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
[ 76, 10, 33, 64 ]
97
[ "76-10=66", "64-33=31", "66+31=97" ]
Current State: 97:[76, 10, 33, 64], Operations: [] Exploring Operation: 76-10=66, Resulting Numbers: [33, 64, 66] Generated Node #2: [33, 64, 66] from Operation: 76-10=66 Current State: 97:[33, 64, 66], Operations: ['76-10=66'] Exploring Operation: 64-33=31, Resulting Numbers: [66, 31] Generated Node #3: [66, 31] from Operation: 64-33=31 Current State: 97:[66, 31], Operations: ['76-10=66', '64-33=31'] Exploring Operation: 66+31=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[76, 10, 33, 64], Operations: [] Exploring Operation: 76+10=86, Resulting Numbers: [33, 64, 86] Generated Node #0,0: 97:[33, 64, 86] Operation: 76+10=86 Exploring Operation: 10+33=43, Resulting Numbers: [76, 64, 43] Generated Node #0,1: 97:[76, 64, 43] Operation: 10+33=43 Exploring Operation: 33+64=97, Resulting Numbers: [76, 10, 97] Generated Node #0,2: 97:[76, 10, 97] Operation: 33+64=97 Exploring Operation: 10+64=74, Resulting Numbers: [76, 33, 74] Generated Node #0,3: 97:[76, 33, 74] Operation: 10+64=74 Moving to Node #0,0 Current State: 97:[33, 64, 86], Operations: ['76+10=86'] Exploring Operation: 33+64=97, Resulting Numbers: [86, 97] Generated Node #0,0,0: 97:[86, 97] Operation: 33+64=97 Exploring Operation: 33+86=119, Resulting Numbers: [64, 119] Generated Node #0,0,1: 97:[64, 119] Operation: 33+86=119 Exploring Operation: 86-33=53, Resulting Numbers: [64, 53] Generated Node #0,0,2: 97:[64, 53] Operation: 86-33=53 Exploring Operation: 64-33=31, Resulting Numbers: [86, 31] Generated Node #0,0,3: 97:[86, 31] Operation: 64-33=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[86, 97], Operations: ['76+10=86', '33+64=97'] Exploring Operation: 86*97=8342, Resulting Numbers: [8342] 8342,97 unequal: No Solution Exploring Operation: 86+97=183, Resulting Numbers: [183] 183,97 unequal: No Solution Exploring Operation: 97-86=11, Resulting Numbers: [11] 11,97 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:[64, 119], Operations: ['76+10=86', '33+86=119'] Exploring Operation: 64*119=7616, Resulting Numbers: [7616] 7616,97 unequal: No Solution Exploring Operation: 64+119=183, Resulting Numbers: [183] 183,97 unequal: No Solution Exploring Operation: 119-64=55, Resulting Numbers: [55] 55,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[64, 53], Operations: ['76+10=86', '86-33=53'] Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 64+53=117, Resulting Numbers: [117] 117,97 unequal: No Solution Exploring Operation: 64*53=3392, Resulting Numbers: [3392] 3392,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 97:[86, 31], Operations: ['76+10=86', '64-33=31'] Exploring Operation: 86*31=2666, Resulting Numbers: [2666] 2666,97 unequal: No Solution Exploring Operation: 86-31=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 86+31=117, Resulting Numbers: [117] 117,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 97:[76, 10, 97], Operations: ['33+64=97'] Exploring Operation: 76-10=66, Resulting Numbers: [97, 66] Generated Node #0,2,0: 97:[97, 66] Operation: 76-10=66 Exploring Operation: 76+10=86, Resulting Numbers: [97, 86] Generated Node #0,2,1: 97:[97, 86] Operation: 76+10=86 Exploring Operation: 10+97=107, Resulting Numbers: [76, 107] Generated Node #0,2,2: 97:[76, 107] Operation: 10+97=107 Exploring Operation: 97-10=87, Resulting Numbers: [76, 87] Generated Node #0,2,3: 97:[76, 87] Operation: 97-10=87 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[97, 86], Operations: ['33+64=97', '76+10=86'] Exploring Operation: 97-86=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 97*86=8342, Resulting Numbers: [8342] 8342,97 unequal: No Solution Exploring Operation: 97+86=183, Resulting Numbers: [183] 183,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[97, 66], Operations: ['33+64=97', '76-10=66'] Exploring Operation: 97+66=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 97-66=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 97*66=6402, Resulting Numbers: [6402] 6402,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[76, 107], Operations: ['33+64=97', '10+97=107'] Exploring Operation: 107-76=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 76+107=183, Resulting Numbers: [183] 183,97 unequal: No Solution Exploring Operation: 76*107=8132, Resulting Numbers: [8132] 8132,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[76, 87], Operations: ['33+64=97', '97-10=87'] Exploring Operation: 76*87=6612, Resulting Numbers: [6612] 6612,97 unequal: No Solution Exploring Operation: 76+87=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 87-76=11, Resulting Numbers: [11] 11,97 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:[76, 64, 43], Operations: ['10+33=43'] Exploring Operation: 76+64=140, Resulting Numbers: [43, 140] Generated Node #0,1,0: 97:[43, 140] Operation: 76+64=140 Exploring Operation: 64+43=107, Resulting Numbers: [76, 107] Generated Node #0,1,1: 97:[76, 107] Operation: 64+43=107 Exploring Operation: 76-43=33, Resulting Numbers: [64, 33] Generated Node #0,1,2: 97:[64, 33] Operation: 76-43=33 Exploring Operation: 76+43=119, Resulting Numbers: [64, 119] Generated Node #0,1,3: 97:[64, 119] Operation: 76+43=119 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[76, 107], Operations: ['10+33=43', '64+43=107'] Exploring Operation: 107-76=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 76+107=183, Resulting Numbers: [183] 183,97 unequal: No Solution Exploring Operation: 76*107=8132, Resulting Numbers: [8132] 8132,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 97:[64, 119], Operations: ['10+33=43', '76+43=119'] Exploring Operation: 119-64=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 64*119=7616, Resulting Numbers: [7616] 7616,97 unequal: No Solution Exploring Operation: 64+119=183, Resulting Numbers: [183] 183,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[43, 140], Operations: ['10+33=43', '76+64=140'] Exploring Operation: 43*140=6020, Resulting Numbers: [6020] 6020,97 unequal: No Solution Exploring Operation: 140-43=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[76, 10, 33, 64], Operations: [] Exploring Operation: 10+33=43, Resulting Numbers: [76, 64, 43] Generated Node #0,1: 97:[76, 64, 43] Operation: 10+33=43 Moving to Node #0,1 Current State: 97:[76, 64, 43], Operations: ['10+33=43'] Exploring Operation: 76+64=140, Resulting Numbers: [43, 140] Generated Node #0,1,0: 97:[43, 140] Operation: 76+64=140 Moving to Node #0,1,0 Current State: 97:[43, 140], Operations: ['10+33=43', '76+64=140'] Exploring Operation: 140-43=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
mult_heuristic
[ 73, 71, 57, 88 ]
26
[ "73-71=2", "57*2=114", "114-88=26" ]
Current State: 26:[73, 71, 57, 88], Operations: [] Exploring Operation: 73-71=2, Resulting Numbers: [57, 88, 2] Generated Node #2: [57, 88, 2] from Operation: 73-71=2 Current State: 26:[57, 88, 2], Operations: ['73-71=2'] Exploring Operation: 57*2=114, Resulting Numbers: [88, 114] Generated Node #3: [88, 114] from Operation: 57*2=114 Current State: 26:[88, 114], Operations: ['73-71=2', '57*2=114'] Exploring Operation: 114-88=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[73, 71, 57, 88], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [73, 57, 17] Generated Node #0,0: 26:[73, 57, 17] Operation: 88-71=17 Exploring Operation: 73-71=2, Resulting Numbers: [57, 88, 2] Generated Node #0,1: 26:[57, 88, 2] Operation: 73-71=2 Exploring Operation: 88-73=15, Resulting Numbers: [71, 57, 15] Generated Node #0,2: 26:[71, 57, 15] Operation: 88-73=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[71, 57, 15], Operations: ['88-73=15'] Exploring Operation: 57-15=42, Resulting Numbers: [71, 42] Generated Node #0,2,0: 26:[71, 42] Operation: 57-15=42 Exploring Operation: 71-15=56, Resulting Numbers: [57, 56] Generated Node #0,2,1: 26:[57, 56] Operation: 71-15=56 Exploring Operation: 71-57=14, Resulting Numbers: [15, 14] Generated Node #0,2,2: 26:[15, 14] Operation: 71-57=14 Moving to Node #0,2,2 Current State: 26:[15, 14], Operations: ['88-73=15', '71-57=14'] Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,26 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,26 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[71, 42], Operations: ['88-73=15', '57-15=42'] Exploring Operation: 71+42=113, Resulting Numbers: [113] 113,26 unequal: No Solution Exploring Operation: 71-42=29, Resulting Numbers: [29] 29,26 unequal: No Solution Exploring Operation: 71*42=2982, Resulting Numbers: [2982] 2982,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[57, 56], Operations: ['88-73=15', '71-15=56'] Exploring Operation: 57-56=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 57+56=113, Resulting Numbers: [113] 113,26 unequal: No Solution Exploring Operation: 57*56=3192, Resulting Numbers: [3192] 3192,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[73, 57, 17], Operations: ['88-71=17'] Exploring Operation: 73-17=56, Resulting Numbers: [57, 56] Generated Node #0,0,0: 26:[57, 56] Operation: 73-17=56 Exploring Operation: 57-17=40, Resulting Numbers: [73, 40] Generated Node #0,0,1: 26:[73, 40] Operation: 57-17=40 Exploring Operation: 73-57=16, Resulting Numbers: [17, 16] Generated Node #0,0,2: 26:[17, 16] Operation: 73-57=16 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 26:[17, 16], Operations: ['88-71=17', '73-57=16'] Exploring Operation: 17*16=272, Resulting Numbers: [272] 272,26 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 17+16=33, Resulting Numbers: [33] 33,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 26:[57, 56], Operations: ['88-71=17', '73-17=56'] Exploring Operation: 57*56=3192, Resulting Numbers: [3192] 3192,26 unequal: No Solution Exploring Operation: 57+56=113, Resulting Numbers: [113] 113,26 unequal: No Solution Exploring Operation: 57-56=1, Resulting Numbers: [1] 1,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 26:[73, 40], Operations: ['88-71=17', '57-17=40'] Exploring Operation: 73+40=113, Resulting Numbers: [113] 113,26 unequal: No Solution Exploring Operation: 73*40=2920, Resulting Numbers: [2920] 2920,26 unequal: No Solution Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[57, 88, 2], Operations: ['73-71=2'] Exploring Operation: 88/2=44, Resulting Numbers: [57, 44] Generated Node #0,1,0: 26:[57, 44] Operation: 88/2=44 Exploring Operation: 57-2=55, Resulting Numbers: [88, 55] Generated Node #0,1,1: 26:[88, 55] Operation: 57-2=55 Exploring Operation: 88-57=31, Resulting Numbers: [2, 31] Generated Node #0,1,2: 26:[2, 31] Operation: 88-57=31 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 26:[2, 31], Operations: ['73-71=2', '88-57=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,26 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,26 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 26:[57, 44], Operations: ['73-71=2', '88/2=44'] Exploring Operation: 57-44=13, Resulting Numbers: [13] 13,26 unequal: No Solution Exploring Operation: 57*44=2508, Resulting Numbers: [2508] 2508,26 unequal: No Solution Exploring Operation: 57+44=101, Resulting Numbers: [101] 101,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 26:[88, 55], Operations: ['73-71=2', '57-2=55'] Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,26 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,26 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 17, 6, 9, 9 ]
22
[ "17+6=23", "9/9=1", "23-1=22" ]
Current State: 22:[17, 6, 9, 9], Operations: [] Exploring Operation: 17+6=23, Resulting Numbers: [9, 9, 23] Generated Node #2: [9, 9, 23] from Operation: 17+6=23 Current State: 22:[9, 9, 23], Operations: ['17+6=23'] Exploring Operation: 9/9=1, Resulting Numbers: [23, 1] Generated Node #3: [23, 1] from Operation: 9/9=1 Current State: 22:[23, 1], Operations: ['17+6=23', '9/9=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[17, 6, 9, 9], Operations: [] Exploring Operation: 17-6=11, Resulting Numbers: [9, 9, 11] Generated Node #0,0: 22:[9, 9, 11] Operation: 17-6=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[9, 9, 11], Operations: ['17-6=11'] Exploring Operation: 9/9=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 22:[11, 1] Operation: 9/9=1 Moving to Node #0,0,0 Current State: 22:[11, 1], Operations: ['17-6=11', '9/9=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,22 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
[ 37, 47, 58, 12 ]
51
[ "37+47=84", "84/12=7", "58-7=51" ]
Current State: 51:[37, 47, 58, 12], Operations: [] Exploring Operation: 37+47=84, Resulting Numbers: [58, 12, 84] Generated Node #2: [58, 12, 84] from Operation: 37+47=84 Current State: 51:[58, 12, 84], Operations: ['37+47=84'] Exploring Operation: 84/12=7, Resulting Numbers: [58, 7] Generated Node #3: [58, 7] from Operation: 84/12=7 Current State: 51:[58, 7], Operations: ['37+47=84', '84/12=7'] Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[37, 47, 58, 12], Operations: [] Exploring Operation: 37+12=49, Resulting Numbers: [47, 58, 49] Generated Node #0,0: 51:[47, 58, 49] Operation: 37+12=49 Exploring Operation: 58-37=21, Resulting Numbers: [47, 12, 21] Generated Node #0,1: 51:[47, 12, 21] Operation: 58-37=21 Moving to Node #0,0 Current State: 51:[47, 58, 49], Operations: ['37+12=49'] Exploring Operation: 49-47=2, Resulting Numbers: [58, 2] Generated Node #0,0,0: 51:[58, 2] Operation: 49-47=2 Exploring Operation: 58-47=11, Resulting Numbers: [49, 11] Generated Node #0,0,1: 51:[49, 11] Operation: 58-47=11 Moving to Node #0,1 Current State: 51:[47, 12, 21], Operations: ['58-37=21'] Exploring Operation: 47+12=59, Resulting Numbers: [21, 59] Generated Node #0,1,0: 51:[21, 59] Operation: 47+12=59 Exploring Operation: 21-12=9, Resulting Numbers: [47, 9] Generated Node #0,1,1: 51:[47, 9] Operation: 21-12=9 Moving to Node #0,0,0 Current State: 51:[58, 2], Operations: ['37+12=49', '49-47=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[49, 11], Operations: ['37+12=49', '58-47=11'] Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[47, 9], Operations: ['58-37=21', '21-12=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[21, 59], Operations: ['58-37=21', '47+12=59'] Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,51 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 80, 52, 24, 46 ]
50
[ "80-52=28", "46-24=22", "28+22=50" ]
Current State: 50:[80, 52, 24, 46], Operations: [] Exploring Operation: 80-52=28, Resulting Numbers: [24, 46, 28] Generated Node #2: [24, 46, 28] from Operation: 80-52=28 Current State: 50:[24, 46, 28], Operations: ['80-52=28'] Exploring Operation: 46-24=22, Resulting Numbers: [28, 22] Generated Node #3: [28, 22] from Operation: 46-24=22 Current State: 50:[28, 22], Operations: ['80-52=28', '46-24=22'] Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[80, 52, 24, 46], Operations: [] Exploring Operation: 80-24=56, Resulting Numbers: [52, 46, 56] Generated Node #0,0: 50:[52, 46, 56] Operation: 80-24=56 Exploring Operation: 80-52=28, Resulting Numbers: [24, 46, 28] Generated Node #0,1: 50:[24, 46, 28] Operation: 80-52=28 Exploring Operation: 80-46=34, Resulting Numbers: [52, 24, 34] Generated Node #0,2: 50:[52, 24, 34] Operation: 80-46=34 Moving to Node #0,1 Current State: 50:[24, 46, 28], Operations: ['80-52=28'] Exploring Operation: 28-24=4, Resulting Numbers: [46, 4] Generated Node #0,1,0: 50:[46, 4] Operation: 28-24=4 Exploring Operation: 24+28=52, Resulting Numbers: [46, 52] Generated Node #0,1,1: 50:[46, 52] Operation: 24+28=52 Exploring Operation: 46-24=22, Resulting Numbers: [28, 22] Generated Node #0,1,2: 50:[28, 22] Operation: 46-24=22 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[46, 4], Operations: ['80-52=28', '28-24=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,50 unequal: No Solution Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[80, 52, 24, 46], Operations: [] Exploring Operation: 80-52=28, Resulting Numbers: [24, 46, 28] Generated Node #0,1: 50:[24, 46, 28] Operation: 80-52=28 Moving to Node #0,1 Current State: 50:[24, 46, 28], Operations: ['80-52=28'] Exploring Operation: 28-24=4, Resulting Numbers: [46, 4] Generated Node #0,1,0: 50:[46, 4] Operation: 28-24=4 Moving to Node #0,1,0 Current State: 50:[46, 4], Operations: ['80-52=28', '28-24=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 10, 20, 85, 65 ]
45
[ "20/10=2", "65*2=130", "130-85=45" ]
