['85-66=19', '52-49=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[85, 49, 52, 66], Operations: [] Exploring Operation: 85-52=33, Resulting Numbers: [49, 66, 33] Generated Node #0,0: 57:[49, 66, 33] Operation: 85-52=33 Exploring Operation: 85-49=36, Resulting Numbers: [52, 66, 36] Generated Node #0,1: 57:[52, 66, 36] Operation: 85-49=36 Exploring Operation: 85-66=19, Resulting Numbers: [49, 52, 19] Generated Node #0,2: 57:[49, 52, 19] Operation: 85-66=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[49, 52, 19], Operations: ['85-66=19'] Exploring Operation: 49-19=30, Resulting Numbers: [52, 30] Generated Node #0,2,0: 57:[52, 30] Operation: 49-19=30 Exploring Operation: 49+19=68, Resulting Numbers: [52, 68] Generated Node #0,2,1: 57:[52, 68] Operation: 49+19=68 Exploring Operation: 52-49=3, Resulting Numbers: [19, 3] Generated Node #0,2,2: 57:[19, 3] Operation: 52-49=3 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 57:[19, 3], Operations: ['85-66=19', '52-49=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,57 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,57 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[85, 49, 52, 66], Operations: [] Exploring Operation: 85-66=19, Resulting Numbers: [49, 52, 19] Generated Node #0,2: 57:[49, 52, 19] Operation: 85-66=19 Moving to Node #0,2 Current State: 57:[49, 52, 19], Operations: ['85-66=19'] Exploring Operation: 52-49=3, Resulting Numbers: [19, 3] Generated Node #0,2,2: 57:[19, 3] Operation: 52-49=3 Moving to Node #0,2,2 Current State: 57:[19, 3], Operations: ['85-66=19', '52-49=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 78, 36, 10, 24 ]
13
[ "78*10=780", "36+24=60", "780/60=13" ]
Current State: 13:[78, 36, 10, 24], Operations: [] Exploring Operation: 78*10=780, Resulting Numbers: [36, 24, 780] Generated Node #2: [36, 24, 780] from Operation: 78*10=780 Current State: 13:[36, 24, 780], Operations: ['78*10=780'] Exploring Operation: 36+24=60, Resulting Numbers: [780, 60] Generated Node #3: [780, 60] from Operation: 36+24=60 Current State: 13:[780, 60], Operations: ['78*10=780', '36+24=60'] Exploring Operation: 780/60=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[78, 36, 10, 24], Operations: [] Exploring Operation: 78-24=54, Resulting Numbers: [36, 10, 54] Generated Node #0,0: 13:[36, 10, 54] Operation: 78-24=54 Exploring Operation: 78-36=42, Resulting Numbers: [10, 24, 42] Generated Node #0,1: 13:[10, 24, 42] Operation: 78-36=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[10, 24, 42], Operations: ['78-36=42'] Exploring Operation: 24-10=14, Resulting Numbers: [42, 14] Generated Node #0,1,0: 13:[42, 14] Operation: 24-10=14 Exploring Operation: 42-24=18, Resulting Numbers: [10, 18] Generated Node #0,1,1: 13:[10, 18] Operation: 42-24=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[10, 18], Operations: ['78-36=42', '42-24=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,13 unequal: No Solution No 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: 13:[42, 14], Operations: ['78-36=42', '24-10=14'] Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,13 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: 13:[36, 10, 54], Operations: ['78-24=54'] Exploring Operation: 54-36=18, Resulting Numbers: [10, 18] Generated Node #0,0,0: 13:[10, 18] Operation: 54-36=18 Exploring Operation: 36-10=26, Resulting Numbers: [54, 26] Generated Node #0,0,1: 13:[54, 26] Operation: 36-10=26 Moving to Node #0,0,0 Current State: 13:[10, 18], Operations: ['78-24=54', '54-36=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[54, 26], Operations: ['78-24=54', '36-10=26'] Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,13 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,13 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
[ 17, 26, 55, 12 ]
34
[ "26-17=9", "55-12=43", "43-9=34" ]
Current State: 34:[17, 26, 55, 12], Operations: [] Exploring Operation: 26-17=9, Resulting Numbers: [55, 12, 9] Generated Node #2: [55, 12, 9] from Operation: 26-17=9 Current State: 34:[55, 12, 9], Operations: ['26-17=9'] Exploring Operation: 55-12=43, Resulting Numbers: [9, 43] Generated Node #3: [9, 43] from Operation: 55-12=43 Current State: 34:[9, 43], Operations: ['26-17=9', '55-12=43'] Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[17, 26, 55, 12], Operations: [] Exploring Operation: 55-12=43, Resulting Numbers: [17, 26, 43] Generated Node #0,0: 34:[17, 26, 43] Operation: 55-12=43 Exploring Operation: 55-17=38, Resulting Numbers: [26, 12, 38] Generated Node #0,1: 34:[26, 12, 38] Operation: 55-17=38 Exploring Operation: 55-26=29, Resulting Numbers: [17, 12, 29] Generated Node #0,2: 34:[17, 12, 29] Operation: 55-26=29 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[17, 12, 29], Operations: ['55-26=29'] Exploring Operation: 29-12=17, Resulting Numbers: [17, 17] Generated Node #0,2,0: 34:[17, 17] Operation: 29-12=17 Exploring Operation: 12+29=41, Resulting Numbers: [17, 41] Generated Node #0,2,1: 34:[17, 41] Operation: 12+29=41 Exploring Operation: 17-12=5, Resulting Numbers: [29, 5] Generated Node #0,2,2: 34:[29, 5] Operation: 17-12=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 34:[17, 17], Operations: ['55-26=29', '29-12=17'] Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[17, 26, 55, 12], Operations: [] Exploring Operation: 55-26=29, Resulting Numbers: [17, 12, 29] Generated Node #0,2: 34:[17, 12, 29] Operation: 55-26=29 Moving to Node #0,2 Current State: 34:[17, 12, 29], Operations: ['55-26=29'] Exploring Operation: 29-12=17, Resulting Numbers: [17, 17] Generated Node #0,2,0: 34:[17, 17] Operation: 29-12=17 Moving to Node #0,2,0 Current State: 34:[17, 17], Operations: ['55-26=29', '29-12=17'] Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 11, 47, 60, 9 ]
11
[ "11+47=58", "60+9=69", "69-58=11" ]
Current State: 11:[11, 47, 60, 9], Operations: [] Exploring Operation: 11+47=58, Resulting Numbers: [60, 9, 58] Generated Node #2: [60, 9, 58] from Operation: 11+47=58 Current State: 11:[60, 9, 58], Operations: ['11+47=58'] Exploring Operation: 60+9=69, Resulting Numbers: [58, 69] Generated Node #3: [58, 69] from Operation: 60+9=69 Current State: 11:[58, 69], Operations: ['11+47=58', '60+9=69'] Exploring Operation: 69-58=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[11, 47, 60, 9], Operations: [] Exploring Operation: 60-47=13, Resulting Numbers: [11, 9, 13] Generated Node #0,0: 11:[11, 9, 13] Operation: 60-47=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[11, 9, 13], Operations: ['60-47=13'] Exploring Operation: 13-9=4, Resulting Numbers: [11, 4] Generated Node #0,0,0: 11:[11, 4] Operation: 13-9=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[11, 4], Operations: ['60-47=13', '13-9=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 41, 33, 12, 30 ]
37
[ "33-30=3", "12/3=4", "41-4=37" ]
Current State: 37:[41, 33, 12, 30], Operations: [] Exploring Operation: 33-30=3, Resulting Numbers: [41, 12, 3] Generated Node #2: [41, 12, 3] from Operation: 33-30=3 Current State: 37:[41, 12, 3], Operations: ['33-30=3'] Exploring Operation: 12/3=4, Resulting Numbers: [41, 4] Generated Node #3: [41, 4] from Operation: 12/3=4 Current State: 37:[41, 4], Operations: ['33-30=3', '12/3=4'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[41, 33, 12, 30], Operations: [] Exploring Operation: 41-12=29, Resulting Numbers: [33, 30, 29] Generated Node #0,0: 37:[33, 30, 29] Operation: 41-12=29 Exploring Operation: 12+30=42, Resulting Numbers: [41, 33, 42] Generated Node #0,1: 37:[41, 33, 42] Operation: 12+30=42 Exploring Operation: 33+12=45, Resulting Numbers: [41, 30, 45] Generated Node #0,2: 37:[41, 30, 45] Operation: 33+12=45 Moving to Node #0,1 Current State: 37:[41, 33, 42], Operations: ['12+30=42'] Exploring Operation: 42-33=9, Resulting Numbers: [41, 9] Generated Node #0,1,0: 37:[41, 9] Operation: 42-33=9 Exploring Operation: 41-33=8, Resulting Numbers: [42, 8] Generated Node #0,1,1: 37:[42, 8] Operation: 41-33=8 Exploring Operation: 42-41=1, Resulting Numbers: [33, 1] Generated Node #0,1,2: 37:[33, 1] Operation: 42-41=1 Moving to Node #0,0 Current State: 37:[33, 30, 29], Operations: ['41-12=29'] Exploring Operation: 33+30=63, Resulting Numbers: [29, 63] Generated Node #0,0,0: 37:[29, 63] Operation: 33+30=63 Exploring Operation: 33+29=62, Resulting Numbers: [30, 62] Generated Node #0,0,1: 37:[30, 62] Operation: 33+29=62 Exploring Operation: 30+29=59, Resulting Numbers: [33, 59] Generated Node #0,0,2: 37:[33, 59] Operation: 30+29=59 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[33, 59], Operations: ['41-12=29', '30+29=59'] Exploring Operation: 33+59=92, Resulting Numbers: [92] 92,37 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 33*59=1947, Resulting Numbers: [1947] 1947,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[30, 62], Operations: ['41-12=29', '33+29=62'] Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,37 unequal: No Solution Exploring Operation: 30+62=92, Resulting Numbers: [92] 92,37 unequal: No Solution Exploring Operation: 30*62=1860, Resulting Numbers: [1860] 1860,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[29, 63], Operations: ['41-12=29', '33+30=63'] Exploring Operation: 29+63=92, Resulting Numbers: [92] 92,37 unequal: No Solution Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 29*63=1827, Resulting Numbers: [1827] 1827,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 37:[41, 30, 45], Operations: ['33+12=45'] Exploring Operation: 45-30=15, Resulting Numbers: [41, 15] Generated Node #0,2,0: 37:[41, 15] Operation: 45-30=15 Exploring Operation: 45-41=4, Resulting Numbers: [30, 4] Generated Node #0,2,1: 37:[30, 4] Operation: 45-41=4 Exploring Operation: 41-30=11, Resulting Numbers: [45, 11] Generated Node #0,2,2: 37:[45, 11] Operation: 41-30=11 Moving to Node #0,2,0 Current State: 37:[41, 15], Operations: ['33+12=45', '45-30=15'] Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 41+15=56, Resulting Numbers: [56] 56,37 unequal: No Solution Exploring Operation: 41*15=615, Resulting Numbers: [615] 615,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[41, 9], Operations: ['12+30=42', '42-33=9'] Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,37 unequal: No Solution Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,37 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[45, 11], Operations: ['33+12=45', '41-30=11'] Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,37 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[42, 8], Operations: ['12+30=42', '41-33=8'] Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,37 unequal: No Solution Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,37 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[30, 4], Operations: ['33+12=45', '45-41=4'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,37 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[33, 1], Operations: ['12+30=42', '42-41=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,37 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,37 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 42, 80, 13, 11 ]
85
[ "42+13=55", "55/11=5", "80+5=85" ]
Current State: 85:[42, 80, 13, 11], Operations: [] Exploring Operation: 42+13=55, Resulting Numbers: [80, 11, 55] Generated Node #2: [80, 11, 55] from Operation: 42+13=55 Current State: 85:[80, 11, 55], Operations: ['42+13=55'] Exploring Operation: 55/11=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 55/11=5 Current State: 85:[80, 5], Operations: ['42+13=55', '55/11=5'] Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[42, 80, 13, 11], Operations: [] Exploring Operation: 42-13=29, Resulting Numbers: [80, 11, 29] Generated Node #0,0: 85:[80, 11, 29] Operation: 42-13=29 Exploring Operation: 42-11=31, Resulting Numbers: [80, 13, 31] Generated Node #0,1: 85:[80, 13, 31] Operation: 42-11=31 Moving to Node #0,0 Current State: 85:[80, 11, 29], Operations: ['42-13=29'] Exploring Operation: 29-11=18, Resulting Numbers: [80, 18] Generated Node #0,0,0: 85:[80, 18] Operation: 29-11=18 Exploring Operation: 80+11=91, Resulting Numbers: [29, 91] Generated Node #0,0,1: 85:[29, 91] Operation: 80+11=91 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[80, 18], Operations: ['42-13=29', '29-11=18'] Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,85 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[29, 91], Operations: ['42-13=29', '80+11=91'] Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,85 unequal: No Solution Exploring Operation: 29+91=120, Resulting Numbers: [120] 120,85 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: 85:[80, 13, 31], Operations: ['42-11=31'] Exploring Operation: 31-13=18, Resulting Numbers: [80, 18] Generated Node #0,1,0: 85:[80, 18] Operation: 31-13=18 Exploring Operation: 80+13=93, Resulting Numbers: [31, 93] Generated Node #0,1,1: 85:[31, 93] Operation: 80+13=93 Moving to Node #0,1,0 Current State: 85:[80, 18], Operations: ['42-11=31', '31-13=18'] Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,85 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[31, 93], Operations: ['42-11=31', '80+13=93'] Exploring Operation: 93-31=62, Resulting Numbers: [62] 62,85 unequal: No Solution Exploring Operation: 93/31=3, Resulting Numbers: [3] 3,85 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 11, 57, 11, 22 ]
54
[ "11+22=33", "33/11=3", "57-3=54" ]
Current State: 54:[11, 57, 11, 22], Operations: [] Exploring Operation: 11+22=33, Resulting Numbers: [57, 33] Generated Node #2: [57, 33] from Operation: 11+22=33 Current State: 54:[57, 33], Operations: ['11+22=33'] Exploring Operation: 33/11=3, Resulting Numbers: [57, 3] Generated Node #3: [57, 3] from Operation: 33/11=3 Current State: 54:[57, 3], Operations: ['11+22=33', '33/11=3'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[11, 57, 11, 22], Operations: [] Exploring Operation: 22/11=2, Resulting Numbers: [57, 11, 2] Generated Node #0,0: 54:[57, 11, 2] Operation: 22/11=2 Moving to Node #0,0 Current State: 54:[57, 11, 2], Operations: ['22/11=2'] Exploring Operation: 57-2=55, Resulting Numbers: [11, 55] Generated Node #0,0,0: 54:[11, 55] Operation: 57-2=55 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[11, 55], Operations: ['22/11=2', '57-2=55'] Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,54 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
[ 70, 28, 29, 96 ]
31
[ "70+28=98", "96-29=67", "98-67=31" ]
Current State: 31:[70, 28, 29, 96], Operations: [] Exploring Operation: 70+28=98, Resulting Numbers: [29, 96, 98] Generated Node #2: [29, 96, 98] from Operation: 70+28=98 Current State: 31:[29, 96, 98], Operations: ['70+28=98'] Exploring Operation: 96-29=67, Resulting Numbers: [98, 67] Generated Node #3: [98, 67] from Operation: 96-29=67 Current State: 31:[98, 67], Operations: ['70+28=98', '96-29=67'] Exploring Operation: 98-67=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[70, 28, 29, 96], Operations: [] Exploring Operation: 70-29=41, Resulting Numbers: [28, 96, 41] Generated Node #0,0: 31:[28, 96, 41] Operation: 70-29=41 Exploring Operation: 96-70=26, Resulting Numbers: [28, 29, 26] Generated Node #0,1: 31:[28, 29, 26] Operation: 96-70=26 Exploring Operation: 70-28=42, Resulting Numbers: [29, 96, 42] Generated Node #0,2: 31:[29, 96, 42] Operation: 70-28=42 Exploring Operation: 96-28=68, Resulting Numbers: [70, 29, 68] Generated Node #0,3: 31:[70, 29, 68] Operation: 96-28=68 Moving to Node #0,1 Current State: 31:[28, 29, 26], Operations: ['96-70=26'] Exploring Operation: 28-26=2, Resulting Numbers: [29, 2] Generated Node #0,1,0: 31:[29, 2] Operation: 28-26=2 Exploring Operation: 28+26=54, Resulting Numbers: [29, 54] Generated Node #0,1,1: 31:[29, 54] Operation: 28+26=54 Exploring Operation: 29+26=55, Resulting Numbers: [28, 55] Generated Node #0,1,2: 31:[28, 55] Operation: 29+26=55 Exploring Operation: 28+29=57, Resulting Numbers: [26, 57] Generated Node #0,1,3: 31:[26, 57] Operation: 28+29=57 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[29, 54], Operations: ['96-70=26', '28+26=54'] Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,31 unequal: No Solution Exploring Operation: 29+54=83, Resulting Numbers: [83] 83,31 unequal: No Solution Exploring Operation: 29*54=1566, Resulting Numbers: [1566] 1566,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[28, 55], Operations: ['96-70=26', '29+26=55'] Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,31 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[29, 2], Operations: ['96-70=26', '28-26=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[70, 28, 29, 96], Operations: [] Exploring Operation: 96-70=26, Resulting Numbers: [28, 29, 26] Generated Node #0,1: 31:[28, 29, 26] Operation: 96-70=26 Moving to Node #0,1 Current State: 31:[28, 29, 26], Operations: ['96-70=26'] Exploring Operation: 28-26=2, Resulting Numbers: [29, 2] Generated Node #0,1,0: 31:[29, 2] Operation: 28-26=2 Moving to Node #0,1,0 Current State: 31:[29, 2], Operations: ['96-70=26', '28-26=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 64, 10, 54, 62 ]
16
[ "62-54=8", "10*8=80", "80-64=16" ]
Current State: 16:[64, 10, 54, 62], Operations: [] Exploring Operation: 62-54=8, Resulting Numbers: [64, 10, 8] Generated Node #2: [64, 10, 8] from Operation: 62-54=8 Current State: 16:[64, 10, 8], Operations: ['62-54=8'] Exploring Operation: 10*8=80, Resulting Numbers: [64, 80] Generated Node #3: [64, 80] from Operation: 10*8=80 Current State: 16:[64, 80], Operations: ['62-54=8', '10*8=80'] Exploring Operation: 80-64=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[64, 10, 54, 62], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [10, 54, 2] Generated Node #0,0: 16:[10, 54, 2] Operation: 64-62=2 Exploring Operation: 64-54=10, Resulting Numbers: [10, 62, 10] Generated Node #0,1: 16:[10, 62, 10] Operation: 64-54=10 Moving to Node #0,0 Current State: 16:[10, 54, 2], Operations: ['64-62=2'] Exploring Operation: 54/2=27, Resulting Numbers: [10, 27] Generated Node #0,0,0: 16:[10, 27] Operation: 54/2=27 Exploring Operation: 54-10=44, Resulting Numbers: [2, 44] Generated Node #0,0,1: 16:[2, 44] Operation: 54-10=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[10, 27], Operations: ['64-62=2', '54/2=27'] Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,16 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[2, 44], Operations: ['64-62=2', '54-10=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,16 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: 16:[10, 62, 10], Operations: ['64-54=10'] Exploring Operation: 62-10=52, Resulting Numbers: [10, 52] Generated Node #0,1,0: 16:[10, 52] Operation: 62-10=52 Exploring Operation: 62-10=52, Resulting Numbers: [10, 52] Generated Node #0,1,1: 16:[10, 52] Operation: 62-10=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[10, 52], Operations: ['64-54=10', '62-10=52'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 10+52=62, Resulting Numbers: [62] 62,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[10, 52], Operations: ['64-54=10', '62-10=52'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 10+52=62, Resulting Numbers: [62] 62,16 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, 10, 24, 44 ]
84
[ "94+10=104", "44-24=20", "104-20=84" ]
Current State: 84:[94, 10, 24, 44], Operations: [] Exploring Operation: 94+10=104, Resulting Numbers: [24, 44, 104] Generated Node #2: [24, 44, 104] from Operation: 94+10=104 Current State: 84:[24, 44, 104], Operations: ['94+10=104'] Exploring Operation: 44-24=20, Resulting Numbers: [104, 20] Generated Node #3: [104, 20] from Operation: 44-24=20 Current State: 84:[104, 20], Operations: ['94+10=104', '44-24=20'] Exploring Operation: 104-20=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[94, 10, 24, 44], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [94, 10, 20] Generated Node #0,0: 84:[94, 10, 20] Operation: 44-24=20 Exploring Operation: 94-44=50, Resulting Numbers: [10, 24, 50] Generated Node #0,1: 84:[10, 24, 50] Operation: 94-44=50 Exploring Operation: 24-10=14, Resulting Numbers: [94, 44, 14] Generated Node #0,2: 84:[94, 44, 14] Operation: 24-10=14 Exploring Operation: 94-24=70, Resulting Numbers: [10, 44, 70] Generated Node #0,3: 84:[10, 44, 70] Operation: 94-24=70 Exploring Operation: 94-10=84, Resulting Numbers: [24, 44, 84] Generated Node #0,4: 84:[24, 44, 84] Operation: 94-10=84 Start Sub Search at level 1: Moving to Node #0,4 Current State: 84:[24, 44, 84], Operations: ['94-10=84'] Exploring Operation: 84-24=60, Resulting Numbers: [44, 60] Generated Node #0,4,0: 84:[44, 60] Operation: 84-24=60 Exploring Operation: 24+44=68, Resulting Numbers: [84, 68] Generated Node #0,4,1: 84:[84, 68] Operation: 24+44=68 Exploring Operation: 44-24=20, Resulting Numbers: [84, 20] Generated Node #0,4,2: 84:[84, 20] Operation: 44-24=20 Exploring Operation: 84-44=40, Resulting Numbers: [24, 40] Generated Node #0,4,3: 84:[24, 40] Operation: 84-44=40 Exploring Operation: 24+84=108, Resulting Numbers: [44, 108] Generated Node #0,4,4: 84:[44, 108] Operation: 24+84=108 Moving to Node #0,4,2 Current State: 84:[84, 20], Operations: ['94-10=84', '44-24=20'] Exploring Operation: 84+20=104, Resulting Numbers: [104] 104,84 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 84*20=1680, Resulting Numbers: [1680] 1680,84 unequal: No Solution Moving to Node #0,4,3 Current State: 84:[24, 40], Operations: ['94-10=84', '84-44=40'] Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,84 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,84 unequal: No Solution Moving to Node #0,4,1 Current State: 84:[84, 68], Operations: ['94-10=84', '24+44=68'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 84+68=152, Resulting Numbers: [152] 152,84 unequal: No Solution Exploring Operation: 84*68=5712, Resulting Numbers: [5712] 5712,84 unequal: No Solution Moving to Node #0,4,0 Current State: 84:[44, 60], Operations: ['94-10=84', '84-24=60'] Exploring Operation: 44*60=2640, Resulting Numbers: [2640] 2640,84 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 44+60=104, Resulting Numbers: [104] 104,84 unequal: No Solution Moving to Node #0,4,4 Current State: 84:[44, 108], Operations: ['94-10=84', '24+84=108'] Exploring Operation: 44+108=152, Resulting Numbers: [152] 152,84 unequal: No Solution Exploring Operation: 44*108=4752, Resulting Numbers: [4752] 4752,84 unequal: No Solution Exploring Operation: 108-44=64, Resulting Numbers: [64] 64,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[94, 44, 14], Operations: ['24-10=14'] Exploring Operation: 44+14=58, Resulting Numbers: [94, 58] Generated Node #0,2,0: 84:[94, 58] Operation: 44+14=58 Exploring Operation: 94-14=80, Resulting Numbers: [44, 80] Generated Node #0,2,1: 84:[44, 80] Operation: 94-14=80 Exploring Operation: 94+14=108, Resulting Numbers: [44, 108] Generated Node #0,2,2: 84:[44, 108] Operation: 94+14=108 Exploring Operation: 44-14=30, Resulting Numbers: [94, 30] Generated Node #0,2,3: 84:[94, 30] Operation: 44-14=30 Exploring Operation: 94-44=50, Resulting Numbers: [14, 50] Generated Node #0,2,4: 84:[14, 50] Operation: 94-44=50 Moving to Node #0,2,1 Current State: 84:[44, 80], Operations: ['24-10=14', '94-14=80'] Exploring Operation: 44+80=124, Resulting Numbers: [124] 124,84 unequal: No Solution Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 44*80=3520, Resulting Numbers: [3520] 3520,84 unequal: No Solution Moving to Node #0,2,4 Current State: 84:[14, 50], Operations: ['24-10=14', '94-44=50'] Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 14+50=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 14*50=700, Resulting Numbers: [700] 700,84 unequal: No Solution Moving to Node #0,2,3 Current State: 84:[94, 30], Operations: ['24-10=14', '44-14=30'] Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,84 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[94, 58], Operations: ['24-10=14', '44+14=58'] Exploring Operation: 94+58=152, Resulting Numbers: [152] 152,84 unequal: No Solution Exploring Operation: 94*58=5452, Resulting Numbers: [5452] 5452,84 unequal: No Solution Exploring Operation: 94-58=36, Resulting Numbers: [36] 36,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[44, 108], Operations: ['24-10=14', '94+14=108'] Exploring Operation: 108-44=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 44+108=152, Resulting Numbers: [152] 152,84 unequal: No Solution Exploring Operation: 44*108=4752, Resulting Numbers: [4752] 4752,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[94, 10, 20], Operations: ['44-24=20'] Exploring Operation: 94-10=84, Resulting Numbers: [20, 84] Generated Node #0,0,0: 84:[20, 84] Operation: 94-10=84 Exploring Operation: 20/10=2, Resulting Numbers: [94, 2] Generated Node #0,0,1: 84:[94, 2] Operation: 20/10=2 Exploring Operation: 20-10=10, Resulting Numbers: [94, 10] Generated Node #0,0,2: 84:[94, 10] Operation: 20-10=10 Exploring Operation: 94-20=74, Resulting Numbers: [10, 74] Generated Node #0,0,3: 84:[10, 74] Operation: 94-20=74 Exploring Operation: 10+20=30, Resulting Numbers: [94, 30] Generated Node #0,0,4: 84:[94, 30] Operation: 10+20=30 Moving to Node #0,0,0 Current State: 84:[20, 84], Operations: ['44-24=20', '94-10=84'] Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,84 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[94, 2], Operations: ['44-24=20', '20/10=2'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,84 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 94*2=188, Resulting Numbers: [188] 188,84 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[94, 10], Operations: ['44-24=20', '20-10=10'] Exploring Operation: 94*10=940, Resulting Numbers: [940] 940,84 unequal: No Solution Exploring Operation: 94+10=104, Resulting Numbers: [104] 104,84 unequal: No Solution Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[94, 10, 24, 44], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [94, 10, 20] Generated Node #0,0: 84:[94, 10, 20] Operation: 44-24=20 Moving to Node #0,0 Current State: 84:[94, 10, 20], Operations: ['44-24=20'] Exploring Operation: 20-10=10, Resulting Numbers: [94, 10] Generated Node #0,0,2: 84:[94, 10] Operation: 20-10=10 Moving to Node #0,0,2 Current State: 84:[94, 10], Operations: ['44-24=20', '20-10=10'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.944444
hs_5
mult_heuristic
[ 18, 74, 7, 87 ]
12
[ "18+74=92", "87-7=80", "92-80=12" ]
Current State: 12:[18, 74, 7, 87], Operations: [] Exploring Operation: 18+74=92, Resulting Numbers: [7, 87, 92] Generated Node #2: [7, 87, 92] from Operation: 18+74=92 Current State: 12:[7, 87, 92], Operations: ['18+74=92'] Exploring Operation: 87-7=80, Resulting Numbers: [92, 80] Generated Node #3: [92, 80] from Operation: 87-7=80 Current State: 12:[92, 80], Operations: ['18+74=92', '87-7=80'] Exploring Operation: 92-80=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[18, 74, 7, 87], Operations: [] Exploring Operation: 87-18=69, Resulting Numbers: [74, 7, 69] Generated Node #0,0: 12:[74, 7, 69] Operation: 87-18=69 Exploring Operation: 74-7=67, Resulting Numbers: [18, 87, 67] Generated Node #0,1: 12:[18, 87, 67] Operation: 74-7=67 Exploring Operation: 87-74=13, Resulting Numbers: [18, 7, 13] Generated Node #0,2: 12:[18, 7, 13] Operation: 87-74=13 Exploring Operation: 74-18=56, Resulting Numbers: [7, 87, 56] Generated Node #0,3: 12:[7, 87, 56] Operation: 74-18=56 Moving to Node #0,2 Current State: 12:[18, 7, 13], Operations: ['87-74=13'] Exploring Operation: 13-7=6, Resulting Numbers: [18, 6] Generated Node #0,2,0: 12:[18, 6] Operation: 13-7=6 Exploring Operation: 18-7=11, Resulting Numbers: [13, 11] Generated Node #0,2,1: 12:[13, 11] Operation: 18-7=11 Exploring Operation: 18+7=25, Resulting Numbers: [13, 25] Generated Node #0,2,2: 12:[13, 25] Operation: 18+7=25 Exploring Operation: 18-13=5, Resulting Numbers: [7, 5] Generated Node #0,2,3: 12:[7, 5] Operation: 18-13=5 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 12:[13, 11], Operations: ['87-74=13', '18-7=11'] Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,12 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 12:[7, 5], Operations: ['87-74=13', '18-13=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[18, 74, 7, 87], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [18, 7, 13] Generated Node #0,2: 12:[18, 7, 13] Operation: 87-74=13 Moving to Node #0,2 Current State: 12:[18, 7, 13], Operations: ['87-74=13'] Exploring Operation: 18-13=5, Resulting Numbers: [7, 5] Generated Node #0,2,3: 12:[7, 5] Operation: 18-13=5 Moving to Node #0,2,3 Current State: 12:[7, 5], Operations: ['87-74=13', '18-13=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 82, 12, 61, 2 ]
14
[ "82+12=94", "94/2=47", "61-47=14" ]