Current State: 45:[10, 20, 85, 65], Operations: [] Exploring Operation: 20/10=2, Resulting Numbers: [85, 65, 2] Generated Node #2: [85, 65, 2] from Operation: 20/10=2 Current State: 45:[85, 65, 2], Operations: ['20/10=2'] Exploring Operation: 65*2=130, Resulting Numbers: [85, 130] Generated Node #3: [85, 130] from Operation: 65*2=130 Current State: 45:[85, 130], Operations: ['20/10=2', '65*2=130'] Exploring Operation: 130-85=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[10, 20, 85, 65], Operations: [] Exploring Operation: 85-65=20, Resulting Numbers: [10, 20, 20] Generated Node #0,0: 45:[10, 20, 20] Operation: 85-65=20 Exploring Operation: 85-10=75, Resulting Numbers: [20, 65, 75] Generated Node #0,1: 45:[20, 65, 75] Operation: 85-10=75 Exploring Operation: 65-20=45, Resulting Numbers: [10, 85, 45] Generated Node #0,2: 45:[10, 85, 45] Operation: 65-20=45 Exploring Operation: 85-20=65, Resulting Numbers: [10, 65, 65] Generated Node #0,3: 45:[10, 65, 65] Operation: 85-20=65 Moving to Node #0,0 Current State: 45:[10, 20, 20], Operations: ['85-65=20'] Exploring Operation: 20-20=0, Resulting Numbers: [10, 0] Generated Node #0,0,0: 45:[10, 0] Operation: 20-20=0 Exploring Operation: 20/20=1, Resulting Numbers: [10, 1] Generated Node #0,0,1: 45:[10, 1] Operation: 20/20=1 Exploring Operation: 20/10=2, Resulting Numbers: [20, 2] Generated Node #0,0,2: 45:[20, 2] Operation: 20/10=2 Exploring Operation: 20-10=10, Resulting Numbers: [20, 10] Generated Node #0,0,3: 45:[20, 10] Operation: 20-10=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[10, 1], Operations: ['85-65=20', '20/20=1'] Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[10, 0], Operations: ['85-65=20', '20-20=0'] Exploring Operation: 10*0=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 10-0=10, Resulting Numbers: [10] 10,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[20, 2], Operations: ['85-65=20', '20/10=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 45:[20, 10], Operations: ['85-65=20', '20-10=10'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,45 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,45 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: 45:[10, 65, 65], Operations: ['85-20=65'] Exploring Operation: 65-10=55, Resulting Numbers: [65, 55] Generated Node #0,3,0: 45:[65, 55] Operation: 65-10=55 Exploring Operation: 65-10=55, Resulting Numbers: [65, 55] Generated Node #0,3,1: 45:[65, 55] Operation: 65-10=55 Exploring Operation: 65/65=1, Resulting Numbers: [10, 1] Generated Node #0,3,2: 45:[10, 1] Operation: 65/65=1 Exploring Operation: 65-65=0, Resulting Numbers: [10, 0] Generated Node #0,3,3: 45:[10, 0] Operation: 65-65=0 Moving to Node #0,2 Current State: 45:[10, 85, 45], Operations: ['65-20=45'] Exploring Operation: 85-10=75, Resulting Numbers: [45, 75] Generated Node #0,2,0: 45:[45, 75] Operation: 85-10=75 Exploring Operation: 10+45=55, Resulting Numbers: [85, 55] Generated Node #0,2,1: 45:[85, 55] Operation: 10+45=55 Exploring Operation: 10+85=95, Resulting Numbers: [45, 95] Generated Node #0,2,2: 45:[45, 95] Operation: 10+85=95 Exploring Operation: 85-45=40, Resulting Numbers: [10, 40] Generated Node #0,2,3: 45:[10, 40] Operation: 85-45=40 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 45:[10, 40], Operations: ['65-20=45', '85-45=40'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,45 unequal: No Solution Exploring Operation: 10*40=400, Resulting Numbers: [400] 400,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[45, 75], Operations: ['65-20=45', '85-10=75'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 45+75=120, Resulting Numbers: [120] 120,45 unequal: No Solution Exploring Operation: 45*75=3375, Resulting Numbers: [3375] 3375,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[85, 55], Operations: ['65-20=45', '10+45=55'] Exploring Operation: 85*55=4675, Resulting Numbers: [4675] 4675,45 unequal: No Solution Exploring Operation: 85-55=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 85+55=140, Resulting Numbers: [140] 140,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 45:[45, 95], Operations: ['65-20=45', '10+85=95'] Exploring Operation: 45*95=4275, Resulting Numbers: [4275] 4275,45 unequal: No Solution Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,45 unequal: No Solution Exploring Operation: 45+95=140, Resulting Numbers: [140] 140,45 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: 45:[20, 65, 75], Operations: ['85-10=75'] Exploring Operation: 65-20=45, Resulting Numbers: [75, 45] Generated Node #0,1,0: 45:[75, 45] Operation: 65-20=45 Exploring Operation: 75-65=10, Resulting Numbers: [20, 10] Generated Node #0,1,1: 45:[20, 10] Operation: 75-65=10 Exploring Operation: 20+65=85, Resulting Numbers: [75, 85] Generated Node #0,1,2: 45:[75, 85] Operation: 20+65=85 Exploring Operation: 75-20=55, Resulting Numbers: [65, 55] Generated Node #0,1,3: 45:[65, 55] Operation: 75-20=55 Moving to Node #0,3,2 Current State: 45:[10, 1], Operations: ['85-20=65', '65/65=1'] Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[10, 0], Operations: ['85-20=65', '65-65=0'] Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 10*0=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 10-0=10, Resulting Numbers: [10] 10,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[20, 10], Operations: ['85-10=75', '75-65=10'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[65, 55], Operations: ['85-20=65', '65-10=55'] Exploring Operation: 65-55=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 65+55=120, Resulting Numbers: [120] 120,45 unequal: No Solution Exploring Operation: 65*55=3575, Resulting Numbers: [3575] 3575,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[75, 45], Operations: ['85-10=75', '65-20=45'] Exploring Operation: 75*45=3375, Resulting Numbers: [3375] 3375,45 unequal: No Solution Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 75+45=120, Resulting Numbers: [120] 120,45 unequal: No Solution Moving to Node #0,3,1 Current State: 45:[65, 55], Operations: ['85-20=65', '65-10=55'] Exploring Operation: 65-55=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 65*55=3575, Resulting Numbers: [3575] 3575,45 unequal: No Solution Exploring Operation: 65+55=120, Resulting Numbers: [120] 120,45 unequal: No Solution Moving to Node #0,1,3 Current State: 45:[65, 55], Operations: ['85-10=75', '75-20=55'] Exploring Operation: 65-55=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 65*55=3575, Resulting Numbers: [3575] 3575,45 unequal: No Solution Exploring Operation: 65+55=120, Resulting Numbers: [120] 120,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[75, 85], Operations: ['85-10=75', '20+65=85'] Exploring Operation: 75*85=6375, Resulting Numbers: [6375] 6375,45 unequal: No Solution Exploring Operation: 85-75=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 75+85=160, Resulting Numbers: [160] 160,45 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 10, 90, 86, 95 ]
100
[ "10*90=900", "95-86=9", "900/9=100" ]
Current State: 100:[10, 90, 86, 95], Operations: [] Exploring Operation: 10*90=900, Resulting Numbers: [86, 95, 900] Generated Node #2: [86, 95, 900] from Operation: 10*90=900 Current State: 100:[86, 95, 900], Operations: ['10*90=900'] Exploring Operation: 95-86=9, Resulting Numbers: [900, 9] Generated Node #3: [900, 9] from Operation: 95-86=9 Current State: 100:[900, 9], Operations: ['10*90=900', '95-86=9'] Exploring Operation: 900/9=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[10, 90, 86, 95], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [10, 95, 4] Generated Node #0,0: 100:[10, 95, 4] Operation: 90-86=4 Exploring Operation: 95-86=9, Resulting Numbers: [10, 90, 9] Generated Node #0,1: 100:[10, 90, 9] Operation: 95-86=9 Exploring Operation: 95-90=5, Resulting Numbers: [10, 86, 5] Generated Node #0,2: 100:[10, 86, 5] Operation: 95-90=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[10, 95, 4], Operations: ['90-86=4'] Exploring Operation: 10+95=105, Resulting Numbers: [4, 105] Generated Node #0,0,0: 100:[4, 105] Operation: 10+95=105 Exploring Operation: 10-4=6, Resulting Numbers: [95, 6] Generated Node #0,0,1: 100:[95, 6] Operation: 10-4=6 Exploring Operation: 95+4=99, Resulting Numbers: [10, 99] Generated Node #0,0,2: 100:[10, 99] Operation: 95+4=99 Moving to Node #0,0,2 Current State: 100:[10, 99], Operations: ['90-86=4', '95+4=99'] Exploring Operation: 99-10=89, Resulting Numbers: [89] 89,100 unequal: No Solution Exploring Operation: 10*99=990, Resulting Numbers: [990] 990,100 unequal: No Solution Exploring Operation: 10+99=109, Resulting Numbers: [109] 109,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[4, 105], Operations: ['90-86=4', '10+95=105'] Exploring Operation: 4*105=420, Resulting Numbers: [420] 420,100 unequal: No Solution Exploring Operation: 105-4=101, Resulting Numbers: [101] 101,100 unequal: No Solution Exploring Operation: 4+105=109, Resulting Numbers: [109] 109,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[95, 6], Operations: ['90-86=4', '10-4=6'] Exploring Operation: 95*6=570, Resulting Numbers: [570] 570,100 unequal: No Solution Exploring Operation: 95+6=101, Resulting Numbers: [101] 101,100 unequal: No Solution Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[10, 90, 9], Operations: ['95-86=9'] Exploring Operation: 90+9=99, Resulting Numbers: [10, 99] Generated Node #0,1,0: 100:[10, 99] Operation: 90+9=99 Exploring Operation: 10+90=100, Resulting Numbers: [9, 100] Generated Node #0,1,1: 100:[9, 100] Operation: 10+90=100 Exploring Operation: 90/9=10, Resulting Numbers: [10, 10] Generated Node #0,1,2: 100:[10, 10] Operation: 90/9=10 Moving to Node #0,1,2 Current State: 100:[10, 10], Operations: ['95-86=9', '90/9=10'] Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[10, 90, 86, 95], Operations: [] Exploring Operation: 95-86=9, Resulting Numbers: [10, 90, 9] Generated Node #0,1: 100:[10, 90, 9] Operation: 95-86=9 Moving to Node #0,1 Current State: 100:[10, 90, 9], Operations: ['95-86=9'] Exploring Operation: 90/9=10, Resulting Numbers: [10, 10] Generated Node #0,1,2: 100:[10, 10] Operation: 90/9=10 Moving to Node #0,1,2 Current State: 100:[10, 10], Operations: ['95-86=9', '90/9=10'] Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 70, 57, 18, 93 ]
72
[ "93-57=36", "36/18=2", "70+2=72" ]
Current State: 72:[70, 57, 18, 93], Operations: [] Exploring Operation: 93-57=36, Resulting Numbers: [70, 18, 36] Generated Node #2: [70, 18, 36] from Operation: 93-57=36 Current State: 72:[70, 18, 36], Operations: ['93-57=36'] Exploring Operation: 36/18=2, Resulting Numbers: [70, 2] Generated Node #3: [70, 2] from Operation: 36/18=2 Current State: 72:[70, 2], Operations: ['93-57=36', '36/18=2'] Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[70, 57, 18, 93], Operations: [] Exploring Operation: 93-57=36, Resulting Numbers: [70, 18, 36] Generated Node #0,0: 72:[70, 18, 36] Operation: 93-57=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[70, 18, 36], Operations: ['93-57=36'] Exploring Operation: 70-36=34, Resulting Numbers: [18, 34] Generated Node #0,0,0: 72:[18, 34] Operation: 70-36=34 Moving to Node #0,0,0 Current State: 72:[18, 34], Operations: ['93-57=36', '70-36=34'] Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 88, 78, 29, 91 ]
12
[ "88-78=10", "29+91=120", "120/10=12" ]
Current State: 12:[88, 78, 29, 91], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [29, 91, 10] Generated Node #2: [29, 91, 10] from Operation: 88-78=10 Current State: 12:[29, 91, 10], Operations: ['88-78=10'] Exploring Operation: 29+91=120, Resulting Numbers: [10, 120] Generated Node #3: [10, 120] from Operation: 29+91=120 Current State: 12:[10, 120], Operations: ['88-78=10', '29+91=120'] Exploring Operation: 120/10=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[88, 78, 29, 91], Operations: [] Exploring Operation: 88-29=59, Resulting Numbers: [78, 91, 59] Generated Node #0,0: 12:[78, 91, 59] Operation: 88-29=59 Exploring Operation: 88-78=10, Resulting Numbers: [29, 91, 10] Generated Node #0,1: 12:[29, 91, 10] Operation: 88-78=10 Exploring Operation: 78-29=49, Resulting Numbers: [88, 91, 49] Generated Node #0,2: 12:[88, 91, 49] Operation: 78-29=49 Exploring Operation: 91-78=13, Resulting Numbers: [88, 29, 13] Generated Node #0,3: 12:[88, 29, 13] Operation: 91-78=13 Exploring Operation: 91-88=3, Resulting Numbers: [78, 29, 3] Generated Node #0,4: 12:[78, 29, 3] Operation: 91-88=3 Moving to Node #0,4 Current State: 12:[78, 29, 3], Operations: ['91-88=3'] Exploring Operation: 78/3=26, Resulting Numbers: [29, 26] Generated Node #0,4,0: 12:[29, 26] Operation: 78/3=26 Exploring Operation: 78-3=75, Resulting Numbers: [29, 75] Generated Node #0,4,1: 12:[29, 75] Operation: 78-3=75 Exploring Operation: 78+3=81, Resulting Numbers: [29, 81] Generated Node #0,4,2: 12:[29, 81] Operation: 78+3=81 Exploring Operation: 29-3=26, Resulting Numbers: [78, 26] Generated Node #0,4,3: 12:[78, 26] Operation: 29-3=26 Exploring Operation: 78-29=49, Resulting Numbers: [3, 49] Generated Node #0,4,4: 12:[3, 49] Operation: 78-29=49 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 12:[29, 26], Operations: ['91-88=3', '78/3=26'] Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,12 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,12 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 #0,4,4 Current State: 12:[3, 49], Operations: ['91-88=3', '78-29=49'] Exploring Operation: 3+49=52, Resulting Numbers: [52] 52,12 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 3*49=147, Resulting Numbers: [147] 147,12 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 #0,4,1 Current State: 12:[29, 75], Operations: ['91-88=3', '78-3=75'] Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 29+75=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 29*75=2175, Resulting Numbers: [2175] 2175,12 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 #0,4,3 Current State: 12:[78, 26], Operations: ['91-88=3', '29-3=26'] Exploring Operation: 78*26=2028, Resulting Numbers: [2028] 2028,12 unequal: No Solution Exploring Operation: 78-26=52, Resulting Numbers: [52] 52,12 unequal: No Solution Exploring Operation: 78+26=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 78/26=3, Resulting Numbers: [3] 3,12 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 #0,4,2 Current State: 12:[29, 81], Operations: ['91-88=3', '78+3=81'] Exploring Operation: 29+81=110, Resulting Numbers: [110] 110,12 unequal: No Solution Exploring Operation: 81-29=52, Resulting Numbers: [52] 52,12 unequal: No Solution Exploring Operation: 29*81=2349, Resulting Numbers: [2349] 2349,12 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: 12:[88, 29, 13], Operations: ['91-78=13'] Exploring Operation: 88+29=117, Resulting Numbers: [13, 117] Generated Node #0,3,0: 12:[13, 117] Operation: 88+29=117 Exploring Operation: 88+13=101, Resulting Numbers: [29, 101] Generated Node #0,3,1: 12:[29, 101] Operation: 88+13=101 Exploring Operation: 88-29=59, Resulting Numbers: [13, 59] Generated Node #0,3,2: 12:[13, 59] Operation: 88-29=59 Exploring Operation: 29-13=16, Resulting Numbers: [88, 16] Generated Node #0,3,3: 12:[88, 16] Operation: 29-13=16 Exploring Operation: 88-13=75, Resulting Numbers: [29, 75] Generated Node #0,3,4: 12:[29, 75] Operation: 88-13=75 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 12:[13, 59], Operations: ['91-78=13', '88-29=59'] Exploring Operation: 13+59=72, Resulting Numbers: [72] 72,12 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 13*59=767, Resulting Numbers: [767] 767,12 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 #0,3,3 Current State: 12:[88, 16], Operations: ['91-78=13', '29-13=16'] Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,12 unequal: No Solution Exploring Operation: 88*16=1408, Resulting Numbers: [1408] 1408,12 unequal: No Solution Exploring Operation: 88+16=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 #0,3,4 Current State: 12:[29, 75], Operations: ['91-78=13', '88-13=75'] Exploring Operation: 29*75=2175, Resulting Numbers: [2175] 2175,12 unequal: No Solution Exploring Operation: 29+75=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,12 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 #0,3,0 Current State: 12:[13, 117], Operations: ['91-78=13', '88+29=117'] Exploring Operation: 117-13=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 117/13=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 13+117=130, Resulting Numbers: [130] 130,12 unequal: No Solution Exploring Operation: 13*117=1521, Resulting Numbers: [1521] 1521,12 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 #0,3,1 Current State: 12:[29, 101], Operations: ['91-78=13', '88+13=101'] Exploring Operation: 29*101=2929, Resulting Numbers: [2929] 2929,12 unequal: No Solution Exploring Operation: 29+101=130, Resulting Numbers: [130] 130,12 unequal: No Solution Exploring Operation: 101-29=72, Resulting Numbers: [72] 72,12 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: 12:[29, 91, 10], Operations: ['88-78=10'] Exploring Operation: 91-29=62, Resulting Numbers: [10, 62] Generated Node #0,1,0: 12:[10, 62] Operation: 91-29=62 Exploring Operation: 29-10=19, Resulting Numbers: [91, 19] Generated Node #0,1,1: 12:[91, 19] Operation: 29-10=19 Exploring Operation: 91-10=81, Resulting Numbers: [29, 81] Generated Node #0,1,2: 12:[29, 81] Operation: 91-10=81 Exploring Operation: 29+10=39, Resulting Numbers: [91, 39] Generated Node #0,1,3: 12:[91, 39] Operation: 29+10=39 Exploring Operation: 91+10=101, Resulting Numbers: [29, 101] Generated Node #0,1,4: 12:[29, 101] Operation: 91+10=101 Moving to Node #0,0 Current State: 12:[78, 91, 59], Operations: ['88-29=59'] Exploring Operation: 78+91=169, Resulting Numbers: [59, 169] Generated Node #0,0,0: 12:[59, 169] Operation: 78+91=169 Exploring Operation: 78+59=137, Resulting Numbers: [91, 137] Generated Node #0,0,1: 12:[91, 137] Operation: 78+59=137 Exploring Operation: 91-59=32, Resulting Numbers: [78, 32] Generated Node #0,0,2: 12:[78, 32] Operation: 91-59=32 Exploring Operation: 78-59=19, Resulting Numbers: [91, 19] Generated Node #0,0,3: 12:[91, 19] Operation: 78-59=19 Exploring Operation: 91-78=13, Resulting Numbers: [59, 13] Generated Node #0,0,4: 12:[59, 13] Operation: 91-78=13 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 12:[59, 13], Operations: ['88-29=59', '91-78=13'] Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,12 unequal: No Solution Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,12 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 #0,0,2 Current State: 12:[78, 32], Operations: ['88-29=59', '91-59=32'] Exploring Operation: 78*32=2496, Resulting Numbers: [2496] 2496,12 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 78+32=110, Resulting Numbers: [110] 110,12 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 #0,0,3 Current State: 12:[91, 19], Operations: ['88-29=59', '78-59=19'] Exploring Operation: 91*19=1729, Resulting Numbers: [1729] 1729,12 unequal: No Solution Exploring Operation: 91-19=72, Resulting Numbers: [72] 72,12 unequal: No Solution Exploring Operation: 91+19=110, Resulting Numbers: [110] 110,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[59, 169], Operations: ['88-29=59', '78+91=169'] Exploring Operation: 59*169=9971, Resulting Numbers: [9971] 9971,12 unequal: No Solution Exploring Operation: 59+169=228, Resulting Numbers: [228] 228,12 unequal: No Solution Exploring Operation: 169-59=110, Resulting Numbers: [110] 110,12 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 #0,0,1 Current State: 12:[91, 137], Operations: ['88-29=59', '78+59=137'] Exploring Operation: 91+137=228, Resulting Numbers: [228] 228,12 unequal: No Solution Exploring Operation: 91*137=12467, Resulting Numbers: [12467] 12467,12 unequal: No Solution Exploring Operation: 137-91=46, Resulting Numbers: [46] 46,12 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: 12:[88, 91, 49], Operations: ['78-29=49'] Exploring Operation: 88+49=137, Resulting Numbers: [91, 137] Generated Node #0,2,0: 12:[91, 137] Operation: 88+49=137 Exploring Operation: 91-49=42, Resulting Numbers: [88, 42] Generated Node #0,2,1: 12:[88, 42] Operation: 91-49=42 Exploring Operation: 91-88=3, Resulting Numbers: [49, 3] Generated Node #0,2,2: 12:[49, 3] Operation: 91-88=3 Exploring Operation: 88-49=39, Resulting Numbers: [91, 39] Generated Node #0,2,3: 12:[91, 39] Operation: 88-49=39 Exploring Operation: 88+91=179, Resulting Numbers: [49, 179] Generated Node #0,2,4: 12:[49, 179] Operation: 88+91=179 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 12:[49, 3], Operations: ['78-29=49', '91-88=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,12 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,12 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,12 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 #0,2,1 Current State: 12:[88, 42], Operations: ['78-29=49', '91-49=42'] Exploring Operation: 88*42=3696, Resulting Numbers: [3696] 3696,12 unequal: No Solution Exploring Operation: 88-42=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 88+42=130, Resulting Numbers: [130] 130,12 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:[91, 39], Operations: ['78-29=49', '88-49=39'] Exploring Operation: 91+39=130, Resulting Numbers: [130] 130,12 unequal: No Solution Exploring Operation: 91*39=3549, Resulting Numbers: [3549] 3549,12 unequal: No Solution Exploring Operation: 91-39=52, Resulting Numbers: [52] 52,12 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 #0,2,0 Current State: 12:[91, 137], Operations: ['78-29=49', '88+49=137'] Exploring Operation: 137-91=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 91+137=228, Resulting Numbers: [228] 228,12 unequal: No Solution Exploring Operation: 91*137=12467, Resulting Numbers: [12467] 12467,12 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 #0,2,4 Current State: 12:[49, 179], Operations: ['78-29=49', '88+91=179'] Exploring Operation: 179-49=130, Resulting Numbers: [130] 130,12 unequal: No Solution Exploring Operation: 49*179=8771, Resulting Numbers: [8771] 8771,12 unequal: No Solution Exploring Operation: 49+179=228, Resulting Numbers: [228] 228,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 12:[10, 62], Operations: ['88-78=10', '91-29=62'] Exploring Operation: 10+62=72, Resulting Numbers: [72] 72,12 unequal: No Solution Exploring Operation: 10*62=620, Resulting Numbers: [620] 620,12 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[29, 81], Operations: ['88-78=10', '91-10=81'] Exploring Operation: 81-29=52, Resulting Numbers: [52] 52,12 unequal: No Solution Exploring Operation: 29*81=2349, Resulting Numbers: [2349] 2349,12 unequal: No Solution Exploring Operation: 29+81=110, Resulting Numbers: [110] 110,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[91, 19], Operations: ['88-78=10', '29-10=19'] Exploring Operation: 91-19=72, Resulting Numbers: [72] 72,12 unequal: No Solution Exploring Operation: 91*19=1729, Resulting Numbers: [1729] 1729,12 unequal: No Solution Exploring Operation: 91+19=110, Resulting Numbers: [110] 110,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[91, 39], Operations: ['88-78=10', '29+10=39'] Exploring Operation: 91+39=130, Resulting Numbers: [130] 130,12 unequal: No Solution Exploring Operation: 91*39=3549, Resulting Numbers: [3549] 3549,12 unequal: No Solution Exploring Operation: 91-39=52, Resulting Numbers: [52] 52,12 unequal: No Solution Moving to Node #0,1,4 Current State: 12:[29, 101], Operations: ['88-78=10', '91+10=101'] Exploring Operation: 29+101=130, Resulting Numbers: [130] 130,12 unequal: No Solution Exploring Operation: 29*101=2929, Resulting Numbers: [2929] 2929,12 unequal: No Solution Exploring Operation: 101-29=72, Resulting Numbers: [72] 72,12 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 20, 55, 10, 50 ]
11
[ "20-10=10", "55*10=550", "550/50=11" ]
Current State: 11:[20, 55, 10, 50], Operations: [] Exploring Operation: 20-10=10, Resulting Numbers: [55, 50, 10] Generated Node #2: [55, 50, 10] from Operation: 20-10=10 Current State: 11:[55, 50, 10], Operations: ['20-10=10'] Exploring Operation: 55*10=550, Resulting Numbers: [50, 550] Generated Node #3: [50, 550] from Operation: 55*10=550 Current State: 11:[50, 550], Operations: ['20-10=10', '55*10=550'] Exploring Operation: 550/50=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[20, 55, 10, 50], Operations: [] Exploring Operation: 55-50=5, Resulting Numbers: [20, 10, 5] Generated Node #0,0: 11:[20, 10, 5] Operation: 55-50=5 Moving to Node #0,0 Current State: 11:[20, 10, 5], Operations: ['55-50=5'] Exploring Operation: 20-5=15, Resulting Numbers: [10, 15] Generated Node #0,0,0: 11:[10, 15] Operation: 20-5=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[10, 15], Operations: ['55-50=5', '20-5=15'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,11 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
[ 1, 35, 34, 70 ]
31
[ "34-1=33", "70/35=2", "33-2=31" ]
Current State: 31:[1, 35, 34, 70], Operations: [] Exploring Operation: 34-1=33, Resulting Numbers: [35, 70, 33] Generated Node #2: [35, 70, 33] from Operation: 34-1=33 Current State: 31:[35, 70, 33], Operations: ['34-1=33'] Exploring Operation: 70/35=2, Resulting Numbers: [33, 2] Generated Node #3: [33, 2] from Operation: 70/35=2 Current State: 31:[33, 2], Operations: ['34-1=33', '70/35=2'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[1, 35, 34, 70], Operations: [] Exploring Operation: 35-1=34, Resulting Numbers: [34, 70, 34] Generated Node #0,0: 31:[34, 70, 34] Operation: 35-1=34 Exploring Operation: 70-35=35, Resulting Numbers: [1, 34, 35] Generated Node #0,1: 31:[1, 34, 35] Operation: 70-35=35 Exploring Operation: 34-1=33, Resulting Numbers: [35, 70, 33] Generated Node #0,2: 31:[35, 70, 33] Operation: 34-1=33 Exploring Operation: 70-34=36, Resulting Numbers: [1, 35, 36] Generated Node #0,3: 31:[1, 35, 36] Operation: 70-34=36 Moving to Node #0,1 Current State: 31:[1, 34, 35], Operations: ['70-35=35'] Exploring Operation: 35-1=34, Resulting Numbers: [34, 34] Generated Node #0,1,0: 31:[34, 34] Operation: 35-1=34 Exploring Operation: 34/1=34, Resulting Numbers: [35, 34] Generated Node #0,1,1: 31:[35, 34] Operation: 34/1=34 Exploring Operation: 1*34=34, Resulting Numbers: [35, 34] Generated Node #0,1,2: 31:[35, 34] Operation: 1*34=34 Exploring Operation: 34-1=33, Resulting Numbers: [35, 33] Generated Node #0,1,3: 31:[35, 33] Operation: 34-1=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[34, 34], Operations: ['70-35=35', '35-1=34'] Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,31 unequal: No Solution Exploring Operation: 34*34=1156, Resulting Numbers: [1156] 1156,31 unequal: No Solution Exploring Operation: 34/34=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,31 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 #0,1,3 Current State: 31:[35, 33], Operations: ['70-35=35', '34-1=33'] Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,31 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,31 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 #0,1,1 Current State: 31:[35, 34], Operations: ['70-35=35', '34/1=34'] Exploring Operation: 35+34=69, Resulting Numbers: [69] 69,31 unequal: No Solution Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 35*34=1190, Resulting Numbers: [1190] 1190,31 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:[35, 34], Operations: ['70-35=35', '1*34=34'] Exploring Operation: 35*34=1190, Resulting Numbers: [1190] 1190,31 unequal: No Solution Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 35+34=69, Resulting Numbers: [69] 69,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 31:[1, 35, 36], Operations: ['70-34=36'] Exploring Operation: 35-1=34, Resulting Numbers: [36, 34] Generated Node #0,3,0: 31:[36, 34] Operation: 35-1=34 Exploring Operation: 36-1=35, Resulting Numbers: [35, 35] Generated Node #0,3,1: 31:[35, 35] Operation: 36-1=35 Exploring Operation: 35/1=35, Resulting Numbers: [36, 35] Generated Node #0,3,2: 31:[36, 35] Operation: 35/1=35 Exploring Operation: 1*35=35, Resulting Numbers: [36, 35] Generated Node #0,3,3: 31:[36, 35] Operation: 1*35=35 Moving to Node #0,2 Current State: 31:[35, 70, 33], Operations: ['34-1=33'] Exploring Operation: 35-33=2, Resulting Numbers: [70, 2] Generated Node #0,2,0: 31:[70, 2] Operation: 35-33=2 Exploring Operation: 70-33=37, Resulting Numbers: [35, 37] Generated Node #0,2,1: 31:[35, 37] Operation: 70-33=37 Exploring Operation: 70/35=2, Resulting Numbers: [33, 2] Generated Node #0,2,2: 31:[33, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [33, 35] Generated Node #0,2,3: 31:[33, 35] Operation: 70-35=35 Moving to Node #0,0 Current State: 31:[34, 70, 34], Operations: ['35-1=34'] Exploring Operation: 34-34=0, Resulting Numbers: [70, 0] Generated Node #0,0,0: 31:[70, 0] Operation: 34-34=0 Exploring Operation: 34/34=1, Resulting Numbers: [70, 1] Generated Node #0,0,1: 31:[70, 1] Operation: 34/34=1 Exploring Operation: 70-34=36, Resulting Numbers: [34, 36] Generated Node #0,0,2: 31:[34, 36] Operation: 70-34=36 Exploring Operation: 70-34=36, Resulting Numbers: [34, 36] Generated Node #0,0,3: 31:[34, 36] Operation: 70-34=36 Moving to Node #0,2,3 Current State: 31:[33, 35], Operations: ['34-1=33', '70-35=35'] Exploring Operation: 33*35=1155, Resulting Numbers: [1155] 1155,31 unequal: No Solution Exploring Operation: 33+35=68, Resulting Numbers: [68] 68,31 unequal: No Solution Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,3,0 Current State: 31:[36, 34], Operations: ['70-34=36', '35-1=34'] Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 36+34=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 36*34=1224, Resulting Numbers: [1224] 1224,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[35, 35], Operations: ['70-34=36', '36-1=35'] Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,31 unequal: No Solution Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,31 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[34, 36], Operations: ['35-1=34', '70-34=36'] Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,31 unequal: No Solution Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[34, 36], Operations: ['35-1=34', '70-34=36'] Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,31 unequal: No Solution Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,31 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[36, 35], Operations: ['70-34=36', '35/1=35'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 36*35=1260, Resulting Numbers: [1260] 1260,31 unequal: No Solution Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[36, 35], Operations: ['70-34=36', '1*35=35'] Exploring Operation: 36*35=1260, Resulting Numbers: [1260] 1260,31 unequal: No Solution Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,31 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[35, 37], Operations: ['34-1=33', '70-33=37'] Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 35*37=1295, Resulting Numbers: [1295] 1295,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[33, 2], Operations: ['34-1=33', '70/35=2'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[1, 35, 34, 70], Operations: [] Exploring Operation: 34-1=33, Resulting Numbers: [35, 70, 33] Generated Node #0,2: 31:[35, 70, 33] Operation: 34-1=33 Moving to Node #0,2 Current State: 31:[35, 70, 33], Operations: ['34-1=33'] Exploring Operation: 70/35=2, Resulting Numbers: [33, 2] Generated Node #0,2,2: 31:[33, 2] Operation: 70/35=2 Moving to Node #0,2,2 Current State: 31:[33, 2], Operations: ['34-1=33', '70/35=2'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.945313
hs_4
sum_heuristic
[ 34, 11, 76, 53 ]
15
[ "53-34=19", "76/19=4", "11+4=15" ]
Current State: 15:[34, 11, 76, 53], Operations: [] Exploring Operation: 53-34=19, Resulting Numbers: [11, 76, 19] Generated Node #2: [11, 76, 19] from Operation: 53-34=19 Current State: 15:[11, 76, 19], Operations: ['53-34=19'] Exploring Operation: 76/19=4, Resulting Numbers: [11, 4] Generated Node #3: [11, 4] from Operation: 76/19=4 Current State: 15:[11, 4], Operations: ['53-34=19', '76/19=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[34, 11, 76, 53], Operations: [] Exploring Operation: 76-53=23, Resulting Numbers: [34, 11, 23] Generated Node #0,0: 15:[34, 11, 23] Operation: 76-53=23 Exploring Operation: 53-34=19, Resulting Numbers: [11, 76, 19] Generated Node #0,1: 15:[11, 76, 19] Operation: 53-34=19 Exploring Operation: 76-34=42, Resulting Numbers: [11, 53, 42] Generated Node #0,2: 15:[11, 53, 42] Operation: 76-34=42 Exploring Operation: 34-11=23, Resulting Numbers: [76, 53, 23] Generated Node #0,3: 15:[76, 53, 23] Operation: 34-11=23 Exploring Operation: 76-11=65, Resulting Numbers: [34, 53, 65] Generated Node #0,4: 15:[34, 53, 65] Operation: 76-11=65 Moving to Node #0,0 Current State: 15:[34, 11, 23], Operations: ['76-53=23'] Exploring Operation: 34+11=45, Resulting Numbers: [23, 45] Generated Node #0,0,0: 15:[23, 45] Operation: 34+11=45 Exploring Operation: 34-23=11, Resulting Numbers: [11, 11] Generated Node #0,0,1: 15:[11, 11] Operation: 34-23=11 Exploring Operation: 23-11=12, Resulting Numbers: [34, 12] Generated Node #0,0,2: 15:[34, 12] Operation: 23-11=12 Exploring Operation: 11+23=34, Resulting Numbers: [34, 34] Generated Node #0,0,3: 15:[34, 34] Operation: 11+23=34 Exploring Operation: 34-11=23, Resulting Numbers: [23, 23] Generated Node #0,0,4: 15:[23, 23] Operation: 34-11=23 Moving to Node #0,2 Current State: 15:[11, 53, 42], Operations: ['76-34=42'] Exploring Operation: 42-11=31, Resulting Numbers: [53, 31] Generated Node #0,2,0: 15:[53, 31] Operation: 42-11=31 Exploring Operation: 11+42=53, Resulting Numbers: [53, 53] Generated Node #0,2,1: 15:[53, 53] Operation: 11+42=53 Exploring Operation: 53-42=11, Resulting Numbers: [11, 11] Generated Node #0,2,2: 15:[11, 11] Operation: 53-42=11 Exploring Operation: 53-11=42, Resulting Numbers: [42, 42] Generated Node #0,2,3: 15:[42, 42] Operation: 53-11=42 Exploring Operation: 11+53=64, Resulting Numbers: [42, 64] Generated Node #0,2,4: 15:[42, 64] Operation: 11+53=64 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[11, 11], Operations: ['76-34=42', '53-42=11'] Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,15 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:[53, 31], Operations: ['76-34=42', '42-11=31'] Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,15 unequal: No Solution Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,15 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:[42, 42], Operations: ['76-34=42', '53-11=42'] Exploring Operation: 42*42=1764, Resulting Numbers: [1764] 1764,15 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,15 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:[53, 53], Operations: ['76-34=42', '11+42=53'] Exploring Operation: 53*53=2809, Resulting Numbers: [2809] 2809,15 unequal: No Solution Exploring Operation: 53-53=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 53/53=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 53+53=106, Resulting Numbers: [106] 106,15 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 #0,2,4 Current State: 15:[42, 64], Operations: ['76-34=42', '11+53=64'] Exploring Operation: 42*64=2688, Resulting Numbers: [2688] 2688,15 unequal: No Solution Exploring Operation: 42+64=106, Resulting Numbers: [106] 106,15 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,15 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: 15:[11, 76, 19], Operations: ['53-34=19'] Exploring Operation: 76/19=4, Resulting Numbers: [11, 4] Generated Node #0,1,0: 15:[11, 4] Operation: 76/19=4 Exploring Operation: 19-11=8, Resulting Numbers: [76, 8] Generated Node #0,1,1: 15:[76, 8] Operation: 19-11=8 Exploring Operation: 76-19=57, Resulting Numbers: [11, 57] Generated Node #0,1,2: 15:[11, 57] Operation: 76-19=57 Exploring Operation: 76-11=65, Resulting Numbers: [19, 65] Generated Node #0,1,3: 15:[19, 65] Operation: 76-11=65 Exploring Operation: 11+76=87, Resulting Numbers: [19, 87] Generated Node #0,1,4: 15:[19, 87] Operation: 11+76=87 Moving to Node #0,3 Current State: 15:[76, 53, 23], Operations: ['34-11=23'] Exploring Operation: 76+53=129, Resulting Numbers: [23, 129] Generated Node #0,3,0: 15:[23, 129] Operation: 76+53=129 Exploring Operation: 76-23=53, Resulting Numbers: [53, 53] Generated Node #0,3,1: 15:[53, 53] Operation: 76-23=53 Exploring Operation: 