Current State: 14:[82, 12, 61, 2], Operations: [] Exploring Operation: 82+12=94, Resulting Numbers: [61, 2, 94] Generated Node #2: [61, 2, 94] from Operation: 82+12=94 Current State: 14:[61, 2, 94], Operations: ['82+12=94'] Exploring Operation: 94/2=47, Resulting Numbers: [61, 47] Generated Node #3: [61, 47] from Operation: 94/2=47 Current State: 14:[61, 47], Operations: ['82+12=94', '94/2=47'] Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[82, 12, 61, 2], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [12, 61, 41] Generated Node #0,0: 14:[12, 61, 41] Operation: 82/2=41 Exploring Operation: 82-61=21, Resulting Numbers: [12, 2, 21] Generated Node #0,1: 14:[12, 2, 21] Operation: 82-61=21 Exploring Operation: 82-2=80, Resulting Numbers: [12, 61, 80] Generated Node #0,2: 14:[12, 61, 80] Operation: 82-2=80 Exploring Operation: 82-12=70, Resulting Numbers: [61, 2, 70] Generated Node #0,3: 14:[61, 2, 70] Operation: 82-12=70 Exploring Operation: 61-12=49, Resulting Numbers: [82, 2, 49] Generated Node #0,4: 14:[82, 2, 49] Operation: 61-12=49 Moving to Node #0,1 Current State: 14:[12, 2, 21], Operations: ['82-61=21'] Exploring Operation: 21-12=9, Resulting Numbers: [2, 9] Generated Node #0,1,0: 14:[2, 9] Operation: 21-12=9 Exploring Operation: 12/2=6, Resulting Numbers: [21, 6] Generated Node #0,1,1: 14:[21, 6] Operation: 12/2=6 Exploring Operation: 12-2=10, Resulting Numbers: [21, 10] Generated Node #0,1,2: 14:[21, 10] Operation: 12-2=10 Exploring Operation: 21-2=19, Resulting Numbers: [12, 19] Generated Node #0,1,3: 14:[12, 19] Operation: 21-2=19 Exploring Operation: 12+2=14, Resulting Numbers: [21, 14] Generated Node #0,1,4: 14:[21, 14] Operation: 12+2=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[2, 9], Operations: ['82-61=21', '21-12=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 14:[12, 19], Operations: ['82-61=21', '21-2=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 14:[21, 14], Operations: ['82-61=21', '12+2=14'] Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,14 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 14:[21, 6], Operations: ['82-61=21', '12/2=6'] Exploring Operation: 21*6=126, Resulting Numbers: [126] 126,14 unequal: No Solution Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 14:[21, 10], Operations: ['82-61=21', '12-2=10'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,14 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: 14:[12, 61, 41], Operations: ['82/2=41'] Exploring Operation: 12+61=73, Resulting Numbers: [41, 73] Generated Node #0,0,0: 14:[41, 73] Operation: 12+61=73 Exploring Operation: 61-12=49, Resulting Numbers: [41, 49] Generated Node #0,0,1: 14:[41, 49] Operation: 61-12=49 Exploring Operation: 12+41=53, Resulting Numbers: [61, 53] Generated Node #0,0,2: 14:[61, 53] Operation: 12+41=53 Exploring Operation: 61-41=20, Resulting Numbers: [12, 20] Generated Node #0,0,3: 14:[12, 20] Operation: 61-41=20 Exploring Operation: 41-12=29, Resulting Numbers: [61, 29] Generated Node #0,0,4: 14:[61, 29] Operation: 41-12=29 Moving to Node #0,3 Current State: 14:[61, 2, 70], Operations: ['82-12=70'] Exploring Operation: 61+2=63, Resulting Numbers: [70, 63] Generated Node #0,3,0: 14:[70, 63] Operation: 61+2=63 Exploring Operation: 70/2=35, Resulting Numbers: [61, 35] Generated Node #0,3,1: 14:[61, 35] Operation: 70/2=35 Exploring Operation: 61-2=59, Resulting Numbers: [70, 59] Generated Node #0,3,2: 14:[70, 59] Operation: 61-2=59 Exploring Operation: 70-2=68, Resulting Numbers: [61, 68] Generated Node #0,3,3: 14:[61, 68] Operation: 70-2=68 Exploring Operation: 70-61=9, Resulting Numbers: [2, 9] Generated Node #0,3,4: 14:[2, 9] Operation: 70-61=9 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 14:[2, 9], Operations: ['82-12=70', '70-61=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 14:[61, 35], Operations: ['82-12=70', '70/2=35'] Exploring Operation: 61*35=2135, Resulting Numbers: [2135] 2135,14 unequal: No Solution Exploring Operation: 61+35=96, Resulting Numbers: [96] 96,14 unequal: No Solution Exploring Operation: 61-35=26, Resulting Numbers: [26] 26,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 14:[70, 59], Operations: ['82-12=70', '61-2=59'] Exploring Operation: 70*59=4130, Resulting Numbers: [4130] 4130,14 unequal: No Solution Exploring Operation: 70-59=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 70+59=129, Resulting Numbers: [129] 129,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 14:[61, 68], Operations: ['82-12=70', '70-2=68'] Exploring Operation: 68-61=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 61*68=4148, Resulting Numbers: [4148] 4148,14 unequal: No Solution Exploring Operation: 61+68=129, Resulting Numbers: [129] 129,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 14:[70, 63], Operations: ['82-12=70', '61+2=63'] Exploring Operation: 70*63=4410, Resulting Numbers: [4410] 4410,14 unequal: No Solution Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 70+63=133, Resulting Numbers: [133] 133,14 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: 14:[82, 2, 49], Operations: ['61-12=49'] Exploring Operation: 82+2=84, Resulting Numbers: [49, 84] Generated Node #0,4,0: 14:[49, 84] Operation: 82+2=84 Exploring Operation: 82/2=41, Resulting Numbers: [49, 41] Generated Node #0,4,1: 14:[49, 41] Operation: 82/2=41 Exploring Operation: 82-2=80, Resulting Numbers: [49, 80] Generated Node #0,4,2: 14:[49, 80] Operation: 82-2=80 Exploring Operation: 49-2=47, Resulting Numbers: [82, 47] Generated Node #0,4,3: 14:[82, 47] Operation: 49-2=47 Exploring Operation: 82-49=33, Resulting Numbers: [2, 33] Generated Node #0,4,4: 14:[2, 33] Operation: 82-49=33 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 14:[2, 33], Operations: ['61-12=49', '82-49=33'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,14 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 14:[49, 41], Operations: ['61-12=49', '82/2=41'] Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 49*41=2009, Resulting Numbers: [2009] 2009,14 unequal: No Solution Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 14:[49, 80], Operations: ['61-12=49', '82-2=80'] Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 14:[82, 47], Operations: ['61-12=49', '49-2=47'] Exploring Operation: 82-47=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 82+47=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 82*47=3854, Resulting Numbers: [3854] 3854,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 14:[49, 84], Operations: ['61-12=49', '82+2=84'] Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 49*84=4116, Resulting Numbers: [4116] 4116,14 unequal: No Solution Exploring Operation: 49+84=133, Resulting Numbers: [133] 133,14 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: 14:[12, 61, 80], Operations: ['82-2=80'] Exploring Operation: 12+80=92, Resulting Numbers: [61, 92] Generated Node #0,2,0: 14:[61, 92] Operation: 12+80=92 Exploring Operation: 12+61=73, Resulting Numbers: [80, 73] Generated Node #0,2,1: 14:[80, 73] Operation: 12+61=73 Exploring Operation: 80-12=68, Resulting Numbers: [61, 68] Generated Node #0,2,2: 14:[61, 68] Operation: 80-12=68 Exploring Operation: 80-61=19, Resulting Numbers: [12, 19] Generated Node #0,2,3: 14:[12, 19] Operation: 80-61=19 Exploring Operation: 61-12=49, Resulting Numbers: [80, 49] Generated Node #0,2,4: 14:[80, 49] Operation: 61-12=49 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 14:[12, 19], Operations: ['82-2=80', '80-61=19'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 14:[61, 68], Operations: ['82-2=80', '80-12=68'] Exploring Operation: 61+68=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 68-61=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 61*68=4148, Resulting Numbers: [4148] 4148,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 14:[80, 49], Operations: ['82-2=80', '61-12=49'] Exploring Operation: 80+49=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 80*49=3920, Resulting Numbers: [3920] 3920,14 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[61, 92], Operations: ['82-2=80', '12+80=92'] Exploring Operation: 92-61=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 61*92=5612, Resulting Numbers: [5612] 5612,14 unequal: No Solution Exploring Operation: 61+92=153, Resulting Numbers: [153] 153,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[80, 73], Operations: ['82-2=80', '12+61=73'] Exploring Operation: 80*73=5840, Resulting Numbers: [5840] 5840,14 unequal: No Solution Exploring Operation: 80-73=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 80+73=153, Resulting Numbers: [153] 153,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 14:[12, 20], Operations: ['82/2=41', '61-41=20'] Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 12*20=240, Resulting Numbers: [240] 240,14 unequal: No Solution Moving to Node #0,0,4 Current State: 14:[61, 29], Operations: ['82/2=41', '41-12=29'] Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 61*29=1769, Resulting Numbers: [1769] 1769,14 unequal: No Solution Exploring Operation: 61+29=90, Resulting Numbers: [90] 90,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[41, 49], Operations: ['82/2=41', '61-12=49'] Exploring Operation: 41+49=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 41*49=2009, Resulting Numbers: [2009] 2009,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[41, 73], Operations: ['82/2=41', '12+61=73'] Exploring Operation: 41*73=2993, Resulting Numbers: [2993] 2993,14 unequal: No Solution Exploring Operation: 41+73=114, Resulting Numbers: [114] 114,14 unequal: No Solution Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,14 unequal: No Solution Moving to Node #0,0,2 Current State: 14:[61, 53], Operations: ['82/2=41', '12+41=53'] Exploring Operation: 61+53=114, Resulting Numbers: [114] 114,14 unequal: No Solution Exploring Operation: 61*53=3233, Resulting Numbers: [3233] 3233,14 unequal: No Solution Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,14 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 99, 10, 15, 75 ]
96
[ "10+15=25", "75/25=3", "99-3=96" ]
Current State: 96:[99, 10, 15, 75], Operations: [] Exploring Operation: 10+15=25, Resulting Numbers: [99, 75, 25] Generated Node #2: [99, 75, 25] from Operation: 10+15=25 Current State: 96:[99, 75, 25], Operations: ['10+15=25'] Exploring Operation: 75/25=3, Resulting Numbers: [99, 3] Generated Node #3: [99, 3] from Operation: 75/25=3 Current State: 96:[99, 3], Operations: ['10+15=25', '75/25=3'] Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[99, 10, 15, 75], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [10, 15, 24] Generated Node #0,0: 96:[10, 15, 24] Operation: 99-75=24 Exploring Operation: 75/15=5, Resulting Numbers: [99, 10, 5] Generated Node #0,1: 96:[99, 10, 5] Operation: 75/15=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[10, 15, 24], Operations: ['99-75=24'] Exploring Operation: 10+15=25, Resulting Numbers: [24, 25] Generated Node #0,0,0: 96:[24, 25] Operation: 10+15=25 Exploring Operation: 15-10=5, Resulting Numbers: [24, 5] Generated Node #0,0,1: 96:[24, 5] Operation: 15-10=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[24, 25], Operations: ['99-75=24', '10+15=25'] Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 24+25=49, Resulting Numbers: [49] 49,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[24, 5], Operations: ['99-75=24', '15-10=5'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[99, 10, 5], Operations: ['75/15=5'] Exploring Operation: 10/5=2, Resulting Numbers: [99, 2] Generated Node #0,1,0: 96:[99, 2] Operation: 10/5=2 Exploring Operation: 99-5=94, Resulting Numbers: [10, 94] Generated Node #0,1,1: 96:[10, 94] Operation: 99-5=94 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[99, 2], Operations: ['75/15=5', '10/5=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,96 unequal: No Solution Exploring Operation: 99+2=101, Resulting Numbers: [101] 101,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[10, 94], Operations: ['75/15=5', '99-5=94'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,96 unequal: No Solution Exploring Operation: 10+94=104, Resulting Numbers: [104] 104,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 23, 52, 62, 2 ]
80
[ "52+62=114", "114/2=57", "23+57=80" ]
Current State: 80:[23, 52, 62, 2], Operations: [] Exploring Operation: 52+62=114, Resulting Numbers: [23, 2, 114] Generated Node #2: [23, 2, 114] from Operation: 52+62=114 Current State: 80:[23, 2, 114], Operations: ['52+62=114'] Exploring Operation: 114/2=57, Resulting Numbers: [23, 57] Generated Node #3: [23, 57] from Operation: 114/2=57 Current State: 80:[23, 57], Operations: ['52+62=114', '114/2=57'] Exploring Operation: 23+57=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[23, 52, 62, 2], Operations: [] Exploring Operation: 62-52=10, Resulting Numbers: [23, 2, 10] Generated Node #0,0: 80:[23, 2, 10] Operation: 62-52=10 Exploring Operation: 62-23=39, Resulting Numbers: [52, 2, 39] Generated Node #0,1: 80:[52, 2, 39] Operation: 62-23=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[23, 2, 10], Operations: ['62-52=10'] Exploring Operation: 23-10=13, Resulting Numbers: [2, 13] Generated Node #0,0,0: 80:[2, 13] Operation: 23-10=13 Exploring Operation: 23-2=21, Resulting Numbers: [10, 21] Generated Node #0,0,1: 80:[10, 21] Operation: 23-2=21 Moving to Node #0,0,1 Current State: 80:[10, 21], Operations: ['62-52=10', '23-2=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[2, 13], Operations: ['62-52=10', '23-10=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,80 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[52, 2, 39], Operations: ['62-23=39'] Exploring Operation: 52/2=26, Resulting Numbers: [39, 26] Generated Node #0,1,0: 80:[39, 26] Operation: 52/2=26 Exploring Operation: 52-39=13, Resulting Numbers: [2, 13] Generated Node #0,1,1: 80:[2, 13] Operation: 52-39=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[2, 13], Operations: ['62-23=39', '52-39=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,80 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,80 unequal: No Solution No 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: 80:[39, 26], Operations: ['62-23=39', '52/2=26'] Exploring Operation: 39+26=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 81, 97, 36, 29 ]
23
[ "97-81=16", "36-29=7", "16+7=23" ]
Current State: 23:[81, 97, 36, 29], Operations: [] Exploring Operation: 97-81=16, Resulting Numbers: [36, 29, 16] Generated Node #2: [36, 29, 16] from Operation: 97-81=16 Current State: 23:[36, 29, 16], Operations: ['97-81=16'] Exploring Operation: 36-29=7, Resulting Numbers: [16, 7] Generated Node #3: [16, 7] from Operation: 36-29=7 Current State: 23:[16, 7], Operations: ['97-81=16', '36-29=7'] Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[81, 97, 36, 29], Operations: [] Exploring Operation: 81-29=52, Resulting Numbers: [97, 36, 52] Generated Node #0,0: 23:[97, 36, 52] Operation: 81-29=52 Exploring Operation: 97-36=61, Resulting Numbers: [81, 29, 61] Generated Node #0,1: 23:[81, 29, 61] Operation: 97-36=61 Exploring Operation: 97-81=16, Resulting Numbers: [36, 29, 16] Generated Node #0,2: 23:[36, 29, 16] Operation: 97-81=16 Exploring Operation: 81-36=45, Resulting Numbers: [97, 29, 45] Generated Node #0,3: 23:[97, 29, 45] Operation: 81-36=45 Exploring Operation: 97-29=68, Resulting Numbers: [81, 36, 68] Generated Node #0,4: 23:[81, 36, 68] Operation: 97-29=68 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[36, 29, 16], Operations: ['97-81=16'] Exploring Operation: 36-29=7, Resulting Numbers: [16, 7] Generated Node #0,2,0: 23:[16, 7] Operation: 36-29=7 Exploring Operation: 36-16=20, Resulting Numbers: [29, 20] Generated Node #0,2,1: 23:[29, 20] Operation: 36-16=20 Exploring Operation: 29-16=13, Resulting Numbers: [36, 13] Generated Node #0,2,2: 23:[36, 13] Operation: 29-16=13 Exploring Operation: 29+16=45, Resulting Numbers: [36, 45] Generated Node #0,2,3: 23:[36, 45] Operation: 29+16=45 Exploring Operation: 36+16=52, Resulting Numbers: [29, 52] Generated Node #0,2,4: 23:[29, 52] Operation: 36+16=52 Moving to Node #0,2,1 Current State: 23:[29, 20], Operations: ['97-81=16', '36-16=20'] Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,23 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,23 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[36, 13], Operations: ['97-81=16', '29-16=13'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[81, 97, 36, 29], Operations: [] Exploring Operation: 97-81=16, Resulting Numbers: [36, 29, 16] Generated Node #0,2: 23:[36, 29, 16] Operation: 97-81=16 Moving to Node #0,2 Current State: 23:[36, 29, 16], Operations: ['97-81=16'] Exploring Operation: 29-16=13, Resulting Numbers: [36, 13] Generated Node #0,2,2: 23:[36, 13] Operation: 29-16=13 Moving to Node #0,2,2 Current State: 23:[36, 13], Operations: ['97-81=16', '29-16=13'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 9, 87, 44, 26 ]
47
[ "87-9=78", "78/26=3", "44+3=47" ]
Current State: 47:[9, 87, 44, 26], Operations: [] Exploring Operation: 87-9=78, Resulting Numbers: [44, 26, 78] Generated Node #2: [44, 26, 78] from Operation: 87-9=78 Current State: 47:[44, 26, 78], Operations: ['87-9=78'] Exploring Operation: 78/26=3, Resulting Numbers: [44, 3] Generated Node #3: [44, 3] from Operation: 78/26=3 Current State: 47:[44, 3], Operations: ['87-9=78', '78/26=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[9, 87, 44, 26], Operations: [] Exploring Operation: 87-9=78, Resulting Numbers: [44, 26, 78] Generated Node #0,0: 47:[44, 26, 78] Operation: 87-9=78 Exploring Operation: 9+26=35, Resulting Numbers: [87, 44, 35] Generated Node #0,1: 47:[87, 44, 35] Operation: 9+26=35 Exploring Operation: 87-26=61, Resulting Numbers: [9, 44, 61] Generated Node #0,2: 47:[9, 44, 61] Operation: 87-26=61 Exploring Operation: 87-44=43, Resulting Numbers: [9, 26, 43] Generated Node #0,3: 47:[9, 26, 43] Operation: 87-44=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[44, 26, 78], Operations: ['87-9=78'] Exploring Operation: 44+26=70, Resulting Numbers: [78, 70] Generated Node #0,0,0: 47:[78, 70] Operation: 44+26=70 Exploring Operation: 78/26=3, Resulting Numbers: [44, 3] Generated Node #0,0,1: 47:[44, 3] Operation: 78/26=3 Exploring Operation: 78-44=34, Resulting Numbers: [26, 34] Generated Node #0,0,2: 47:[26, 34] Operation: 78-44=34 Exploring Operation: 78-26=52, Resulting Numbers: [44, 52] Generated Node #0,0,3: 47:[44, 52] Operation: 78-26=52 Moving to Node #0,0,3 Current State: 47:[44, 52], Operations: ['87-9=78', '78-26=52'] Exploring Operation: 44*52=2288, Resulting Numbers: [2288] 2288,47 unequal: No Solution Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,47 unequal: No Solution Exploring Operation: 44+52=96, Resulting Numbers: [96] 96,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[26, 34], Operations: ['87-9=78', '78-44=34'] Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,47 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,47 unequal: No Solution Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[44, 3], Operations: ['87-9=78', '78/26=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[9, 87, 44, 26], Operations: [] Exploring Operation: 87-9=78, Resulting Numbers: [44, 26, 78] Generated Node #0,0: 47:[44, 26, 78] Operation: 87-9=78 Moving to Node #0,0 Current State: 47:[44, 26, 78], Operations: ['87-9=78'] Exploring Operation: 78/26=3, Resulting Numbers: [44, 3] Generated Node #0,0,1: 47:[44, 3] Operation: 78/26=3 Moving to Node #0,0,1 Current State: 47:[44, 3], Operations: ['87-9=78', '78/26=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 57, 74, 73, 12 ]
44
[ "74-57=17", "73-12=61", "61-17=44" ]
Current State: 44:[57, 74, 73, 12], Operations: [] Exploring Operation: 74-57=17, Resulting Numbers: [73, 12, 17] Generated Node #2: [73, 12, 17] from Operation: 74-57=17 Current State: 44:[73, 12, 17], Operations: ['74-57=17'] Exploring Operation: 73-12=61, Resulting Numbers: [17, 61] Generated Node #3: [17, 61] from Operation: 73-12=61 Current State: 44:[17, 61], Operations: ['74-57=17', '73-12=61'] Exploring Operation: 61-17=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[57, 74, 73, 12], Operations: [] Exploring Operation: 74-57=17, Resulting Numbers: [73, 12, 17] Generated Node #0,0: 44:[73, 12, 17] Operation: 74-57=17 Exploring Operation: 74-73=1, Resulting Numbers: [57, 12, 1] Generated Node #0,1: 44:[57, 12, 1] Operation: 74-73=1 Exploring Operation: 57-12=45, Resulting Numbers: [74, 73, 45] Generated Node #0,2: 44:[74, 73, 45] Operation: 57-12=45 Exploring Operation: 73-57=16, Resulting Numbers: [74, 12, 16] Generated Node #0,3: 44:[74, 12, 16] Operation: 73-57=16 Moving to Node #0,1 Current State: 44:[57, 12, 1], Operations: ['74-73=1'] Exploring Operation: 57-1=56, Resulting Numbers: [12, 56] Generated Node #0,1,0: 44:[12, 56] Operation: 57-1=56 Exploring Operation: 57*1=57, Resulting Numbers: [12, 57] Generated Node #0,1,1: 44:[12, 57] Operation: 57*1=57 Exploring Operation: 12-1=11, Resulting Numbers: [57, 11] Generated Node #0,1,2: 44:[57, 11] Operation: 12-1=11 Exploring Operation: 57-12=45, Resulting Numbers: [1, 45] Generated Node #0,1,3: 44:[1, 45] Operation: 57-12=45 Moving to Node #0,0 Current State: 44:[73, 12, 17], Operations: ['74-57=17'] Exploring Operation: 73-17=56, Resulting Numbers: [12, 56] Generated Node #0,0,0: 44:[12, 56] Operation: 73-17=56 Exploring Operation: 17-12=5, Resulting Numbers: [73, 5] Generated Node #0,0,1: 44:[73, 5] Operation: 17-12=5 Exploring Operation: 12+17=29, Resulting Numbers: [73, 29] Generated Node #0,0,2: 44:[73, 29] Operation: 12+17=29 Exploring Operation: 73-12=61, Resulting Numbers: [17, 61] Generated Node #0,0,3: 44:[17, 61] Operation: 73-12=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[12, 56], Operations: ['74-57=17', '73-17=56'] Exploring Operation: 12*56=672, Resulting Numbers: [672] 672,44 unequal: No Solution Exploring Operation: 12+56=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 56-12=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[57, 74, 73, 12], Operations: [] Exploring Operation: 74-57=17, Resulting Numbers: [73, 12, 17] Generated Node #0,0: 44:[73, 12, 17] Operation: 74-57=17 Moving to Node #0,0 Current State: 44:[73, 12, 17], Operations: ['74-57=17'] Exploring Operation: 73-17=56, Resulting Numbers: [12, 56] Generated Node #0,0,0: 44:[12, 56] Operation: 73-17=56 Moving to Node #0,0,0 Current State: 44:[12, 56], Operations: ['74-57=17', '73-17=56'] Exploring Operation: 56-12=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 47, 27, 4, 7 ]
12
[ "47-27=20", "20/4=5", "7+5=12" ]
Current State: 12:[47, 27, 4, 7], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [4, 7, 20] Generated Node #2: [4, 7, 20] from Operation: 47-27=20 Current State: 12:[4, 7, 20], Operations: ['47-27=20'] Exploring Operation: 20/4=5, Resulting Numbers: [7, 5] Generated Node #3: [7, 5] from Operation: 20/4=5 Current State: 12:[7, 5], Operations: ['47-27=20', '20/4=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[47, 27, 4, 7], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [4, 7, 20] Generated Node #0,0: 12:[4, 7, 20] Operation: 47-27=20 Moving to Node #0,0 Current State: 12:[4, 7, 20], Operations: ['47-27=20'] Exploring Operation: 20-7=13, Resulting Numbers: [4, 13] Generated Node #0,0,0: 12:[4, 13] Operation: 20-7=13 Moving to Node #0,0,0 Current State: 12:[4, 13], Operations: ['47-27=20', '20-7=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,12 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 26, 20, 66, 75 ]
15
[ "26-20=6", "75-66=9", "6+9=15" ]
Current State: 15:[26, 20, 66, 75], Operations: [] Exploring Operation: 26-20=6, Resulting Numbers: [66, 75, 6] Generated Node #2: [66, 75, 6] from Operation: 26-20=6 Current State: 15:[66, 75, 6], Operations: ['26-20=6'] Exploring Operation: 75-66=9, Resulting Numbers: [6, 9] Generated Node #3: [6, 9] from Operation: 75-66=9 Current State: 15:[6, 9], Operations: ['26-20=6', '75-66=9'] Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[26, 20, 66, 75], Operations: [] Exploring Operation: 75-66=9, Resulting Numbers: [26, 20, 9] Generated Node #0,0: 15:[26, 20, 9] Operation: 75-66=9 Exploring Operation: 66-26=40, Resulting Numbers: [20, 75, 40] Generated Node #0,1: 15:[20, 75, 40] Operation: 66-26=40 Exploring Operation: 75-26=49, Resulting Numbers: [20, 66, 49] Generated Node #0,2: 15:[20, 66, 49] Operation: 75-26=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[26, 20, 9], Operations: ['75-66=9'] Exploring Operation: 26-20=6, Resulting Numbers: [9, 6] Generated Node #0,0,0: 15:[9, 6] Operation: 26-20=6 Exploring Operation: 26-9=17, Resulting Numbers: [20, 17] Generated Node #0,0,1: 15:[20, 17] Operation: 26-9=17 Exploring Operation: 20-9=11, Resulting Numbers: [26, 11] Generated Node #0,0,2: 15:[26, 11] Operation: 20-9=11 Moving to Node #0,0,0 Current State: 15:[9, 6], Operations: ['75-66=9', '26-20=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,15 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[26, 20, 66, 75], Operations: [] Exploring Operation: 75-66=9, Resulting Numbers: [26, 20, 9] Generated Node #0,0: 15:[26, 20, 9] Operation: 75-66=9 Moving to Node #0,0 Current State: 15:[26, 20, 9], Operations: ['75-66=9'] Exploring Operation: 26-20=6, Resulting Numbers: [9, 6] Generated Node #0,0,0: 15:[9, 6] Operation: 26-20=6 Moving to Node #0,0,0 Current State: 15:[9, 6], Operations: ['75-66=9', '26-20=6'] Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 28, 12, 2, 17 ]
63
[ "28+12=40", "2*40=80", "80-17=63" ]
Current State: 63:[28, 12, 2, 17], Operations: [] Exploring Operation: 28+12=40, Resulting Numbers: [2, 17, 40] Generated Node #2: [2, 17, 40] from Operation: 28+12=40 Current State: 63:[2, 17, 40], Operations: ['28+12=40'] Exploring Operation: 2*40=80, Resulting Numbers: [17, 80] Generated Node #3: [17, 80] from Operation: 2*40=80 Current State: 63:[17, 80], Operations: ['28+12=40', '2*40=80'] Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[28, 12, 2, 17], Operations: [] Exploring Operation: 28-17=11, Resulting Numbers: [12, 2, 11] Generated Node #0,0: 63:[12, 2, 11] Operation: 28-17=11 Moving to Node #0,0 Current State: 63:[12, 2, 11], Operations: ['28-17=11'] Exploring Operation: 12-2=10, Resulting Numbers: [11, 10] Generated Node #0,0,0: 63:[11, 10] Operation: 12-2=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[11, 10], Operations: ['28-17=11', '12-2=10'] Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,63 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
[ 23, 96, 2, 56 ]
62
[ "23+56=79", "2*79=158", "158-96=62" ]