76+23=99, Resulting Numbers: [53, 99] Generated Node #0,3,2: 15:[53, 99] Operation: 76+23=99 Exploring Operation: 53-23=30, Resulting Numbers: [76, 30] Generated Node #0,3,3: 15:[76, 30] Operation: 53-23=30 Exploring Operation: 76-53=23, Resulting Numbers: [23, 23] Generated Node #0,3,4: 15:[23, 23] Operation: 76-53=23 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 15:[23, 23], Operations: ['34-11=23', '76-53=23'] Exploring Operation: 23*23=529, Resulting Numbers: [529] 529,15 unequal: No Solution Exploring Operation: 23-23=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 23+23=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 23/23=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 #0,3,1 Current State: 15:[53, 53], Operations: ['34-11=23', '76-23=53'] Exploring Operation: 53/53=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 53*53=2809, Resulting Numbers: [2809] 2809,15 unequal: No Solution Exploring Operation: 53-53=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 53+53=106, Resulting Numbers: [106] 106,15 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 #0,3,3 Current State: 15:[76, 30], Operations: ['34-11=23', '53-23=30'] Exploring Operation: 76+30=106, Resulting Numbers: [106] 106,15 unequal: No Solution Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 76*30=2280, Resulting Numbers: [2280] 2280,15 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 #0,3,0 Current State: 15:[23, 129], Operations: ['34-11=23', '76+53=129'] Exploring Operation: 129-23=106, Resulting Numbers: [106] 106,15 unequal: No Solution Exploring Operation: 23*129=2967, Resulting Numbers: [2967] 2967,15 unequal: No Solution Exploring Operation: 23+129=152, Resulting Numbers: [152] 152,15 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 #0,3,2 Current State: 15:[53, 99], Operations: ['34-11=23', '76+23=99'] Exploring Operation: 53+99=152, Resulting Numbers: [152] 152,15 unequal: No Solution Exploring Operation: 99-53=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 53*99=5247, Resulting Numbers: [5247] 5247,15 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: 15:[34, 53, 65], Operations: ['76-11=65'] Exploring Operation: 65-34=31, Resulting Numbers: [53, 31] Generated Node #0,4,0: 15:[53, 31] Operation: 65-34=31 Exploring Operation: 34+65=99, Resulting Numbers: [53, 99] Generated Node #0,4,1: 15:[53, 99] Operation: 34+65=99 Exploring Operation: 53-34=19, Resulting Numbers: [65, 19] Generated Node #0,4,2: 15:[65, 19] Operation: 53-34=19 Exploring Operation: 65-53=12, Resulting Numbers: [34, 12] Generated Node #0,4,3: 15:[34, 12] Operation: 65-53=12 Exploring Operation: 34+53=87, Resulting Numbers: [65, 87] Generated Node #0,4,4: 15:[65, 87] Operation: 34+53=87 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 15:[34, 12], Operations: ['76-11=65', '65-53=12'] Exploring Operation: 34*12=408, Resulting Numbers: [408] 408,15 unequal: No Solution Exploring Operation: 34+12=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,15 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:[53, 31], Operations: ['76-11=65', '65-34=31'] Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,15 unequal: No Solution Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,15 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 #0,4,2 Current State: 15:[65, 19], Operations: ['76-11=65', '53-34=19'] Exploring Operation: 65*19=1235, Resulting Numbers: [1235] 1235,15 unequal: No Solution Exploring Operation: 65+19=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,15 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:[53, 99], Operations: ['76-11=65', '34+65=99'] Exploring Operation: 99-53=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 53+99=152, Resulting Numbers: [152] 152,15 unequal: No Solution Exploring Operation: 53*99=5247, Resulting Numbers: [5247] 5247,15 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:[65, 87], Operations: ['76-11=65', '34+53=87'] Exploring Operation: 65*87=5655, Resulting Numbers: [5655] 5655,15 unequal: No Solution Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 65+87=152, Resulting Numbers: [152] 152,15 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: 15:[11, 4], Operations: ['53-34=19', '76/19=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,15 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[34, 11, 76, 53], Operations: [] Exploring Operation: 53-34=19, Resulting Numbers: [11, 76, 19] Generated Node #0,1: 15:[11, 76, 19] Operation: 53-34=19 Moving to Node #0,1 Current State: 15:[11, 76, 19], Operations: ['53-34=19'] Exploring Operation: 76/19=4, Resulting Numbers: [11, 4] Generated Node #0,1,0: 15:[11, 4] Operation: 76/19=4 Moving to Node #0,1,0 Current State: 15:[11, 4], Operations: ['53-34=19', '76/19=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
0.924479
hs_5
sum_heuristic
[ 58, 19, 56, 26 ]
14
[ "58-56=2", "26-19=7", "2*7=14" ]
Current State: 14:[58, 19, 56, 26], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [19, 26, 2] Generated Node #2: [19, 26, 2] from Operation: 58-56=2 Current State: 14:[19, 26, 2], Operations: ['58-56=2'] Exploring Operation: 26-19=7, Resulting Numbers: [2, 7] Generated Node #3: [2, 7] from Operation: 26-19=7 Current State: 14:[2, 7], Operations: ['58-56=2', '26-19=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[58, 19, 56, 26], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [19, 26, 2] Generated Node #0,0: 14:[19, 26, 2] Operation: 58-56=2 Exploring Operation: 58-26=32, Resulting Numbers: [19, 56, 32] Generated Node #0,1: 14:[19, 56, 32] Operation: 58-26=32 Moving to Node #0,0 Current State: 14:[19, 26, 2], Operations: ['58-56=2'] Exploring Operation: 26-19=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 14:[2, 7] Operation: 26-19=7 Exploring Operation: 26/2=13, Resulting Numbers: [19, 13] Generated Node #0,0,1: 14:[19, 13] Operation: 26/2=13 Moving to Node #0,1 Current State: 14:[19, 56, 32], Operations: ['58-26=32'] Exploring Operation: 56-32=24, Resulting Numbers: [19, 24] Generated Node #0,1,0: 14:[19, 24] Operation: 56-32=24 Exploring Operation: 56-19=37, Resulting Numbers: [32, 37] Generated Node #0,1,1: 14:[32, 37] Operation: 56-19=37 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[19, 24], Operations: ['58-26=32', '56-32=24'] Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,14 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:[32, 37], Operations: ['58-26=32', '56-19=37'] Exploring Operation: 32+37=69, Resulting Numbers: [69] 69,14 unequal: No Solution Exploring Operation: 37-32=5, Resulting Numbers: [5] 5,14 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: 14:[2, 7], Operations: ['58-56=2', '26-19=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[58, 19, 56, 26], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [19, 26, 2] Generated Node #0,0: 14:[19, 26, 2] Operation: 58-56=2 Moving to Node #0,0 Current State: 14:[19, 26, 2], Operations: ['58-56=2'] Exploring Operation: 26-19=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 14:[2, 7] Operation: 26-19=7 Moving to Node #0,0,0 Current State: 14:[2, 7], Operations: ['58-56=2', '26-19=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 20, 24, 11, 6 ]
78
[ "20-11=9", "6*9=54", "24+54=78" ]
Current State: 78:[20, 24, 11, 6], Operations: [] Exploring Operation: 20-11=9, Resulting Numbers: [24, 6, 9] Generated Node #2: [24, 6, 9] from Operation: 20-11=9 Current State: 78:[24, 6, 9], Operations: ['20-11=9'] Exploring Operation: 6*9=54, Resulting Numbers: [24, 54] Generated Node #3: [24, 54] from Operation: 6*9=54 Current State: 78:[24, 54], Operations: ['20-11=9', '6*9=54'] Exploring Operation: 24+54=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[20, 24, 11, 6], Operations: [] Exploring Operation: 24-20=4, Resulting Numbers: [11, 6, 4] Generated Node #0,0: 78:[11, 6, 4] Operation: 24-20=4 Exploring Operation: 20+6=26, Resulting Numbers: [24, 11, 26] Generated Node #0,1: 78:[24, 11, 26] Operation: 20+6=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[11, 6, 4], Operations: ['24-20=4'] Exploring Operation: 11-4=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 78:[6, 7] Operation: 11-4=7 Exploring Operation: 11-6=5, Resulting Numbers: [4, 5] Generated Node #0,0,1: 78:[4, 5] Operation: 11-6=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[6, 7], Operations: ['24-20=4', '11-4=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,78 unequal: No Solution No 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: 78:[4, 5], Operations: ['24-20=4', '11-6=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,78 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: 78:[24, 11, 26], Operations: ['20+6=26'] Exploring Operation: 24-11=13, Resulting Numbers: [26, 13] Generated Node #0,1,0: 78:[26, 13] Operation: 24-11=13 Exploring Operation: 26-24=2, Resulting Numbers: [11, 2] Generated Node #0,1,1: 78:[11, 2] Operation: 26-24=2 Moving to Node #0,1,0 Current State: 78:[26, 13], Operations: ['20+6=26', '24-11=13'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 26+13=39, Resulting Numbers: [39] 39,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[11, 2], Operations: ['20+6=26', '26-24=2'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,78 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,78 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
[ 74, 76, 94, 75 ]
96
[ "74+76=150", "150/75=2", "94+2=96" ]
Current State: 96:[74, 76, 94, 75], Operations: [] Exploring Operation: 74+76=150, Resulting Numbers: [94, 75, 150] Generated Node #2: [94, 75, 150] from Operation: 74+76=150 Current State: 96:[94, 75, 150], Operations: ['74+76=150'] Exploring Operation: 150/75=2, Resulting Numbers: [94, 2] Generated Node #3: [94, 2] from Operation: 150/75=2 Current State: 96:[94, 2], Operations: ['74+76=150', '150/75=2'] Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[74, 76, 94, 75], Operations: [] Exploring Operation: 75-74=1, Resulting Numbers: [76, 94, 1] Generated Node #0,0: 96:[76, 94, 1] Operation: 75-74=1 Exploring Operation: 76-75=1, Resulting Numbers: [74, 94, 1] Generated Node #0,1: 96:[74, 94, 1] Operation: 76-75=1 Exploring Operation: 76-74=2, Resulting Numbers: [94, 75, 2] Generated Node #0,2: 96:[94, 75, 2] Operation: 76-74=2 Moving to Node #0,0 Current State: 96:[76, 94, 1], Operations: ['75-74=1'] Exploring Operation: 94-76=18, Resulting Numbers: [1, 18] Generated Node #0,0,0: 96:[1, 18] Operation: 94-76=18 Exploring Operation: 76+1=77, Resulting Numbers: [94, 77] Generated Node #0,0,1: 96:[94, 77] Operation: 76+1=77 Exploring Operation: 94+1=95, Resulting Numbers: [76, 95] Generated Node #0,0,2: 96:[76, 95] Operation: 94+1=95 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[1, 18], Operations: ['75-74=1', '94-76=18'] Exploring Operation: 1*18=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 96:[94, 77], Operations: ['75-74=1', '76+1=77'] Exploring Operation: 94*77=7238, Resulting Numbers: [7238] 7238,96 unequal: No Solution Exploring Operation: 94+77=171, Resulting Numbers: [171] 171,96 unequal: No Solution Exploring Operation: 94-77=17, Resulting Numbers: [17] 17,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 96:[76, 95], Operations: ['75-74=1', '94+1=95'] Exploring Operation: 76*95=7220, Resulting Numbers: [7220] 7220,96 unequal: No Solution Exploring Operation: 76+95=171, Resulting Numbers: [171] 171,96 unequal: No Solution Exploring Operation: 95-76=19, Resulting Numbers: [19] 19,96 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: 96:[94, 75, 2], Operations: ['76-74=2'] Exploring Operation: 94+2=96, Resulting Numbers: [75, 96] Generated Node #0,2,0: 96:[75, 96] Operation: 94+2=96 Exploring Operation: 94-75=19, Resulting Numbers: [2, 19] Generated Node #0,2,1: 96:[2, 19] Operation: 94-75=19 Exploring Operation: 75+2=77, Resulting Numbers: [94, 77] Generated Node #0,2,2: 96:[94, 77] Operation: 75+2=77 Moving to Node #0,1 Current State: 96:[74, 94, 1], Operations: ['76-75=1'] Exploring Operation: 74+1=75, Resulting Numbers: [94, 75] Generated Node #0,1,0: 96:[94, 75] Operation: 74+1=75 Exploring Operation: 94+1=95, Resulting Numbers: [74, 95] Generated Node #0,1,1: 96:[74, 95] Operation: 94+1=95 Exploring Operation: 94-74=20, Resulting Numbers: [1, 20] Generated Node #0,1,2: 96:[1, 20] Operation: 94-74=20 Moving to Node #0,2,1 Current State: 96:[2, 19], Operations: ['76-74=2', '94-75=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,96 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[1, 20], Operations: ['76-75=1', '94-74=20'] Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[94, 77], Operations: ['76-74=2', '75+2=77'] Exploring Operation: 94+77=171, Resulting Numbers: [171] 171,96 unequal: No Solution Exploring Operation: 94*77=7238, Resulting Numbers: [7238] 7238,96 unequal: No Solution Exploring Operation: 94-77=17, Resulting Numbers: [17] 17,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[75, 96], Operations: ['76-74=2', '94+2=96'] Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 75+96=171, Resulting Numbers: [171] 171,96 unequal: No Solution Exploring Operation: 75*96=7200, Resulting Numbers: [7200] 7200,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[74, 95], Operations: ['76-75=1', '94+1=95'] Exploring Operation: 74+95=169, Resulting Numbers: [169] 169,96 unequal: No Solution Exploring Operation: 95-74=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 74*95=7030, Resulting Numbers: [7030] 7030,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[94, 75], Operations: ['76-75=1', '74+1=75'] Exploring Operation: 94-75=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 94*75=7050, Resulting Numbers: [7050] 7050,96 unequal: No Solution Exploring Operation: 94+75=169, Resulting Numbers: [169] 169,96 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 25, 18, 86, 94 ]
92
[ "25+18=43", "86/43=2", "94-2=92" ]
Current State: 92:[25, 18, 86, 94], Operations: [] Exploring Operation: 25+18=43, Resulting Numbers: [86, 94, 43] Generated Node #2: [86, 94, 43] from Operation: 25+18=43 Current State: 92:[86, 94, 43], Operations: ['25+18=43'] Exploring Operation: 86/43=2, Resulting Numbers: [94, 2] Generated Node #3: [94, 2] from Operation: 86/43=2 Current State: 92:[94, 2], Operations: ['25+18=43', '86/43=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[25, 18, 86, 94], Operations: [] Exploring Operation: 25+18=43, Resulting Numbers: [86, 94, 43] Generated Node #0,0: 92:[86, 94, 43] Operation: 25+18=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[86, 94, 43], Operations: ['25+18=43'] Exploring Operation: 86/43=2, Resulting Numbers: [94, 2] Generated Node #0,0,0: 92:[94, 2] Operation: 86/43=2 Moving to Node #0,0,0 Current State: 92:[94, 2], Operations: ['25+18=43', '86/43=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[25, 18, 86, 94], Operations: [] Exploring Operation: 25+18=43, Resulting Numbers: [86, 94, 43] Generated Node #0,0: 92:[86, 94, 43] Operation: 25+18=43 Moving to Node #0,0 Current State: 92:[86, 94, 43], Operations: ['25+18=43'] Exploring Operation: 86/43=2, Resulting Numbers: [94, 2] Generated Node #0,0,0: 92:[94, 2] Operation: 86/43=2 Moving to Node #0,0,0 Current State: 92:[94, 2], Operations: ['25+18=43', '86/43=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 7, 16, 29, 83 ]
45
[ "16-7=9", "83-29=54", "54-9=45" ]
Current State: 45:[7, 16, 29, 83], Operations: [] Exploring Operation: 16-7=9, Resulting Numbers: [29, 83, 9] Generated Node #2: [29, 83, 9] from Operation: 16-7=9 Current State: 45:[29, 83, 9], Operations: ['16-7=9'] Exploring Operation: 83-29=54, Resulting Numbers: [9, 54] Generated Node #3: [9, 54] from Operation: 83-29=54 Current State: 45:[9, 54], Operations: ['16-7=9', '83-29=54'] Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[7, 16, 29, 83], Operations: [] Exploring Operation: 83-29=54, Resulting Numbers: [7, 16, 54] Generated Node #0,0: 45:[7, 16, 54] Operation: 83-29=54 Moving to Node #0,0 Current State: 45:[7, 16, 54], Operations: ['83-29=54'] Exploring Operation: 54-7=47, Resulting Numbers: [16, 47] Generated Node #0,0,0: 45:[16, 47] Operation: 54-7=47 Moving to Node #0,0,0 Current State: 45:[16, 47], Operations: ['83-29=54', '54-7=47'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,45 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 39, 43, 40, 76 ]
59
[ "43-39=4", "76/4=19", "40+19=59" ]
Current State: 59:[39, 43, 40, 76], Operations: [] Exploring Operation: 43-39=4, Resulting Numbers: [40, 76, 4] Generated Node #2: [40, 76, 4] from Operation: 43-39=4 Current State: 59:[40, 76, 4], Operations: ['43-39=4'] Exploring Operation: 76/4=19, Resulting Numbers: [40, 19] Generated Node #3: [40, 19] from Operation: 76/4=19 Current State: 59:[40, 19], Operations: ['43-39=4', '76/4=19'] Exploring Operation: 40+19=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[39, 43, 40, 76], Operations: [] Exploring Operation: 76-39=37, Resulting Numbers: [43, 40, 37] Generated Node #0,0: 59:[43, 40, 37] Operation: 76-39=37 Exploring Operation: 39+40=79, Resulting Numbers: [43, 76, 79] Generated Node #0,1: 59:[43, 76, 79] Operation: 39+40=79 Moving to Node #0,1 Current State: 59:[43, 76, 79], Operations: ['39+40=79'] Exploring Operation: 79-43=36, Resulting Numbers: [76, 36] Generated Node #0,1,0: 59:[76, 36] Operation: 79-43=36 Exploring Operation: 76-43=33, Resulting Numbers: [79, 33] Generated Node #0,1,1: 59:[79, 33] Operation: 76-43=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[76, 36], Operations: ['39+40=79', '79-43=36'] Exploring Operation: 76+36=112, Resulting Numbers: [112] 112,59 unequal: No Solution Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,59 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 #0,1,1 Current State: 59:[79, 33], Operations: ['39+40=79', '76-43=33'] Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 79+33=112, Resulting Numbers: [112] 112,59 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: 59:[43, 40, 37], Operations: ['76-39=37'] Exploring Operation: 40+37=77, Resulting Numbers: [43, 77] Generated Node #0,0,0: 59:[43, 77] Operation: 40+37=77 Exploring Operation: 43+37=80, Resulting Numbers: [40, 80] Generated Node #0,0,1: 59:[40, 80] Operation: 43+37=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[43, 77], Operations: ['76-39=37', '40+37=77'] Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,59 unequal: No Solution Exploring Operation: 43+77=120, Resulting Numbers: [120] 120,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[40, 80], Operations: ['76-39=37', '43+37=80'] Exploring Operation: 80/40=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 80-40=40, Resulting Numbers: [40] 40,59 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
[ 26, 79, 36, 20 ]
49
[ "26+79=105", "36+20=56", "105-56=49" ]
Current State: 49:[26, 79, 36, 20], Operations: [] Exploring Operation: 26+79=105, Resulting Numbers: [36, 20, 105] Generated Node #2: [36, 20, 105] from Operation: 26+79=105 Current State: 49:[36, 20, 105], Operations: ['26+79=105'] Exploring Operation: 36+20=56, Resulting Numbers: [105, 56] Generated Node #3: [105, 56] from Operation: 36+20=56 Current State: 49:[105, 56], Operations: ['26+79=105', '36+20=56'] Exploring Operation: 105-56=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[26, 79, 36, 20], Operations: [] Exploring Operation: 79-20=59, Resulting Numbers: [26, 36, 59] Generated Node #0,0: 49:[26, 36, 59] Operation: 79-20=59 Exploring Operation: 79-26=53, Resulting Numbers: [36, 20, 53] Generated Node #0,1: 49:[36, 20, 53] Operation: 79-26=53 Exploring Operation: 79-36=43, Resulting Numbers: [26, 20, 43] Generated Node #0,2: 49:[26, 20, 43] Operation: 79-36=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[36, 20, 53], Operations: ['79-26=53'] Exploring Operation: 36+20=56, Resulting Numbers: [53, 56] Generated Node #0,1,0: 49:[53, 56] Operation: 36+20=56 Exploring Operation: 36-20=16, Resulting Numbers: [53, 16] Generated Node #0,1,1: 49:[53, 16] Operation: 36-20=16 Exploring Operation: 53-36=17, Resulting Numbers: [20, 17] Generated Node #0,1,2: 49:[20, 17] Operation: 53-36=17 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[53, 56], Operations: ['79-26=53', '36+20=56'] Exploring Operation: 53*56=2968, Resulting Numbers: [2968] 2968,49 unequal: No Solution Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 53+56=109, Resulting Numbers: [109] 109,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[53, 16], Operations: ['79-26=53', '36-20=16'] Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 53*16=848, Resulting Numbers: [848] 848,49 unequal: No Solution Exploring Operation: 53+16=69, Resulting Numbers: [69] 69,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 49:[20, 17], Operations: ['79-26=53', '53-36=17'] Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,49 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[26, 20, 43], Operations: ['79-36=43'] Exploring Operation: 26-20=6, Resulting Numbers: [43, 6] Generated Node #0,2,0: 49:[43, 6] Operation: 26-20=6 Exploring Operation: 26+20=46, Resulting Numbers: [43, 46] Generated Node #0,2,1: 49:[43, 46] Operation: 26+20=46 Exploring Operation: 43-26=17, Resulting Numbers: [20, 17] Generated Node #0,2,2: 49:[20, 17] Operation: 43-26=17 Moving to Node #0,2,0 Current State: 49:[43, 6], Operations: ['79-36=43', '26-20=6'] Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[26, 79, 36, 20], Operations: [] Exploring Operation: 79-36=43, Resulting Numbers: [26, 20, 43] Generated Node #0,2: 49:[26, 20, 43] Operation: 79-36=43 Moving to Node #0,2 Current State: 49:[26, 20, 43], Operations: ['79-36=43'] Exploring Operation: 26-20=6, Resulting Numbers: [43, 6] Generated Node #0,2,0: 49:[43, 6] Operation: 26-20=6 Moving to Node #0,2,0 Current State: 49:[43, 6], Operations: ['79-36=43', '26-20=6'] Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 47, 64, 73, 90 ]
52
[ "47+64=111", "73+90=163", "163-111=52" ]
Current State: 52:[47, 64, 73, 90], Operations: [] Exploring Operation: 47+64=111, Resulting Numbers: [73, 90, 111] Generated Node #2: [73, 90, 111] from Operation: 47+64=111 Current State: 52:[73, 90, 111], Operations: ['47+64=111'] Exploring Operation: 73+90=163, Resulting Numbers: [111, 163] Generated Node #3: [111, 163] from Operation: 73+90=163 Current State: 52:[111, 163], Operations: ['47+64=111', '73+90=163'] Exploring Operation: 163-111=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[47, 64, 73, 90], Operations: [] Exploring Operation: 90-73=17, Resulting Numbers: [47, 64, 17] Generated Node #0,0: 52:[47, 64, 17] Operation: 90-73=17 Exploring Operation: 90-64=26, Resulting Numbers: [47, 73, 26] Generated Node #0,1: 52:[47, 73, 26] Operation: 90-64=26 Moving to Node #0,0 Current State: 52:[47, 64, 17], Operations: ['90-73=17'] Exploring Operation: 64-47=17, Resulting Numbers: [17, 17] Generated Node #0,0,0: 52:[17, 17] Operation: 64-47=17 Exploring Operation: 64-17=47, Resulting Numbers: [47, 47] Generated Node #0,0,1: 52:[47, 47] Operation: 64-17=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[17, 17], Operations: ['90-73=17', '64-47=17'] Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,52 unequal: No Solution Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[47, 47], Operations: ['90-73=17', '64-17=47'] Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 47-47=0, Resulting Numbers: [0] 0,52 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: 52:[47, 73, 26], Operations: ['90-64=26'] Exploring Operation: 73-47=26, Resulting Numbers: [26, 26] Generated Node #0,1,0: 52:[26, 26] Operation: 73-47=26 Exploring Operation: 73-26=47, Resulting Numbers: [47, 47] Generated Node #0,1,1: 52:[47, 47] Operation: 73-26=47 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 52:[26, 26], Operations: ['90-64=26', '73-47=26'] Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[47, 64, 73, 90], Operations: [] Exploring Operation: 90-64=26, Resulting Numbers: [47, 73, 26] Generated Node #0,1: 52:[47, 73, 26] Operation: 90-64=26 Moving to Node #0,1 Current State: 52:[47, 73, 26], Operations: ['90-64=26'] Exploring Operation: 73-47=26, Resulting Numbers: [26, 26] Generated Node #0,1,0: 52:[26, 26] Operation: 73-47=26 Moving to Node #0,1,0 Current State: 52:[26, 26], Operations: ['90-64=26', '73-47=26'] Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 35, 89, 42, 71 ]
83
[ "89-35=54", "71-42=29", "54+29=83" ]
Current State: 83:[35, 89, 42, 71], Operations: [] Exploring Operation: 89-35=54, Resulting Numbers: [42, 71, 54] Generated Node #2: [42, 71, 54] from Operation: 89-35=54 Current State: 83:[42, 71, 54], Operations: ['89-35=54'] Exploring Operation: 71-42=29, Resulting Numbers: [54, 29] Generated Node #3: [54, 29] from Operation: 71-42=29 Current State: 83:[54, 29], Operations: ['89-35=54', '71-42=29'] Exploring Operation: 54+29=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[35, 89, 42, 71], Operations: [] Exploring Operation: 35+71=106, Resulting Numbers: [89, 42, 106] Generated Node #0,0: 83:[89, 42, 106] Operation: 35+71=106 Exploring Operation: 35+42=77, Resulting Numbers: [89, 71, 77] Generated Node #0,1: 83:[89, 71, 77] Operation: 35+42=77 Exploring Operation: 89-35=54, Resulting Numbers: [42, 71, 54] Generated Node #0,2: 83:[42, 71, 54] Operation: 89-35=54 Moving to Node #0,1 Current State: 83:[89, 71, 77], Operations: ['35+42=77'] Exploring Operation: 89+71=160, Resulting Numbers: [77, 160] Generated Node #0,1,0: 83:[77, 160] Operation: 89+71=160 Exploring Operation: 71+77=148, Resulting Numbers: [89, 148] Generated Node #0,1,1: 83:[89, 148] Operation: 71+77=148 Exploring Operation: 89-71=18, Resulting Numbers: [77, 18] Generated Node #0,1,2: 83:[77, 18] Operation: 89-71=18 Moving to Node #0,0 Current State: 83:[89, 42, 106], Operations: ['35+71=106'] Exploring Operation: 89+42=131, Resulting Numbers: [106, 131] Generated Node #0,0,0: 83:[106, 131] Operation: 89+42=131 Exploring Operation: 89-42=47, Resulting Numbers: [106, 47] Generated Node #0,0,1: 83:[106, 47] Operation: 89-42=47 Exploring Operation: 106-42=64, Resulting Numbers: [89, 64] Generated Node #0,0,2: 83:[89, 64] Operation: 106-42=64 Moving to Node #0,2 Current State: 83:[42, 71, 54], Operations: ['89-35=54'] Exploring Operation: 71-42=29, Resulting Numbers: [54, 29] Generated Node #0,2,0: 83:[54, 29] Operation: 71-42=29 Exploring Operation: 42+54=96, Resulting Numbers: [71, 96] Generated Node #0,2,1: 83:[71, 96] Operation: 42+54=96 Exploring Operation: 42+71=113, Resulting Numbers: [54, 113] Generated Node #0,2,2: 83:[54, 113] Operation: 42+71=113 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[71, 96], Operations: ['89-35=54', '42+54=96'] Exploring Operation: 71+96=167, Resulting Numbers: [167] 167,83 unequal: No Solution Exploring Operation: 96-71=25, Resulting Numbers: [25] 25,83 unequal: No Solution Exploring Operation: 71*96=6816, Resulting Numbers: [6816] 6816,83 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 #0,2,2 Current State: 83:[54, 113], Operations: ['89-35=54', '42+71=113'] Exploring Operation: 54*113=6102, Resulting Numbers: [6102] 6102,83 unequal: No Solution Exploring Operation: 54+113=167, Resulting Numbers: [167] 167,83 unequal: No Solution Exploring Operation: 113-54=59, Resulting Numbers: [59] 59,83 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 #0,2,0 Current State: 83:[54, 29], Operations: ['89-35=54', '71-42=29'] Exploring Operation: 54+29=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[35, 89, 42, 71], Operations: [] Exploring Operation: 89-35=54, Resulting Numbers: [42, 71, 54] Generated Node #0,2: 83:[42, 71, 54] Operation: 89-35=54 Moving to Node #0,2 Current State: 83:[42, 71, 54], Operations: ['89-35=54'] Exploring Operation: 71-42=29, Resulting Numbers: [54, 29] Generated Node #0,2,0: 83:[54, 29] Operation: 71-42=29 Moving to Node #0,2,0 Current State: 83:[54, 29], Operations: ['89-35=54', '71-42=29'] Exploring Operation: 54+29=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 24, 98, 12, 84 ]
93
[ "84-24=60", "60/12=5", "98-5=93" ]
Current State: 93:[24, 98, 12, 84], Operations: [] Exploring Operation: 84-24=60, Resulting Numbers: [98, 12, 60] Generated Node #2: [98, 12, 60] from Operation: 84-24=60 Current State: 93:[98, 12, 60], Operations: ['84-24=60'] Exploring Operation: 60/12=5, Resulting Numbers: [98, 5] Generated Node #3: [98, 5] from Operation: 60/12=5 Current State: 93:[98, 5], Operations: ['84-24=60', '60/12=5'] Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[24, 98, 12, 84], Operations: [] Exploring Operation: 24+12=36, Resulting Numbers: [98, 84, 36] Generated Node #0,0: 93:[98, 84, 36] Operation: 24+12=36 Exploring Operation: 24/12=2, Resulting Numbers: [98, 84, 2] Generated Node #0,1: 93:[98, 84, 2] Operation: 24/12=2 Exploring Operation: 12+84=96, Resulting Numbers: [24, 98, 96] Generated Node #0,2: 93:[24, 98, 96] Operation: 12+84=96 Exploring Operation: 84/12=7, Resulting Numbers: [24, 98, 7] Generated Node #0,3: 93:[24, 98, 7] Operation: 84/12=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[98, 84, 2], Operations: ['24/12=2'] Exploring Operation: 98+2=100, Resulting Numbers: [84, 100] Generated Node #0,1,0: 93:[84, 100] Operation: 98+2=100 Exploring Operation: 84+2=86, Resulting Numbers: [98, 86] Generated Node #0,1,1: 93:[98, 86] Operation: 84+2=86 Exploring Operation: 98-2=96, Resulting Numbers: [84, 96] Generated Node #0,1,2: 93:[84, 96] Operation: 98-2=96 Exploring Operation: 98-84=14, Resulting Numbers: [2, 14] Generated Node #0,1,3: 93:[2, 14] Operation: 98-84=14 Moving to Node #0,1,1 Current State: 93:[98, 86], Operations: ['24/12=2', '84+2=86'] Exploring Operation: 98*86=8428, Resulting Numbers: [8428] 8428,93 unequal: No Solution Exploring Operation: 98-86=12, Resulting Numbers: [12] 12,93 unequal: No Solution Exploring Operation: 98+86=184, Resulting Numbers: [184] 184,93 unequal: No Solution Moving to Node #0,1,3 Current State: 93:[2, 14], Operations: ['24/12=2', '98-84=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,93 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,93 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[84, 96], Operations: ['24/12=2', '98-2=96'] Exploring Operation: 84+96=180, Resulting Numbers: [180] 180,93 unequal: No Solution Exploring Operation: 84*96=8064, Resulting Numbers: [8064] 8064,93 unequal: No Solution Exploring Operation: 96-84=12, Resulting Numbers: [12] 12,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[84, 100], Operations: ['24/12=2', '98+2=100'] Exploring Operation: 84+100=184, Resulting Numbers: [184] 184,93 unequal: No Solution Exploring Operation: 100-84=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 84*100=8400, Resulting Numbers: [8400] 8400,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[24, 98, 96], Operations: ['12+84=96'] Exploring Operation: 96-24=72, Resulting Numbers: [98, 72] Generated Node #0,2,0: 93:[98, 72] Operation: 96-24=72 Exploring Operation: 98-24=74, Resulting Numbers: [96, 74] Generated Node #0,2,1: 93:[96, 74] Operation: 98-24=74 Exploring Operation: 96/24=4, Resulting Numbers: [98, 4] Generated Node #0,2,2: 93:[98, 4] Operation: 96/24=4 Exploring Operation: 98-96=2, Resulting Numbers: [24, 2] Generated Node #0,2,3: 93:[24, 2] Operation: 98-96=2 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 93:[98, 4], Operations: ['12+84=96', '96/24=4'] Exploring Operation: 98+4=102, Resulting Numbers: [102] 102,93 unequal: No Solution Exploring Operation: 98*4=392, Resulting Numbers: [392] 392,93 unequal: No Solution Exploring Operation: 98-4=94, Resulting Numbers: [94] 94,93 unequal: No Solution No 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: 93:[24, 2], Operations: ['12+84=96', '98-96=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,93 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,93 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,93 unequal: No Solution No 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: 93:[96, 74], Operations: ['12+84=96', '98-24=74'] Exploring Operation: 96*74=7104, Resulting Numbers: [7104] 7104,93 unequal: No Solution Exploring Operation: 96+74=170, Resulting Numbers: [170] 170,93 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,93 unequal: No Solution No 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: 93:[98, 72], Operations: ['12+84=96', '96-24=72'] Exploring Operation: 98+72=170, Resulting Numbers: [170] 170,93 unequal: No Solution Exploring Operation: 98-72=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 98*72=7056, Resulting Numbers: [7056] 7056,93 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: 93:[24, 98, 7], Operations: ['84/12=7'] Exploring Operation: 24-7=17, Resulting Numbers: [98, 17] Generated Node #0,3,0: 93:[98, 17] Operation: 24-7=17 Exploring Operation: 98-7=91, Resulting Numbers: [24, 91] Generated Node #0,3,1: 93:[24, 91] Operation: 98-7=91 Exploring Operation: 24+7=31, Resulting Numbers: [98, 31] Generated Node #0,3,2: 93:[98, 31] Operation: 24+7=31 Exploring Operation: 98/7=14, Resulting Numbers: [24, 14] Generated Node #0,3,3: 93:[24, 14] Operation: 98/7=14 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 93:[98, 31], Operations: ['84/12=7', '24+7=31'] Exploring Operation: 98-31=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 98*31=3038, Resulting Numbers: [3038] 3038,93 unequal: No Solution Exploring Operation: 98+31=129, Resulting Numbers: [129] 129,93 unequal: No Solution No 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: 93:[24, 91], Operations: ['84/12=7', '98-7=91'] Exploring Operation: 24+91=115, Resulting Numbers: [115] 115,93 unequal: No Solution Exploring Operation: 91-24=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 24*91=2184, Resulting Numbers: [2184] 2184,93 unequal: No Solution No 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: 93:[24, 14], Operations: ['84/12=7', '98/7=14'] Exploring Operation: 24*14=336, Resulting Numbers: [336] 336,93 unequal: No Solution Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,93 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,93 unequal: No Solution No 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: 93:[98, 17], Operations: ['84/12=7', '24-7=17'] Exploring Operation: 98+17=115, Resulting Numbers: [115] 115,93 unequal: No Solution Exploring Operation: 98*17=1666, Resulting Numbers: [1666] 1666,93 unequal: No Solution Exploring Operation: 98-17=81, Resulting Numbers: [81] 81,93 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: 93:[98, 84, 36], Operations: ['24+12=36'] Exploring Operation: 98-84=14, Resulting Numbers: [36, 14] Generated Node #0,0,0: 93:[36, 14] Operation: 98-84=14 Exploring Operation: 84+36=120, Resulting Numbers: [98, 120] Generated Node #0,0,1: 93:[98, 120] Operation: 84+36=120 Exploring Operation: 98-36=62, Resulting Numbers: [84, 62] Generated Node #0,0,2: 93:[84, 62] Operation: 98-36=62 Exploring Operation: 84-36=48, Resulting Numbers: [98, 48] Generated Node #0,0,3: 93:[98, 48] Operation: 84-36=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[36, 14], Operations: ['24+12=36', '98-84=14'] Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,93 unequal: No Solution Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,93 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,93 unequal: No Solution No 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: 93:[98, 48], Operations: ['24+12=36', '84-36=48'] Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,93 unequal: No Solution Exploring Operation: 98+48=146, Resulting Numbers: [146] 146,93 unequal: No Solution Exploring Operation: 98*48=4704, Resulting Numbers: [4704] 4704,93 unequal: No Solution No 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: 93:[98, 120], Operations: ['24+12=36', '84+36=120'] Exploring Operation: 98+120=218, Resulting Numbers: [218] 218,93 unequal: No Solution Exploring Operation: 98*120=11760, Resulting Numbers: [11760] 11760,93 unequal: No Solution Exploring Operation: 120-98=22, Resulting Numbers: [22] 22,93 unequal: No Solution No 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: 93:[84, 62], Operations: ['24+12=36', '98-36=62'] Exploring Operation: 84+62=146, Resulting Numbers: [146] 146,93 unequal: No Solution Exploring Operation: 84*62=5208, Resulting Numbers: [5208] 5208,93 unequal: No Solution Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,93 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