Current State: 62:[23, 96, 2, 56], Operations: [] Exploring Operation: 23+56=79, Resulting Numbers: [96, 2, 79] Generated Node #2: [96, 2, 79] from Operation: 23+56=79 Current State: 62:[96, 2, 79], Operations: ['23+56=79'] Exploring Operation: 2*79=158, Resulting Numbers: [96, 158] Generated Node #3: [96, 158] from Operation: 2*79=158 Current State: 62:[96, 158], Operations: ['23+56=79', '2*79=158'] Exploring Operation: 158-96=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[23, 96, 2, 56], Operations: [] Exploring Operation: 96-56=40, Resulting Numbers: [23, 2, 40] Generated Node #0,0: 62:[23, 2, 40] Operation: 96-56=40 Exploring Operation: 96-23=73, Resulting Numbers: [2, 56, 73] Generated Node #0,1: 62:[2, 56, 73] Operation: 96-23=73 Exploring Operation: 56-23=33, Resulting Numbers: [96, 2, 33] Generated Node #0,2: 62:[96, 2, 33] Operation: 56-23=33 Exploring Operation: 96/2=48, Resulting Numbers: [23, 56, 48] Generated Node #0,3: 62:[23, 56, 48] Operation: 96/2=48 Moving to Node #0,0 Current State: 62:[23, 2, 40], Operations: ['96-56=40'] Exploring Operation: 23+2=25, Resulting Numbers: [40, 25] Generated Node #0,0,0: 62:[40, 25] Operation: 23+2=25 Exploring Operation: 23+40=63, Resulting Numbers: [2, 63] Generated Node #0,0,1: 62:[2, 63] Operation: 23+40=63 Exploring Operation: 40-2=38, Resulting Numbers: [23, 38] Generated Node #0,0,2: 62:[23, 38] Operation: 40-2=38 Exploring Operation: 40-23=17, Resulting Numbers: [2, 17] Generated Node #0,0,3: 62:[2, 17] Operation: 40-23=17 Moving to Node #0,1 Current State: 62:[2, 56, 73], Operations: ['96-23=73'] Exploring Operation: 56/2=28, Resulting Numbers: [73, 28] Generated Node #0,1,0: 62:[73, 28] Operation: 56/2=28 Exploring Operation: 2+56=58, Resulting Numbers: [73, 58] Generated Node #0,1,1: 62:[73, 58] Operation: 2+56=58 Exploring Operation: 73-2=71, Resulting Numbers: [56, 71] Generated Node #0,1,2: 62:[56, 71] Operation: 73-2=71 Exploring Operation: 73-56=17, Resulting Numbers: [2, 17] Generated Node #0,1,3: 62:[2, 17] Operation: 73-56=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[73, 28], Operations: ['96-23=73', '56/2=28'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 62:[2, 17], Operations: ['96-23=73', '73-56=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[73, 58], Operations: ['96-23=73', '2+56=58'] Exploring Operation: 73-58=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 73*58=4234, Resulting Numbers: [4234] 4234,62 unequal: No Solution Exploring Operation: 73+58=131, Resulting Numbers: [131] 131,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[56, 71], Operations: ['96-23=73', '73-2=71'] Exploring Operation: 56*71=3976, Resulting Numbers: [3976] 3976,62 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 56+71=127, Resulting Numbers: [127] 127,62 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: 62:[23, 56, 48], Operations: ['96/2=48'] Exploring Operation: 23+48=71, Resulting Numbers: [56, 71] Generated Node #0,3,0: 62:[56, 71] Operation: 23+48=71 Exploring Operation: 56-23=33, Resulting Numbers: [48, 33] Generated Node #0,3,1: 62:[48, 33] Operation: 56-23=33 Exploring Operation: 56-48=8, Resulting Numbers: [23, 8] Generated Node #0,3,2: 62:[23, 8] Operation: 56-48=8 Exploring Operation: 48-23=25, Resulting Numbers: [56, 25] Generated Node #0,3,3: 62:[56, 25] Operation: 48-23=25 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 62:[56, 25], Operations: ['96/2=48', '48-23=25'] Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 56+25=81, Resulting Numbers: [81] 81,62 unequal: No Solution Exploring Operation: 56*25=1400, Resulting Numbers: [1400] 1400,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 62:[23, 8], Operations: ['96/2=48', '56-48=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 62:[56, 71], Operations: ['96/2=48', '23+48=71'] Exploring Operation: 56+71=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 56*71=3976, Resulting Numbers: [3976] 3976,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 62:[48, 33], Operations: ['96/2=48', '56-23=33'] Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 48*33=1584, Resulting Numbers: [1584] 1584,62 unequal: No Solution Exploring Operation: 48+33=81, Resulting Numbers: [81] 81,62 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: 62:[96, 2, 33], Operations: ['56-23=33'] Exploring Operation: 96-2=94, Resulting Numbers: [33, 94] Generated Node #0,2,0: 62:[33, 94] Operation: 96-2=94 Exploring Operation: 33-2=31, Resulting Numbers: [96, 31] Generated Node #0,2,1: 62:[96, 31] Operation: 33-2=31 Exploring Operation: 96-33=63, Resulting Numbers: [2, 63] Generated Node #0,2,2: 62:[2, 63] Operation: 96-33=63 Exploring Operation: 96/2=48, Resulting Numbers: [33, 48] Generated Node #0,2,3: 62:[33, 48] Operation: 96/2=48 Moving to Node #0,0,1 Current State: 62:[2, 63], Operations: ['96-56=40', '23+40=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,62 unequal: No Solution Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,62 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[2, 63], Operations: ['56-23=33', '96-33=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,62 unequal: No Solution Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,62 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,62 unequal: No Solution Moving to Node #0,0,3 Current State: 62:[2, 17], Operations: ['96-56=40', '40-23=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[40, 25], Operations: ['96-56=40', '23+2=25'] Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 40*25=1000, Resulting Numbers: [1000] 1000,62 unequal: No Solution Exploring Operation: 40+25=65, Resulting Numbers: [65] 65,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[23, 38], Operations: ['96-56=40', '40-2=38'] Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 23*38=874, Resulting Numbers: [874] 874,62 unequal: No Solution Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[33, 48], Operations: ['56-23=33', '96/2=48'] Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,62 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[33, 94], Operations: ['56-23=33', '96-2=94'] Exploring Operation: 33+94=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 94-33=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 33*94=3102, Resulting Numbers: [3102] 3102,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[96, 31], Operations: ['56-23=33', '33-2=31'] Exploring Operation: 96*31=2976, Resulting Numbers: [2976] 2976,62 unequal: No Solution Exploring Operation: 96+31=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 96-31=65, Resulting Numbers: [65] 65,62 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 66, 79, 68, 19 ]
74
[ "79-66=13", "68+19=87", "87-13=74" ]
Current State: 74:[66, 79, 68, 19], Operations: [] Exploring Operation: 79-66=13, Resulting Numbers: [68, 19, 13] Generated Node #2: [68, 19, 13] from Operation: 79-66=13 Current State: 74:[68, 19, 13], Operations: ['79-66=13'] Exploring Operation: 68+19=87, Resulting Numbers: [13, 87] Generated Node #3: [13, 87] from Operation: 68+19=87 Current State: 74:[13, 87], Operations: ['79-66=13', '68+19=87'] Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[66, 79, 68, 19], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [79, 19, 2] Generated Node #0,0: 74:[79, 19, 2] Operation: 68-66=2 Exploring Operation: 66-19=47, Resulting Numbers: [79, 68, 47] Generated Node #0,1: 74:[79, 68, 47] Operation: 66-19=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[79, 68, 47], Operations: ['66-19=47'] Exploring Operation: 79-68=11, Resulting Numbers: [47, 11] Generated Node #0,1,0: 74:[47, 11] Operation: 79-68=11 Exploring Operation: 79-47=32, Resulting Numbers: [68, 32] Generated Node #0,1,1: 74:[68, 32] Operation: 79-47=32 Moving to Node #0,1,1 Current State: 74:[68, 32], Operations: ['66-19=47', '79-47=32'] Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,74 unequal: No Solution Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,74 unequal: No Solution Moving to Node #0,1,0 Current State: 74:[47, 11], Operations: ['66-19=47', '79-68=11'] Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 47+11=58, Resulting Numbers: [58] 58,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[79, 19, 2], Operations: ['68-66=2'] Exploring Operation: 79-19=60, Resulting Numbers: [2, 60] Generated Node #0,0,0: 74:[2, 60] Operation: 79-19=60 Exploring Operation: 19*2=38, Resulting Numbers: [79, 38] Generated Node #0,0,1: 74:[79, 38] Operation: 19*2=38 Moving to Node #0,0,1 Current State: 74:[79, 38], Operations: ['68-66=2', '19*2=38'] Exploring Operation: 79+38=117, Resulting Numbers: [117] 117,74 unequal: No Solution Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,74 unequal: No Solution Moving to Node #0,0,0 Current State: 74:[2, 60], Operations: ['68-66=2', '79-19=60'] Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,74 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,74 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
[ 67, 21, 3, 11 ]
60
[ "67-21=46", "3+11=14", "46+14=60" ]
Current State: 60:[67, 21, 3, 11], Operations: [] Exploring Operation: 67-21=46, Resulting Numbers: [3, 11, 46] Generated Node #2: [3, 11, 46] from Operation: 67-21=46 Current State: 60:[3, 11, 46], Operations: ['67-21=46'] Exploring Operation: 3+11=14, Resulting Numbers: [46, 14] Generated Node #3: [46, 14] from Operation: 3+11=14 Current State: 60:[46, 14], Operations: ['67-21=46', '3+11=14'] Exploring Operation: 46+14=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[67, 21, 3, 11], Operations: [] Exploring Operation: 21-11=10, Resulting Numbers: [67, 3, 10] Generated Node #0,0: 60:[67, 3, 10] Operation: 21-11=10 Exploring Operation: 67-11=56, Resulting Numbers: [21, 3, 56] Generated Node #0,1: 60:[21, 3, 56] Operation: 67-11=56 Exploring Operation: 67-3=64, Resulting Numbers: [21, 11, 64] Generated Node #0,2: 60:[21, 11, 64] Operation: 67-3=64 Moving to Node #0,1 Current State: 60:[21, 3, 56], Operations: ['67-11=56'] Exploring Operation: 21/3=7, Resulting Numbers: [56, 7] Generated Node #0,1,0: 60:[56, 7] Operation: 21/3=7 Exploring Operation: 56-21=35, Resulting Numbers: [3, 35] Generated Node #0,1,1: 60:[3, 35] Operation: 56-21=35 Exploring Operation: 3+56=59, Resulting Numbers: [21, 59] Generated Node #0,1,2: 60:[21, 59] Operation: 3+56=59 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[21, 59], Operations: ['67-11=56', '3+56=59'] Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,60 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[56, 7], Operations: ['67-11=56', '21/3=7'] Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,60 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[3, 35], Operations: ['67-11=56', '56-21=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,60 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 60:[21, 11, 64], Operations: ['67-3=64'] Exploring Operation: 64-11=53, Resulting Numbers: [21, 53] Generated Node #0,2,0: 60:[21, 53] Operation: 64-11=53 Exploring Operation: 21-11=10, Resulting Numbers: [64, 10] Generated Node #0,2,1: 60:[64, 10] Operation: 21-11=10 Exploring Operation: 21+11=32, Resulting Numbers: [64, 32] Generated Node #0,2,2: 60:[64, 32] Operation: 21+11=32 Moving to Node #0,0 Current State: 60:[67, 3, 10], Operations: ['21-11=10'] Exploring Operation: 67-10=57, Resulting Numbers: [3, 57] Generated Node #0,0,0: 60:[3, 57] Operation: 67-10=57 Exploring Operation: 3*10=30, Resulting Numbers: [67, 30] Generated Node #0,0,1: 60:[67, 30] Operation: 3*10=30 Exploring Operation: 67-3=64, Resulting Numbers: [10, 64] Generated Node #0,0,2: 60:[10, 64] Operation: 67-3=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[3, 57], Operations: ['21-11=10', '67-10=57'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,60 unequal: No Solution Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[67, 21, 3, 11], Operations: [] Exploring Operation: 21-11=10, Resulting Numbers: [67, 3, 10] Generated Node #0,0: 60:[67, 3, 10] Operation: 21-11=10 Moving to Node #0,0 Current State: 60:[67, 3, 10], Operations: ['21-11=10'] Exploring Operation: 67-10=57, Resulting Numbers: [3, 57] Generated Node #0,0,0: 60:[3, 57] Operation: 67-10=57 Moving to Node #0,0,0 Current State: 60:[3, 57], Operations: ['21-11=10', '67-10=57'] Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 55, 78, 32, 78 ]
32
[ "78-78=0", "55*0=0", "32+0=32" ]
Current State: 32:[55, 78, 32, 78], Operations: [] Exploring Operation: 78-78=0, Resulting Numbers: [55, 32, 0] Generated Node #2: [55, 32, 0] from Operation: 78-78=0 Current State: 32:[55, 32, 0], Operations: ['78-78=0'] Exploring Operation: 55*0=0, Resulting Numbers: [32, 0] Generated Node #3: [32, 0] from Operation: 55*0=0 Current State: 32:[32, 0], Operations: ['78-78=0', '55*0=0'] Exploring Operation: 32+0=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[55, 78, 32, 78], Operations: [] Exploring Operation: 78-55=23, Resulting Numbers: [32, 78, 23] Generated Node #0,0: 32:[32, 78, 23] Operation: 78-55=23 Exploring Operation: 78/78=1, Resulting Numbers: [55, 32, 1] Generated Node #0,1: 32:[55, 32, 1] Operation: 78/78=1 Exploring Operation: 78-78=0, Resulting Numbers: [55, 32, 0] Generated Node #0,2: 32:[55, 32, 0] Operation: 78-78=0 Exploring Operation: 78-55=23, Resulting Numbers: [78, 32, 23] Generated Node #0,3: 32:[78, 32, 23] Operation: 78-55=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[55, 32, 1], Operations: ['78/78=1'] Exploring Operation: 55-1=54, Resulting Numbers: [32, 54] Generated Node #0,1,0: 32:[32, 54] Operation: 55-1=54 Exploring Operation: 55-32=23, Resulting Numbers: [1, 23] Generated Node #0,1,1: 32:[1, 23] Operation: 55-32=23 Exploring Operation: 55*1=55, Resulting Numbers: [32, 55] Generated Node #0,1,2: 32:[32, 55] Operation: 55*1=55 Exploring Operation: 55/1=55, Resulting Numbers: [32, 55] Generated Node #0,1,3: 32:[32, 55] Operation: 55/1=55 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 32:[1, 23], Operations: ['78/78=1', '55-32=23'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,32 unequal: No Solution No 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: 32:[32, 54], Operations: ['78/78=1', '55-1=54'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 32+54=86, Resulting Numbers: [86] 86,32 unequal: No Solution Exploring Operation: 32*54=1728, Resulting Numbers: [1728] 1728,32 unequal: No Solution No 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: 32:[32, 55], Operations: ['78/78=1', '55*1=55'] Exploring Operation: 32*55=1760, Resulting Numbers: [1760] 1760,32 unequal: No Solution Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,32 unequal: No Solution No 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: 32:[32, 55], Operations: ['78/78=1', '55/1=55'] Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 32*55=1760, Resulting Numbers: [1760] 1760,32 unequal: No Solution Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,32 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: 32:[55, 32, 0], Operations: ['78-78=0'] Exploring Operation: 55-32=23, Resulting Numbers: [0, 23] Generated Node #0,2,0: 32:[0, 23] Operation: 55-32=23 Exploring Operation: 55+0=55, Resulting Numbers: [32, 55] Generated Node #0,2,1: 32:[32, 55] Operation: 55+0=55 Exploring Operation: 55-0=55, Resulting Numbers: [32, 55] Generated Node #0,2,2: 32:[32, 55] Operation: 55-0=55 Exploring Operation: 55*0=0, Resulting Numbers: [32, 0] Generated Node #0,2,3: 32:[32, 0] Operation: 55*0=0 Moving to Node #0,2,3 Current State: 32:[32, 0], Operations: ['78-78=0', '55*0=0'] Exploring Operation: 32+0=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[55, 78, 32, 78], Operations: [] Exploring Operation: 78-78=0, Resulting Numbers: [55, 32, 0] Generated Node #0,2: 32:[55, 32, 0] Operation: 78-78=0 Moving to Node #0,2 Current State: 32:[55, 32, 0], Operations: ['78-78=0'] Exploring Operation: 55*0=0, Resulting Numbers: [32, 0] Generated Node #0,2,3: 32:[32, 0] Operation: 55*0=0 Moving to Node #0,2,3 Current State: 32:[32, 0], Operations: ['78-78=0', '55*0=0'] Exploring Operation: 32+0=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 2, 23, 98, 9 ]
34
[ "23+9=32", "2*32=64", "98-64=34" ]
Current State: 34:[2, 23, 98, 9], Operations: [] Exploring Operation: 23+9=32, Resulting Numbers: [2, 98, 32] Generated Node #2: [2, 98, 32] from Operation: 23+9=32 Current State: 34:[2, 98, 32], Operations: ['23+9=32'] Exploring Operation: 2*32=64, Resulting Numbers: [98, 64] Generated Node #3: [98, 64] from Operation: 2*32=64 Current State: 34:[98, 64], Operations: ['23+9=32', '2*32=64'] Exploring Operation: 98-64=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[2, 23, 98, 9], Operations: [] Exploring Operation: 23+9=32, Resulting Numbers: [2, 98, 32] Generated Node #0,0: 34:[2, 98, 32] Operation: 23+9=32 Exploring Operation: 98-23=75, Resulting Numbers: [2, 9, 75] Generated Node #0,1: 34:[2, 9, 75] Operation: 98-23=75 Exploring Operation: 98/2=49, Resulting Numbers: [23, 9, 49] Generated Node #0,2: 34:[23, 9, 49] Operation: 98/2=49 Exploring Operation: 98-9=89, Resulting Numbers: [2, 23, 89] Generated Node #0,3: 34:[2, 23, 89] Operation: 98-9=89 Moving to Node #0,2 Current State: 34:[23, 9, 49], Operations: ['98/2=49'] Exploring Operation: 49-9=40, Resulting Numbers: [23, 40] Generated Node #0,2,0: 34:[23, 40] Operation: 49-9=40 Exploring Operation: 23+9=32, Resulting Numbers: [49, 32] Generated Node #0,2,1: 34:[49, 32] Operation: 23+9=32 Exploring Operation: 23-9=14, Resulting Numbers: [49, 14] Generated Node #0,2,2: 34:[49, 14] Operation: 23-9=14 Exploring Operation: 49-23=26, Resulting Numbers: [9, 26] Generated Node #0,2,3: 34:[9, 26] Operation: 49-23=26 Moving to Node #0,1 Current State: 34:[2, 9, 75], Operations: ['98-23=75'] Exploring Operation: 75-9=66, Resulting Numbers: [2, 66] Generated Node #0,1,0: 34:[2, 66] Operation: 75-9=66 Exploring Operation: 75-2=73, Resulting Numbers: [9, 73] Generated Node #0,1,1: 34:[9, 73] Operation: 75-2=73 Exploring Operation: 2*9=18, Resulting Numbers: [75, 18] Generated Node #0,1,2: 34:[75, 18] Operation: 2*9=18 Exploring Operation: 9-2=7, Resulting Numbers: [75, 7] Generated Node #0,1,3: 34:[75, 7] Operation: 9-2=7 Moving to Node #0,3 Current State: 34:[2, 23, 89], Operations: ['98-9=89'] Exploring Operation: 89-23=66, Resulting Numbers: [2, 66] Generated Node #0,3,0: 34:[2, 66] Operation: 89-23=66 Exploring Operation: 2+23=25, Resulting Numbers: [89, 25] Generated Node #0,3,1: 34:[89, 25] Operation: 2+23=25 Exploring Operation: 23-2=21, Resulting Numbers: [89, 21] Generated Node #0,3,2: 34:[89, 21] Operation: 23-2=21 Exploring Operation: 89-2=87, Resulting Numbers: [23, 87] Generated Node #0,3,3: 34:[23, 87] Operation: 89-2=87 Moving to Node #0,0 Current State: 34:[2, 98, 32], Operations: ['23+9=32'] Exploring Operation: 2+32=34, Resulting Numbers: [98, 34] Generated Node #0,0,0: 34:[98, 34] Operation: 2+32=34 Exploring Operation: 98/2=49, Resulting Numbers: [32, 49] Generated Node #0,0,1: 34:[32, 49] Operation: 98/2=49 Exploring Operation: 98-32=66, Resulting Numbers: [2, 66] Generated Node #0,0,2: 34:[2, 66] Operation: 98-32=66 Exploring Operation: 98-2=96, Resulting Numbers: [32, 96] Generated Node #0,0,3: 34:[32, 96] Operation: 98-2=96 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[32, 49], Operations: ['23+9=32', '98/2=49'] Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,34 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 34:[2, 66], Operations: ['23+9=32', '98-32=66'] Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,34 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[98, 34], Operations: ['23+9=32', '2+32=34'] Exploring Operation: 98*34=3332, Resulting Numbers: [3332] 3332,34 unequal: No Solution Exploring Operation: 98+34=132, Resulting Numbers: [132] 132,34 unequal: No Solution Exploring Operation: 98-34=64, Resulting Numbers: [64] 64,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 34:[32, 96], Operations: ['23+9=32', '98-2=96'] Exploring Operation: 32+96=128, Resulting Numbers: [128] 128,34 unequal: No Solution Exploring Operation: 96-32=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 32*96=3072, Resulting Numbers: [3072] 3072,34 unequal: No Solution Exploring Operation: 96/32=3, Resulting Numbers: [3] 3,34 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: 34:[23, 40], Operations: ['98/2=49', '49-9=40'] Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 23*40=920, Resulting Numbers: [920] 920,34 unequal: No Solution Exploring Operation: 23+40=63, Resulting Numbers: [63] 63,34 unequal: No Solution Moving to Node #0,2,3 Current State: 34:[9, 26], Operations: ['98/2=49', '49-23=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,34 unequal: No Solution Exploring Operation: 9*26=234, Resulting Numbers: [234] 234,34 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[49, 32], Operations: ['98/2=49', '23+9=32'] Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,34 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[49, 14], Operations: ['98/2=49', '23-9=14'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,34 unequal: No Solution Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,34 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[2, 66], Operations: ['98-23=75', '75-9=66'] Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,34 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,34 unequal: No Solution Moving to Node #0,3,0 Current State: 34:[2, 66], Operations: ['98-9=89', '89-23=66'] Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[75, 18], Operations: ['98-23=75', '2*9=18'] Exploring Operation: 75*18=1350, Resulting Numbers: [1350] 1350,34 unequal: No Solution Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,34 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[9, 73], Operations: ['98-23=75', '75-2=73'] Exploring Operation: 9+73=82, Resulting Numbers: [82] 82,34 unequal: No Solution Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 9*73=657, Resulting Numbers: [657] 657,34 unequal: No Solution Moving to Node #0,1,3 Current State: 34:[75, 7], Operations: ['98-23=75', '9-2=7'] Exploring Operation: 75*7=525, Resulting Numbers: [525] 525,34 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,34 unequal: No Solution Moving to Node #0,3,3 Current State: 34:[23, 87], Operations: ['98-9=89', '89-2=87'] Exploring Operation: 23+87=110, Resulting Numbers: [110] 110,34 unequal: No Solution Exploring Operation: 23*87=2001, Resulting Numbers: [2001] 2001,34 unequal: No Solution Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,34 unequal: No Solution Moving to Node #0,3,2 Current State: 34:[89, 21], Operations: ['98-9=89', '23-2=21'] Exploring Operation: 89+21=110, Resulting Numbers: [110] 110,34 unequal: No Solution Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 89*21=1869, Resulting Numbers: [1869] 1869,34 unequal: No Solution Moving to Node #0,3,1 Current State: 34:[89, 25], Operations: ['98-9=89', '2+23=25'] Exploring Operation: 89-25=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 89*25=2225, Resulting Numbers: [2225] 2225,34 unequal: No Solution Exploring Operation: 89+25=114, Resulting Numbers: [114] 114,34 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 55, 41, 9, 63 ]
63
[ "55-41=14", "9*14=126", "126-63=63" ]
Current State: 63:[55, 41, 9, 63], Operations: [] Exploring Operation: 55-41=14, Resulting Numbers: [9, 63, 14] Generated Node #2: [9, 63, 14] from Operation: 55-41=14 Current State: 63:[9, 63, 14], Operations: ['55-41=14'] Exploring Operation: 9*14=126, Resulting Numbers: [63, 126] Generated Node #3: [63, 126] from Operation: 9*14=126 Current State: 63:[63, 126], Operations: ['55-41=14', '9*14=126'] Exploring Operation: 126-63=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[55, 41, 9, 63], Operations: [] Exploring Operation: 41-9=32, Resulting Numbers: [55, 63, 32] Generated Node #0,0: 63:[55, 63, 32] Operation: 41-9=32 Exploring Operation: 55-41=14, Resulting Numbers: [9, 63, 14] Generated Node #0,1: 63:[9, 63, 14] Operation: 55-41=14 Exploring Operation: 63-41=22, Resulting Numbers: [55, 9, 22] Generated Node #0,2: 63:[55, 9, 22] Operation: 63-41=22 Exploring Operation: 55+9=64, Resulting Numbers: [41, 63, 64] Generated Node #0,3: 63:[41, 63, 64] Operation: 55+9=64 Moving to Node #0,1 Current State: 63:[9, 63, 14], Operations: ['55-41=14'] Exploring Operation: 14-9=5, Resulting Numbers: [63, 5] Generated Node #0,1,0: 63:[63, 5] Operation: 14-9=5 Exploring Operation: 63/9=7, Resulting Numbers: [14, 7] Generated Node #0,1,1: 63:[14, 7] Operation: 63/9=7 Exploring Operation: 9+14=23, Resulting Numbers: [63, 23] Generated Node #0,1,2: 63:[63, 23] Operation: 9+14=23 Exploring Operation: 9+63=72, Resulting Numbers: [14, 72] Generated Node #0,1,3: 63:[14, 72] Operation: 9+63=72 Moving to Node #0,2 Current State: 63:[55, 9, 22], Operations: ['63-41=22'] Exploring Operation: 22-9=13, Resulting Numbers: [55, 13] Generated Node #0,2,0: 63:[55, 13] Operation: 22-9=13 Exploring Operation: 55+9=64, Resulting Numbers: [22, 64] Generated Node #0,2,1: 63:[22, 64] Operation: 55+9=64 Exploring Operation: 55-22=33, Resulting Numbers: [9, 33] Generated Node #0,2,2: 63:[9, 33] Operation: 55-22=33 Exploring Operation: 55+22=77, Resulting Numbers: [9, 77] Generated Node #0,2,3: 63:[9, 77] Operation: 55+22=77 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[22, 64], Operations: ['63-41=22', '55+9=64'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 22*64=1408, Resulting Numbers: [1408] 1408,63 unequal: No Solution Exploring Operation: 22+64=86, Resulting Numbers: [86] 86,63 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:[55, 13], Operations: ['63-41=22', '22-9=13'] Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 55*13=715, Resulting Numbers: [715] 715,63 unequal: No Solution Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,63 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 #0,2,2 Current State: 63:[9, 33], Operations: ['63-41=22', '55-22=33'] Exploring Operation: 9*33=297, Resulting Numbers: [297] 297,63 unequal: No Solution Exploring Operation: 9+33=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,63 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:[9, 77], Operations: ['63-41=22', '55+22=77'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,63 unequal: No Solution Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 9*77=693, Resulting Numbers: [693] 693,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 63:[55, 63, 32], Operations: ['41-9=32'] Exploring Operation: 63-55=8, Resulting Numbers: [32, 8] Generated Node #0,0,0: 63:[32, 8] Operation: 63-55=8 Exploring Operation: 63-32=31, Resulting Numbers: [55, 31] Generated Node #0,0,1: 63:[55, 31] Operation: 63-32=31 Exploring Operation: 55+32=87, Resulting Numbers: [63, 87] Generated Node #0,0,2: 63:[63, 87] Operation: 55+32=87 Exploring Operation: 55-32=23, Resulting Numbers: [63, 23] Generated Node #0,0,3: 63:[63, 23] Operation: 55-32=23 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 63:[63, 23], Operations: ['41-9=32', '55-32=23'] Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 63*23=1449, Resulting Numbers: [1449] 1449,63 unequal: No Solution Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[32, 8], Operations: ['41-9=32', '63-55=8'] Exploring Operation: 32*8=256, Resulting Numbers: [256] 256,63 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,63 unequal: No Solution Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[55, 31], Operations: ['41-9=32', '63-32=31'] Exploring Operation: 55+31=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,63 unequal: No Solution Exploring Operation: 55*31=1705, Resulting Numbers: [1705] 1705,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[63, 87], Operations: ['41-9=32', '55+32=87'] Exploring Operation: 63*87=5481, Resulting Numbers: [5481] 5481,63 unequal: No Solution Exploring Operation: 87-63=24, Resulting Numbers: [24] 24,63 unequal: No Solution Exploring Operation: 63+87=150, Resulting Numbers: [150] 150,63 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: 63:[41, 63, 64], Operations: ['55+9=64'] Exploring Operation: 41+63=104, Resulting Numbers: [64, 104] Generated Node #0,3,0: 63:[64, 104] Operation: 41+63=104 Exploring Operation: 64-41=23, Resulting Numbers: [63, 23] Generated Node #0,3,1: 63:[63, 23] Operation: 64-41=23 Exploring Operation: 64-63=1, Resulting Numbers: [41, 1] Generated Node #0,3,2: 63:[41, 1] Operation: 64-63=1 Exploring Operation: 63-41=22, Resulting Numbers: [64, 22] Generated Node #0,3,3: 63:[64, 22] Operation: 63-41=22 Moving to Node #0,1,0 Current State: 63:[63, 5], Operations: ['55-41=14', '14-9=5'] Exploring Operation: 63*5=315, Resulting Numbers: [315] 315,63 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,63 unequal: No Solution Exploring Operation: 63+5=68, Resulting Numbers: [68] 68,63 unequal: No Solution Moving to Node #0,3,3 Current State: 63:[64, 22], Operations: ['55+9=64', '63-41=22'] Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,63 unequal: No Solution Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[63, 23], Operations: ['55-41=14', '9+14=23'] Exploring Operation: 63*23=1449, Resulting Numbers: [1449] 1449,63 unequal: No Solution Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,63 unequal: No Solution Moving to Node #0,3,1 Current State: 63:[63, 23], Operations: ['55+9=64', '64-41=23'] Exploring Operation: 63*23=1449, Resulting Numbers: [1449] 1449,63 unequal: No Solution Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[14, 7], Operations: ['55-41=14', '63/9=7'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,63 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,63 unequal: No Solution Moving to Node #0,1,3 Current State: 63:[14, 72], Operations: ['55-41=14', '9+63=72'] Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,63 unequal: No Solution Exploring Operation: 14*72=1008, Resulting Numbers: [1008] 1008,63 unequal: No Solution Exploring Operation: 14+72=86, Resulting Numbers: [86] 86,63 unequal: No Solution Moving to Node #0,3,2 Current State: 63:[41, 1], Operations: ['55+9=64', '64-63=1'] Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,63 unequal: No Solution Moving to Node #0,3,0 Current State: 63:[64, 104], Operations: ['55+9=64', '41+63=104'] Exploring Operation: 64*104=6656, Resulting Numbers: [6656] 6656,63 unequal: No Solution Exploring Operation: 64+104=168, Resulting Numbers: [168] 168,63 unequal: No Solution Exploring Operation: 104-64=40, Resulting Numbers: [40] 40,63 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 97, 2, 38, 24 ]
54
[ "97-24=73", "38/2=19", "73-19=54" ]