[ 62, 25, 23, 82 ]
22
[ "62-25=37", "82-23=59", "59-37=22" ]
Current State: 22:[62, 25, 23, 82], Operations: [] Exploring Operation: 62-25=37, Resulting Numbers: [23, 82, 37] Generated Node #2: [23, 82, 37] from Operation: 62-25=37 Current State: 22:[23, 82, 37], Operations: ['62-25=37'] Exploring Operation: 82-23=59, Resulting Numbers: [37, 59] Generated Node #3: [37, 59] from Operation: 82-23=59 Current State: 22:[37, 59], Operations: ['62-25=37', '82-23=59'] Exploring Operation: 59-37=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[62, 25, 23, 82], Operations: [] Exploring Operation: 82-62=20, Resulting Numbers: [25, 23, 20] Generated Node #0,0: 22:[25, 23, 20] Operation: 82-62=20 Exploring Operation: 62-25=37, Resulting Numbers: [23, 82, 37] Generated Node #0,1: 22:[23, 82, 37] Operation: 62-25=37 Exploring Operation: 82-25=57, Resulting Numbers: [62, 23, 57] Generated Node #0,2: 22:[62, 23, 57] Operation: 82-25=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[25, 23, 20], Operations: ['82-62=20'] Exploring Operation: 23-20=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 22:[25, 3] Operation: 23-20=3 Exploring Operation: 25-20=5, Resulting Numbers: [23, 5] Generated Node #0,0,1: 22:[23, 5] Operation: 25-20=5 Exploring Operation: 25-23=2, Resulting Numbers: [20, 2] Generated Node #0,0,2: 22:[20, 2] Operation: 25-23=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 22:[20, 2], Operations: ['82-62=20', '25-23=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[62, 25, 23, 82], Operations: [] Exploring Operation: 82-62=20, Resulting Numbers: [25, 23, 20] Generated Node #0,0: 22:[25, 23, 20] Operation: 82-62=20 Moving to Node #0,0 Current State: 22:[25, 23, 20], Operations: ['82-62=20'] Exploring Operation: 25-23=2, Resulting Numbers: [20, 2] Generated Node #0,0,2: 22:[20, 2] Operation: 25-23=2 Moving to Node #0,0,2 Current State: 22:[20, 2], Operations: ['82-62=20', '25-23=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 65, 41, 3, 46 ]
94
[ "41+46=87", "87/3=29", "65+29=94" ]
Current State: 94:[65, 41, 3, 46], Operations: [] Exploring Operation: 41+46=87, Resulting Numbers: [65, 3, 87] Generated Node #2: [65, 3, 87] from Operation: 41+46=87 Current State: 94:[65, 3, 87], Operations: ['41+46=87'] Exploring Operation: 87/3=29, Resulting Numbers: [65, 29] Generated Node #3: [65, 29] from Operation: 87/3=29 Current State: 94:[65, 29], Operations: ['41+46=87', '87/3=29'] Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[65, 41, 3, 46], Operations: [] Exploring Operation: 65+41=106, Resulting Numbers: [3, 46, 106] Generated Node #0,0: 94:[3, 46, 106] Operation: 65+41=106 Exploring Operation: 65-3=62, Resulting Numbers: [41, 46, 62] Generated Node #0,1: 94:[41, 46, 62] Operation: 65-3=62 Moving to Node #0,0 Current State: 94:[3, 46, 106], Operations: ['65+41=106'] Exploring Operation: 3+46=49, Resulting Numbers: [106, 49] Generated Node #0,0,0: 94:[106, 49] Operation: 3+46=49 Exploring Operation: 106-3=103, Resulting Numbers: [46, 103] Generated Node #0,0,1: 94:[46, 103] Operation: 106-3=103 Moving to Node #0,1 Current State: 94:[41, 46, 62], Operations: ['65-3=62'] Exploring Operation: 41+62=103, Resulting Numbers: [46, 103] Generated Node #0,1,0: 94:[46, 103] Operation: 41+62=103 Exploring Operation: 46-41=5, Resulting Numbers: [62, 5] Generated Node #0,1,1: 94:[62, 5] Operation: 46-41=5 Moving to Node #0,0,1 Current State: 94:[46, 103], Operations: ['65+41=106', '106-3=103'] Exploring Operation: 103-46=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 46+103=149, Resulting Numbers: [149] 149,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[46, 103], Operations: ['65-3=62', '41+62=103'] Exploring Operation: 46+103=149, Resulting Numbers: [149] 149,94 unequal: No Solution Exploring Operation: 103-46=57, Resulting Numbers: [57] 57,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[106, 49], Operations: ['65+41=106', '3+46=49'] Exploring Operation: 106-49=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 106+49=155, Resulting Numbers: [155] 155,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[62, 5], Operations: ['65-3=62', '46-41=5'] Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,94 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 8, 72, 28, 45 ]
63
[ "8+72=80", "45-28=17", "80-17=63" ]
Current State: 63:[8, 72, 28, 45], Operations: [] Exploring Operation: 8+72=80, Resulting Numbers: [28, 45, 80] Generated Node #2: [28, 45, 80] from Operation: 8+72=80 Current State: 63:[28, 45, 80], Operations: ['8+72=80'] Exploring Operation: 45-28=17, Resulting Numbers: [80, 17] Generated Node #3: [80, 17] from Operation: 45-28=17 Current State: 63:[80, 17], Operations: ['8+72=80', '45-28=17'] Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[8, 72, 28, 45], Operations: [] Exploring Operation: 72-45=27, Resulting Numbers: [8, 28, 27] Generated Node #0,0: 63:[8, 28, 27] Operation: 72-45=27 Moving to Node #0,0 Current State: 63:[8, 28, 27], Operations: ['72-45=27'] Exploring Operation: 28-27=1, Resulting Numbers: [8, 1] Generated Node #0,0,0: 63:[8, 1] Operation: 28-27=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[8, 1], Operations: ['72-45=27', '28-27=1'] Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,63 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
[ 82, 75, 60, 82 ]
75
[ "82-82=0", "60*0=0", "75+0=75" ]
Current State: 75:[82, 75, 60, 82], Operations: [] Exploring Operation: 82-82=0, Resulting Numbers: [75, 60, 0] Generated Node #2: [75, 60, 0] from Operation: 82-82=0 Current State: 75:[75, 60, 0], Operations: ['82-82=0'] Exploring Operation: 60*0=0, Resulting Numbers: [75, 0] Generated Node #3: [75, 0] from Operation: 60*0=0 Current State: 75:[75, 0], Operations: ['82-82=0', '60*0=0'] Exploring Operation: 75+0=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[82, 75, 60, 82], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [75, 82, 22] Generated Node #0,0: 75:[75, 82, 22] Operation: 82-60=22 Exploring Operation: 82-60=22, Resulting Numbers: [82, 75, 22] Generated Node #0,1: 75:[82, 75, 22] Operation: 82-60=22 Exploring Operation: 75-60=15, Resulting Numbers: [82, 82, 15] Generated Node #0,2: 75:[82, 82, 15] Operation: 75-60=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[75, 82, 22], Operations: ['82-60=22'] Exploring Operation: 75+22=97, Resulting Numbers: [82, 97] Generated Node #0,0,0: 75:[82, 97] Operation: 75+22=97 Exploring Operation: 82-75=7, Resulting Numbers: [22, 7] Generated Node #0,0,1: 75:[22, 7] Operation: 82-75=7 Exploring Operation: 82-22=60, Resulting Numbers: [75, 60] Generated Node #0,0,2: 75:[75, 60] Operation: 82-22=60 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[22, 7], Operations: ['82-60=22', '82-75=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,75 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 22*7=154, Resulting Numbers: [154] 154,75 unequal: No Solution No 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: 75:[75, 60], Operations: ['82-60=22', '82-22=60'] Exploring Operation: 75*60=4500, Resulting Numbers: [4500] 4500,75 unequal: No Solution Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 75+60=135, Resulting Numbers: [135] 135,75 unequal: No Solution No 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: 75:[82, 97], Operations: ['82-60=22', '75+22=97'] Exploring Operation: 82*97=7954, Resulting Numbers: [7954] 7954,75 unequal: No Solution Exploring Operation: 97-82=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 82+97=179, Resulting Numbers: [179] 179,75 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[82, 75, 22], Operations: ['82-60=22'] Exploring Operation: 82-22=60, Resulting Numbers: [75, 60] Generated Node #0,1,0: 75:[75, 60] Operation: 82-22=60 Exploring Operation: 82-75=7, Resulting Numbers: [22, 7] Generated Node #0,1,1: 75:[22, 7] Operation: 82-75=7 Exploring Operation: 82+22=104, Resulting Numbers: [75, 104] Generated Node #0,1,2: 75:[75, 104] Operation: 82+22=104 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[22, 7], Operations: ['82-60=22', '82-75=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,75 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 22*7=154, Resulting Numbers: [154] 154,75 unequal: No Solution No 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: 75:[75, 60], Operations: ['82-60=22', '82-22=60'] Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 75*60=4500, Resulting Numbers: [4500] 4500,75 unequal: No Solution Exploring Operation: 75+60=135, Resulting Numbers: [135] 135,75 unequal: No Solution No 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: 75:[75, 104], Operations: ['82-60=22', '82+22=104'] Exploring Operation: 75+104=179, Resulting Numbers: [179] 179,75 unequal: No Solution Exploring Operation: 104-75=29, Resulting Numbers: [29] 29,75 unequal: No Solution Exploring Operation: 75*104=7800, Resulting Numbers: [7800] 7800,75 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[82, 82, 15], Operations: ['75-60=15'] Exploring Operation: 82-82=0, Resulting Numbers: [15, 0] Generated Node #0,2,0: 75:[15, 0] Operation: 82-82=0 Exploring Operation: 82/82=1, Resulting Numbers: [15, 1] Generated Node #0,2,1: 75:[15, 1] Operation: 82/82=1 Exploring Operation: 82-15=67, Resulting Numbers: [82, 67] Generated Node #0,2,2: 75:[82, 67] Operation: 82-15=67 Moving to Node #0,2,1 Current State: 75:[15, 1], Operations: ['75-60=15', '82/82=1'] Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,75 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[15, 0], Operations: ['75-60=15', '82-82=0'] Exploring Operation: 15+0=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 15*0=0, Resulting Numbers: [0] 0,75 unequal: No Solution Exploring Operation: 15-0=15, Resulting Numbers: [15] 15,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[82, 67], Operations: ['75-60=15', '82-15=67'] Exploring Operation: 82+67=149, Resulting Numbers: [149] 149,75 unequal: No Solution Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 82*67=5494, Resulting Numbers: [5494] 5494,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 3, 46, 31, 73 ]
50
[ "46+31=77", "73+77=150", "150/3=50" ]
Current State: 50:[3, 46, 31, 73], Operations: [] Exploring Operation: 46+31=77, Resulting Numbers: [3, 73, 77] Generated Node #2: [3, 73, 77] from Operation: 46+31=77 Current State: 50:[3, 73, 77], Operations: ['46+31=77'] Exploring Operation: 73+77=150, Resulting Numbers: [3, 150] Generated Node #3: [3, 150] from Operation: 73+77=150 Current State: 50:[3, 150], Operations: ['46+31=77', '73+77=150'] Exploring Operation: 150/3=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[3, 46, 31, 73], Operations: [] Exploring Operation: 3+46=49, Resulting Numbers: [31, 73, 49] Generated Node #0,0: 50:[31, 73, 49] Operation: 3+46=49 Exploring Operation: 73-46=27, Resulting Numbers: [3, 31, 27] Generated Node #0,1: 50:[3, 31, 27] Operation: 73-46=27 Exploring Operation: 46-31=15, Resulting Numbers: [3, 73, 15] Generated Node #0,2: 50:[3, 73, 15] Operation: 46-31=15 Exploring Operation: 73-31=42, Resulting Numbers: [3, 46, 42] Generated Node #0,3: 50:[3, 46, 42] Operation: 73-31=42 Moving to Node #0,1 Current State: 50:[3, 31, 27], Operations: ['73-46=27'] Exploring Operation: 31-27=4, Resulting Numbers: [3, 4] Generated Node #0,1,0: 50:[3, 4] Operation: 31-27=4 Exploring Operation: 31-3=28, Resulting Numbers: [27, 28] Generated Node #0,1,1: 50:[27, 28] Operation: 31-3=28 Exploring Operation: 27/3=9, Resulting Numbers: [31, 9] Generated Node #0,1,2: 50:[31, 9] Operation: 27/3=9 Exploring Operation: 27-3=24, Resulting Numbers: [31, 24] Generated Node #0,1,3: 50:[31, 24] Operation: 27-3=24 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[3, 4], Operations: ['73-46=27', '31-27=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,50 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:[27, 28], Operations: ['73-46=27', '31-3=28'] Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,50 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:[31, 9], Operations: ['73-46=27', '27/3=9'] Exploring Operation: 31*9=279, Resulting Numbers: [279] 279,50 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,50 unequal: No Solution Exploring Operation: 31+9=40, Resulting Numbers: [40] 40,50 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 #0,1,3 Current State: 50:[31, 24], Operations: ['73-46=27', '27-3=24'] Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,50 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: 50:[3, 46, 42], Operations: ['73-31=42'] Exploring Operation: 42/3=14, Resulting Numbers: [46, 14] Generated Node #0,3,0: 50:[46, 14] Operation: 42/3=14 Exploring Operation: 46-42=4, Resulting Numbers: [3, 4] Generated Node #0,3,1: 50:[3, 4] Operation: 46-42=4 Exploring Operation: 3+46=49, Resulting Numbers: [42, 49] Generated Node #0,3,2: 50:[42, 49] Operation: 3+46=49 Exploring Operation: 3+42=45, Resulting Numbers: [46, 45] Generated Node #0,3,3: 50:[46, 45] Operation: 3+42=45 Moving to Node #0,2 Current State: 50:[3, 73, 15], Operations: ['46-31=15'] Exploring Operation: 73-15=58, Resulting Numbers: [3, 58] Generated Node #0,2,0: 50:[3, 58] Operation: 73-15=58 Exploring Operation: 15-3=12, Resulting Numbers: [73, 12] Generated Node #0,2,1: 50:[73, 12] Operation: 15-3=12 Exploring Operation: 15/3=5, Resulting Numbers: [73, 5] Generated Node #0,2,2: 50:[73, 5] Operation: 15/3=5 Exploring Operation: 73-3=70, Resulting Numbers: [15, 70] Generated Node #0,2,3: 50:[15, 70] Operation: 73-3=70 Moving to Node #0,0 Current State: 50:[31, 73, 49], Operations: ['3+46=49'] Exploring Operation: 49-31=18, Resulting Numbers: [73, 18] Generated Node #0,0,0: 50:[73, 18] Operation: 49-31=18 Exploring Operation: 73-49=24, Resulting Numbers: [31, 24] Generated Node #0,0,1: 50:[31, 24] Operation: 73-49=24 Exploring Operation: 31+49=80, Resulting Numbers: [73, 80] Generated Node #0,0,2: 50:[73, 80] Operation: 31+49=80 Exploring Operation: 73-31=42, Resulting Numbers: [49, 42] Generated Node #0,0,3: 50:[49, 42] Operation: 73-31=42 Moving to Node #0,3,1 Current State: 50:[3, 4], Operations: ['73-31=42', '46-42=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[31, 24], Operations: ['3+46=49', '73-49=24'] Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,50 unequal: No Solution Moving to Node #0,3,0 Current State: 50:[46, 14], Operations: ['73-31=42', '42/3=14'] Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,50 unequal: No Solution Exploring Operation: 46+14=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 46*14=644, Resulting Numbers: [644] 644,50 unequal: No Solution Moving to Node #0,3,2 Current State: 50:[42, 49], Operations: ['73-31=42', '3+46=49'] Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 42+49=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 42*49=2058, Resulting Numbers: [2058] 2058,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[3, 58], Operations: ['46-31=15', '73-15=58'] Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,50 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,50 unequal: No Solution Moving to Node #0,0,3 Current State: 50:[49, 42], Operations: ['3+46=49', '73-31=42'] Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 49*42=2058, Resulting Numbers: [2058] 2058,50 unequal: No Solution Moving to Node #0,3,3 Current State: 50:[46, 45], Operations: ['73-31=42', '3+42=45'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,50 unequal: No Solution Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[73, 5], Operations: ['46-31=15', '15/3=5'] Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,50 unequal: No Solution Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,50 unequal: No Solution Exploring Operation: 73*5=365, Resulting Numbers: [365] 365,50 unequal: No Solution Moving to Node #0,2,3 Current State: 50:[15, 70], Operations: ['46-31=15', '73-3=70'] Exploring Operation: 15+70=85, Resulting Numbers: [85] 85,50 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 15*70=1050, Resulting Numbers: [1050] 1050,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[73, 12], Operations: ['46-31=15', '15-3=12'] Exploring Operation: 73+12=85, Resulting Numbers: [85] 85,50 unequal: No Solution Exploring Operation: 73-12=61, Resulting Numbers: [61] 61,50 unequal: No Solution Exploring Operation: 73*12=876, Resulting Numbers: [876] 876,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[73, 18], Operations: ['3+46=49', '49-31=18'] Exploring Operation: 73-18=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 73+18=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 73*18=1314, Resulting Numbers: [1314] 1314,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[73, 80], Operations: ['3+46=49', '31+49=80'] Exploring Operation: 80-73=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 73+80=153, Resulting Numbers: [153] 153,50 unequal: No Solution Exploring Operation: 73*80=5840, Resulting Numbers: [5840] 5840,50 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 84, 76, 85, 38 ]
43
[ "84*38=3192", "3192/76=42", "85-42=43" ]
Current State: 43:[84, 76, 85, 38], Operations: [] Exploring Operation: 84*38=3192, Resulting Numbers: [76, 85, 3192] Generated Node #2: [76, 85, 3192] from Operation: 84*38=3192 Current State: 43:[76, 85, 3192], Operations: ['84*38=3192'] Exploring Operation: 3192/76=42, Resulting Numbers: [85, 42] Generated Node #3: [85, 42] from Operation: 3192/76=42 Current State: 43:[85, 42], Operations: ['84*38=3192', '3192/76=42'] Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[84, 76, 85, 38], Operations: [] Exploring Operation: 85-38=47, Resulting Numbers: [84, 76, 47] Generated Node #0,0: 43:[84, 76, 47] Operation: 85-38=47 Exploring Operation: 84-38=46, Resulting Numbers: [76, 85, 46] Generated Node #0,1: 43:[76, 85, 46] Operation: 84-38=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[84, 76, 47], Operations: ['85-38=47'] Exploring Operation: 84-76=8, Resulting Numbers: [47, 8] Generated Node #0,0,0: 43:[47, 8] Operation: 84-76=8 Exploring Operation: 84-47=37, Resulting Numbers: [76, 37] Generated Node #0,0,1: 43:[76, 37] Operation: 84-47=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[47, 8], Operations: ['85-38=47', '84-76=8'] Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[76, 37], Operations: ['85-38=47', '84-47=37'] Exploring Operation: 76-37=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 76+37=113, Resulting Numbers: [113] 113,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[76, 85, 46], Operations: ['84-38=46'] Exploring Operation: 85-46=39, Resulting Numbers: [76, 39] Generated Node #0,1,0: 43:[76, 39] Operation: 85-46=39 Exploring Operation: 85-76=9, Resulting Numbers: [46, 9] Generated Node #0,1,1: 43:[46, 9] Operation: 85-76=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[76, 39], Operations: ['84-38=46', '85-46=39'] Exploring Operation: 76+39=115, Resulting Numbers: [115] 115,43 unequal: No Solution Exploring Operation: 76-39=37, Resulting Numbers: [37] 37,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[46, 9], Operations: ['84-38=46', '85-76=9'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,43 unequal: No Solution Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 50, 95, 97, 27 ]
79
[ "95-50=45", "97+27=124", "124-45=79" ]
Current State: 79:[50, 95, 97, 27], Operations: [] Exploring Operation: 95-50=45, Resulting Numbers: [97, 27, 45] Generated Node #2: [97, 27, 45] from Operation: 95-50=45 Current State: 79:[97, 27, 45], Operations: ['95-50=45'] Exploring Operation: 97+27=124, Resulting Numbers: [45, 124] Generated Node #3: [45, 124] from Operation: 97+27=124 Current State: 79:[45, 124], Operations: ['95-50=45', '97+27=124'] Exploring Operation: 124-45=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[50, 95, 97, 27], Operations: [] Exploring Operation: 50+27=77, Resulting Numbers: [95, 97, 77] Generated Node #0,0: 79:[95, 97, 77] Operation: 50+27=77 Moving to Node #0,0 Current State: 79:[95, 97, 77], Operations: ['50+27=77'] Exploring Operation: 97-77=20, Resulting Numbers: [95, 20] Generated Node #0,0,0: 79:[95, 20] Operation: 97-77=20 Moving to Node #0,0,0 Current State: 79:[95, 20], Operations: ['50+27=77', '97-77=20'] Exploring Operation: 95-20=75, Resulting Numbers: [75] 75,79 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 16, 64, 33, 41 ]
91
[ "64/16=4", "33*4=132", "132-41=91" ]
Current State: 91:[16, 64, 33, 41], Operations: [] Exploring Operation: 64/16=4, Resulting Numbers: [33, 41, 4] Generated Node #2: [33, 41, 4] from Operation: 64/16=4 Current State: 91:[33, 41, 4], Operations: ['64/16=4'] Exploring Operation: 33*4=132, Resulting Numbers: [41, 132] Generated Node #3: [41, 132] from Operation: 33*4=132 Current State: 91:[41, 132], Operations: ['64/16=4', '33*4=132'] Exploring Operation: 132-41=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[16, 64, 33, 41], Operations: [] Exploring Operation: 64-41=23, Resulting Numbers: [16, 33, 23] Generated Node #0,0: 91:[16, 33, 23] Operation: 64-41=23 Exploring Operation: 64+33=97, Resulting Numbers: [16, 41, 97] Generated Node #0,1: 91:[16, 41, 97] Operation: 64+33=97 Exploring Operation: 41-33=8, Resulting Numbers: [16, 64, 8] Generated Node #0,2: 91:[16, 64, 8] Operation: 41-33=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[16, 64, 8], Operations: ['41-33=8'] Exploring Operation: 64/8=8, Resulting Numbers: [16, 8] Generated Node #0,2,0: 91:[16, 8] Operation: 64/8=8 Exploring Operation: 64/16=4, Resulting Numbers: [8, 4] Generated Node #0,2,1: 91:[8, 4] Operation: 64/16=4 Exploring Operation: 16+64=80, Resulting Numbers: [8, 80] Generated Node #0,2,2: 91:[8, 80] Operation: 16+64=80 Moving to Node #0,2,0 Current State: 91:[16, 8], Operations: ['41-33=8', '64/8=8'] Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[8, 4], Operations: ['41-33=8', '64/16=4'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[8, 80], Operations: ['41-33=8', '16+64=80'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,91 unequal: No Solution Exploring Operation: 8+80=88, Resulting Numbers: [88] 88,91 unequal: No Solution Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[16, 33, 23], Operations: ['64-41=23'] Exploring Operation: 33-23=10, Resulting Numbers: [16, 10] Generated Node #0,0,0: 91:[16, 10] Operation: 33-23=10 Exploring Operation: 33-16=17, Resulting Numbers: [23, 17] Generated Node #0,0,1: 91:[23, 17] Operation: 33-16=17 Exploring Operation: 23-16=7, Resulting Numbers: [33, 7] Generated Node #0,0,2: 91:[33, 7] Operation: 23-16=7 Moving to Node #0,0,0 Current State: 91:[16, 10], Operations: ['64-41=23', '33-23=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,91 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[23, 17], Operations: ['64-41=23', '33-16=17'] Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 23*17=391, Resulting Numbers: [391] 391,91 unequal: No Solution Exploring Operation: 23+17=40, Resulting Numbers: [40] 40,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[33, 7], Operations: ['64-41=23', '23-16=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,91 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,91 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,91 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 #0,1 Current State: 91:[16, 41, 97], Operations: ['64+33=97'] Exploring Operation: 41-16=25, Resulting Numbers: [97, 25] Generated Node #0,1,0: 91:[97, 25] Operation: 41-16=25 Exploring Operation: 97-41=56, Resulting Numbers: [16, 56] Generated Node #0,1,1: 91:[16, 56] Operation: 97-41=56 Exploring Operation: 97-16=81, Resulting Numbers: [41, 81] Generated Node #0,1,2: 91:[41, 81] Operation: 97-16=81 Moving to Node #0,1,0 Current State: 91:[97, 25], Operations: ['64+33=97', '41-16=25'] Exploring Operation: 97+25=122, Resulting Numbers: [122] 122,91 unequal: No Solution Exploring Operation: 97*25=2425, Resulting Numbers: [2425] 2425,91 unequal: No Solution Exploring Operation: 97-25=72, Resulting Numbers: [72] 72,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[16, 56], Operations: ['64+33=97', '97-41=56'] Exploring Operation: 56-16=40, Resulting Numbers: [40] 40,91 unequal: No Solution Exploring Operation: 16+56=72, Resulting Numbers: [72] 72,91 unequal: No Solution Exploring Operation: 16*56=896, Resulting Numbers: [896] 896,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[41, 81], Operations: ['64+33=97', '97-16=81'] Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,91 unequal: No Solution Exploring Operation: 41*81=3321, Resulting Numbers: [3321] 3321,91 unequal: No Solution Exploring Operation: 41+81=122, Resulting Numbers: [122] 122,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 66, 38, 32, 95 ]
84
[ "38-32=6", "66/6=11", "95-11=84" ]
Current State: 84:[66, 38, 32, 95], Operations: [] Exploring Operation: 38-32=6, Resulting Numbers: [66, 95, 6] Generated Node #2: [66, 95, 6] from Operation: 38-32=6 Current State: 84:[66, 95, 6], Operations: ['38-32=6'] Exploring Operation: 66/6=11, Resulting Numbers: [95, 11] Generated Node #3: [95, 11] from Operation: 66/6=11 Current State: 84:[95, 11], Operations: ['38-32=6', '66/6=11'] Exploring Operation: 95-11=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[66, 38, 32, 95], Operations: [] Exploring Operation: 66-38=28, Resulting Numbers: [32, 95, 28] Generated Node #0,0: 84:[32, 95, 28] Operation: 66-38=28 Exploring Operation: 38-32=6, Resulting Numbers: [66, 95, 6] Generated Node #0,1: 84:[66, 95, 6] Operation: 38-32=6 Exploring Operation: 95-66=29, Resulting Numbers: [38, 32, 29] Generated Node #0,2: 84:[38, 32, 29] Operation: 95-66=29 Exploring Operation: 66+32=98, Resulting Numbers: [38, 95, 98] Generated Node #0,3: 84:[38, 95, 98] Operation: 66+32=98 Exploring Operation: 66-32=34, Resulting Numbers: [38, 95, 34] Generated Node #0,4: 84:[38, 95, 34] Operation: 66-32=34 Moving to Node #0,2 Current State: 84:[38, 32, 29], Operations: ['95-66=29'] Exploring Operation: 32-29=3, Resulting Numbers: [38, 3] Generated Node #0,2,0: 84:[38, 3] Operation: 32-29=3 Exploring Operation: 38-32=6, Resulting Numbers: [29, 6] Generated Node #0,2,1: 84:[29, 6] Operation: 38-32=6 Exploring Operation: 38+32=70, Resulting Numbers: [29, 70] Generated Node #0,2,2: 84:[29, 70] Operation: 38+32=70 Exploring Operation: 38-29=9, Resulting Numbers: [32, 9] Generated Node #0,2,3: 84:[32, 9] Operation: 38-29=9 Exploring Operation: 38+29=67, Resulting Numbers: [32, 67] Generated Node #0,2,4: 84:[32, 67] Operation: 38+29=67 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[29, 6], Operations: ['95-66=29', '38-32=6'] Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,84 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,84 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 #0,2,0 Current State: 84:[38, 3], Operations: ['95-66=29', '32-29=3'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 38*3=114, Resulting Numbers: [114] 114,84 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 #0,2,3 Current State: 84:[32, 9], Operations: ['95-66=29', '38-29=9'] Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,84 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 #0,2,2 Current State: 84:[29, 70], Operations: ['95-66=29', '38+32=70'] Exploring Operation: 70-29=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 29*70=2030, Resulting Numbers: [2030] 2030,84 unequal: No Solution Exploring Operation: 29+70=99, Resulting Numbers: [99] 99,84 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 #0,2,4 Current State: 84:[32, 67], Operations: ['95-66=29', '38+29=67'] Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 32+67=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 32*67=2144, Resulting Numbers: [2144] 2144,84 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: 84:[32, 95, 28], Operations: ['66-38=28'] Exploring Operation: 32+95=127, Resulting Numbers: [28, 127] Generated Node #0,0,0: 84:[28, 127] Operation: 32+95=127 Exploring Operation: 95-28=67, Resulting Numbers: [32, 67] Generated Node #0,0,1: 84:[32, 67] Operation: 95-28=67 Exploring Operation: 95-32=63, Resulting Numbers: [28, 63] Generated Node #0,0,2: 84:[28, 63] Operation: 95-32=63 Exploring Operation: 32-28=4, Resulting Numbers: [95, 4] Generated Node #0,0,3: 84:[95, 4] Operation: 32-28=4 Exploring Operation: 32+28=60, Resulting Numbers: [95, 60] Generated Node #0,0,4: 84:[95, 60] Operation: 32+28=60 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[95, 4], Operations: ['66-38=28', '32-28=4'] Exploring Operation: 95*4=380, Resulting Numbers: [380] 380,84 unequal: No Solution Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,84 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 #0,0,1 Current State: 84:[32, 67], Operations: ['66-38=28', '95-28=67'] Exploring Operation: 32+67=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 32*67=2144, Resulting Numbers: [2144] 2144,84 unequal: No Solution Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[28, 63], Operations: ['66-38=28', '95-32=63'] Exploring Operation: 28*63=1764, Resulting Numbers: [1764] 1764,84 unequal: No Solution Exploring Operation: 63-28=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 28+63=91, Resulting Numbers: [91] 91,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 84:[95, 60], Operations: ['66-38=28', '32+28=60'] Exploring Operation: 95+60=155, Resulting Numbers: [155] 155,84 unequal: No Solution Exploring Operation: 95-60=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 95*60=5700, Resulting Numbers: [5700] 5700,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[28, 127], Operations: ['66-38=28', '32+95=127'] Exploring Operation: 127-28=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 28*127=3556, Resulting Numbers: [3556] 3556,84 unequal: No Solution Exploring Operation: 28+127=155, Resulting Numbers: [155] 155,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 84:[38, 95, 34], Operations: ['66-32=34'] Exploring Operation: 95-34=61, Resulting Numbers: [38, 61] Generated Node #0,4,0: 84:[38, 61] Operation: 95-34=61 Exploring Operation: 38+34=72, Resulting Numbers: [95, 72] Generated Node #0,4,1: 84:[95, 72] Operation: 38+34=72 Exploring Operation: 38-34=4, Resulting Numbers: [95, 4] Generated Node #0,4,2: 84:[95, 4] Operation: 38-34=4 Exploring Operation: 95+34=129, Resulting Numbers: [38, 129] Generated Node #0,4,3: 84:[38, 129] Operation: 95+34=129 Exploring Operation: 95-38=57, Resulting Numbers: [34, 57] Generated Node #0,4,4: 84:[34, 57] Operation: 95-38=57 Moving to Node #0,1 Current State: 84:[66, 95, 6], Operations: ['38-32=6'] Exploring Operation: 95-6=89, Resulting Numbers: [66, 89] Generated Node #0,1,0: 84:[66, 89] Operation: 95-6=89 Exploring Operation: 66/6=11, Resulting Numbers: [95, 11] Generated Node #0,1,1: 84:[95, 11] Operation: 66/6=11 Exploring Operation: 66-6=60, Resulting Numbers: [95, 60] Generated Node #0,1,2: 84:[95, 60] Operation: 66-6=60 Exploring Operation: 95-66=29, Resulting Numbers: [6, 29] Generated Node #0,1,3: 84:[6, 29] Operation: 95-66=29 Exploring Operation: 66+6=72, Resulting Numbers: [95, 72] Generated Node #0,1,4: 84:[95, 72] Operation: 66+6=72 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[6, 29], Operations: ['38-32=6', '95-66=29'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,84 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[95, 11], Operations: ['38-32=6', '66/6=11'] Exploring Operation: 95+11=106, Resulting Numbers: [106] 106,84 unequal: No Solution Exploring Operation: 95*11=1045, Resulting Numbers: [1045] 1045,84 unequal: No Solution Exploring Operation: 95-11=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[66, 38, 32, 95], Operations: [] Exploring Operation: 38-32=6, Resulting Numbers: [66, 95, 6] Generated Node #0,1: 84:[66, 95, 6] Operation: 38-32=6 Moving to Node #0,1 Current State: 84:[66, 95, 6], Operations: ['38-32=6'] Exploring Operation: 66/6=11, Resulting Numbers: [95, 11] Generated Node #0,1,1: 84:[95, 11] Operation: 66/6=11 Moving to Node #0,1,1 Current State: 84:[95, 11], Operations: ['38-32=6', '66/6=11'] Exploring Operation: 95-11=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.943576
hs_5
sum_heuristic
[ 92, 40, 20, 45 ]
25
[ "92-20=72", "40*45=1800", "1800/72=25" ]
Current State: 25:[92, 40, 20, 45], Operations: [] Exploring Operation: 92-20=72, Resulting Numbers: [40, 45, 72] Generated Node #2: [40, 45, 72] from Operation: 92-20=72 Current State: 25:[40, 45, 72], Operations: ['92-20=72'] Exploring Operation: 40*45=1800, Resulting Numbers: [72, 1800] Generated Node #3: [72, 1800] from Operation: 40*45=1800 Current State: 25:[72, 1800], Operations: ['92-20=72', '40*45=1800'] Exploring Operation: 1800/72=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[92, 40, 20, 45], Operations: [] Exploring Operation: 92-40=52, Resulting Numbers: [20, 45, 52] Generated Node #0,0: 25:[20, 45, 52] Operation: 92-40=52 Exploring Operation: 92-45=47, Resulting Numbers: [40, 20, 47] Generated Node #0,1: 25:[40, 20, 47] Operation: 92-45=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[40, 20, 47], Operations: ['92-45=47'] Exploring Operation: 47-40=7, Resulting Numbers: [20, 7] Generated Node #0,1,0: 25:[20, 7] Operation: 47-40=7 Exploring Operation: 47-20=27, Resulting Numbers: [40, 27] Generated Node #0,1,1: 25:[40, 27] Operation: 47-20=27 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[20, 7], Operations: ['92-45=47', '47-40=7'] Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[40, 27], Operations: ['92-45=47', '47-20=27'] Exploring Operation: 40+27=67, Resulting Numbers: [67] 67,25 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[20, 45, 52], Operations: ['92-40=52'] Exploring Operation: 52-45=7, Resulting Numbers: [20, 7] Generated Node #0,0,0: 25:[20, 7] Operation: 52-45=7 Exploring Operation: 45-20=25, Resulting Numbers: [52, 25] Generated Node #0,0,1: 25:[52, 25] Operation: 45-20=25 Moving to Node #0,0,0 Current State: 25:[20, 7], Operations: ['92-40=52', '52-45=7'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[52, 25], Operations: ['92-40=52', '45-20=25'] Exploring Operation: 52+25=77, Resulting Numbers: [77] 77,25 unequal: No Solution Exploring Operation: 52-25=27, Resulting Numbers: [27] 27,25 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