Current State: 54:[97, 2, 38, 24], Operations: [] Exploring Operation: 97-24=73, Resulting Numbers: [2, 38, 73] Generated Node #2: [2, 38, 73] from Operation: 97-24=73 Current State: 54:[2, 38, 73], Operations: ['97-24=73'] Exploring Operation: 38/2=19, Resulting Numbers: [73, 19] Generated Node #3: [73, 19] from Operation: 38/2=19 Current State: 54:[73, 19], Operations: ['97-24=73', '38/2=19'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[97, 2, 38, 24], Operations: [] Exploring Operation: 97-24=73, Resulting Numbers: [2, 38, 73] Generated Node #0,0: 54:[2, 38, 73] Operation: 97-24=73 Exploring Operation: 97-38=59, Resulting Numbers: [2, 24, 59] Generated Node #0,1: 54:[2, 24, 59] Operation: 97-38=59 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[2, 24, 59], Operations: ['97-38=59'] Exploring Operation: 2+24=26, Resulting Numbers: [59, 26] Generated Node #0,1,0: 54:[59, 26] Operation: 2+24=26 Exploring Operation: 59-2=57, Resulting Numbers: [24, 57] Generated Node #0,1,1: 54:[24, 57] Operation: 59-2=57 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[59, 26], Operations: ['97-38=59', '2+24=26'] Exploring Operation: 59-26=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 59+26=85, Resulting Numbers: [85] 85,54 unequal: No Solution No 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: 54:[24, 57], Operations: ['97-38=59', '59-2=57'] Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 24+57=81, Resulting Numbers: [81] 81,54 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: 54:[2, 38, 73], Operations: ['97-24=73'] Exploring Operation: 38/2=19, Resulting Numbers: [73, 19] Generated Node #0,0,0: 54:[73, 19] Operation: 38/2=19 Exploring Operation: 73-38=35, Resulting Numbers: [2, 35] Generated Node #0,0,1: 54:[2, 35] Operation: 73-38=35 Moving to Node #0,0,1 Current State: 54:[2, 35], Operations: ['97-24=73', '73-38=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[73, 19], Operations: ['97-24=73', '38/2=19'] Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,54 unequal: No Solution Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[97, 2, 38, 24], Operations: [] Exploring Operation: 97-24=73, Resulting Numbers: [2, 38, 73] Generated Node #0,0: 54:[2, 38, 73] Operation: 97-24=73 Moving to Node #0,0 Current State: 54:[2, 38, 73], Operations: ['97-24=73'] Exploring Operation: 38/2=19, Resulting Numbers: [73, 19] Generated Node #0,0,0: 54:[73, 19] Operation: 38/2=19 Moving to Node #0,0,0 Current State: 54:[73, 19], Operations: ['97-24=73', '38/2=19'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 93, 3, 7, 42 ]
25
[ "93/3=31", "42/7=6", "31-6=25" ]
Current State: 25:[93, 3, 7, 42], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [7, 42, 31] Generated Node #2: [7, 42, 31] from Operation: 93/3=31 Current State: 25:[7, 42, 31], Operations: ['93/3=31'] Exploring Operation: 42/7=6, Resulting Numbers: [31, 6] Generated Node #3: [31, 6] from Operation: 42/7=6 Current State: 25:[31, 6], Operations: ['93/3=31', '42/7=6'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[93, 3, 7, 42], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [7, 42, 31] Generated Node #0,0: 25:[7, 42, 31] Operation: 93/3=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[7, 42, 31], Operations: ['93/3=31'] Exploring Operation: 42/7=6, Resulting Numbers: [31, 6] Generated Node #0,0,0: 25:[31, 6] Operation: 42/7=6 Moving to Node #0,0,0 Current State: 25:[31, 6], Operations: ['93/3=31', '42/7=6'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[93, 3, 7, 42], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [7, 42, 31] Generated Node #0,0: 25:[7, 42, 31] Operation: 93/3=31 Moving to Node #0,0 Current State: 25:[7, 42, 31], Operations: ['93/3=31'] Exploring Operation: 42/7=6, Resulting Numbers: [31, 6] Generated Node #0,0,0: 25:[31, 6] Operation: 42/7=6 Moving to Node #0,0,0 Current State: 25:[31, 6], Operations: ['93/3=31', '42/7=6'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 70, 24, 74, 70 ]
90
[ "70+24=94", "74-70=4", "94-4=90" ]
Current State: 90:[70, 24, 74, 70], Operations: [] Exploring Operation: 70+24=94, Resulting Numbers: [74, 94] Generated Node #2: [74, 94] from Operation: 70+24=94 Current State: 90:[74, 94], Operations: ['70+24=94'] Exploring Operation: 74-70=4, Resulting Numbers: [94, 4] Generated Node #3: [94, 4] from Operation: 74-70=4 Current State: 90:[94, 4], Operations: ['70+24=94', '74-70=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[70, 24, 74, 70], Operations: [] Exploring Operation: 70/70=1, Resulting Numbers: [24, 74, 1] Generated Node #0,0: 90:[24, 74, 1] Operation: 70/70=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[24, 74, 1], Operations: ['70/70=1'] Exploring Operation: 74-24=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 90:[1, 50] Operation: 74-24=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[1, 50], Operations: ['70/70=1', '74-24=50'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,90 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
[ 45, 3, 83, 24 ]
28
[ "45*3=135", "83+24=107", "135-107=28" ]
Current State: 28:[45, 3, 83, 24], Operations: [] Exploring Operation: 45*3=135, Resulting Numbers: [83, 24, 135] Generated Node #2: [83, 24, 135] from Operation: 45*3=135 Current State: 28:[83, 24, 135], Operations: ['45*3=135'] Exploring Operation: 83+24=107, Resulting Numbers: [135, 107] Generated Node #3: [135, 107] from Operation: 83+24=107 Current State: 28:[135, 107], Operations: ['45*3=135', '83+24=107'] Exploring Operation: 135-107=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[45, 3, 83, 24], Operations: [] Exploring Operation: 83-45=38, Resulting Numbers: [3, 24, 38] Generated Node #0,0: 28:[3, 24, 38] Operation: 83-45=38 Exploring Operation: 45-24=21, Resulting Numbers: [3, 83, 21] Generated Node #0,1: 28:[3, 83, 21] Operation: 45-24=21 Exploring Operation: 83-24=59, Resulting Numbers: [45, 3, 59] Generated Node #0,2: 28:[45, 3, 59] Operation: 83-24=59 Exploring Operation: 45/3=15, Resulting Numbers: [83, 24, 15] Generated Node #0,3: 28:[83, 24, 15] Operation: 45/3=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[3, 24, 38], Operations: ['83-45=38'] Exploring Operation: 3+24=27, Resulting Numbers: [38, 27] Generated Node #0,0,0: 28:[38, 27] Operation: 3+24=27 Exploring Operation: 38-24=14, Resulting Numbers: [3, 14] Generated Node #0,0,1: 28:[3, 14] Operation: 38-24=14 Exploring Operation: 24/3=8, Resulting Numbers: [38, 8] Generated Node #0,0,2: 28:[38, 8] Operation: 24/3=8 Exploring Operation: 38-3=35, Resulting Numbers: [24, 35] Generated Node #0,0,3: 28:[24, 35] Operation: 38-3=35 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[3, 14], Operations: ['83-45=38', '38-24=14'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,28 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[38, 27], Operations: ['83-45=38', '3+24=27'] Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,28 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 28:[38, 8], Operations: ['83-45=38', '24/3=8'] Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,28 unequal: No Solution Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,28 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 28:[24, 35], Operations: ['83-45=38', '38-3=35'] Exploring Operation: 24+35=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 24*35=840, Resulting Numbers: [840] 840,28 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,28 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 #0,2 Current State: 28:[45, 3, 59], Operations: ['83-24=59'] Exploring Operation: 45-3=42, Resulting Numbers: [59, 42] Generated Node #0,2,0: 28:[59, 42] Operation: 45-3=42 Exploring Operation: 59-3=56, Resulting Numbers: [45, 56] Generated Node #0,2,1: 28:[45, 56] Operation: 59-3=56 Exploring Operation: 59-45=14, Resulting Numbers: [3, 14] Generated Node #0,2,2: 28:[3, 14] Operation: 59-45=14 Exploring Operation: 45/3=15, Resulting Numbers: [59, 15] Generated Node #0,2,3: 28:[59, 15] Operation: 45/3=15 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 28:[3, 14], Operations: ['83-24=59', '59-45=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,28 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,28 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 #0,2,3 Current State: 28:[59, 15], Operations: ['83-24=59', '45/3=15'] Exploring Operation: 59-15=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 59*15=885, Resulting Numbers: [885] 885,28 unequal: No Solution Exploring Operation: 59+15=74, Resulting Numbers: [74] 74,28 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:[59, 42], Operations: ['83-24=59', '45-3=42'] Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,28 unequal: No Solution Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,28 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,28 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:[45, 56], Operations: ['83-24=59', '59-3=56'] Exploring Operation: 45*56=2520, Resulting Numbers: [2520] 2520,28 unequal: No Solution Exploring Operation: 45+56=101, Resulting Numbers: [101] 101,28 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,28 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 #0,3 Current State: 28:[83, 24, 15], Operations: ['45/3=15'] Exploring Operation: 83-15=68, Resulting Numbers: [24, 68] Generated Node #0,3,0: 28:[24, 68] Operation: 83-15=68 Exploring Operation: 24-15=9, Resulting Numbers: [83, 9] Generated Node #0,3,1: 28:[83, 9] Operation: 24-15=9 Exploring Operation: 83-24=59, Resulting Numbers: [15, 59] Generated Node #0,3,2: 28:[15, 59] Operation: 83-24=59 Exploring Operation: 24+15=39, Resulting Numbers: [83, 39] Generated Node #0,3,3: 28:[83, 39] Operation: 24+15=39 Moving to Node #0,3,2 Current State: 28:[15, 59], Operations: ['45/3=15', '83-24=59'] Exploring Operation: 59-15=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 15*59=885, Resulting Numbers: [885] 885,28 unequal: No Solution Exploring Operation: 15+59=74, Resulting Numbers: [74] 74,28 unequal: No Solution Moving to Node #0,3,0 Current State: 28:[24, 68], Operations: ['45/3=15', '83-15=68'] Exploring Operation: 24+68=92, Resulting Numbers: [92] 92,28 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 24*68=1632, Resulting Numbers: [1632] 1632,28 unequal: No Solution Moving to Node #0,3,1 Current State: 28:[83, 9], Operations: ['45/3=15', '24-15=9'] Exploring Operation: 83+9=92, Resulting Numbers: [92] 92,28 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 83*9=747, Resulting Numbers: [747] 747,28 unequal: No Solution Moving to Node #0,3,3 Current State: 28:[83, 39], Operations: ['45/3=15', '24+15=39'] Exploring Operation: 83*39=3237, Resulting Numbers: [3237] 3237,28 unequal: No Solution Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 83+39=122, Resulting Numbers: [122] 122,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[3, 83, 21], Operations: ['45-24=21'] Exploring Operation: 21/3=7, Resulting Numbers: [83, 7] Generated Node #0,1,0: 28:[83, 7] Operation: 21/3=7 Exploring Operation: 83-21=62, Resulting Numbers: [3, 62] Generated Node #0,1,1: 28:[3, 62] Operation: 83-21=62 Exploring Operation: 83-3=80, Resulting Numbers: [21, 80] Generated Node #0,1,2: 28:[21, 80] Operation: 83-3=80 Exploring Operation: 3+21=24, Resulting Numbers: [83, 24] Generated Node #0,1,3: 28:[83, 24] Operation: 3+21=24 Moving to Node #0,1,1 Current State: 28:[3, 62], Operations: ['45-24=21', '83-21=62'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[83, 7], Operations: ['45-24=21', '21/3=7'] Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,28 unequal: No Solution Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,28 unequal: No Solution Moving to Node #0,1,3 Current State: 28:[83, 24], Operations: ['45-24=21', '3+21=24'] Exploring Operation: 83+24=107, Resulting Numbers: [107] 107,28 unequal: No Solution Exploring Operation: 83*24=1992, Resulting Numbers: [1992] 1992,28 unequal: No Solution Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,28 unequal: No Solution Moving to Node #0,1,2 Current State: 28:[21, 80], Operations: ['45-24=21', '83-3=80'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 21*80=1680, Resulting Numbers: [1680] 1680,28 unequal: No Solution Exploring Operation: 21+80=101, Resulting Numbers: [101] 101,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 39, 33, 1, 64 ]
59
[ "39-33=6", "1+64=65", "65-6=59" ]
Current State: 59:[39, 33, 1, 64], Operations: [] Exploring Operation: 39-33=6, Resulting Numbers: [1, 64, 6] Generated Node #2: [1, 64, 6] from Operation: 39-33=6 Current State: 59:[1, 64, 6], Operations: ['39-33=6'] Exploring Operation: 1+64=65, Resulting Numbers: [6, 65] Generated Node #3: [6, 65] from Operation: 1+64=65 Current State: 59:[6, 65], Operations: ['39-33=6', '1+64=65'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[39, 33, 1, 64], Operations: [] Exploring Operation: 39+1=40, Resulting Numbers: [33, 64, 40] Generated Node #0,0: 59:[33, 64, 40] Operation: 39+1=40 Exploring Operation: 64-1=63, Resulting Numbers: [39, 33, 63] Generated Node #0,1: 59:[39, 33, 63] Operation: 64-1=63 Exploring Operation: 33+1=34, Resulting Numbers: [39, 64, 34] Generated Node #0,2: 59:[39, 64, 34] Operation: 33+1=34 Exploring Operation: 39*1=39, Resulting Numbers: [33, 64, 39] Generated Node #0,3: 59:[33, 64, 39] Operation: 39*1=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[33, 64, 40], Operations: ['39+1=40'] Exploring Operation: 33+40=73, Resulting Numbers: [64, 73] Generated Node #0,0,0: 59:[64, 73] Operation: 33+40=73 Exploring Operation: 40-33=7, Resulting Numbers: [64, 7] Generated Node #0,0,1: 59:[64, 7] Operation: 40-33=7 Exploring Operation: 64-33=31, Resulting Numbers: [40, 31] Generated Node #0,0,2: 59:[40, 31] Operation: 64-33=31 Exploring Operation: 33+64=97, Resulting Numbers: [40, 97] Generated Node #0,0,3: 59:[40, 97] Operation: 33+64=97 Moving to Node #0,0,0 Current State: 59:[64, 73], Operations: ['39+1=40', '33+40=73'] Exploring Operation: 73-64=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 64+73=137, Resulting Numbers: [137] 137,59 unequal: No Solution Exploring Operation: 64*73=4672, Resulting Numbers: [4672] 4672,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[40, 31], Operations: ['39+1=40', '64-33=31'] Exploring Operation: 40+31=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 40*31=1240, Resulting Numbers: [1240] 1240,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[40, 97], Operations: ['39+1=40', '33+64=97'] Exploring Operation: 40*97=3880, Resulting Numbers: [3880] 3880,59 unequal: No Solution Exploring Operation: 97-40=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 40+97=137, Resulting Numbers: [137] 137,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[64, 7], Operations: ['39+1=40', '40-33=7'] Exploring Operation: 64*7=448, Resulting Numbers: [448] 448,59 unequal: No Solution Exploring Operation: 64+7=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[39, 33, 63], Operations: ['64-1=63'] Exploring Operation: 39+33=72, Resulting Numbers: [63, 72] Generated Node #0,1,0: 59:[63, 72] Operation: 39+33=72 Exploring Operation: 33+63=96, Resulting Numbers: [39, 96] Generated Node #0,1,1: 59:[39, 96] Operation: 33+63=96 Exploring Operation: 63-33=30, Resulting Numbers: [39, 30] Generated Node #0,1,2: 59:[39, 30] Operation: 63-33=30 Exploring Operation: 39-33=6, Resulting Numbers: [63, 6] Generated Node #0,1,3: 59:[63, 6] Operation: 39-33=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[63, 72], Operations: ['64-1=63', '39+33=72'] Exploring Operation: 72-63=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 63*72=4536, Resulting Numbers: [4536] 4536,59 unequal: No Solution Exploring Operation: 63+72=135, Resulting Numbers: [135] 135,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 59:[39, 30], Operations: ['64-1=63', '63-33=30'] Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,59 unequal: No Solution Exploring Operation: 39*30=1170, Resulting Numbers: [1170] 1170,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[39, 96], Operations: ['64-1=63', '33+63=96'] Exploring Operation: 96-39=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 39+96=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 39*96=3744, Resulting Numbers: [3744] 3744,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 59:[63, 6], Operations: ['64-1=63', '39-33=6'] Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,59 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[39, 64, 34], Operations: ['33+1=34'] Exploring Operation: 39+34=73, Resulting Numbers: [64, 73] Generated Node #0,2,0: 59:[64, 73] Operation: 39+34=73 Exploring Operation: 39-34=5, Resulting Numbers: [64, 5] Generated Node #0,2,1: 59:[64, 5] Operation: 39-34=5 Exploring Operation: 64-34=30, Resulting Numbers: [39, 30] Generated Node #0,2,2: 59:[39, 30] Operation: 64-34=30 Exploring Operation: 64-39=25, Resulting Numbers: [34, 25] Generated Node #0,2,3: 59:[34, 25] Operation: 64-39=25 Moving to Node #0,2,0 Current State: 59:[64, 73], Operations: ['33+1=34', '39+34=73'] Exploring Operation: 64*73=4672, Resulting Numbers: [4672] 4672,59 unequal: No Solution Exploring Operation: 73-64=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 64+73=137, Resulting Numbers: [137] 137,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[39, 30], Operations: ['33+1=34', '64-34=30'] Exploring Operation: 39*30=1170, Resulting Numbers: [1170] 1170,59 unequal: No Solution Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,59 unequal: No Solution Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[34, 25], Operations: ['33+1=34', '64-39=25'] Exploring Operation: 34*25=850, Resulting Numbers: [850] 850,59 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 34+25=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[39, 33, 1, 64], Operations: [] Exploring Operation: 33+1=34, Resulting Numbers: [39, 64, 34] Generated Node #0,2: 59:[39, 64, 34] Operation: 33+1=34 Moving to Node #0,2 Current State: 59:[39, 64, 34], Operations: ['33+1=34'] Exploring Operation: 64-39=25, Resulting Numbers: [34, 25] Generated Node #0,2,3: 59:[34, 25] Operation: 64-39=25 Moving to Node #0,2,3 Current State: 59:[34, 25], Operations: ['33+1=34', '64-39=25'] Exploring Operation: 34+25=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_4
sum_heuristic
[ 6, 97, 24, 55 ]
11
[ "97+24=121", "121-55=66", "66/6=11" ]
Current State: 11:[6, 97, 24, 55], Operations: [] Exploring Operation: 97+24=121, Resulting Numbers: [6, 55, 121] Generated Node #2: [6, 55, 121] from Operation: 97+24=121 Current State: 11:[6, 55, 121], Operations: ['97+24=121'] Exploring Operation: 121-55=66, Resulting Numbers: [6, 66] Generated Node #3: [6, 66] from Operation: 121-55=66 Current State: 11:[6, 66], Operations: ['97+24=121', '121-55=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[6, 97, 24, 55], Operations: [] Exploring Operation: 97-6=91, Resulting Numbers: [24, 55, 91] Generated Node #0,0: 11:[24, 55, 91] Operation: 97-6=91 Exploring Operation: 55-24=31, Resulting Numbers: [6, 97, 31] Generated Node #0,1: 11:[6, 97, 31] Operation: 55-24=31 Exploring Operation: 97-24=73, Resulting Numbers: [6, 55, 73] Generated Node #0,2: 11:[6, 55, 73] Operation: 97-24=73 Exploring Operation: 97-55=42, Resulting Numbers: [6, 24, 42] Generated Node #0,3: 11:[6, 24, 42] Operation: 97-55=42 Moving to Node #0,3 Current State: 11:[6, 24, 42], Operations: ['97-55=42'] Exploring Operation: 42-24=18, Resulting Numbers: [6, 18] Generated Node #0,3,0: 11:[6, 18] Operation: 42-24=18 Exploring Operation: 42/6=7, Resulting Numbers: [24, 7] Generated Node #0,3,1: 11:[24, 7] Operation: 42/6=7 Exploring Operation: 24-6=18, Resulting Numbers: [42, 18] Generated Node #0,3,2: 11:[42, 18] Operation: 24-6=18 Exploring Operation: 24/6=4, Resulting Numbers: [42, 4] Generated Node #0,3,3: 11:[42, 4] Operation: 24/6=4 Moving to Node #0,2 Current State: 11:[6, 55, 73], Operations: ['97-24=73'] Exploring Operation: 6+55=61, Resulting Numbers: [73, 61] Generated Node #0,2,0: 11:[73, 61] Operation: 6+55=61 Exploring Operation: 73-6=67, Resulting Numbers: [55, 67] Generated Node #0,2,1: 11:[55, 67] Operation: 73-6=67 Exploring Operation: 73-55=18, Resulting Numbers: [6, 18] Generated Node #0,2,2: 11:[6, 18] Operation: 73-55=18 Exploring Operation: 55-6=49, Resulting Numbers: [73, 49] Generated Node #0,2,3: 11:[73, 49] Operation: 55-6=49 Moving to Node #0,1 Current State: 11:[6, 97, 31], Operations: ['55-24=31'] Exploring Operation: 31-6=25, Resulting Numbers: [97, 25] Generated Node #0,1,0: 11:[97, 25] Operation: 31-6=25 Exploring Operation: 6+97=103, Resulting Numbers: [31, 103] Generated Node #0,1,1: 11:[31, 103] Operation: 6+97=103 Exploring Operation: 97-31=66, Resulting Numbers: [6, 66] Generated Node #0,1,2: 11:[6, 66] Operation: 97-31=66 Exploring Operation: 97-6=91, Resulting Numbers: [31, 91] Generated Node #0,1,3: 11:[31, 91] Operation: 97-6=91 Moving to Node #0,0 Current State: 11:[24, 55, 91], Operations: ['97-6=91'] Exploring Operation: 24+55=79, Resulting Numbers: [91, 79] Generated Node #0,0,0: 11:[91, 79] Operation: 24+55=79 Exploring Operation: 91-55=36, Resulting Numbers: [24, 36] Generated Node #0,0,1: 11:[24, 36] Operation: 91-55=36 Exploring Operation: 91-24=67, Resulting Numbers: [55, 67] Generated Node #0,0,2: 11:[55, 67] Operation: 91-24=67 Exploring Operation: 55-24=31, Resulting Numbers: [91, 31] Generated Node #0,0,3: 11:[91, 31] Operation: 55-24=31 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[24, 36], Operations: ['97-6=91', '91-55=36'] Exploring Operation: 24*36=864, Resulting Numbers: [864] 864,11 unequal: No Solution Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 24+36=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[55, 67], Operations: ['97-6=91', '91-24=67'] Exploring Operation: 55+67=122, Resulting Numbers: [122] 122,11 unequal: No Solution Exploring Operation: 67-55=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 55*67=3685, Resulting Numbers: [3685] 3685,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 11:[91, 31], Operations: ['97-6=91', '55-24=31'] Exploring Operation: 91*31=2821, Resulting Numbers: [2821] 2821,11 unequal: No Solution Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 91+31=122, Resulting Numbers: [122] 122,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[91, 79], Operations: ['97-6=91', '24+55=79'] Exploring Operation: 91-79=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 91+79=170, Resulting Numbers: [170] 170,11 unequal: No Solution Exploring Operation: 91*79=7189, Resulting Numbers: [7189] 7189,11 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: 11:[6, 18], Operations: ['97-55=42', '42-24=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 6*18=108, Resulting Numbers: [108] 108,11 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,11 unequal: No Solution Moving to Node #0,2,2 Current State: 11:[6, 18], Operations: ['97-24=73', '73-55=18'] Exploring Operation: 6*18=108, Resulting Numbers: [108] 108,11 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[24, 7], Operations: ['97-55=42', '42/6=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,11 unequal: No Solution Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[42, 18], Operations: ['97-55=42', '24-6=18'] Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,11 unequal: No Solution Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[42, 4], Operations: ['97-55=42', '24/6=4'] Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,11 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[6, 66], Operations: ['55-24=31', '97-31=66'] Exploring Operation: 6+66=72, Resulting Numbers: [72] 72,11 unequal: No Solution Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[6, 97, 24, 55], Operations: [] Exploring Operation: 55-24=31, Resulting Numbers: [6, 97, 31] Generated Node #0,1: 11:[6, 97, 31] Operation: 55-24=31 Moving to Node #0,1 Current State: 11:[6, 97, 31], Operations: ['55-24=31'] Exploring Operation: 97-31=66, Resulting Numbers: [6, 66] Generated Node #0,1,2: 11:[6, 66] Operation: 97-31=66 Moving to Node #0,1,2 Current State: 11:[6, 66], Operations: ['55-24=31', '97-31=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.952257
hs_4
sum_heuristic
[ 76, 36, 49, 5 ]
84
[ "76-36=40", "49-5=44", "40+44=84" ]
Current State: 84:[76, 36, 49, 5], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [49, 5, 40] Generated Node #2: [49, 5, 40] from Operation: 76-36=40 Current State: 84:[49, 5, 40], Operations: ['76-36=40'] Exploring Operation: 49-5=44, Resulting Numbers: [40, 44] Generated Node #3: [40, 44] from Operation: 49-5=44 Current State: 84:[40, 44], Operations: ['76-36=40', '49-5=44'] Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[76, 36, 49, 5], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [76, 5, 13] Generated Node #0,0: 84:[76, 5, 13] Operation: 49-36=13 Exploring Operation: 76-36=40, Resulting Numbers: [49, 5, 40] Generated Node #0,1: 84:[49, 5, 40] Operation: 76-36=40 Exploring Operation: 36+49=85, Resulting Numbers: [76, 5, 85] Generated Node #0,2: 84:[76, 5, 85] Operation: 36+49=85 Exploring Operation: 76-49=27, Resulting Numbers: [36, 5, 27] Generated Node #0,3: 84:[36, 5, 27] Operation: 76-49=27 Moving to Node #0,3 Current State: 84:[36, 5, 27], Operations: ['76-49=27'] Exploring Operation: 36+5=41, Resulting Numbers: [27, 41] Generated Node #0,3,0: 84:[27, 41] Operation: 36+5=41 Exploring Operation: 36-27=9, Resulting Numbers: [5, 9] Generated Node #0,3,1: 84:[5, 9] Operation: 36-27=9 Exploring Operation: 27-5=22, Resulting Numbers: [36, 22] Generated Node #0,3,2: 84:[36, 22] Operation: 27-5=22 Exploring Operation: 36-5=31, Resulting Numbers: [27, 31] Generated Node #0,3,3: 84:[27, 31] Operation: 36-5=31 Moving to Node #0,1 Current State: 84:[49, 5, 40], Operations: ['76-36=40'] Exploring Operation: 40/5=8, Resulting Numbers: [49, 8] Generated Node #0,1,0: 84:[49, 8] Operation: 40/5=8 Exploring Operation: 49-5=44, Resulting Numbers: [40, 44] Generated Node #0,1,1: 84:[40, 44] Operation: 49-5=44 Exploring Operation: 49-40=9, Resulting Numbers: [5, 9] Generated Node #0,1,2: 84:[5, 9] Operation: 49-40=9 Exploring Operation: 49+40=89, Resulting Numbers: [5, 89] Generated Node #0,1,3: 84:[5, 89] Operation: 49+40=89 Moving to Node #0,0 Current State: 84:[76, 5, 13], Operations: ['49-36=13'] Exploring Operation: 76+5=81, Resulting Numbers: [13, 81] Generated Node #0,0,0: 84:[13, 81] Operation: 76+5=81 Exploring Operation: 76+13=89, Resulting Numbers: [5, 89] Generated Node #0,0,1: 84:[5, 89] Operation: 76+13=89 Exploring Operation: 13-5=8, Resulting Numbers: [76, 8] Generated Node #0,0,2: 84:[76, 8] Operation: 13-5=8 Exploring Operation: 5+13=18, Resulting Numbers: [76, 18] Generated Node #0,0,3: 84:[76, 18] Operation: 5+13=18 Moving to Node #0,2 Current State: 84:[76, 5, 85], Operations: ['36+49=85'] Exploring Operation: 85/5=17, Resulting Numbers: [76, 17] Generated Node #0,2,0: 84:[76, 17] Operation: 85/5=17 Exploring Operation: 85-76=9, Resulting Numbers: [5, 9] Generated Node #0,2,1: 84:[5, 9] Operation: 85-76=9 Exploring Operation: 76+5=81, Resulting Numbers: [85, 81] Generated Node #0,2,2: 84:[85, 81] Operation: 76+5=81 Exploring Operation: 85-5=80, Resulting Numbers: [76, 80] Generated Node #0,2,3: 84:[76, 80] Operation: 85-5=80 Moving to Node #0,3,0 Current State: 84:[27, 41], Operations: ['76-49=27', '36+5=41'] Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,84 unequal: No Solution Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,84 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[5, 9], Operations: ['36+49=85', '85-76=9'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[5, 9], Operations: ['76-49=27', '36-27=9'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[5, 9], Operations: ['76-36=40', '49-40=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,84 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[85, 81], Operations: ['36+49=85', '76+5=81'] Exploring Operation: 85+81=166, Resulting Numbers: [166] 166,84 unequal: No Solution Exploring Operation: 85-81=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 85*81=6885, Resulting Numbers: [6885] 6885,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[27, 31], Operations: ['76-49=27', '36-5=31'] Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,84 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[40, 44], Operations: ['76-36=40', '49-5=44'] Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,84 unequal: No Solution Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[76, 36, 49, 5], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [49, 5, 40] Generated Node #0,1: 84:[49, 5, 40] Operation: 76-36=40 Moving to Node #0,1 Current State: 84:[49, 5, 40], Operations: ['76-36=40'] Exploring Operation: 49-5=44, Resulting Numbers: [40, 44] Generated Node #0,1,1: 84:[40, 44] Operation: 49-5=44 Moving to Node #0,1,1 Current State: 84:[40, 44], Operations: ['76-36=40', '49-5=44'] Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.961806
hs_4
sum_heuristic
[ 31, 29, 76, 95 ]
19
[ "31*76=2356", "29+95=124", "2356/124=19" ]
Current State: 19:[31, 29, 76, 95], Operations: [] Exploring Operation: 31*76=2356, Resulting Numbers: [29, 95, 2356] Generated Node #2: [29, 95, 2356] from Operation: 31*76=2356 Current State: 19:[29, 95, 2356], Operations: ['31*76=2356'] Exploring Operation: 29+95=124, Resulting Numbers: [2356, 124] Generated Node #3: [2356, 124] from Operation: 29+95=124 Current State: 19:[2356, 124], Operations: ['31*76=2356', '29+95=124'] Exploring Operation: 2356/124=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[31, 29, 76, 95], Operations: [] Exploring Operation: 95-76=19, Resulting Numbers: [31, 29, 19] Generated Node #0,0: 19:[31, 29, 19] Operation: 95-76=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[31, 29, 19], Operations: ['95-76=19'] Exploring Operation: 31-29=2, Resulting Numbers: [19, 2] Generated Node #0,0,0: 19:[19, 2] Operation: 31-29=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[19, 2], Operations: ['95-76=19', '31-29=2'] Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,19 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
sum_heuristic
[ 75, 64, 88, 40 ]
91
[ "75+64=139", "88-40=48", "139-48=91" ]
Current State: 91:[75, 64, 88, 40], Operations: [] Exploring Operation: 75+64=139, Resulting Numbers: [88, 40, 139] Generated Node #2: [88, 40, 139] from Operation: 75+64=139 Current State: 91:[88, 40, 139], Operations: ['75+64=139'] Exploring Operation: 88-40=48, Resulting Numbers: [139, 48] Generated Node #3: [139, 48] from Operation: 88-40=48 Current State: 91:[139, 48], Operations: ['75+64=139', '88-40=48'] Exploring Operation: 139-48=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[75, 64, 88, 40], Operations: [] Exploring Operation: 64-40=24, Resulting Numbers: [75, 88, 24] Generated Node #0,0: 91:[75, 88, 24] Operation: 64-40=24 Exploring Operation: 88-75=13, Resulting Numbers: [64, 40, 13] Generated Node #0,1: 91:[64, 40, 13] Operation: 88-75=13 Exploring Operation: 75-40=35, Resulting Numbers: [64, 88, 35] Generated Node #0,2: 91:[64, 88, 35] Operation: 75-40=35 Exploring Operation: 75-64=11, Resulting Numbers: [88, 40, 11] Generated Node #0,3: 91:[88, 40, 11] Operation: 75-64=11 Exploring Operation: 64+40=104, Resulting Numbers: [75, 88, 104] Generated Node #0,4: 91:[75, 88, 104] Operation: 64+40=104 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[75, 88, 24], Operations: ['64-40=24'] Exploring Operation: 88-75=13, Resulting Numbers: [24, 13] Generated Node #0,0,0: 91:[24, 13] Operation: 88-75=13 Exploring Operation: 75+24=99, Resulting Numbers: [88, 99] Generated Node #0,0,1: 91:[88, 99] Operation: 75+24=99 Exploring Operation: 88+24=112, Resulting Numbers: [75, 112] Generated Node #0,0,2: 91:[75, 112] Operation: 88+24=112 Exploring Operation: 88-24=64, Resulting Numbers: [75, 64] Generated Node #0,0,3: 91:[75, 64] Operation: 88-24=64 Exploring Operation: 75-24=51, Resulting Numbers: [88, 51] Generated Node #0,0,4: 91:[88, 51] Operation: 75-24=51 Moving to Node #0,0,0 Current State: 91:[24, 13], Operations: ['64-40=24', '88-75=13'] Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,91 unequal: No Solution Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[88, 99], Operations: ['64-40=24', '75+24=99'] Exploring Operation: 99-88=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 88*99=8712, Resulting Numbers: [8712] 8712,91 unequal: No Solution Exploring Operation: 88+99=187, Resulting Numbers: [187] 187,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[75, 112], Operations: ['64-40=24', '88+24=112'] Exploring Operation: 75*112=8400, Resulting Numbers: [8400] 8400,91 unequal: No Solution Exploring Operation: 112-75=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 75+112=187, Resulting Numbers: [187] 187,91 unequal: No Solution Moving to Node #0,0,4 Current State: 91:[88, 51], Operations: ['64-40=24', '75-24=51'] Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,91 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[75, 64], Operations: ['64-40=24', '88-24=64'] Exploring Operation: 75*64=4800, Resulting Numbers: [4800] 4800,91 unequal: No Solution Exploring Operation: 75+64=139, Resulting Numbers: [139] 139,91 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[88, 40, 11], Operations: ['75-64=11'] Exploring Operation: 88+40=128, Resulting Numbers: [11, 128] Generated Node #0,3,0: 91:[11, 128] Operation: 88+40=128 Exploring Operation: 88-40=48, Resulting Numbers: [11, 48] Generated Node #0,3,1: 91:[11, 48] Operation: 88-40=48 Exploring Operation: 40-11=29, Resulting Numbers: [88, 29] Generated Node #0,3,2: 91:[88, 29] Operation: 40-11=29 Exploring Operation: 88/11=8, Resulting Numbers: [40, 8] Generated Node #0,3,3: 91:[40, 8] Operation: 88/11=8 Exploring Operation: 88+11=99, Resulting Numbers: [40, 99] Generated Node #0,3,4: 91:[40, 99] Operation: 88+11=99 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 91:[88, 29], Operations: ['75-64=11', '40-11=29'] Exploring Operation: 88*29=2552, Resulting Numbers: [2552] 2552,91 unequal: No Solution Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,91 unequal: No Solution Exploring Operation: 88+29=117, Resulting Numbers: [117] 117,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 91:[40, 8], Operations: ['75-64=11', '88/11=8'] Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,91 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,91 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 91:[40, 99], Operations: ['75-64=11', '88+11=99'] Exploring Operation: 99-40=59, Resulting Numbers: [59] 59,91 unequal: No Solution Exploring Operation: 40*99=3960, Resulting Numbers: [3960] 3960,91 unequal: No Solution Exploring Operation: 40+99=139, Resulting Numbers: [139] 139,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 91:[11, 48], Operations: ['75-64=11', '88-40=48'] Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 11*48=528, Resulting Numbers: [528] 528,91 unequal: No Solution Exploring Operation: 11+48=59, Resulting Numbers: [59] 59,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 91:[11, 128], Operations: ['75-64=11', '88+40=128'] Exploring Operation: 11+128=139, Resulting Numbers: [139] 139,91 unequal: No Solution Exploring Operation: 128-11=117, Resulting Numbers: [117] 117,91 unequal: No Solution Exploring Operation: 11*128=1408, Resulting Numbers: [1408] 1408,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 91:[75, 88, 104], Operations: ['64+40=104'] Exploring Operation: 75+88=163, Resulting Numbers: [104, 163] Generated Node #0,4,0: 91:[104, 163] Operation: 75+88=163 Exploring Operation: 75+104=179, Resulting Numbers: [88, 179] Generated Node #0,4,1: 91:[88, 179] Operation: 75+104=179 Exploring Operation: 88-75=13, Resulting Numbers: [104, 13] Generated Node #0,4,2: 91:[104, 13] Operation: 88-75=13 Exploring Operation: 104-75=29, Resulting Numbers: [88, 29] Generated Node #0,4,3: 91:[88, 29] Operation: 104-75=29 Exploring Operation: 104-88=16, Resulting Numbers: [75, 16] Generated Node #0,4,4: 91:[75, 16] Operation: 104-88=16 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 91:[104, 13], Operations: ['64+40=104', '88-75=13'] Exploring Operation: 104*13=1352, Resulting Numbers: [1352] 1352,91 unequal: No Solution Exploring Operation: 104/13=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 104-13=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[75, 64, 88, 40], Operations: [] Exploring Operation: 64+40=104, Resulting Numbers: [75, 88, 104] Generated Node #0,4: 91:[75, 88, 104] Operation: 64+40=104 Moving to Node #0,4 Current State: 91:[75, 88, 104], Operations: ['64+40=104'] Exploring Operation: 88-75=13, Resulting Numbers: [104, 13] Generated Node #0,4,2: 91:[104, 13] Operation: 88-75=13 Moving to Node #0,4,2 Current State: 91:[104, 13], Operations: ['64+40=104', '88-75=13'] Exploring Operation: 104-13=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 51, 52, 12, 90 ]
26
[ "51*52=2652", "12+90=102", "2652/102=26" ]
Current State: 26:[51, 52, 12, 90], Operations: [] Exploring Operation: 51*52=2652, Resulting Numbers: [12, 90, 2652] Generated Node #2: [12, 90, 2652] from Operation: 51*52=2652 Current State: 26:[12, 90, 2652], Operations: ['51*52=2652'] Exploring Operation: 12+90=102, Resulting Numbers: [2652, 102] Generated Node #3: [2652, 102] from Operation: 12+90=102 Current State: 26:[2652, 102], Operations: ['51*52=2652', '12+90=102'] Exploring Operation: 2652/102=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[51, 52, 12, 90], Operations: [] Exploring Operation: 52-51=1, Resulting Numbers: [12, 90, 1] Generated Node #0,0: 26:[12, 90, 1] Operation: 52-51=1 Exploring Operation: 52-12=40, Resulting Numbers: [51, 90, 40] Generated Node #0,1: 26:[51, 90, 40] Operation: 52-12=40 Exploring Operation: 90-51=39, Resulting Numbers: [52, 12, 39] Generated Node #0,2: 26:[52, 12, 39] Operation: 90-51=39 Exploring Operation: 51-12=39, Resulting Numbers: [52, 90, 39] Generated Node #0,3: 26:[52, 90, 39] Operation: 51-12=39 Exploring Operation: 90-52=38, Resulting Numbers: [51, 12, 38] Generated Node #0,4: 26:[51, 12, 38] Operation: 90-52=38 Moving to Node #0,4 Current State: 26:[51, 12, 38], Operations: ['90-52=38'] Exploring Operation: 51-38=13, Resulting Numbers: [12, 13] Generated Node #0,4,0: 26:[12, 13] Operation: 51-38=13 Exploring Operation: 38-12=26, Resulting Numbers: [51, 26] Generated Node #0,4,1: 26:[51, 26] Operation: 38-12=26 Exploring Operation: 12+38=50, Resulting Numbers: [51, 50] Generated Node #0,4,2: 26:[51, 50] Operation: 12+38=50 Exploring Operation: 51-12=39, Resulting Numbers: [38, 39] Generated Node #0,4,3: 26:[38, 39] Operation: 51-12=39 Exploring Operation: 51+12=63, Resulting Numbers: [38, 63] Generated Node #0,4,4: 26:[38, 63] Operation: 51+12=63 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 26:[12, 13], Operations: ['90-52=38', '51-38=13'] Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,26 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,26 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 #0,4,1 Current State: 26:[51, 26], Operations: ['90-52=38', '38-12=26'] Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,26 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,26 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 #0,4,3 Current State: 26:[38, 39], Operations: ['90-52=38', '51-12=39'] Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 38*39=1482, Resulting Numbers: [1482] 1482,26 unequal: No Solution Exploring Operation: 38+39=77, Resulting Numbers: [77] 77,26 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 #0,4,2 Current State: 26:[51, 50], Operations: ['90-52=38', '12+38=50'] Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 51*50=2550, Resulting Numbers: [2550] 2550,26 unequal: No Solution Exploring Operation: 51+50=101, Resulting Numbers: [101] 101,26 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 #0,4,4 Current State: 26:[38, 63], Operations: ['90-52=38', '51+12=63'] Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 38+63=101, Resulting Numbers: [101] 101,26 unequal: No Solution Exploring Operation: 38*63=2394, Resulting Numbers: [2394] 2394,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 26:[52, 12, 39], Operations: ['90-51=39'] Exploring Operation: 52-12=40, Resulting Numbers: [39, 40] Generated Node #0,2,0: 26:[39, 40] Operation: 52-12=40 Exploring Operation: 12+39=51, Resulting Numbers: [52, 51] Generated Node #0,2,1: 26:[52, 51] Operation: 12+39=51 Exploring Operation: 52-39=13, Resulting Numbers: [12, 13] Generated Node #0,2,2: 26:[12, 13] Operation: 52-39=13 Exploring Operation: 39-12=27, Resulting Numbers: [52, 27] Generated Node #0,2,3: 26:[52, 27] Operation: 39-12=27 Exploring Operation: 52+12=64, Resulting Numbers: [39, 64] Generated Node #0,2,4: 26:[39, 64] Operation: 52+12=64 Moving to Node #0,0 Current State: 26:[12, 90, 1], Operations: ['52-51=1'] Exploring Operation: 12/1=12, Resulting Numbers: [90, 12] Generated Node #0,0,0: 26:[90, 12] Operation: 12/1=12 Exploring Operation: 12*1=12, Resulting Numbers: [90, 12] Generated Node #0,0,1: 26:[90, 12] Operation: 12*1=12 Exploring Operation: 12+1=13, Resulting Numbers: [90, 13] Generated Node #0,0,2: 26:[90, 13] Operation: 12+1=13 Exploring Operation: 90-12=78, Resulting Numbers: [1, 78] Generated Node #0,0,3: 26:[1, 78] Operation: 90-12=78 Exploring Operation: 90-1=89, Resulting Numbers: [12, 89] Generated Node #0,0,4: 26:[12, 89] Operation: 90-1=89 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 26:[1, 78], Operations: ['52-51=1', '90-12=78'] Exploring Operation: 1+78=79, Resulting Numbers: [79] 79,26 unequal: No Solution Exploring Operation: 78/1=78, Resulting Numbers: [78] 78,26 unequal: No Solution Exploring Operation: 1*78=78, Resulting Numbers: [78] 78,26 unequal: No Solution Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[90, 13], Operations: ['52-51=1', '12+1=13'] Exploring Operation: 90*13=1170, Resulting Numbers: [1170] 1170,26 unequal: No Solution Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,26 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 #0,0,4 Current State: 26:[12, 89], Operations: ['52-51=1', '90-1=89'] Exploring Operation: 12*89=1068, Resulting Numbers: [1068] 1068,26 unequal: No Solution Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,26 unequal: No Solution Exploring Operation: 12+89=101, Resulting Numbers: [101] 101,26 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:[90, 12], Operations: ['52-51=1', '12/1=12'] Exploring Operation: 90+12=102, Resulting Numbers: [102] 102,26 unequal: No Solution Exploring Operation: 90*12=1080, Resulting Numbers: [1080] 1080,26 unequal: No Solution Exploring Operation: 90-12=78, Resulting Numbers: [78] 78,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[90, 12], Operations: ['52-51=1', '12*1=12'] Exploring Operation: 90+12=102, Resulting Numbers: [102] 102,26 unequal: No Solution Exploring Operation: 90*12=1080, Resulting Numbers: [1080] 1080,26 unequal: No Solution Exploring Operation: 90-12=78, Resulting Numbers: [78] 78,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 26:[51, 90, 40], Operations: ['52-12=40'] Exploring Operation: 51+90=141, Resulting Numbers: [40, 141] Generated Node #0,1,0: 26:[40, 141] Operation: 51+90=141 Exploring Operation: 90-40=50, Resulting Numbers: [51, 50] Generated Node #0,1,1: 26:[51, 50] Operation: 90-40=50 Exploring Operation: 51-40=11, Resulting Numbers: [90, 11] Generated Node #0,1,2: 26:[90, 11] Operation: 51-40=11 Exploring Operation: 51+40=91, Resulting Numbers: [90, 91] Generated Node #0,1,3: 26:[90, 91] Operation: 51+40=91 Exploring Operation: 90-51=39, Resulting Numbers: [40, 39] Generated Node #0,1,4: 26:[40, 39] Operation: 90-51=39 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 26:[40, 39], Operations: ['52-12=40', '90-51=39'] Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,26 unequal: No Solution Exploring Operation: 40*39=1560, Resulting Numbers: [1560] 1560,26 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[51, 50], Operations: ['52-12=40', '90-40=50'] Exploring Operation: 51+50=101, Resulting Numbers: [101] 101,26 unequal: No Solution Exploring Operation: 51*50=2550, Resulting Numbers: [2550] 2550,26 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[90, 11], Operations: ['52-12=40', '51-40=11'] Exploring Operation: 90*11=990, Resulting Numbers: [990] 990,26 unequal: No Solution Exploring Operation: 90-11=79, Resulting Numbers: [79] 79,26 unequal: No Solution Exploring Operation: 90+11=101, Resulting Numbers: [101] 101,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[40, 141], Operations: ['52-12=40', '51+90=141'] Exploring Operation: 40*141=5640, Resulting Numbers: [5640] 5640,26 unequal: No Solution Exploring Operation: 141-40=101, Resulting Numbers: [101] 101,26 unequal: No Solution Exploring Operation: 40+141=181, Resulting Numbers: [181] 181,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 26:[90, 91], Operations: ['52-12=40', '51+40=91'] Exploring Operation: 90*91=8190, Resulting Numbers: [8190] 8190,26 unequal: No Solution Exploring Operation: 91-90=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 90+91=181, Resulting Numbers: [181] 181,26 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: 26:[52, 90, 39], Operations: ['51-12=39'] Exploring Operation: 52+39=91, Resulting Numbers: [90, 91] Generated Node #0,3,0: 26:[90, 91] Operation: 52+39=91 Exploring Operation: 52+90=142, Resulting Numbers: [39, 142] Generated Node #0,3,1: 26:[39, 142] Operation: 52+90=142 Exploring Operation: 90-39=51, Resulting Numbers: [52, 51] Generated Node #0,3,2: 26:[52, 51] Operation: 90-39=51 Exploring Operation: 52-39=13, Resulting Numbers: [90, 13] Generated Node #0,3,3: 26:[90, 13] Operation: 52-39=13 Exploring Operation: 90-52=38, Resulting Numbers: [39, 38] Generated Node #0,3,4: 26:[39, 38] Operation: 90-52=38 Moving to Node #0,2,2 Current State: 26:[12, 13], Operations: ['90-51=39', '52-39=13'] Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,26 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,3,4 Current State: 26:[39, 38], Operations: ['51-12=39', '90-52=38'] Exploring Operation: 39*38=1482, Resulting Numbers: [1482] 1482,26 unequal: No Solution Exploring Operation: 39+38=77, Resulting Numbers: [77] 77,26 unequal: No Solution Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[52, 27], Operations: ['90-51=39', '39-12=27'] Exploring Operation: 52+27=79, Resulting Numbers: [79] 79,26 unequal: No Solution Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 52*27=1404, Resulting Numbers: [1404] 1404,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[39, 40], Operations: ['90-51=39', '52-12=40'] Exploring Operation: 39*40=1560, Resulting Numbers: [1560] 1560,26 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 39+40=79, Resulting Numbers: [79] 79,26 unequal: No Solution Moving to Node #0,3,2 Current State: 26:[52, 51], Operations: ['51-12=39', '90-39=51'] Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,26 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,26 unequal: No Solution Moving to Node #0,2,4 Current State: 26:[39, 64], Operations: ['90-51=39', '52+12=64'] Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 39*64=2496, Resulting Numbers: [2496] 2496,26 unequal: No Solution Exploring Operation: 39+64=103, Resulting Numbers: [103] 103,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[52, 51], Operations: ['90-51=39', '12+39=51'] Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,26 unequal: No Solution Moving to Node #0,3,3 Current State: 26:[90, 13], Operations: ['51-12=39', '52-39=13'] Exploring Operation: 90*13=1170, Resulting Numbers: [1170] 1170,26 unequal: No Solution Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,26 unequal: No Solution Moving to Node #0,3,0 Current State: 26:[90, 91], Operations: ['51-12=39', '52+39=91'] Exploring Operation: 90+91=181, Resulting Numbers: [181] 181,26 unequal: No Solution Exploring Operation: 90*91=8190, Resulting Numbers: [8190] 8190,26 unequal: No Solution Exploring Operation: 91-90=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,3,1 Current State: 26:[39, 142], Operations: ['51-12=39', '52+90=142'] Exploring Operation: 142-39=103, Resulting Numbers: [103] 103,26 unequal: No Solution Exploring Operation: 39*142=5538, Resulting Numbers: [5538] 5538,26 unequal: No Solution Exploring Operation: 39+142=181, Resulting Numbers: [181] 181,26 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 51, 68, 20, 68 ]
16
[ "68-51=17", "68/17=4", "20-4=16" ]
Current State: 16:[51, 68, 20, 68], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [20, 17] Generated Node #2: [20, 17] from Operation: 68-51=17 Current State: 16:[20, 17], Operations: ['68-51=17'] Exploring Operation: 68/17=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 68/17=4 Current State: 16:[20, 4], Operations: ['68-51=17', '68/17=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[51, 68, 20, 68], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [68, 20, 17] Generated Node #0,0: 16:[68, 20, 17] Operation: 68-51=17 Exploring Operation: 68-68=0, Resulting Numbers: [51, 20, 0] Generated Node #0,1: 16:[51, 20, 0] Operation: 68-68=0 Exploring Operation: 68/68=1, Resulting Numbers: [51, 20, 1] Generated Node #0,2: 16:[51, 20, 1] Operation: 68/68=1 Exploring Operation: 68-51=17, Resulting Numbers: [20, 68, 17] Generated Node #0,3: 16:[20, 68, 17] Operation: 68-51=17 Moving to Node #0,2 Current State: 16:[51, 20, 1], Operations: ['68/68=1'] Exploring Operation: 51*1=51, Resulting Numbers: [20, 51] Generated Node #0,2,0: 16:[20, 51] Operation: 51*1=51 Exploring Operation: 51-1=50, Resulting Numbers: [20, 50] Generated Node #0,2,1: 16:[20, 50] Operation: 51-1=50 Exploring Operation: 20-1=19, Resulting Numbers: [51, 19] Generated Node #0,2,2: 16:[51, 19] Operation: 20-1=19 Exploring Operation: 51-20=31, Resulting Numbers: [1, 31] Generated Node #0,2,3: 16:[1, 31] Operation: 51-20=31 Moving to Node #0,1 Current State: 16:[51, 20, 0], Operations: ['68-68=0'] Exploring Operation: 20*0=0, Resulting Numbers: [51, 0] Generated Node #0,1,0: 16:[51, 0] Operation: 20*0=0 Exploring Operation: 51*0=0, Resulting Numbers: [20, 0] Generated Node #0,1,1: 16:[20, 0] Operation: 51*0=0 Exploring Operation: 51-20=31, Resulting Numbers: [0, 31] Generated Node #0,1,2: 16:[0, 31] Operation: 51-20=31 Exploring Operation: 51+0=51, Resulting Numbers: [20, 51] Generated Node #0,1,3: 16:[20, 51] Operation: 51+0=51 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[20, 0], Operations: ['68-68=0', '51*0=0'] Exploring Operation: 20+0=20, Resulting Numbers: [20] 20,16 unequal: No Solution Exploring Operation: 20*0=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 20-0=20, Resulting Numbers: [20] 20,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 16:[0, 31], Operations: ['68-68=0', '51-20=31'] Exploring Operation: 31-0=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 0+31=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 0*31=0, Resulting Numbers: [0] 0,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[51, 0], Operations: ['68-68=0', '20*0=0'] Exploring Operation: 51*0=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 51-0=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 51+0=51, Resulting Numbers: [51] 51,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 16:[20, 51], Operations: ['68-68=0', '51+0=51'] Exploring Operation: 20*51=1020, Resulting Numbers: [1020] 1020,16 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 20+51=71, Resulting Numbers: [71] 71,16 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: 16:[20, 68, 17], Operations: ['68-51=17'] Exploring Operation: 20-17=3, Resulting Numbers: [68, 3] Generated Node #0,3,0: 16:[68, 3] Operation: 20-17=3 Exploring Operation: 68-20=48, Resulting Numbers: [17, 48] Generated Node #0,3,1: 16:[17, 48] Operation: 68-20=48 Exploring Operation: 68-17=51, Resulting Numbers: [20, 51] Generated Node #0,3,2: 16:[20, 51] Operation: 68-17=51 Exploring Operation: 68/17=4, Resulting Numbers: [20, 4] Generated Node #0,3,3: 16:[20, 4] Operation: 68/17=4 Moving to Node #0,0 Current State: 16:[68, 20, 17], Operations: ['68-51=17'] Exploring Operation: 20-17=3, Resulting Numbers: [68, 3] Generated Node #0,0,0: 16:[68, 3] Operation: 20-17=3 Exploring Operation: 68-17=51, Resulting Numbers: [20, 51] Generated Node #0,0,1: 16:[20, 51] Operation: 68-17=51 Exploring Operation: 68/17=4, Resulting Numbers: [20, 4] Generated Node #0,0,2: 16:[20, 4] Operation: 68/17=4 Exploring Operation: 68-20=48, Resulting Numbers: [17, 48] Generated Node #0,0,3: 16:[17, 48] Operation: 68-20=48 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[20, 4], Operations: ['68-51=17', '68/17=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[51, 68, 20, 68], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [68, 20, 17] Generated Node #0,0: 16:[68, 20, 17] Operation: 68-51=17 Moving to Node #0,0 Current State: 16:[68, 20, 17], Operations: ['68-51=17'] Exploring Operation: 68/17=4, Resulting Numbers: [20, 4] Generated Node #0,0,2: 16:[20, 4] Operation: 68/17=4 Moving to Node #0,0,2 Current State: 16:[20, 4], Operations: ['68-51=17', '68/17=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
sum_heuristic
[ 10, 36, 86, 15 ]
75
[ "36-10=26", "86+15=101", "101-26=75" ]
Current State: 75:[10, 36, 86, 15], Operations: [] Exploring Operation: 36-10=26, Resulting Numbers: [86, 15, 26] Generated Node #2: [86, 15, 26] from Operation: 36-10=26 Current State: 75:[86, 15, 26], Operations: ['36-10=26'] Exploring Operation: 86+15=101, Resulting Numbers: [26, 101] Generated Node #3: [26, 101] from Operation: 86+15=101 Current State: 75:[26, 101], Operations: ['36-10=26', '86+15=101'] Exploring Operation: 101-26=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[10, 36, 86, 15], Operations: [] Exploring Operation: 36-10=26, Resulting Numbers: [86, 15, 26] Generated Node #0,0: 75:[86, 15, 26] Operation: 36-10=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[86, 15, 26], Operations: ['36-10=26'] Exploring Operation: 86-15=71, Resulting Numbers: [26, 71] Generated Node #0,0,0: 75:[26, 71] Operation: 86-15=71 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[26, 71], Operations: ['36-10=26', '86-15=71'] Exploring Operation: 71-26=45, Resulting Numbers: [45] 45,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 22, 24, 98, 33 ]
63
[ "24-22=2", "98-33=65", "65-2=63" ]
Current State: 63:[22, 24, 98, 33], Operations: [] Exploring Operation: 24-22=2, Resulting Numbers: [98, 33, 2] Generated Node #2: [98, 33, 2] from Operation: 24-22=2 Current State: 63:[98, 33, 2], Operations: ['24-22=2'] Exploring Operation: 98-33=65, Resulting Numbers: [2, 65] Generated Node #3: [2, 65] from Operation: 98-33=65 Current State: 63:[2, 65], Operations: ['24-22=2', '98-33=65'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[22, 24, 98, 33], Operations: [] Exploring Operation: 98-33=65, Resulting Numbers: [22, 24, 65] Generated Node #0,0: 63:[22, 24, 65] Operation: 98-33=65 Exploring Operation: 33-22=11, Resulting Numbers: [24, 98, 11] Generated Node #0,1: 63:[24, 98, 11] Operation: 33-22=11 Exploring Operation: 33-24=9, Resulting Numbers: [22, 98, 9] Generated Node #0,2: 63:[22, 98, 9] Operation: 33-24=9 Exploring Operation: 98-22=76, Resulting Numbers: [24, 33, 76] Generated Node #0,3: 63:[24, 33, 76] Operation: 98-22=76 Exploring Operation: 98-24=74, Resulting Numbers: [22, 33, 74] Generated Node #0,4: 63:[22, 33, 74] Operation: 98-24=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[22, 24, 65], Operations: ['98-33=65'] Exploring Operation: 65-22=43, Resulting Numbers: [24, 43] Generated Node #0,0,0: 63:[24, 43] Operation: 65-22=43 Exploring Operation: 22+24=46, Resulting Numbers: [65, 46] Generated Node #0,0,1: 63:[65, 46] Operation: 22+24=46 Exploring Operation: 65-24=41, Resulting Numbers: [22, 41] Generated Node #0,0,2: 63:[22, 41] Operation: 65-24=41 Exploring Operation: 22+65=87, Resulting Numbers: [24, 87] Generated Node #0,0,3: 63:[24, 87] Operation: 22+65=87 Exploring Operation: 24-22=2, Resulting Numbers: [65, 2] Generated Node #0,0,4: 63:[65, 2] Operation: 24-22=2 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 63:[65, 2], Operations: ['98-33=65', '24-22=2'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[22, 24, 98, 33], Operations: [] Exploring Operation: 98-33=65, Resulting Numbers: [22, 24, 65] Generated Node #0,0: 63:[22, 24, 65] Operation: 98-33=65 Moving to Node #0,0 Current State: 63:[22, 24, 65], Operations: ['98-33=65'] Exploring Operation: 24-22=2, Resulting Numbers: [65, 2] Generated Node #0,0,4: 63:[65, 2] Operation: 24-22=2 Moving to Node #0,0,4 Current State: 63:[65, 2], Operations: ['98-33=65', '24-22=2'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 23, 56, 10, 3 ]
15
[ "10-3=7", "56/7=8", "23-8=15" ]