[ 3, 70, 54, 68 ]
80
[ "3*68=204", "70+54=124", "204-124=80" ]
Current State: 80:[3, 70, 54, 68], Operations: [] Exploring Operation: 3*68=204, Resulting Numbers: [70, 54, 204] Generated Node #2: [70, 54, 204] from Operation: 3*68=204 Current State: 80:[70, 54, 204], Operations: ['3*68=204'] Exploring Operation: 70+54=124, Resulting Numbers: [204, 124] Generated Node #3: [204, 124] from Operation: 70+54=124 Current State: 80:[204, 124], Operations: ['3*68=204', '70+54=124'] Exploring Operation: 204-124=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[3, 70, 54, 68], Operations: [] Exploring Operation: 68-54=14, Resulting Numbers: [3, 70, 14] Generated Node #0,0: 80:[3, 70, 14] Operation: 68-54=14 Exploring Operation: 70-54=16, Resulting Numbers: [3, 68, 16] Generated Node #0,1: 80:[3, 68, 16] Operation: 70-54=16 Exploring Operation: 70-68=2, Resulting Numbers: [3, 54, 2] Generated Node #0,2: 80:[3, 54, 2] Operation: 70-68=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[3, 70, 14], Operations: ['68-54=14'] Exploring Operation: 70+14=84, Resulting Numbers: [3, 84] Generated Node #0,0,0: 80:[3, 84] Operation: 70+14=84 Exploring Operation: 3+70=73, Resulting Numbers: [14, 73] Generated Node #0,0,1: 80:[14, 73] Operation: 3+70=73 Exploring Operation: 70/14=5, Resulting Numbers: [3, 5] Generated Node #0,0,2: 80:[3, 5] Operation: 70/14=5 Moving to Node #0,0,2 Current State: 80:[3, 5], Operations: ['68-54=14', '70/14=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[3, 84], Operations: ['68-54=14', '70+14=84'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[14, 73], Operations: ['68-54=14', '3+70=73'] Exploring Operation: 14*73=1022, Resulting Numbers: [1022] 1022,80 unequal: No Solution Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 14+73=87, Resulting Numbers: [87] 87,80 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:[3, 68, 16], Operations: ['70-54=16'] Exploring Operation: 3+68=71, Resulting Numbers: [16, 71] Generated Node #0,1,0: 80:[16, 71] Operation: 3+68=71 Exploring Operation: 68+16=84, Resulting Numbers: [3, 84] Generated Node #0,1,1: 80:[3, 84] Operation: 68+16=84 Exploring Operation: 3+16=19, Resulting Numbers: [68, 19] Generated Node #0,1,2: 80:[68, 19] Operation: 3+16=19 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[3, 84], Operations: ['70-54=16', '68+16=84'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,80 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:[16, 71], Operations: ['70-54=16', '3+68=71'] Exploring Operation: 16+71=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 71-16=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 16*71=1136, Resulting Numbers: [1136] 1136,80 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 #0,1,2 Current State: 80:[68, 19], Operations: ['70-54=16', '3+16=19'] Exploring Operation: 68*19=1292, Resulting Numbers: [1292] 1292,80 unequal: No Solution Exploring Operation: 68-19=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 68+19=87, Resulting Numbers: [87] 87,80 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[3, 54, 2], Operations: ['70-68=2'] Exploring Operation: 54/3=18, Resulting Numbers: [2, 18] Generated Node #0,2,0: 80:[2, 18] Operation: 54/3=18 Exploring Operation: 54-3=51, Resulting Numbers: [2, 51] Generated Node #0,2,1: 80:[2, 51] Operation: 54-3=51 Exploring Operation: 54/2=27, Resulting Numbers: [3, 27] Generated Node #0,2,2: 80:[3, 27] Operation: 54/2=27 Moving to Node #0,2,0 Current State: 80:[2, 18], Operations: ['70-68=2', '54/3=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[3, 27], Operations: ['70-68=2', '54/2=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[2, 51], Operations: ['70-68=2', '54-3=51'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 11, 94, 37, 58 ]
74
[ "58-11=47", "94*37=3478", "3478/47=74" ]
Current State: 74:[11, 94, 37, 58], Operations: [] Exploring Operation: 58-11=47, Resulting Numbers: [94, 37, 47] Generated Node #2: [94, 37, 47] from Operation: 58-11=47 Current State: 74:[94, 37, 47], Operations: ['58-11=47'] Exploring Operation: 94*37=3478, Resulting Numbers: [47, 3478] Generated Node #3: [47, 3478] from Operation: 94*37=3478 Current State: 74:[47, 3478], Operations: ['58-11=47', '94*37=3478'] Exploring Operation: 3478/47=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[11, 94, 37, 58], Operations: [] Exploring Operation: 94-58=36, Resulting Numbers: [11, 37, 36] Generated Node #0,0: 74:[11, 37, 36] Operation: 94-58=36 Exploring Operation: 94-11=83, Resulting Numbers: [37, 58, 83] Generated Node #0,1: 74:[37, 58, 83] Operation: 94-11=83 Moving to Node #0,0 Current State: 74:[11, 37, 36], Operations: ['94-58=36'] Exploring Operation: 11+36=47, Resulting Numbers: [37, 47] Generated Node #0,0,0: 74:[37, 47] Operation: 11+36=47 Exploring Operation: 37+36=73, Resulting Numbers: [11, 73] Generated Node #0,0,1: 74:[11, 73] Operation: 37+36=73 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[37, 47], Operations: ['94-58=36', '11+36=47'] Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,74 unequal: No Solution Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,74 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 #0,0,1 Current State: 74:[11, 73], Operations: ['94-58=36', '37+36=73'] Exploring Operation: 11+73=84, Resulting Numbers: [84] 84,74 unequal: No Solution Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,74 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: 74:[37, 58, 83], Operations: ['94-11=83'] Exploring Operation: 83-58=25, Resulting Numbers: [37, 25] Generated Node #0,1,0: 74:[37, 25] Operation: 83-58=25 Exploring Operation: 58-37=21, Resulting Numbers: [83, 21] Generated Node #0,1,1: 74:[83, 21] Operation: 58-37=21 Moving to Node #0,1,0 Current State: 74:[37, 25], Operations: ['94-11=83', '83-58=25'] Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,74 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[83, 21], Operations: ['94-11=83', '58-37=21'] Exploring Operation: 83+21=104, Resulting Numbers: [104] 104,74 unequal: No Solution Exploring Operation: 83-21=62, Resulting Numbers: [62] 62,74 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 10, 61, 10, 2 ]
37
[ "10*10=100", "61+2=63", "100-63=37" ]
Current State: 37:[10, 61, 10, 2], Operations: [] Exploring Operation: 10*10=100, Resulting Numbers: [61, 2, 100] Generated Node #2: [61, 2, 100] from Operation: 10*10=100 Current State: 37:[61, 2, 100], Operations: ['10*10=100'] Exploring Operation: 61+2=63, Resulting Numbers: [100, 63] Generated Node #3: [100, 63] from Operation: 61+2=63 Current State: 37:[100, 63], Operations: ['10*10=100', '61+2=63'] Exploring Operation: 100-63=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[10, 61, 10, 2], Operations: [] Exploring Operation: 10*2=20, Resulting Numbers: [10, 61, 20] Generated Node #0,0: 37:[10, 61, 20] Operation: 10*2=20 Exploring Operation: 10+10=20, Resulting Numbers: [61, 2, 20] Generated Node #0,1: 37:[61, 2, 20] Operation: 10+10=20 Exploring Operation: 10*2=20, Resulting Numbers: [61, 10, 20] Generated Node #0,2: 37:[61, 10, 20] Operation: 10*2=20 Exploring Operation: 61-10=51, Resulting Numbers: [10, 2, 51] Generated Node #0,3: 37:[10, 2, 51] Operation: 61-10=51 Moving to Node #0,0 Current State: 37:[10, 61, 20], Operations: ['10*2=20'] Exploring Operation: 61-10=51, Resulting Numbers: [20, 51] Generated Node #0,0,0: 37:[20, 51] Operation: 61-10=51 Exploring Operation: 61-20=41, Resulting Numbers: [10, 41] Generated Node #0,0,1: 37:[10, 41] Operation: 61-20=41 Exploring Operation: 10+61=71, Resulting Numbers: [20, 71] Generated Node #0,0,2: 37:[20, 71] Operation: 10+61=71 Exploring Operation: 10+20=30, Resulting Numbers: [61, 30] Generated Node #0,0,3: 37:[61, 30] Operation: 10+20=30 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[20, 51], Operations: ['10*2=20', '61-10=51'] Exploring Operation: 20+51=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 20*51=1020, Resulting Numbers: [1020] 1020,37 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,37 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:[10, 41], Operations: ['10*2=20', '61-20=41'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,37 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[61, 30], Operations: ['10*2=20', '10+20=30'] Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 61*30=1830, Resulting Numbers: [1830] 1830,37 unequal: No Solution Exploring Operation: 61+30=91, Resulting Numbers: [91] 91,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[20, 71], Operations: ['10*2=20', '10+61=71'] Exploring Operation: 71-20=51, Resulting Numbers: [51] 51,37 unequal: No Solution Exploring Operation: 20*71=1420, Resulting Numbers: [1420] 1420,37 unequal: No Solution Exploring Operation: 20+71=91, Resulting Numbers: [91] 91,37 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:[61, 10, 20], Operations: ['10*2=20'] Exploring Operation: 10+20=30, Resulting Numbers: [61, 30] Generated Node #0,2,0: 37:[61, 30] Operation: 10+20=30 Exploring Operation: 61-10=51, Resulting Numbers: [20, 51] Generated Node #0,2,1: 37:[20, 51] Operation: 61-10=51 Exploring Operation: 61-20=41, Resulting Numbers: [10, 41] Generated Node #0,2,2: 37:[10, 41] Operation: 61-20=41 Exploring Operation: 61+10=71, Resulting Numbers: [20, 71] Generated Node #0,2,3: 37:[20, 71] Operation: 61+10=71 Moving to Node #0,3 Current State: 37:[10, 2, 51], Operations: ['61-10=51'] Exploring Operation: 51-2=49, Resulting Numbers: [10, 49] Generated Node #0,3,0: 37:[10, 49] Operation: 51-2=49 Exploring Operation: 51-10=41, Resulting Numbers: [2, 41] Generated Node #0,3,1: 37:[2, 41] Operation: 51-10=41 Exploring Operation: 10*2=20, Resulting Numbers: [51, 20] Generated Node #0,3,2: 37:[51, 20] Operation: 10*2=20 Exploring Operation: 10+2=12, Resulting Numbers: [51, 12] Generated Node #0,3,3: 37:[51, 12] Operation: 10+2=12 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 37:[51, 20], Operations: ['61-10=51', '10*2=20'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 37:[10, 49], Operations: ['61-10=51', '51-2=49'] Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,37 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 37:[2, 41], Operations: ['61-10=51', '51-10=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,37 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 37:[51, 12], Operations: ['61-10=51', '10+2=12'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 37:[61, 2, 20], Operations: ['10+10=20'] Exploring Operation: 61-20=41, Resulting Numbers: [2, 41] Generated Node #0,1,0: 37:[2, 41] Operation: 61-20=41 Exploring Operation: 2+20=22, Resulting Numbers: [61, 22] Generated Node #0,1,1: 37:[61, 22] Operation: 2+20=22 Exploring Operation: 2*20=40, Resulting Numbers: [61, 40] Generated Node #0,1,2: 37:[61, 40] Operation: 2*20=40 Exploring Operation: 61-2=59, Resulting Numbers: [20, 59] Generated Node #0,1,3: 37:[20, 59] Operation: 61-2=59 Moving to Node #0,1,2 Current State: 37:[61, 40], Operations: ['10+10=20', '2*20=40'] Exploring Operation: 61+40=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 61*40=2440, Resulting Numbers: [2440] 2440,37 unequal: No Solution Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[10, 41], Operations: ['10*2=20', '61-20=41'] Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,37 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[61, 30], Operations: ['10*2=20', '10+20=30'] Exploring Operation: 61*30=1830, Resulting Numbers: [1830] 1830,37 unequal: No Solution Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 61+30=91, Resulting Numbers: [91] 91,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[20, 51], Operations: ['10*2=20', '61-10=51'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 20*51=1020, Resulting Numbers: [1020] 1020,37 unequal: No Solution Exploring Operation: 20+51=71, Resulting Numbers: [71] 71,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[61, 22], Operations: ['10+10=20', '2+20=22'] Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 61*22=1342, Resulting Numbers: [1342] 1342,37 unequal: No Solution Exploring Operation: 61+22=83, Resulting Numbers: [83] 83,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[20, 59], Operations: ['10+10=20', '61-2=59'] Exploring Operation: 20+59=79, Resulting Numbers: [79] 79,37 unequal: No Solution Exploring Operation: 20*59=1180, Resulting Numbers: [1180] 1180,37 unequal: No Solution Exploring Operation: 59-20=39, Resulting Numbers: [39] 39,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[2, 41], Operations: ['10+10=20', '61-20=41'] Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,37 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[20, 71], Operations: ['10*2=20', '61+10=71'] Exploring Operation: 20*71=1420, Resulting Numbers: [1420] 1420,37 unequal: No Solution Exploring Operation: 20+71=91, Resulting Numbers: [91] 91,37 unequal: No Solution Exploring Operation: 71-20=51, Resulting Numbers: [51] 51,37 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 77, 99, 96, 72 ]
53
[ "99-96=3", "72/3=24", "77-24=53" ]
Current State: 53:[77, 99, 96, 72], Operations: [] Exploring Operation: 99-96=3, Resulting Numbers: [77, 72, 3] Generated Node #2: [77, 72, 3] from Operation: 99-96=3 Current State: 53:[77, 72, 3], Operations: ['99-96=3'] Exploring Operation: 72/3=24, Resulting Numbers: [77, 24] Generated Node #3: [77, 24] from Operation: 72/3=24 Current State: 53:[77, 24], Operations: ['99-96=3', '72/3=24'] Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[77, 99, 96, 72], Operations: [] Exploring Operation: 99-77=22, Resulting Numbers: [96, 72, 22] Generated Node #0,0: 53:[96, 72, 22] Operation: 99-77=22 Moving to Node #0,0 Current State: 53:[96, 72, 22], Operations: ['99-77=22'] Exploring Operation: 96-22=74, Resulting Numbers: [72, 74] Generated Node #0,0,0: 53:[72, 74] Operation: 96-22=74 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[72, 74], Operations: ['99-77=22', '96-22=74'] Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 6, 55, 49, 2 ]
17
[ "55+49=104", "104-2=102", "102/6=17" ]
Current State: 17:[6, 55, 49, 2], Operations: [] Exploring Operation: 55+49=104, Resulting Numbers: [6, 2, 104] Generated Node #2: [6, 2, 104] from Operation: 55+49=104 Current State: 17:[6, 2, 104], Operations: ['55+49=104'] Exploring Operation: 104-2=102, Resulting Numbers: [6, 102] Generated Node #3: [6, 102] from Operation: 104-2=102 Current State: 17:[6, 102], Operations: ['55+49=104', '104-2=102'] Exploring Operation: 102/6=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[6, 55, 49, 2], Operations: [] Exploring Operation: 6*2=12, Resulting Numbers: [55, 49, 12] Generated Node #0,0: 17:[55, 49, 12] Operation: 6*2=12 Exploring Operation: 6+2=8, Resulting Numbers: [55, 49, 8] Generated Node #0,1: 17:[55, 49, 8] Operation: 6+2=8 Exploring Operation: 49-6=43, Resulting Numbers: [55, 2, 43] Generated Node #0,2: 17:[55, 2, 43] Operation: 49-6=43 Exploring Operation: 55-6=49, Resulting Numbers: [49, 2, 49] Generated Node #0,3: 17:[49, 2, 49] Operation: 55-6=49 Exploring Operation: 55-49=6, Resulting Numbers: [6, 2, 6] Generated Node #0,4: 17:[6, 2, 6] Operation: 55-49=6 Start Sub Search at level 1: Moving to Node #0,4 Current State: 17:[6, 2, 6], Operations: ['55-49=6'] Exploring Operation: 2*6=12, Resulting Numbers: [6, 12] Generated Node #0,4,0: 17:[6, 12] Operation: 2*6=12 Exploring Operation: 6*2=12, Resulting Numbers: [6, 12] Generated Node #0,4,1: 17:[6, 12] Operation: 6*2=12 Exploring Operation: 6+6=12, Resulting Numbers: [2, 12] Generated Node #0,4,2: 17:[2, 12] Operation: 6+6=12 Exploring Operation: 6+2=8, Resulting Numbers: [6, 8] Generated Node #0,4,3: 17:[6, 8] Operation: 6+2=8 Exploring Operation: 2+6=8, Resulting Numbers: [6, 8] Generated Node #0,4,4: 17:[6, 8] Operation: 2+6=8 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 17:[6, 12], Operations: ['55-49=6', '2*6=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,17 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 17:[6, 12], Operations: ['55-49=6', '6*2=12'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 17:[2, 12], Operations: ['55-49=6', '6+6=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 17:[6, 8], Operations: ['55-49=6', '6+2=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 17:[6, 8], Operations: ['55-49=6', '2+6=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[55, 49, 12], Operations: ['6*2=12'] Exploring Operation: 55+12=67, Resulting Numbers: [49, 67] Generated Node #0,0,0: 17:[49, 67] Operation: 55+12=67 Exploring Operation: 49-12=37, Resulting Numbers: [55, 37] Generated Node #0,0,1: 17:[55, 37] Operation: 49-12=37 Exploring Operation: 55-12=43, Resulting Numbers: [49, 43] Generated Node #0,0,2: 17:[49, 43] Operation: 55-12=43 Exploring Operation: 49+12=61, Resulting Numbers: [55, 61] Generated Node #0,0,3: 17:[55, 61] Operation: 49+12=61 Exploring Operation: 55-49=6, Resulting Numbers: [12, 6] Generated Node #0,0,4: 17:[12, 6] Operation: 55-49=6 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 17:[12, 6], Operations: ['6*2=12', '55-49=6'] Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 17:[55, 37], Operations: ['6*2=12', '49-12=37'] Exploring Operation: 55+37=92, Resulting Numbers: [92] 92,17 unequal: No Solution Exploring Operation: 55*37=2035, Resulting