Current State: 15:[23, 56, 10, 3], Operations: [] Exploring Operation: 10-3=7, Resulting Numbers: [23, 56, 7] Generated Node #2: [23, 56, 7] from Operation: 10-3=7 Current State: 15:[23, 56, 7], Operations: ['10-3=7'] Exploring Operation: 56/7=8, Resulting Numbers: [23, 8] Generated Node #3: [23, 8] from Operation: 56/7=8 Current State: 15:[23, 8], Operations: ['10-3=7', '56/7=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[23, 56, 10, 3], Operations: [] Exploring Operation: 23-10=13, Resulting Numbers: [56, 3, 13] Generated Node #0,0: 15:[56, 3, 13] Operation: 23-10=13 Exploring Operation: 56-23=33, Resulting Numbers: [10, 3, 33] Generated Node #0,1: 15:[10, 3, 33] Operation: 56-23=33 Exploring Operation: 23-3=20, Resulting Numbers: [56, 10, 20] Generated Node #0,2: 15:[56, 10, 20] Operation: 23-3=20 Exploring Operation: 56-3=53, Resulting Numbers: [23, 10, 53] Generated Node #0,3: 15:[23, 10, 53] Operation: 56-3=53 Exploring Operation: 56-10=46, Resulting Numbers: [23, 3, 46] Generated Node #0,4: 15:[23, 3, 46] Operation: 56-10=46 Moving to Node #0,1 Current State: 15:[10, 3, 33], Operations: ['56-23=33'] Exploring Operation: 33-10=23, Resulting Numbers: [3, 23] Generated Node #0,1,0: 15:[3, 23] Operation: 33-10=23 Exploring Operation: 33/3=11, Resulting Numbers: [10, 11] Generated Node #0,1,1: 15:[10, 11] Operation: 33/3=11 Exploring Operation: 10-3=7, Resulting Numbers: [33, 7] Generated Node #0,1,2: 15:[33, 7] Operation: 10-3=7 Exploring Operation: 10+3=13, Resulting Numbers: [33, 13] Generated Node #0,1,3: 15:[33, 13] Operation: 10+3=13 Exploring Operation: 33-3=30, Resulting Numbers: [10, 30] Generated Node #0,1,4: 15:[10, 30] Operation: 33-3=30 Moving to Node #0,4 Current State: 15:[23, 3, 46], Operations: ['56-10=46'] Exploring Operation: 46-23=23, Resulting Numbers: [3, 23] Generated Node #0,4,0: 15:[3, 23] Operation: 46-23=23 Exploring Operation: 23-3=20, Resulting Numbers: [46, 20] Generated Node #0,4,1: 15:[46, 20] Operation: 23-3=20 Exploring Operation: 46/23=2, Resulting Numbers: [3, 2] Generated Node #0,4,2: 15:[3, 2] Operation: 46/23=2 Exploring Operation: 23+3=26, Resulting Numbers: [46, 26] Generated Node #0,4,3: 15:[46, 26] Operation: 23+3=26 Exploring Operation: 46-3=43, Resulting Numbers: [23, 43] Generated Node #0,4,4: 15:[23, 43] Operation: 46-3=43 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 15:[3, 2], Operations: ['56-10=46', '46/23=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,15 unequal: No Solution No 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: 15:[3, 23], Operations: ['56-10=46', '46-23=23'] Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,15 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 15:[46, 20], Operations: ['56-10=46', '23-3=20'] Exploring Operation: 46*20=920, Resulting Numbers: [920] 920,15 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 46+20=66, Resulting Numbers: [66] 66,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 15:[23, 43], Operations: ['56-10=46', '46-3=43'] Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 23*43=989, Resulting Numbers: [989] 989,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 15:[46, 26], Operations: ['56-10=46', '23+3=26'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 46+26=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 46*26=1196, Resulting Numbers: [1196] 1196,15 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: 15:[56, 3, 13], Operations: ['23-10=13'] Exploring Operation: 56-3=53, Resulting Numbers: [13, 53] Generated Node #0,0,0: 15:[13, 53] Operation: 56-3=53 Exploring Operation: 3+13=16, Resulting Numbers: [56, 16] Generated Node #0,0,1: 15:[56, 16] Operation: 3+13=16 Exploring Operation: 13-3=10, Resulting Numbers: [56, 10] Generated Node #0,0,2: 15:[56, 10] Operation: 13-3=10 Exploring Operation: 56-13=43, Resulting Numbers: [3, 43] Generated Node #0,0,3: 15:[3, 43] Operation: 56-13=43 Exploring Operation: 56+3=59, Resulting Numbers: [13, 59] Generated Node #0,0,4: 15:[13, 59] Operation: 56+3=59 Moving to Node #0,2 Current State: 15:[56, 10, 20], Operations: ['23-3=20'] Exploring Operation: 20/10=2, Resulting Numbers: [56, 2] Generated Node #0,2,0: 15:[56, 2] Operation: 20/10=2 Exploring Operation: 56-10=46, Resulting Numbers: [20, 46] Generated Node #0,2,1: 15:[20, 46] Operation: 56-10=46 Exploring Operation: 20-10=10, Resulting Numbers: [56, 10] Generated Node #0,2,2: 15:[56, 10] Operation: 20-10=10 Exploring Operation: 56+10=66, Resulting Numbers: [20, 66] Generated Node #0,2,3: 15:[20, 66] Operation: 56+10=66 Exploring Operation: 56-20=36, Resulting Numbers: [10, 36] Generated Node #0,2,4: 15:[10, 36] Operation: 56-20=36 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 15:[10, 36], Operations: ['23-3=20', '56-20=36'] Exploring Operation: 10+36=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 10*36=360, Resulting Numbers: [360] 360,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[20, 46], Operations: ['23-3=20', '56-10=46'] Exploring Operation: 20*46=920, Resulting Numbers: [920] 920,15 unequal: No Solution Exploring Operation: 20+46=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[56, 2], Operations: ['23-3=20', '20/10=2'] Exploring Operation: 56*2=112, Resulting Numbers: [112] 112,15 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,15 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,15 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[56, 10], Operations: ['23-3=20', '20-10=10'] Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,15 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 15:[20, 66], Operations: ['23-3=20', '56+10=66'] Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 20*66=1320, Resulting Numbers: [1320] 1320,15 unequal: No Solution Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,15 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: 15:[23, 10, 53], Operations: ['56-3=53'] Exploring Operation: 53-23=30, Resulting Numbers: [10, 30] Generated Node #0,3,0: 15:[10, 30] Operation: 53-23=30 Exploring Operation: 23+10=33, Resulting Numbers: [53, 33] Generated Node #0,3,1: 15:[53, 33] Operation: 23+10=33 Exploring Operation: 23-10=13, Resulting Numbers: [53, 13] Generated Node #0,3,2: 15:[53, 13] Operation: 23-10=13 Exploring Operation: 53-10=43, Resulting Numbers: [23, 43] Generated Node #0,3,3: 15:[23, 43] Operation: 53-10=43 Exploring Operation: 10+53=63, Resulting Numbers: [23, 63] Generated Node #0,3,4: 15:[23, 63] Operation: 10+53=63 Moving to Node #0,1,0 Current State: 15:[3, 23], Operations: ['56-23=33', '33-10=23'] Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[10, 11], Operations: ['56-23=33', '33/3=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,15 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[33, 7], Operations: ['56-23=33', '10-3=7'] Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,15 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,15 unequal: No Solution Moving to Node #0,1,4 Current State: 15:[10, 30], Operations: ['56-23=33', '33-3=30'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,15 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[10, 30], Operations: ['56-3=53', '53-23=30'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,15 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[33, 13], Operations: ['56-23=33', '10+3=13'] Exploring Operation: 33+13=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 33*13=429, Resulting Numbers: [429] 429,15 unequal: No Solution Moving to Node #0,0,3 Current State: 15:[3, 43], Operations: ['23-10=13', '56-13=43'] Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,15 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,15 unequal: No Solution Moving to Node #0,3,3 Current State: 15:[23, 43], Operations: ['56-3=53', '53-10=43'] Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 23*43=989, Resulting Numbers: [989] 989,15 unequal: No Solution Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,15 unequal: No Solution Moving to Node #0,0,0 Current State: 15:[13, 53], Operations: ['23-10=13', '56-3=53'] Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,15 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,15 unequal: No Solution Moving to Node #0,3,2 Current State: 15:[53, 13], Operations: ['56-3=53', '23-10=13'] Exploring Operation: 53+13=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 53*13=689, Resulting Numbers: [689] 689,15 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[56, 16], Operations: ['23-10=13', '3+13=16'] Exploring Operation: 56-16=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 56+16=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 56*16=896, Resulting Numbers: [896] 896,15 unequal: No Solution Moving to Node #0,0,2 Current State: 15:[56, 10], Operations: ['23-10=13', '13-3=10'] Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,15 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,15 unequal: No Solution Moving to Node #0,0,4 Current State: 15:[13, 59], Operations: ['23-10=13', '56+3=59'] Exploring Operation: 13+59=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 13*59=767, Resulting Numbers: [767] 767,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[53, 33], Operations: ['56-3=53', '23+10=33'] Exploring Operation: 53+33=86, Resulting Numbers: [86] 86,15 unequal: No Solution Exploring Operation: 53*33=1749, Resulting Numbers: [1749] 1749,15 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,15 unequal: No Solution Moving to Node #0,3,4 Current State: 15:[23, 63], Operations: ['56-3=53', '10+53=63'] Exploring Operation: 23*63=1449, Resulting Numbers: [1449] 1449,15 unequal: No Solution Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 23+63=86, Resulting Numbers: [86] 86,15 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 9, 20, 30, 14 ]
15
[ "9+20=29", "30+14=44", "44-29=15" ]
Current State: 15:[9, 20, 30, 14], Operations: [] Exploring Operation: 9+20=29, Resulting Numbers: [30, 14, 29] Generated Node #2: [30, 14, 29] from Operation: 9+20=29 Current State: 15:[30, 14, 29], Operations: ['9+20=29'] Exploring Operation: 30+14=44, Resulting Numbers: [29, 44] Generated Node #3: [29, 44] from Operation: 30+14=44 Current State: 15:[29, 44], Operations: ['9+20=29', '30+14=44'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[9, 20, 30, 14], Operations: [] Exploring Operation: 20-9=11, Resulting Numbers: [30, 14, 11] Generated Node #0,0: 15:[30, 14, 11] Operation: 20-9=11 Exploring Operation: 30-14=16, Resulting Numbers: [9, 20, 16] Generated Node #0,1: 15:[9, 20, 16] Operation: 30-14=16 Exploring Operation: 30-20=10, Resulting Numbers: [9, 14, 10] Generated Node #0,2: 15:[9, 14, 10] Operation: 30-20=10 Exploring Operation: 14-9=5, Resulting Numbers: [20, 30, 5] Generated Node #0,3: 15:[20, 30, 5] Operation: 14-9=5 Exploring Operation: 30-9=21, Resulting Numbers: [20, 14, 21] Generated Node #0,4: 15:[20, 14, 21] Operation: 30-9=21 Moving to Node #0,1 Current State: 15:[9, 20, 16], Operations: ['30-14=16'] Exploring Operation: 9+20=29, Resulting Numbers: [16, 29] Generated Node #0,1,0: 15:[16, 29] Operation: 9+20=29 Exploring Operation: 16-9=7, Resulting Numbers: [20, 7] Generated Node #0,1,1: 15:[20, 7] Operation: 16-9=7 Exploring Operation: 20-9=11, Resulting Numbers: [16, 11] Generated Node #0,1,2: 15:[16, 11] Operation: 20-9=11 Exploring Operation: 20-16=4, Resulting Numbers: [9, 4] Generated Node #0,1,3: 15:[9, 4] Operation: 20-16=4 Exploring Operation: 9+16=25, Resulting Numbers: [20, 25] Generated Node #0,1,4: 15:[20, 25] Operation: 9+16=25 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 15:[16, 11], Operations: ['30-14=16', '20-9=11'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 16+11=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 16*11=176, Resulting Numbers: [176] 176,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 15:[9, 4], Operations: ['30-14=16', '20-16=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,15 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,15 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 15:[20, 7], Operations: ['30-14=16', '16-9=7'] Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,15 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,15 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[16, 29], Operations: ['30-14=16', '9+20=29'] Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,15 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,15 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 15:[20, 25], Operations: ['30-14=16', '9+16=25'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,15 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,15 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: 15:[9, 14, 10], Operations: ['30-20=10'] Exploring Operation: 10-9=1, Resulting Numbers: [14, 1] Generated Node #0,2,0: 15:[14, 1] Operation: 10-9=1 Exploring Operation: 9+10=19, Resulting Numbers: [14, 19] Generated Node #0,2,1: 15:[14, 19] Operation: 9+10=19 Exploring Operation: 14-10=4, Resulting Numbers: [9, 4] Generated Node #0,2,2: 15:[9, 4] Operation: 14-10=4 Exploring Operation: 9+14=23, Resulting Numbers: [10, 23] Generated Node #0,2,3: 15:[10, 23] Operation: 9+14=23 Exploring Operation: 14-9=5, Resulting Numbers: [10, 5] Generated Node #0,2,4: 15:[10, 5] Operation: 14-9=5 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[14, 1], Operations: ['30-20=10', '10-9=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,15 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[9, 20, 30, 14], Operations: [] Exploring Operation: 30-20=10, Resulting Numbers: [9, 14, 10] Generated Node #0,2: 15:[9, 14, 10] Operation: 30-20=10 Moving to Node #0,2 Current State: 15:[9, 14, 10], Operations: ['30-20=10'] Exploring Operation: 10-9=1, Resulting Numbers: [14, 1] Generated Node #0,2,0: 15:[14, 1] Operation: 10-9=1 Moving to Node #0,2,0 Current State: 15:[14, 1], Operations: ['30-20=10', '10-9=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
sum_heuristic
[ 26, 26, 34, 1 ]
85
[ "26+26=52", "34-1=33", "52+33=85" ]
Current State: 85:[26, 26, 34, 1], Operations: [] Exploring Operation: 26+26=52, Resulting Numbers: [34, 1, 52] Generated Node #2: [34, 1, 52] from Operation: 26+26=52 Current State: 85:[34, 1, 52], Operations: ['26+26=52'] Exploring Operation: 34-1=33, Resulting Numbers: [52, 33] Generated Node #3: [52, 33] from Operation: 34-1=33 Current State: 85:[52, 33], Operations: ['26+26=52', '34-1=33'] Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[26, 26, 34, 1], Operations: [] Exploring Operation: 34-26=8, Resulting Numbers: [26, 1, 8] Generated Node #0,0: 85:[26, 1, 8] Operation: 34-26=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[26, 1, 8], Operations: ['34-26=8'] Exploring Operation: 26-8=18, Resulting Numbers: [1, 18] Generated Node #0,0,0: 85:[1, 18] Operation: 26-8=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[1, 18], Operations: ['34-26=8', '26-8=18'] Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 42, 11, 21, 77 ]
68
[ "42/21=2", "77-11=66", "2+66=68" ]
Current State: 68:[42, 11, 21, 77], Operations: [] Exploring Operation: 42/21=2, Resulting Numbers: [11, 77, 2] Generated Node #2: [11, 77, 2] from Operation: 42/21=2 Current State: 68:[11, 77, 2], Operations: ['42/21=2'] Exploring Operation: 77-11=66, Resulting Numbers: [2, 66] Generated Node #3: [2, 66] from Operation: 77-11=66 Current State: 68:[2, 66], Operations: ['42/21=2', '77-11=66'] Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[42, 11, 21, 77], Operations: [] Exploring Operation: 77/11=7, Resulting Numbers: [42, 21, 7] Generated Node #0,0: 68:[42, 21, 7] Operation: 77/11=7 Exploring Operation: 77-11=66, Resulting Numbers: [42, 21, 66] Generated Node #0,1: 68:[42, 21, 66] Operation: 77-11=66 Exploring Operation: 77-42=35, Resulting Numbers: [11, 21, 35] Generated Node #0,2: 68:[11, 21, 35] Operation: 77-42=35 Exploring Operation: 42/21=2, Resulting Numbers: [11, 77, 2] Generated Node #0,3: 68:[11, 77, 2] Operation: 42/21=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[11, 21, 35], Operations: ['77-42=35'] Exploring Operation: 21-11=10, Resulting Numbers: [35, 10] Generated Node #0,2,0: 68:[35, 10] Operation: 21-11=10 Exploring Operation: 35-21=14, Resulting Numbers: [11, 14] Generated Node #0,2,1: 68:[11, 14] Operation: 35-21=14 Exploring Operation: 35-11=24, Resulting Numbers: [21, 24] Generated Node #0,2,2: 68:[21, 24] Operation: 35-11=24 Exploring Operation: 11+21=32, Resulting Numbers: [35, 32] Generated Node #0,2,3: 68:[35, 32] Operation: 11+21=32 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 68:[35, 32], Operations: ['77-42=35', '11+21=32'] Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,68 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,68 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 #0,2,0 Current State: 68:[35, 10], Operations: ['77-42=35', '21-11=10'] Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,68 unequal: No Solution Exploring Operation: 35*10=350, Resulting Numbers: [350] 350,68 unequal: No Solution Exploring Operation: 35+10=45, Resulting Numbers: [45] 45,68 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 #0,2,1 Current State: 68:[11, 14], Operations: ['77-42=35', '35-21=14'] Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,68 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,68 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,68 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 #0,2,2 Current State: 68:[21, 24], Operations: ['77-42=35', '35-11=24'] Exploring Operation: 21*24=504, Resulting Numbers: [504] 504,68 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,68 unequal: No Solution Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,68 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[42, 21, 66], Operations: ['77-11=66'] Exploring Operation: 42/21=2, Resulting Numbers: [66, 2] Generated Node #0,1,0: 68:[66, 2] Operation: 42/21=2 Exploring Operation: 42-21=21, Resulting Numbers: [66, 21] Generated Node #0,1,1: 68:[66, 21] Operation: 42-21=21 Exploring Operation: 66-42=24, Resulting Numbers: [21, 24] Generated Node #0,1,2: 68:[21, 24] Operation: 66-42=24 Exploring Operation: 42+21=63, Resulting Numbers: [66, 63] Generated Node #0,1,3: 68:[66, 63] Operation: 42+21=63 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[66, 2], Operations: ['77-11=66', '42/21=2'] Exploring Operation: 66*2=132, Resulting Numbers: [132] 132,68 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,68 unequal: No Solution Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[42, 11, 21, 77], Operations: [] Exploring Operation: 77-11=66, Resulting Numbers: [42, 21, 66] Generated Node #0,1: 68:[42, 21, 66] Operation: 77-11=66 Moving to Node #0,1 Current State: 68:[42, 21, 66], Operations: ['77-11=66'] Exploring Operation: 42/21=2, Resulting Numbers: [66, 2] Generated Node #0,1,0: 68:[66, 2] Operation: 42/21=2 Moving to Node #0,1,0 Current State: 68:[66, 2], Operations: ['77-11=66', '42/21=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 87, 79, 68, 35 ]
25
[ "87-79=8", "68-35=33", "33-8=25" ]
Current State: 25:[87, 79, 68, 35], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [68, 35, 8] Generated Node #2: [68, 35, 8] from Operation: 87-79=8 Current State: 25:[68, 35, 8], Operations: ['87-79=8'] Exploring Operation: 68-35=33, Resulting Numbers: [8, 33] Generated Node #3: [8, 33] from Operation: 68-35=33 Current State: 25:[8, 33], Operations: ['87-79=8', '68-35=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[87, 79, 68, 35], Operations: [] Exploring Operation: 79-68=11, Resulting Numbers: [87, 35, 11] Generated Node #0,0: 25:[87, 35, 11] Operation: 79-68=11 Exploring Operation: 79-35=44, Resulting Numbers: [87, 68, 44] Generated Node #0,1: 25:[87, 68, 44] Operation: 79-35=44 Exploring Operation: 87-35=52, Resulting Numbers: [79, 68, 52] Generated Node #0,2: 25:[79, 68, 52] Operation: 87-35=52 Exploring Operation: 87-79=8, Resulting Numbers: [68, 35, 8] Generated Node #0,3: 25:[68, 35, 8] Operation: 87-79=8 Exploring Operation: 87-68=19, Resulting Numbers: [79, 35, 19] Generated Node #0,4: 25:[79, 35, 19] Operation: 87-68=19 Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[68, 35, 8], Operations: ['87-79=8'] Exploring Operation: 68+8=76, Resulting Numbers: [35, 76] Generated Node #0,3,0: 25:[35, 76] Operation: 68+8=76 Exploring Operation: 68-8=60, Resulting Numbers: [35, 60] Generated Node #0,3,1: 25:[35, 60] Operation: 68-8=60 Exploring Operation: 68-35=33, Resulting Numbers: [8, 33] Generated Node #0,3,2: 25:[8, 33] Operation: 68-35=33 Exploring Operation: 35+8=43, Resulting Numbers: [68, 43] Generated Node #0,3,3: 25:[68, 43] Operation: 35+8=43 Exploring Operation: 35-8=27, Resulting Numbers: [68, 27] Generated Node #0,3,4: 25:[68, 27] Operation: 35-8=27 Moving to Node #0,3,2 Current State: 25:[8, 33], Operations: ['87-79=8', '68-35=33'] Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,25 unequal: No Solution Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[87, 79, 68, 35], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [68, 35, 8] Generated Node #0,3: 25:[68, 35, 8] Operation: 87-79=8 Moving to Node #0,3 Current State: 25:[68, 35, 8], Operations: ['87-79=8'] Exploring Operation: 68-35=33, Resulting Numbers: [8, 33] Generated Node #0,3,2: 25:[8, 33] Operation: 68-35=33 Moving to Node #0,3,2 Current State: 25:[8, 33], Operations: ['87-79=8', '68-35=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 56, 45, 7, 7 ]
45
[ "56/7=8", "8-7=1", "45*1=45" ]
Current State: 45:[56, 45, 7, 7], Operations: [] Exploring Operation: 56/7=8, Resulting Numbers: [45, 8] Generated Node #2: [45, 8] from Operation: 56/7=8 Current State: 45:[45, 8], Operations: ['56/7=8'] Exploring Operation: 8-7=1, Resulting Numbers: [45, 1] Generated Node #3: [45, 1] from Operation: 8-7=1 Current State: 45:[45, 1], Operations: ['56/7=8', '8-7=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[56, 45, 7, 7], Operations: [] Exploring Operation: 56/7=8, Resulting Numbers: [45, 7, 8] Generated Node #0,0: 45:[45, 7, 8] Operation: 56/7=8 Exploring Operation: 56-45=11, Resulting Numbers: [7, 7, 11] Generated Node #0,1: 45:[7, 7, 11] Operation: 56-45=11 Exploring Operation: 56/7=8, Resulting Numbers: [45, 7, 8] Generated Node #0,2: 45:[45, 7, 8] Operation: 56/7=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[45, 7, 8], Operations: ['56/7=8'] Exploring Operation: 45+7=52, Resulting Numbers: [8, 52] Generated Node #0,0,0: 45:[8, 52] Operation: 45+7=52 Exploring Operation: 8-7=1, Resulting Numbers: [45, 1] Generated Node #0,0,1: 45:[45, 1] Operation: 8-7=1 Exploring Operation: 7+8=15, Resulting Numbers: [45, 15] Generated Node #0,0,2: 45:[45, 15] Operation: 7+8=15 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 45:[45, 15], Operations: ['56/7=8', '7+8=15'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[45, 1], Operations: ['56/7=8', '8-7=1'] Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[56, 45, 7, 7], Operations: [] Exploring Operation: 56/7=8, Resulting Numbers: [45, 7, 8] Generated Node #0,0: 45:[45, 7, 8] Operation: 56/7=8 Moving to Node #0,0 Current State: 45:[45, 7, 8], Operations: ['56/7=8'] Exploring Operation: 8-7=1, Resulting Numbers: [45, 1] Generated Node #0,0,1: 45:[45, 1] Operation: 8-7=1 Moving to Node #0,0,1 Current State: 45:[45, 1], Operations: ['56/7=8', '8-7=1'] Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 93, 53, 95, 59 ]
47
[ "95-93=2", "53*2=106", "106-59=47" ]
Current State: 47:[93, 53, 95, 59], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [53, 59, 2] Generated Node #2: [53, 59, 2] from Operation: 95-93=2 Current State: 47:[53, 59, 2], Operations: ['95-93=2'] Exploring Operation: 53*2=106, Resulting Numbers: [59, 106] Generated Node #3: [59, 106] from Operation: 53*2=106 Current State: 47:[59, 106], Operations: ['95-93=2', '53*2=106'] Exploring Operation: 106-59=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[93, 53, 95, 59], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [53, 59, 2] Generated Node #0,0: 47:[53, 59, 2] Operation: 95-93=2 Moving to Node #0,0 Current State: 47:[53, 59, 2], Operations: ['95-93=2'] Exploring Operation: 53-2=51, Resulting Numbers: [59, 51] Generated Node #0,0,0: 47:[59, 51] Operation: 53-2=51 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[59, 51], Operations: ['95-93=2', '53-2=51'] Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,47 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
[ 13, 55, 72, 24 ]
45
[ "55-13=42", "72/24=3", "42+3=45" ]
Current State: 45:[13, 55, 72, 24], Operations: [] Exploring Operation: 55-13=42, Resulting Numbers: [72, 24, 42] Generated Node #2: [72, 24, 42] from Operation: 55-13=42 Current State: 45:[72, 24, 42], Operations: ['55-13=42'] Exploring Operation: 72/24=3, Resulting Numbers: [42, 3] Generated Node #3: [42, 3] from Operation: 72/24=3 Current State: 45:[42, 3], Operations: ['55-13=42', '72/24=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[13, 55, 72, 24], Operations: [] Exploring Operation: 72-55=17, Resulting Numbers: [13, 24, 17] Generated Node #0,0: 45:[13, 24, 17] Operation: 72-55=17 Exploring Operation: 72-13=59, Resulting Numbers: [55, 24, 59] Generated Node #0,1: 45:[55, 24, 59] Operation: 72-13=59 Exploring Operation: 72-24=48, Resulting Numbers: [13, 55, 48] Generated Node #0,2: 45:[13, 55, 48] Operation: 72-24=48 Exploring Operation: 55-13=42, Resulting Numbers: [72, 24, 42] Generated Node #0,3: 45:[72, 24, 42] Operation: 55-13=42 Exploring Operation: 72/24=3, Resulting Numbers: [13, 55, 3] Generated Node #0,4: 45:[13, 55, 3] Operation: 72/24=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 45:[13, 55, 3], Operations: ['72/24=3'] Exploring Operation: 55+3=58, Resulting Numbers: [13, 58] Generated Node #0,4,0: 45:[13, 58] Operation: 55+3=58 Exploring Operation: 55-3=52, Resulting Numbers: [13, 52] Generated Node #0,4,1: 45:[13, 52] Operation: 55-3=52 Exploring Operation: 13+3=16, Resulting Numbers: [55, 16] Generated Node #0,4,2: 45:[55, 16] Operation: 13+3=16 Exploring Operation: 13-3=10, Resulting Numbers: [55, 10] Generated Node #0,4,3: 45:[55, 10] Operation: 13-3=10 Exploring Operation: 55-13=42, Resulting Numbers: [3, 42] Generated Node #0,4,4: 45:[3, 42] Operation: 55-13=42 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 45:[3, 42], Operations: ['72/24=3', '55-13=42'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[13, 55, 72, 24], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [13, 55, 3] Generated Node #0,4: 45:[13, 55, 3] Operation: 72/24=3 Moving to Node #0,4 Current State: 45:[13, 55, 3], Operations: ['72/24=3'] Exploring Operation: 55-13=42, Resulting Numbers: [3, 42] Generated Node #0,4,4: 45:[3, 42] Operation: 55-13=42 Moving to Node #0,4,4 Current State: 45:[3, 42], Operations: ['72/24=3', '55-13=42'] Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 72, 10, 69, 55 ]
15
[ "72-69=3", "55-10=45", "45/3=15" ]
Current State: 15:[72, 10, 69, 55], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [10, 55, 3] Generated Node #2: [10, 55, 3] from Operation: 72-69=3 Current State: 15:[10, 55, 3], Operations: ['72-69=3'] Exploring Operation: 55-10=45, Resulting Numbers: [3, 45] Generated Node #3: [3, 45] from Operation: 55-10=45 Current State: 15:[3, 45], Operations: ['72-69=3', '55-10=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[72, 10, 69, 55], Operations: [] Exploring Operation: 72-55=17, Resulting Numbers: [10, 69, 17] Generated Node #0,0: 15:[10, 69, 17] Operation: 72-55=17 Exploring Operation: 69-55=14, Resulting Numbers: [72, 10, 14] Generated Node #0,1: 15:[72, 10, 14] Operation: 69-55=14 Exploring Operation: 72-69=3, Resulting Numbers: [10, 55, 3] Generated Node #0,2: 15:[10, 55, 3] Operation: 72-69=3 Moving to Node #0,2 Current State: 15:[10, 55, 3], Operations: ['72-69=3'] Exploring Operation: 10+3=13, Resulting Numbers: [55, 13] Generated Node #0,2,0: 15:[55, 13] Operation: 10+3=13 Exploring Operation: 10-3=7, Resulting Numbers: [55, 7] Generated Node #0,2,1: 15:[55, 7] Operation: 10-3=7 Exploring Operation: 55-10=45, Resulting Numbers: [3, 45] Generated Node #0,2,2: 15:[3, 45] Operation: 55-10=45 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[3, 45], Operations: ['72-69=3', '55-10=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[72, 10, 69, 55], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [10, 55, 3] Generated Node #0,2: 15:[10, 55, 3] Operation: 72-69=3 Moving to Node #0,2 Current State: 15:[10, 55, 3], Operations: ['72-69=3'] Exploring Operation: 55-10=45, Resulting Numbers: [3, 45] Generated Node #0,2,2: 15:[3, 45] Operation: 55-10=45 Moving to Node #0,2,2 Current State: 15:[3, 45], Operations: ['72-69=3', '55-10=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 47, 43, 46, 9 ]
33
[ "47-43=4", "46-9=37", "37-4=33" ]
Current State: 33:[47, 43, 46, 9], Operations: [] Exploring Operation: 47-43=4, Resulting Numbers: [46, 9, 4] Generated Node #2: [46, 9, 4] from Operation: 47-43=4 Current State: 33:[46, 9, 4], Operations: ['47-43=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: ['47-43=4', '46-9=37'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[47, 43, 46, 9], Operations: [] Exploring Operation: 47-46=1, Resulting Numbers: [43, 9, 1] Generated Node #0,0: 33:[43, 9, 1] Operation: 47-46=1 Exploring Operation: 46-43=3, Resulting Numbers: [47, 9, 3] Generated Node #0,1: 33:[47, 9, 3] Operation: 46-43=3 Exploring Operation: 47-43=4, Resulting Numbers: [46, 9, 4] Generated Node #0,2: 33:[46, 9, 4] Operation: 47-43=4 Moving to Node #0,0 Current State: 33:[43, 9, 1], Operations: ['47-46=1'] Exploring Operation: 9+1=10, Resulting Numbers: [43, 10] Generated Node #0,0,0: 33:[43, 10] Operation: 9+1=10 Exploring Operation: 43-1=42, Resulting Numbers: [9, 42] Generated Node #0,0,1: 33:[9, 42] Operation: 43-1=42 Exploring Operation: 43-9=34, Resulting Numbers: [1, 34] Generated Node #0,0,2: 33:[1, 34] Operation: 43-9=34 Moving to Node #0,1 Current State: 33:[47, 9, 3], Operations: ['46-43=3'] Exploring Operation: 47-9=38, Resulting Numbers: [3, 38] Generated Node #0,1,0: 33:[3, 38] Operation: 47-9=38 Exploring Operation: 9/3=3, Resulting Numbers: [47, 3] Generated Node #0,1,1: 33:[47, 3] Operation: 9/3=3 Exploring Operation: 47-3=44, Resulting Numbers: [9, 44] Generated Node #0,1,2: 33:[9, 44] Operation: 47-3=44 Moving to Node #0,2 Current State: 33:[46, 9, 4], Operations: ['47-43=4'] Exploring Operation: 9+4=13, Resulting Numbers: [46, 13] Generated Node #0,2,0: 33:[46, 13] Operation: 9+4=13 Exploring Operation: 46-4=42, Resulting Numbers: [9, 42] Generated Node #0,2,1: 33:[9, 42] Operation: 46-4=42 Exploring Operation: 46-9=37, Resulting Numbers: [4, 37] Generated Node #0,2,2: 33:[4, 37] Operation: 46-9=37 Moving to Node #0,0,2 Current State: 33:[1, 34], Operations: ['47-46=1', '43-9=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,33 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,33 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[47, 43, 46, 9], Operations: [] Exploring Operation: 47-46=1, Resulting Numbers: [43, 9, 1] Generated Node #0,0: 33:[43, 9, 1] Operation: 47-46=1 Moving to Node #0,0 Current State: 33:[43, 9, 1], Operations: ['47-46=1'] Exploring Operation: 43-9=34, Resulting Numbers: [1, 34] Generated Node #0,0,2: 33:[1, 34] Operation: 43-9=34 Moving to Node #0,0,2 Current State: 33:[1, 34], Operations: ['47-46=1', '43-9=34'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.983507
hs_3
sum_heuristic
[ 77, 70, 63, 89 ]
97
[ "77*89=6853", "6853-63=6790", "6790/70=97" ]
Current State: 97:[77, 70, 63, 89], Operations: [] Exploring Operation: 77*89=6853, Resulting Numbers: [70, 63, 6853] Generated Node #2: [70, 63, 6853] from Operation: 77*89=6853 Current State: 97:[70, 63, 6853], Operations: ['77*89=6853'] Exploring Operation: 6853-63=6790, Resulting Numbers: [70, 6790] Generated Node #3: [70, 6790] from Operation: 6853-63=6790 Current State: 97:[70, 6790], Operations: ['77*89=6853', '6853-63=6790'] Exploring Operation: 6790/70=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[77, 70, 63, 89], Operations: [] Exploring Operation: 70+63=133, Resulting Numbers: [77, 89, 133] Generated Node #0,0: 97:[77, 89, 133] Operation: 70+63=133 Exploring Operation: 77+63=140, Resulting Numbers: [70, 89, 140] Generated Node #0,1: 97:[70, 89, 140] Operation: 77+63=140 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[77, 89, 133], Operations: ['70+63=133'] Exploring Operation: 133-77=56, Resulting Numbers: [89, 56] Generated Node #0,0,0: 97:[89, 56] Operation: 133-77=56 Exploring Operation: 133-89=44, Resulting Numbers: [77, 44] Generated Node #0,0,1: 97:[77, 44] Operation: 133-89=44 Moving to Node #0,0,0 Current State: 97:[89, 56], Operations: ['70+63=133', '133-77=56'] Exploring Operation: 89-56=33, Resulting Numbers: [33] 33,97 unequal: No Solution Exploring Operation: 89+56=145, Resulting Numbers: [145] 145,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[77, 44], Operations: ['70+63=133', '133-89=44'] Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[70, 89, 140], Operations: ['77+63=140'] Exploring Operation: 140-70=70, Resulting Numbers: [89, 70] Generated Node #0,1,0: 97:[89, 70] Operation: 140-70=70 Exploring Operation: 140-89=51, Resulting Numbers: [70, 51] Generated Node #0,1,1: 97:[70, 51] Operation: 140-89=51 Moving to Node #0,1,0 Current State: 97:[89, 70], Operations: ['77+63=140', '140-70=70'] Exploring Operation: 89+70=159, Resulting Numbers: [159] 159,97 unequal: No Solution Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[70, 51], Operations: ['77+63=140', '140-89=51'] Exploring Operation: 70+51=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,97 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
[ 96, 34, 80, 26 ]
92
[ "34-26=8", "96/8=12", "80+12=92" ]
Current State: 92:[96, 34, 80, 26], Operations: [] Exploring Operation: 34-26=8, Resulting Numbers: [96, 80, 8] Generated Node #2: [96, 80, 8] from Operation: 34-26=8 Current State: 92:[96, 80, 8], Operations: ['34-26=8'] Exploring Operation: 96/8=12, Resulting Numbers: [80, 12] Generated Node #3: [80, 12] from Operation: 96/8=12 Current State: 92:[80, 12], Operations: ['34-26=8', '96/8=12'] Exploring Operation: 80+12=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[96, 34, 80, 26], Operations: [] Exploring Operation: 80-34=46, Resulting Numbers: [96, 26, 46] Generated Node #0,0: 92:[96, 26, 46] Operation: 80-34=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[96, 26, 46], Operations: ['80-34=46'] Exploring Operation: 96-46=50, Resulting Numbers: [26, 50] Generated Node #0,0,0: 92:[26, 50] Operation: 96-46=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[26, 50], Operations: ['80-34=46', '96-46=50'] Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 33, 90, 13, 19 ]
89
[ "90-33=57", "13+19=32", "57+32=89" ]
Current State: 89:[33, 90, 13, 19], Operations: [] Exploring Operation: 90-33=57, Resulting Numbers: [13, 19, 57] Generated Node #2: [13, 19, 57] from Operation: 90-33=57 Current State: 89:[13, 19, 57], Operations: ['90-33=57'] Exploring Operation: 13+19=32, Resulting Numbers: [57, 32] Generated Node #3: [57, 32] from Operation: 13+19=32 Current State: 89:[57, 32], Operations: ['90-33=57', '13+19=32'] Exploring Operation: 57+32=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[33, 90, 13, 19], Operations: [] Exploring Operation: 33+19=52, Resulting Numbers: [90, 13, 52] Generated Node #0,0: 89:[90, 13, 52] Operation: 33+19=52 Exploring Operation: 33+13=46, Resulting Numbers: [90, 19, 46] Generated Node #0,1: 89:[90, 19, 46] Operation: 33+13=46 Exploring Operation: 13+19=32, Resulting Numbers: [33, 90, 32] Generated Node #0,2: 89:[33, 90, 32] Operation: 13+19=32 Moving to Node #0,0 Current State: 89:[90, 13, 52], Operations: ['33+19=52'] Exploring Operation: 90+13=103, Resulting Numbers: [52, 103] Generated Node #0,0,0: 89:[52, 103] Operation: 90+13=103 Exploring Operation: 13+52=65, Resulting Numbers: [90, 65] Generated Node #0,0,1: 89:[90, 65] Operation: 13+52=65 Exploring Operation: 90-13=77, Resulting Numbers: [52, 77] Generated Node #0,0,2: 89:[52, 77] Operation: 90-13=77 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[90, 65], Operations: ['33+19=52', '13+52=65'] Exploring Operation: 90*65=5850, Resulting Numbers: [5850] 5850,89 unequal: No Solution Exploring Operation: 90+65=155, Resulting Numbers: [155] 155,89 unequal: No Solution Exploring Operation: 90-65=25, Resulting Numbers: [25] 25,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[52, 77], Operations: ['33+19=52', '90-13=77'] Exploring Operation: 52+77=129, Resulting Numbers: [129] 129,89 unequal: No Solution Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 52*77=4004, Resulting Numbers: [4004] 4004,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[52, 103], Operations: ['33+19=52', '90+13=103'] Exploring Operation: 52*103=5356, Resulting Numbers: [5356] 5356,89 unequal: No Solution Exploring Operation: 52+103=155, Resulting Numbers: [155] 155,89 unequal: No Solution Exploring Operation: 103-52=51, Resulting Numbers: [51] 51,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[90, 19, 46], Operations: ['33+13=46'] Exploring Operation: 90+19=109, Resulting Numbers: [46, 109] Generated Node #0,1,0: 89:[46, 109] Operation: 90+19=109 Exploring Operation: 19+46=65, Resulting Numbers: [90, 65] Generated Node #0,1,1: 89:[90, 65] Operation: 19+46=65 Exploring Operation: 90-19=71, Resulting Numbers: [46, 71] Generated Node #0,1,2: 89:[46, 71] Operation: 90-19=71 Moving to Node #0,2 Current State: 89:[33, 90, 32], Operations: ['13+19=32'] Exploring Operation: 33+32=65, Resulting Numbers: [90, 65] Generated Node #0,2,0: 89:[90, 65] Operation: 33+32=65 Exploring Operation: 90-32=58, Resulting Numbers: [33, 58] Generated Node #0,2,1: 89:[33, 58] Operation: 90-32=58 Exploring Operation: 90-33=57, Resulting Numbers: [32, 57] Generated Node #0,2,2: 89:[32, 57] Operation: 90-33=57 Moving to Node #0,1,1 Current State: 89:[90, 65], Operations: ['33+13=46', '19+46=65'] Exploring Operation: 90+65=155, Resulting Numbers: [155] 155,89 unequal: No Solution Exploring Operation: 90-65=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 90*65=5850, Resulting Numbers: [5850] 5850,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[90, 65], Operations: ['13+19=32', '33+32=65'] Exploring Operation: 90*65=5850, Resulting Numbers: [5850] 5850,89 unequal: No Solution Exploring Operation: 90+65=155, Resulting Numbers: [155] 155,89 unequal: No Solution Exploring Operation: 90-65=25, Resulting Numbers: [25] 25,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[46, 71], Operations: ['33+13=46', '90-19=71'] Exploring Operation: 71-46=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 46+71=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 46*71=3266, Resulting Numbers: [3266] 3266,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[46, 109], Operations: ['33+13=46', '90+19=109'] Exploring Operation: 109-46=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 46*109=5014, Resulting Numbers: [5014] 5014,89 unequal: No Solution Exploring Operation: 46+109=155, Resulting Numbers: [155] 155,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[33, 58], Operations: ['13+19=32', '90-32=58'] Exploring Operation: 33*58=1914, Resulting Numbers: [1914] 1914,89 unequal: No Solution Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 33+58=91, Resulting Numbers: [91] 91,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[32, 57], Operations: ['13+19=32', '90-33=57'] Exploring Operation: 32+57=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[33, 90, 13, 19], Operations: [] Exploring Operation: 13+19=32, Resulting Numbers: [33, 90, 32] Generated Node #0,2: 89:[33, 90, 32] Operation: 13+19=32 Moving to Node #0,2 Current State: 89:[33, 90, 32], Operations: ['13+19=32'] Exploring Operation: 90-33=57, Resulting Numbers: [32, 57] Generated Node #0,2,2: 89:[32, 57] Operation: 90-33=57 Moving to Node #0,2,2 Current State: 89:[32, 57], Operations: ['13+19=32', '90-33=57'] Exploring Operation: 32+57=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
0.96441
hs_3
sum_heuristic
[ 80, 76, 96, 92 ]
39
[ "80+76=156", "96-92=4", "156/4=39" ]
Current State: 39:[80, 76, 96, 92], Operations: [] Exploring Operation: 80+76=156, Resulting Numbers: [96, 92, 156] Generated Node #2: [96, 92, 156] from Operation: 80+76=156 Current State: 39:[96, 92, 156], Operations: ['80+76=156'] Exploring Operation: 96-92=4, Resulting Numbers: [156, 4] Generated Node #3: [156, 4] from Operation: 96-92=4 Current State: 39:[156, 4], Operations: ['80+76=156', '96-92=4'] Exploring Operation: 156/4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[80, 76, 96, 92], Operations: [] Exploring Operation: 96-80=16, Resulting Numbers: [76, 92, 16] Generated Node #0,0: 39:[76, 92, 16] Operation: 96-80=16 Exploring Operation: 92-80=12, Resulting Numbers: [76, 96, 12] Generated Node #0,1: 39:[76, 96, 12] Operation: 92-80=12 Exploring Operation: 96-92=4, Resulting Numbers: [80, 76, 4] Generated Node #0,2: 39:[80, 76, 4] Operation: 96-92=4 Moving to Node #0,2 Current State: 39:[80, 76, 4], Operations: ['96-92=4'] Exploring Operation: 76/4=19, Resulting Numbers: [80, 19] Generated Node #0,2,0: 39:[80, 19] Operation: 76/4=19 Exploring Operation: 80/4=20, Resulting Numbers: [76, 20] Generated Node #0,2,1: 39:[76, 20] Operation: 80/4=20 Exploring Operation: 80-76=4, Resulting Numbers: [4, 4] Generated Node #0,2,2: 39:[4, 4] Operation: 80-76=4 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[4, 4], Operations: ['96-92=4', '80-76=4'] Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[76, 20], Operations: ['96-92=4', '80/4=20'] Exploring Operation: 76*20=1520, Resulting Numbers: [1520] 1520,39 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,39 unequal: No Solution Exploring Operation: 76+20=96, Resulting Numbers: [96] 96,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[80, 19], Operations: ['96-92=4', '76/4=19'] Exploring Operation: 80*19=1520, Resulting Numbers: [1520] 1520,39 unequal: No Solution Exploring Operation: 80+19=99, Resulting Numbers: [99] 99,39 unequal: No Solution Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 39:[76, 92, 16], Operations: ['96-80=16'] Exploring Operation: 92-76=16, Resulting Numbers: [16, 16] Generated Node #0,0,0: 39:[16, 16] Operation: 92-76=16 Exploring Operation: 92-16=76, Resulting Numbers: [76, 76] Generated Node #0,0,1: 39:[76, 76] Operation: 92-16=76 Exploring Operation: 76-16=60, Resulting Numbers: [92, 60] Generated Node #0,0,2: 39:[92, 60] Operation: 76-16=60 Moving to Node #0,1 Current State: 39:[76, 96, 12], Operations: ['92-80=12'] Exploring Operation: 76-12=64, Resulting Numbers: [96, 64] Generated Node #0,1,0: 39:[96, 64] Operation: 76-12=64 Exploring Operation: 96/12=8, Resulting Numbers: [76, 8] Generated Node #0,1,1: 39:[76, 8] Operation: 96/12=8 Exploring Operation: 96-76=20, Resulting Numbers: [12, 20] Generated Node #0,1,2: 39:[12, 20] Operation: 96-76=20 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 39:[12, 20], Operations: ['92-80=12', '96-76=20'] Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 12*20=240, Resulting Numbers: [240] 240,39 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[76, 8], Operations: ['92-80=12', '96/12=8'] Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 76*8=608, Resulting Numbers: [608] 608,39 unequal: No Solution Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[96, 64], Operations: ['92-80=12', '76-12=64'] Exploring Operation: 96-64=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 96+64=160, Resulting Numbers: [160] 160,39 unequal: No Solution Exploring Operation: 96*64=6144, Resulting Numbers: [6144] 6144,39 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: 39:[16, 16], Operations: ['96-80=16', '92-76=16'] Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[76, 76], Operations: ['96-80=16', '92-16=76'] Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[92, 60], Operations: ['96-80=16', '76-16=60'] Exploring Operation: 92-60=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 92*60=5520, Resulting Numbers: [5520] 5520,39 unequal: No Solution Exploring Operation: 92+60=152, Resulting Numbers: [152] 152,39 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 15, 11, 17, 10 ]
57
[ "15-11=4", "10*4=40", "17+40=57" ]
Current State: 57:[15, 11, 17, 10], Operations: [] Exploring Operation: 15-11=4, Resulting Numbers: [17, 10, 4] Generated Node #2: [17, 10, 4] from Operation: 15-11=4 Current State: 57:[17, 10, 4], Operations: ['15-11=4'] Exploring Operation: 10*4=40, Resulting Numbers: [17, 40] Generated Node #3: [17, 40] from Operation: 10*4=40 Current State: 57:[17, 40], Operations: ['15-11=4', '10*4=40'] Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[15, 11, 17, 10], Operations: [] Exploring Operation: 11+10=21, Resulting Numbers: [15, 17, 21] Generated Node #0,0: 57:[15, 17, 21] Operation: 11+10=21 Exploring Operation: 11-10=1, Resulting Numbers: [15, 17, 1] Generated Node #0,1: 57:[15, 17, 1] Operation: 11-10=1 Moving to Node #0,0 Current State: 57:[15, 17, 21], Operations: ['11+10=21'] Exploring Operation: 17-15=2, Resulting Numbers: [21, 2] Generated Node #0,0,0: 57:[21, 2] Operation: 17-15=2 Exploring Operation: 21-15=6, Resulting Numbers: [17, 6] Generated Node #0,0,1: 57:[17, 6] Operation: 21-15=6 Moving to Node #0,1 Current State: 57:[15, 17, 1], Operations: ['11-10=1'] Exploring Operation: 17-15=2, Resulting Numbers: [1, 2] Generated Node #0,1,0: 57:[1, 2] Operation: 17-15=2 Exploring Operation: 15+1=16, Resulting Numbers: [17, 16] Generated Node #0,1,1: 57:[17, 16] Operation: 15+1=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[1, 2], Operations: ['11-10=1', '17-15=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,57 unequal: No Solution No 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: 57:[17, 16], Operations: ['11-10=1', '15+1=16'] Exploring Operation: 17+16=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,57 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: 57:[21, 2], Operations: ['11+10=21', '17-15=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,57 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[17, 6], Operations: ['11+10=21', '21-15=6'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,57 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 63, 55, 30, 47 ]
25
[ "63-55=8", "47-30=17", "8+17=25" ]
Current State: 25:[63, 55, 30, 47], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [30, 47, 8] Generated Node #2: [30, 47, 8] from Operation: 63-55=8 Current State: 25:[30, 47, 8], Operations: ['63-55=8'] Exploring Operation: 47-30=17, Resulting Numbers: [8, 17] Generated Node #3: [8, 17] from Operation: 47-30=17 Current State: 25:[8, 17], Operations: ['63-55=8', '47-30=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[63, 55, 30, 47], Operations: [] Exploring Operation: 63-47=16, Resulting Numbers: [55, 30, 16] Generated Node #0,0: 25:[55, 30, 16] Operation: 63-47=16 Exploring Operation: 63-55=8, Resulting Numbers: [30, 47, 8] Generated Node #0,1: 25:[30, 47, 8] Operation: 63-55=8 Moving to Node #0,1 Current State: 25:[30, 47, 8], Operations: ['63-55=8'] Exploring Operation: 47-8=39, Resulting Numbers: [30, 39] Generated Node #0,1,0: 25:[30, 39] Operation: 47-8=39 Exploring Operation: 47-30=17, Resulting Numbers: [8, 17] Generated Node #0,1,1: 25:[8, 17] Operation: 47-30=17 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[8, 17], Operations: ['63-55=8', '47-30=17'] Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[63, 55, 30, 47], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [30, 47, 8] Generated Node #0,1: 25:[30, 47, 8] Operation: 63-55=8 Moving to Node #0,1 Current State: 25:[30, 47, 8], Operations: ['63-55=8'] Exploring Operation: 47-30=17, Resulting Numbers: [8, 17] Generated Node #0,1,1: 25:[8, 17] Operation: 47-30=17 Moving to Node #0,1,1 Current State: 25:[8, 17], Operations: ['63-55=8', '47-30=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 70, 23, 17, 17 ]
47
[ "70-23=47", "17-17=0", "47+0=47" ]
Current State: 47:[70, 23, 17, 17], Operations: [] Exploring Operation: 70-23=47, Resulting Numbers: [17, 17, 47] Generated Node #2: [17, 17, 47] from Operation: 70-23=47 Current State: 47:[17, 17, 47], Operations: ['70-23=47'] Exploring Operation: 17-17=0, Resulting Numbers: [47, 0] Generated Node #3: [47, 0] from Operation: 17-17=0 Current State: 47:[47, 0], Operations: ['70-23=47', '17-17=0'] Exploring Operation: 47+0=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[70, 23, 17, 17], Operations: [] Exploring Operation: 70-17=53, Resulting Numbers: [23, 17, 53] Generated Node #0,0: 47:[23, 17, 53] Operation: 70-17=53 Exploring Operation: 70-23=47, Resulting Numbers: [17, 17, 47] Generated Node #0,1: 47:[17, 17, 47] Operation: 70-23=47 Exploring Operation: 23+17=40, Resulting Numbers: [70, 17, 40] Generated Node #0,2: 47:[70, 17, 40] Operation: 23+17=40 Exploring Operation: 70-17=53, Resulting Numbers: [23, 17, 53] Generated Node #0,3: 47:[23, 17, 53] Operation: 70-17=53 Moving to Node #0,0 Current State: 47:[23, 17, 53], Operations: ['70-17=53'] Exploring Operation: 23-17=6, Resulting Numbers: [53, 6] Generated Node #0,0,0: 47:[53, 6] Operation: 23-17=6 Exploring Operation: 53-23=30, Resulting Numbers: [17, 30] Generated Node #0,0,1: 47:[17, 30] Operation: 53-23=30 Exploring Operation: 23+17=40, Resulting Numbers: [53, 40] Generated Node #0,0,2: 47:[53, 40] Operation: 23+17=40 Exploring Operation: 53-17=36, Resulting Numbers: [23, 36] Generated Node #0,0,3: 47:[23, 36] Operation: 53-17=36 Moving to Node #0,2 Current State: 47:[70, 17, 40], Operations: ['23+17=40'] Exploring Operation: 70+17=87, Resulting Numbers: [40, 87] Generated Node #0,2,0: 47:[40, 87] Operation: 70+17=87 Exploring Operation: 17+40=57, Resulting Numbers: [70, 57] Generated Node #0,2,1: 47:[70, 57] Operation: 17+40=57 Exploring Operation: 70-40=30, Resulting Numbers: [17, 30] Generated Node #0,2,2: 47:[17, 30] Operation: 70-40=30 Exploring Operation: 70-17=53, Resulting Numbers: [40, 53] Generated Node #0,2,3: 47:[40, 53] Operation: 70-17=53 Moving to Node #0,1 Current State: 47:[17, 17, 47], Operations: ['70-23=47'] Exploring Operation: 17-17=0, Resulting Numbers: [47, 0] Generated Node #0,1,0: 47:[47, 0] Operation: 17-17=0 Exploring Operation: 17+47=64, Resulting Numbers: [17, 64] Generated Node #0,1,1: 47:[17, 64] Operation: 17+47=64 Exploring Operation: 17+17=34, Resulting Numbers: [47, 34] Generated Node #0,1,2: 47:[47, 34] Operation: 17+17=34 Exploring Operation: 17/17=1, Resulting Numbers: [47, 1] Generated Node #0,1,3: 47:[47, 1] Operation: 17/17=1 Moving to Node #0,3 Current State: 47:[23, 17, 53], Operations: ['70-17=53'] Exploring Operation: 53-17=36, Resulting Numbers: [23, 36] Generated Node #0,3,0: 47:[23, 36] Operation: 53-17=36 Exploring Operation: 23+17=40, Resulting Numbers: [53, 40] Generated Node #0,3,1: 47:[53, 40] Operation: 23+17=40 Exploring Operation: 53-23=30, Resulting Numbers: [17, 30] Generated Node #0,3,2: 47:[17, 30] Operation: 53-23=30 Exploring Operation: 23-17=6, Resulting Numbers: [53, 6] Generated Node #0,3,3: 47:[53, 6] Operation: 23-17=6 Moving to Node #0,0,2 Current State: 47:[53, 40], Operations: ['70-17=53', '23+17=40'] Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 53*40=2120, Resulting Numbers: [2120] 2120,47 unequal: No Solution Exploring Operation: 53+40=93, Resulting Numbers: [93] 93,47 unequal: No Solution Moving to Node #0,3,1 Current State: 47:[53, 40], Operations: ['70-17=53', '23+17=40'] Exploring Operation: 53*40=2120, Resulting Numbers: [2120] 2120,47 unequal: No Solution Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 53+40=93, Resulting Numbers: [93] 93,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[40, 53], Operations: ['23+17=40', '70-17=53'] Exploring Operation: 40*53=2120, Resulting Numbers: [2120] 2120,47 unequal: No Solution Exploring Operation: 40+53=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[47, 34], Operations: ['70-23=47', '17+17=34'] Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 47+34=81, Resulting Numbers: [81] 81,47 unequal: No Solution Exploring Operation: 47*34=1598, Resulting Numbers: [1598] 1598,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[70, 57], Operations: ['23+17=40', '17+40=57'] Exploring Operation: 70*57=3990, Resulting Numbers: [3990] 3990,47 unequal: No Solution Exploring Operation: 70+57=127, Resulting Numbers: [127] 127,47 unequal: No Solution Exploring Operation: 70-57=13, Resulting Numbers: [13] 13,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[23, 36], Operations: ['70-17=53', '53-17=36'] Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,47 unequal: No Solution Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[23, 36], Operations: ['70-17=53', '53-17=36'] Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[47, 1], Operations: ['70-23=47', '17/17=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[70, 23, 17, 17], Operations: [] Exploring Operation: 70-23=47, Resulting Numbers: [17, 17, 47] Generated Node #0,1: 47:[17, 17, 47] Operation: 70-23=47 Moving to Node #0,1 Current State: 47:[17, 17, 47], Operations: ['70-23=47'] Exploring Operation: 17/17=1, Resulting Numbers: [47, 1] Generated Node #0,1,3: 47:[47, 1] Operation: 17/17=1 Moving to Node #0,1,3 Current State: 47:[47, 1], Operations: ['70-23=47', '17/17=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
0.960069
hs_4
mult_heuristic
[ 30, 6, 90, 6 ]
39
[ "30-6=24", "90/6=15", "24+15=39" ]
Current State: 39:[30, 6, 90, 6], Operations: [] Exploring Operation: 30-6=24, Resulting Numbers: [90, 24] Generated Node #2: [90, 24] from Operation: 30-6=24 Current State: 39:[90, 24], Operations: ['30-6=24'] Exploring Operation: 90/6=15, Resulting Numbers: [24, 15] Generated Node #3: [24, 15] from Operation: 90/6=15 Current State: 39:[24, 15], Operations: ['30-6=24', '90/6=15'] Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[30, 6, 90, 6], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [30, 6, 15] Generated Node #0,0: 39:[30, 6, 15] Operation: 90/6=15 Exploring Operation: 90/6=15, Resulting Numbers: [30, 6, 15] Generated Node #0,1: 39:[30, 6, 15] Operation: 90/6=15 Exploring Operation: 90-30=60, Resulting Numbers: [6, 6, 60] Generated Node #0,2: 39:[6, 6, 60] Operation: 90-30=60 Exploring Operation: 30/6=5, Resulting Numbers: [90, 6, 5] Generated Node #0,3: 39:[90, 6, 5] Operation: 30/6=5 Exploring Operation: 90/30=3, Resulting Numbers: [6, 6, 3] Generated Node #0,4: 39:[6, 6, 3] Operation: 90/30=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 39:[6, 6, 3], Operations: ['90/30=3'] Exploring Operation: 6-6=0, Resulting Numbers: [3, 0] Generated Node #0,4,0: 39:[3, 0] Operation: 6-6=0 Exploring Operation: 6/6=1, Resulting Numbers: [3, 1] Generated Node #0,4,1: 39:[3, 1] Operation: 6/6=1 Exploring Operation: 6*6=36, Resulting Numbers: [3, 36] Generated Node #0,4,2: 39:[3, 36] Operation: 6*6=36 Exploring Operation: 6+6=12, Resulting Numbers: [3, 12] Generated Node #0,4,3: 39:[3, 12] Operation: 6+6=12 Exploring Operation: 6-3=3, Resulting Numbers: [6, 3] Generated Node #0,4,4: 39:[6, 3] Operation: 6-3=3 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 39:[3, 12], Operations: ['90/30=3', '6+6=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,39 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 39:[3, 1], Operations: ['90/30=3', '6/6=1'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 39:[3, 0], Operations: ['90/30=3', '6-6=0'] Exploring Operation: 3-0=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 3+0=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 3*0=0, Resulting Numbers: [0] 0,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 39:[3, 36], Operations: ['90/30=3', '6*6=36'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[30, 6, 90, 6], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [6, 6, 3] Generated Node #0,4: 39:[6, 6, 3] Operation: 90/30=3 Moving to Node #0,4 Current State: 39:[6, 6, 3], Operations: ['90/30=3'] Exploring Operation: 6*6=36, Resulting Numbers: [3, 36] Generated Node #0,4,2: 39:[3, 36] Operation: 6*6=36 Moving to Node #0,4,2 Current State: 39:[3, 36], Operations: ['90/30=3', '6*6=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 36, 52, 45, 10 ]
47
[ "36-10=26", "52/26=2", "45+2=47" ]
Current State: 47:[36, 52, 45, 10], Operations: [] Exploring Operation: 36-10=26, Resulting Numbers: [52, 45, 26] Generated Node #2: [52, 45, 26] from Operation: 36-10=26 Current State: 47:[52, 45, 26], Operations: ['36-10=26'] Exploring Operation: 52/26=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 52/26=2 Current State: 47:[45, 2], Operations: ['36-10=26', '52/26=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[36, 52, 45, 10], Operations: [] Exploring Operation: 36-10=26, Resulting Numbers: [52, 45, 26] Generated Node #0,0: 47:[52, 45, 26] Operation: 36-10=26 Exploring Operation: 36+10=46, Resulting Numbers: [52, 45, 46] Generated Node #0,1: 47:[52, 45, 46] Operation: 36+10=46 Exploring Operation: 52-10=42, Resulting Numbers: [36, 45, 42] Generated Node #0,2: 47:[36, 45, 42] Operation: 52-10=42 Exploring Operation: 45+10=55, Resulting Numbers: [36, 52, 55] Generated Node #0,3: 47:[36, 52, 55] Operation: 45+10=55 Moving to Node #0,1 Current State: 47:[52, 45, 46], Operations: ['36+10=46'] Exploring Operation: 52-46=6, Resulting Numbers: [45, 6] Generated Node #0,1,0: 47:[45, 6] Operation: 52-46=6 Exploring Operation: 45+46=91, Resulting Numbers: [52, 91] Generated Node #0,1,1: 47:[52, 91] Operation: 45+46=91 Exploring Operation: 52-45=7, Resulting Numbers: [46, 7] Generated Node #0,1,2: 47:[46, 7] Operation: 52-45=7 Exploring Operation: 52+45=97, Resulting Numbers: [46, 97] Generated Node #0,1,3: 47:[46, 97] Operation: 52+45=97 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[46, 7], Operations: ['36+10=46', '52-45=7'] Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 46*7=322, Resulting Numbers: [322] 322,47 unequal: No Solution Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[45, 6], Operations: ['36+10=46', '52-46=6'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,47 unequal: No Solution Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,47 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:[52, 91], Operations: ['36+10=46', '45+46=91'] Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,47 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,47 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 #0,1,3 Current State: 47:[46, 97], Operations: ['36+10=46', '52+45=97'] Exploring Operation: 97-46=51, Resulting Numbers: [51] 51,47 unequal: No Solution Exploring Operation: 46+97=143, Resulting Numbers: [143] 143,47 unequal: No Solution Exploring Operation: 46*97=4462, Resulting Numbers: [4462] 4462,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 47:[36, 45, 42], Operations: ['52-10=42'] Exploring Operation: 42-36=6, Resulting Numbers: [45, 6] Generated Node #0,2,0: 47:[45, 6] Operation: 42-36=6 Exploring Operation: 36+42=78, Resulting Numbers: [45, 78] Generated Node #0,2,1: 47:[45, 78] Operation: 36+42=78 Exploring Operation: 45-36=9, Resulting Numbers: [42, 9] Generated Node #0,2,2: 47:[42, 9] Operation: 45-36=9 Exploring Operation: 36+45=81, Resulting Numbers: [42, 81] Generated Node #0,2,3: 47:[42, 81] Operation: 36+45=81 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[45, 78], Operations: ['52-10=42', '36+42=78'] Exploring Operation: 45*78=3510, Resulting Numbers: [3510] 3510,47 unequal: No Solution Exploring Operation: 45+78=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,47 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 #0,2,3 Current State: 47:[42, 81], Operations: ['52-10=42', '36+45=81'] Exploring Operation: 42+81=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 42*81=3402, Resulting Numbers: [3402] 3402,47 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 #0,2,0 Current State: 47:[45, 6], Operations: ['52-10=42', '42-36=6'] Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,47 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,47 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[42, 9], Operations: ['52-10=42', '45-36=9'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,47 unequal: No Solution Exploring Operation: 42*9=378, Resulting Numbers: [378] 378,47 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: 47:[36, 52, 55], Operations: ['45+10=55'] Exploring Operation: 36+52=88, Resulting Numbers: [55, 88] Generated Node #0,3,0: 47:[55, 88] Operation: 36+52=88 Exploring Operation: 52-36=16, Resulting Numbers: [55, 16] Generated Node #0,3,1: 47:[55, 16] Operation: 52-36=16 Exploring Operation: 55-36=19, Resulting Numbers: [52, 19] Generated Node #0,3,2: 47:[52, 19] Operation: 55-36=19 Exploring Operation: 36+55=91, Resulting Numbers: [52, 91] Generated Node #0,3,3: 47:[52, 91] Operation: 36+55=91 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 47:[52, 19], Operations: ['45+10=55', '55-36=19'] Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,47 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 #0,3,1 Current State: 47:[55, 16], Operations: ['45+10=55', '52-36=16'] Exploring Operation: 55*16=880, Resulting Numbers: [880] 880,47 unequal: No Solution Exploring Operation: 55+16=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 55-16=39, Resulting Numbers: [39] 39,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 47:[55, 88], Operations: ['45+10=55', '36+52=88'] Exploring Operation: 55*88=4840, Resulting Numbers: [4840] 4840,47 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 55+88=143, Resulting Numbers: [143] 143,47 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 #0,3,3 Current State: 47:[52, 91], Operations: ['45+10=55', '36+55=91'] Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,47 unequal: No Solution Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,47 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 47:[52, 45, 26], Operations: ['36-10=26'] Exploring Operation: 45-26=19, Resulting Numbers: [52, 19] Generated Node #0,0,0: 47:[52, 19] Operation: 45-26=19 Exploring Operation: 52+26=78, Resulting Numbers: [45, 78] Generated Node #0,0,1: 47:[45, 78] Operation: 52+26=78 Exploring Operation: 45+26=71, Resulting Numbers: [52, 71] Generated Node #0,0,2: 47:[52, 71] Operation: 45+26=71 Exploring Operation: 52-26=26, Resulting Numbers: [45, 26] Generated Node #0,0,3: 47:[45, 26] Operation: 52-26=26 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[45, 26], Operations: ['36-10=26', '52-26=26'] Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,47 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[52, 71], Operations: ['36-10=26', '45+26=71'] Exploring Operation: 52*71=3692, Resulting Numbers: [3692] 3692,47 unequal: No Solution Exploring Operation: 52+71=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 71-52=19, Resulting Numbers: [19] 19,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[52, 19], Operations: ['36-10=26', '45-26=19'] Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,47 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[45, 78], Operations: ['36-10=26', '52+26=78'] Exploring Operation: 45+78=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 45*78=3510, Resulting Numbers: [3510] 3510,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 22, 49, 55, 61 ]
50
[ "49+61=110", "110/22=5", "55-5=50" ]
Current State: 50:[22, 49, 55, 61], Operations: [] Exploring Operation: 49+61=110, Resulting Numbers: [22, 55, 110] Generated Node #2: [22, 55, 110] from Operation: 49+61=110 Current State: 50:[22, 55, 110], Operations: ['49+61=110'] Exploring Operation: 110/22=5, Resulting Numbers: [55, 5] Generated Node #3: [55, 5] from Operation: 110/22=5 Current State: 50:[55, 5], Operations: ['49+61=110', '110/22=5'] Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[22, 49, 55, 61], Operations: [] Exploring Operation: 61-55=6, Resulting Numbers: [22, 49, 6] Generated Node #0,0: 50:[22, 49, 6] Operation: 61-55=6 Exploring Operation: 61-49=12, Resulting Numbers: [22, 55, 12] Generated Node #0,1: 50:[22, 55, 12] Operation: 61-49=12 Exploring Operation: 55-49=6, Resulting Numbers: [22, 61, 6] Generated Node #0,2: 50:[22, 61, 6] Operation: 55-49=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[22, 49, 6], Operations: ['61-55=6'] Exploring Operation: 22-6=16, Resulting Numbers: [49, 16] Generated Node #0,0,0: 50:[49, 16] Operation: 22-6=16 Exploring Operation: 22+6=28, Resulting Numbers: [49, 28] Generated Node #0,0,1: 50:[49, 28] Operation: 22+6=28 Exploring Operation: 49-22=27, Resulting Numbers: [6, 27] Generated Node #0,0,2: 50:[6, 27] Operation: 49-22=27 Moving to Node #0,0,2 Current State: 50:[6, 27], Operations: ['61-55=6', '49-22=27'] Exploring Operation: 6*27=162, Resulting Numbers: [162] 162,50 unequal: No Solution Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,50 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[49, 28], Operations: ['61-55=6', '22+6=28'] Exploring Operation: 49*28=1372, Resulting Numbers: [1372] 1372,50 unequal: No Solution Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 49+28=77, Resulting Numbers: [77] 77,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[49, 16], Operations: ['61-55=6', '22-6=16'] Exploring Operation: 49*16=784, Resulting Numbers: [784] 784,50 unequal: No Solution Exploring Operation: 49+16=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[22, 55, 12], Operations: ['61-49=12'] Exploring Operation: 55-22=33, Resulting Numbers: [12, 33] Generated Node #0,1,0: 50:[12, 33] Operation: 55-22=33 Exploring Operation: 22-12=10, Resulting Numbers: [55, 10] Generated Node #0,1,1: 50:[55, 10] Operation: 22-12=10 Exploring Operation: 55-12=43, Resulting Numbers: [22, 43] Generated Node #0,1,2: 50:[22, 43] Operation: 55-12=43 Moving to Node #0,1,1 Current State: 50:[55, 10], Operations: ['61-49=12', '22-12=10'] Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 55+10=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 55*10=550, Resulting Numbers: [550] 550,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[12, 33], Operations: ['61-49=12', '55-22=33'] Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,50 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[22, 43], Operations: ['61-49=12', '55-12=43'] Exploring Operation: 22+43=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 22*43=946, Resulting Numbers: [946] 946,50 unequal: No Solution Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[22, 61, 6], Operations: ['55-49=6'] Exploring Operation: 22+6=28, Resulting Numbers: [61, 28] Generated Node #0,2,0: 50:[61, 28] Operation: 22+6=28 Exploring Operation: 61-22=39, Resulting Numbers: [6, 39] Generated Node #0,2,1: 50:[6, 39] Operation: 61-22=39 Exploring Operation: 61-6=55, Resulting Numbers: [22, 55] Generated Node #0,2,2: 50:[22, 55] Operation: 61-6=55 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 50:[22, 55], Operations: ['55-49=6', '61-6=55'] Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,50 unequal: No Solution Exploring Operation: 22+55=77, Resulting Numbers: [77] 77,50 unequal: No Solution Exploring Operation: 22*55=1210, Resulting Numbers: [1210] 1210,50 unequal: No Solution No 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: 50:[6, 39], Operations: ['55-49=6', '61-22=39'] Exploring Operation: 6+39=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,50 unequal: No Solution Exploring Operation: 6*39=234, Resulting Numbers: [234] 234,50 unequal: No Solution No 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: 50:[61, 28], Operations: ['55-49=6', '22+6=28'] Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,50 unequal: No Solution Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,50 unequal: No Solution Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,50 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
[ 47, 63, 85, 89 ]
62
[ "47*85=3995", "3995-89=3906", "3906/63=62" ]
Current State: 62:[47, 63, 85, 89], Operations: [] Exploring Operation: 47*85=3995, Resulting Numbers: [63, 89, 3995] Generated Node #2: [63, 89, 3995] from Operation: 47*85=3995 Current State: 62:[63, 89, 3995], Operations: ['47*85=3995'] Exploring Operation: 3995-89=3906, Resulting Numbers: [63, 3906] Generated Node #3: [63, 3906] from Operation: 3995-89=3906 Current State: 62:[63, 3906], Operations: ['47*85=3995', '3995-89=3906'] Exploring Operation: 3906/63=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[47, 63, 85, 89], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [47, 63, 4] Generated Node #0,0: 62:[47, 63, 4] Operation: 89-85=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[47, 63, 4], Operations: ['89-85=4'] Exploring Operation: 47+4=51, Resulting Numbers: [63, 51] Generated Node #0,0,0: 62:[63, 51] Operation: 47+4=51 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[63, 51], Operations: ['89-85=4', '47+4=51'] Exploring Operation: 63-51=12, Resulting Numbers: [12] 12,62 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
[ 3, 9, 14, 2 ]
42
[ "9-3=6", "14/2=7", "6*7=42" ]
Current State: 42:[3, 9, 14, 2], Operations: [] Exploring Operation: 9-3=6, Resulting Numbers: [14, 2, 6] Generated Node #2: [14, 2, 6] from Operation: 9-3=6 Current State: 42:[14, 2, 6], Operations: ['9-3=6'] Exploring Operation: 14/2=7, Resulting Numbers: [6, 7] Generated Node #3: [6, 7] from Operation: 14/2=7 Current State: 42:[6, 7], Operations: ['9-3=6', '14/2=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[3, 9, 14, 2], Operations: [] Exploring Operation: 9-2=7, Resulting Numbers: [3, 14, 7] Generated Node #0,0: 42:[3, 14, 7] Operation: 9-2=7 Exploring Operation: 9-3=6, Resulting Numbers: [14, 2, 6] Generated Node #0,1: 42:[14, 2, 6] Operation: 9-3=6 Exploring Operation: 9/3=3, Resulting Numbers: [14, 2, 3] Generated Node #0,2: 42:[14, 2, 3] Operation: 9/3=3 Exploring Operation: 14-9=5, Resulting Numbers: [3, 2, 5] Generated Node #0,3: 42:[3, 2, 5] Operation: 14-9=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[3, 14, 7], Operations: ['9-2=7'] Exploring Operation: 3*14=42, Resulting Numbers: [7, 42] Generated Node #0,0,0: 42:[7, 42] Operation: 3*14=42 Exploring Operation: 14-7=7, Resulting Numbers: [3, 7] Generated Node #0,0,1: 42:[3, 7] Operation: 14-7=7 Exploring Operation: 3*7=21, Resulting Numbers: [14, 21] Generated Node #0,0,2: 42:[14, 21] Operation: 3*7=21 Exploring Operation: 14+7=21, Resulting Numbers: [3, 21] Generated Node #0,0,3: 42:[3, 21] Operation: 14+7=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[7, 42], Operations: ['9-2=7', '3*14=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,42 unequal: No Solution Exploring Operation: 7*42=294, Resulting Numbers: [294] 294,42 unequal: No Solution Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,42 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,42 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 #0,0,1 Current State: 42:[3, 7], Operations: ['9-2=7', '14-7=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,42 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 #0,0,2 Current State: 42:[14, 21], Operations: ['9-2=7', '3*7=21'] Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,42 unequal: No Solution Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,42 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,42 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 #0,0,3 Current State: 42:[3, 21], Operations: ['9-2=7', '14+7=21'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,42 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,42 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,42 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: 42:[14, 2, 6], Operations: ['9-3=6'] Exploring Operation: 14-6=8, Resulting Numbers: [2, 8] Generated Node #0,1,0: 42:[2, 8] Operation: 14-6=8 Exploring Operation: 14+6=20, Resulting Numbers: [2, 20] Generated Node #0,1,1: 42:[2, 20] Operation: 14+6=20 Exploring Operation: 14/2=7, Resulting Numbers: [6, 7] Generated Node #0,1,2: 42:[6, 7] Operation: 14/2=7 Exploring Operation: 6/2=3, Resulting Numbers: [14, 3] Generated Node #0,1,3: 42:[14, 3] Operation: 6/2=3 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 42:[6, 7], Operations: ['9-3=6', '14/2=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[3, 9, 14, 2], Operations: [] Exploring Operation: 9-3=6, Resulting Numbers: [14, 2, 6] Generated Node #0,1: 42:[14, 2, 6] Operation: 9-3=6 Moving to Node #0,1 Current State: 42:[14, 2, 6], Operations: ['9-3=6'] Exploring Operation: 14/2=7, Resulting Numbers: [6, 7] Generated Node #0,1,2: 42:[6, 7] Operation: 14/2=7 Moving to Node #0,1,2 Current State: 42:[6, 7], Operations: ['9-3=6', '14/2=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 15, 82, 72, 72 ]
77
[ "82-15=67", "72+72=144", "144-67=77" ]
Current State: 77:[15, 82, 72, 72], Operations: [] Exploring Operation: 82-15=67, Resulting Numbers: [72, 72, 67] Generated Node #2: [72, 72, 67] from Operation: 82-15=67 Current State: 77:[72, 72, 67], Operations: ['82-15=67'] Exploring Operation: 72+72=144, Resulting Numbers: [67, 144] Generated Node #3: [67, 144] from Operation: 72+72=144 Current State: 77:[67, 144], Operations: ['82-15=67', '72+72=144'] Exploring Operation: 144-67=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[15, 82, 72, 72], Operations: [] Exploring Operation: 82-72=10, Resulting Numbers: [15, 72, 10] Generated Node #0,0: 77:[15, 72, 10] Operation: 82-72=10 Exploring Operation: 72-72=0, Resulting Numbers: [15, 82, 0] Generated Node #0,1: 77:[15, 82, 0] Operation: 72-72=0 Exploring Operation: 82-72=10, Resulting Numbers: [15, 72, 10] Generated Node #0,2: 77:[15, 72, 10] Operation: 82-72=10 Exploring Operation: 82-15=67, Resulting Numbers: [72, 72, 67] Generated Node #0,3: 77:[72, 72, 67] Operation: 82-15=67 Exploring Operation: 72/72=1, Resulting Numbers: [15, 82, 1] Generated Node #0,4: 77:[15, 82, 1] Operation: 72/72=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[15, 72, 10], Operations: ['82-72=10'] Exploring Operation: 15+72=87, Resulting Numbers: [10, 87] Generated Node #0,0,0: 77:[10, 87] Operation: 15+72=87 Exploring Operation: 15-10=5, Resulting Numbers: [72, 5] Generated Node #0,0,1: 77:[72, 5] Operation: 15-10=5 Exploring Operation: 15+10=25, Resulting Numbers: [72, 25] Generated Node #0,0,2: 77:[72, 25] Operation: 15+10=25 Exploring Operation: 72-10=62, Resulting Numbers: [15, 62] Generated Node #0,0,3: 77:[15, 62] Operation: 72-10=62 Exploring Operation: 72+10=82, Resulting Numbers: [15, 82] Generated Node #0,0,4: 77:[15, 82] Operation: 72+10=82 Moving to Node #0,0,1 Current State: 77:[72, 5], Operations: ['82-72=10', '15-10=5'] Exploring Operation: 72*5=360, Resulting Numbers: [360] 360,77 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,77 unequal: No Solution Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[15, 82, 72, 72], Operations: [] Exploring Operation: 82-72=10, Resulting Numbers: [15, 72, 10] Generated Node #0,0: 77:[15, 72, 10] Operation: 82-72=10 Moving to Node #0,0 Current State: 77:[15, 72, 10], Operations: ['82-72=10'] Exploring Operation: 15-10=5, Resulting Numbers: [72, 5] Generated Node #0,0,1: 77:[72, 5] Operation: 15-10=5 Moving to Node #0,0,1 Current State: 77:[72, 5], Operations: ['82-72=10', '15-10=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 54, 32, 28, 98 ]
38
[ "54+98=152", "32-28=4", "152/4=38" ]
Current State: 38:[54, 32, 28, 98], Operations: [] Exploring Operation: 54+98=152, Resulting Numbers: [32, 28, 152] Generated Node #2: [32, 28, 152] from Operation: 54+98=152 Current State: 38:[32, 28, 152], Operations: ['54+98=152'] Exploring Operation: 32-28=4, Resulting Numbers: [152, 4] Generated Node #3: [152, 4] from Operation: 32-28=4 Current State: 38:[152, 4], Operations: ['54+98=152', '32-28=4'] Exploring Operation: 152/4=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[54, 32, 28, 98], Operations: [] Exploring Operation: 98-32=66, Resulting Numbers: [54, 28, 66] Generated Node #0,0: 38:[54, 28, 66] Operation: 98-32=66 Exploring Operation: 98-28=70, Resulting Numbers: [54, 32, 70] Generated Node #0,1: 38:[54, 32, 70] Operation: 98-28=70 Exploring Operation: 98-54=44, Resulting Numbers: [32, 28, 44] Generated Node #0,2: 38:[32, 28, 44] Operation: 98-54=44 Exploring Operation: 54-28=26, Resulting Numbers: [32, 98, 26] Generated Node #0,3: 38:[32, 98, 26] Operation: 54-28=26 Exploring Operation: 54-32=22, Resulting Numbers: [28, 98, 22] Generated Node #0,4: 38:[28, 98, 22] Operation: 54-32=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[32, 28, 44], Operations: ['98-54=44'] Exploring Operation: 28+44=72, Resulting Numbers: [32, 72] Generated Node #0,2,0: 38:[32, 72] Operation: 28+44=72 Exploring Operation: 44-28=16, Resulting Numbers: [32, 16] Generated Node #0,2,1: 38:[32, 16] Operation: 44-28=16 Exploring Operation: 32+28=60, Resulting Numbers: [44, 60] Generated Node #0,2,2: 38:[44, 60] Operation: 32+28=60 Exploring Operation: 44-32=12, Resulting Numbers: [28, 12] Generated Node #0,2,3: 38:[28, 12] Operation: 44-32=12 Exploring Operation: 32-28=4, Resulting Numbers: [44, 4] Generated Node #0,2,4: 38:[44, 4] Operation: 32-28=4 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 38:[44, 4], Operations: ['98-54=44', '32-28=4'] Exploring Operation: 44*4=176, Resulting Numbers: [176] 176,38 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 44+4=48, Resulting Numbers: [48] 48,38 unequal: No Solution No 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: 38:[32, 16], Operations: ['98-54=44', '44-28=16'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 32*16=512, Resulting Numbers: [512] 512,38 unequal: No Solution No 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: 38:[28, 12], Operations: ['98-54=44', '44-32=12'] Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,38 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,38 unequal: No Solution No 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: 38:[44, 60], Operations: ['98-54=44', '32+28=60'] Exploring Operation: 44*60=2640, Resulting Numbers: [2640] 2640,38 unequal: No Solution Exploring Operation: 44+60=104, Resulting Numbers: [104] 104,38 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,38 unequal: No Solution No 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: 38:[32, 72], Operations: ['98-54=44', '28+44=72'] Exploring Operation: 32+72=104, Resulting Numbers: [104] 104,38 unequal: No Solution Exploring Operation: 32*72=2304, Resulting Numbers: [2304] 2304,38 unequal: No Solution Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,38 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: 38:[54, 28, 66], Operations: ['98-32=66'] Exploring Operation: 54+28=82, Resulting Numbers: [66, 82] Generated Node #0,0,0: 38:[66, 82] Operation: 54+28=82 Exploring Operation: 54-28=26, Resulting Numbers: [66, 26] Generated Node #0,0,1: 38:[66, 26] Operation: 54-28=26 Exploring Operation: 66-28=38, Resulting Numbers: [54, 38] Generated Node #0,0,2: 38:[54, 38] Operation: 66-28=38 Exploring Operation: 28+66=94, Resulting Numbers: [54, 94] Generated Node #0,0,3: 38:[54, 94] Operation: 28+66=94 Exploring Operation: 66-54=12, Resulting Numbers: [28, 12] Generated Node #0,0,4: 38:[28, 12] Operation: 66-54=12 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 38:[54, 38], Operations: ['98-32=66', '66-28=38'] Exploring Operation: 54+38=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 54*38=2052, Resulting Numbers: [2052] 2052,38 unequal: No Solution No 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: 38:[28, 12], Operations: ['98-32=66', '66-54=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,38 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,38 unequal: No Solution No 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: 38:[66, 26], Operations: ['98-32=66', '54-28=26'] Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,38 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,38 unequal: No Solution No 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: 38:[66, 82], Operations: ['98-32=66', '54+28=82'] Exploring Operation: 82-66=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 66*82=5412, Resulting Numbers: [5412] 5412,38 unequal: No Solution Exploring Operation: 66+82=148, Resulting Numbers: [148] 148,38 unequal: No Solution No 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: 38:[54, 94], Operations: ['98-32=66', '28+66=94'] Exploring Operation: 94-54=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 54*94=5076, Resulting Numbers: [5076] 5076,38 unequal: No Solution Exploring Operation: 54+94=148, Resulting Numbers: [148] 148,38 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: 38:[54, 32, 70], Operations: ['98-28=70'] Exploring Operation: 32+70=102, Resulting Numbers: [54, 102] Generated Node #0,1,0: 38:[54, 102] Operation: 32+70=102 Exploring Operation: 54-32=22, Resulting Numbers: [70, 22] Generated Node #0,1,1: 38:[70, 22] Operation: 54-32=22 Exploring Operation: 54+32=86, Resulting Numbers: [70, 86] Generated Node #0,1,2: 38:[70, 86] Operation: 54+32=86 Exploring Operation: 70-32=38, Resulting Numbers: [54, 38] Generated Node #0,1,3: 38:[54, 38] Operation: 70-32=38 Exploring Operation: 70-54=16, Resulting Numbers: [32, 16] Generated Node #0,1,4: 38:[32, 16] Operation: 70-54=16 Moving to Node #0,1,4 Current State: 38:[32, 16], Operations: ['98-28=70', '70-54=16'] Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 32*16=512, Resulting Numbers: [512] 512,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[54, 38], Operations: ['98-28=70', '70-32=38'] Exploring Operation: 54+38=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 54*38=2052, Resulting Numbers: [2052] 2052,38 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[70, 22], Operations: ['98-28=70', '54-32=22'] Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,38 unequal: No Solution Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[54, 102], Operations: ['98-28=70', '32+70=102'] Exploring Operation: 102-54=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 54+102=156, Resulting Numbers: [156] 156,38 unequal: No Solution Exploring Operation: 54*102=5508, Resulting Numbers: [5508] 5508,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[70, 86], Operations: ['98-28=70', '54+32=86'] Exploring Operation: 70+86=156, Resulting Numbers: [156] 156,38 unequal: No Solution Exploring Operation: 70*86=6020, Resulting Numbers: [6020] 6020,38 unequal: No Solution Exploring Operation: 86-70=16, Resulting Numbers: [16] 16,38 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 #0,4 Current State: 38:[28, 98, 22], Operations: ['54-32=22'] Exploring Operation: 28+98=126, Resulting Numbers: [22, 126] Generated Node #0,4,0: 38:[22, 126] Operation: 28+98=126 Exploring Operation: 98-28=70, Resulting Numbers: [22, 70] Generated Node #0,4,1: 38:[22, 70] Operation: 98-28=70 Exploring Operation: 98-22=76, Resulting Numbers: [28, 76] Generated Node #0,4,2: 38:[28, 76] Operation: 98-22=76 Exploring Operation: 28+22=50, Resulting Numbers: [98, 50] Generated Node #0,4,3: 38:[98, 50] Operation: 28+22=50 Exploring Operation: 28-22=6, Resulting Numbers: [98, 6] Generated Node #0,4,4: 38:[98, 6] Operation: 28-22=6 Moving to Node #0,4,1 Current State: 38:[22, 70], Operations: ['54-32=22', '98-28=70'] Exploring Operation: 22*70=1540, Resulting Numbers: [1540] 1540,38 unequal: No Solution Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 22+70=92, Resulting Numbers: [92] 92,38 unequal: No Solution Moving to Node #0,4,2 Current State: 38:[28, 76], Operations: ['54-32=22', '98-22=76'] Exploring Operation: 28*76=2128, Resulting Numbers: [2128] 2128,38 unequal: No Solution Exploring Operation: 76-28=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 28+76=104, Resulting Numbers: [104] 104,38 unequal: No Solution Moving to Node #0,4,4 Current State: 38:[98, 6], Operations: ['54-32=22', '28-22=6'] Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 98*6=588, Resulting Numbers: [588] 588,38 unequal: No Solution Exploring Operation: 98+6=104, Resulting Numbers: [104] 104,38 unequal: No Solution Moving to Node #0,4,3 Current State: 38:[98, 50], Operations: ['54-32=22', '28+22=50'] Exploring Operation: 98-50=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 98*50=4900, Resulting Numbers: [4900] 4900,38 unequal: No Solution Exploring Operation: 98+50=148, Resulting Numbers: [148] 148,38 unequal: No Solution Moving to Node #0,4,0 Current State: 38:[22, 126], Operations: ['54-32=22', '28+98=126'] Exploring Operation: 126-22=104, Resulting Numbers: [104] 104,38 unequal: No Solution Exploring Operation: 22*126=2772, Resulting Numbers: [2772] 2772,38 unequal: No Solution Exploring Operation: 22+126=148, Resulting Numbers: [148] 148,38 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 #0,3 Current State: 38:[32, 98, 26], Operations: ['54-28=26'] Exploring Operation: 98-26=72, Resulting Numbers: [32, 72] Generated Node #0,3,0: 38:[32, 72] Operation: 98-26=72 Exploring Operation: 98-32=66, Resulting Numbers: [26, 66] Generated Node #0,3,1: 38:[26, 66] Operation: 98-32=66 Exploring Operation: 98+26=124, Resulting Numbers: [32, 124] Generated Node #0,3,2: 38:[32, 124] Operation: 98+26=124 Exploring Operation: 32+26=58, Resulting Numbers: [98, 58] Generated Node #0,3,3: 38:[98, 58] Operation: 32+26=58 Exploring Operation: 32-26=6, Resulting Numbers: [98, 6] Generated Node #0,3,4: 38:[98, 6] Operation: 32-26=6 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 38:[26, 66], Operations: ['54-28=26', '98-32=66'] Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,38 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,38 unequal: No Solution No 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: 38:[32, 72], Operations: ['54-28=26', '98-26=72'] Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 32+72=104, Resulting Numbers: [104] 104,38 unequal: No Solution Exploring Operation: 32*72=2304, Resulting Numbers: [2304] 2304,38 unequal: No Solution No 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: 38:[98, 6], Operations: ['54-28=26', '32-26=6'] Exploring Operation: 98*6=588, Resulting Numbers: [588] 588,38 unequal: No Solution Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 98+6=104, Resulting Numbers: [104] 104,38 unequal: No Solution No 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: 38:[98, 58], Operations: ['54-28=26', '32+26=58'] Exploring Operation: 98*58=5684, Resulting Numbers: [5684] 5684,38 unequal: No Solution Exploring Operation: 98-58=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 98+58=156, Resulting Numbers: [156] 156,38 unequal: No Solution No 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: 38:[32, 124], Operations: ['54-28=26', '98+26=124'] Exploring Operation: 124-32=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 32*124=3968, Resulting Numbers: [3968] 3968,38 unequal: No Solution Exploring Operation: 32+124=156, Resulting Numbers: [156] 156,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic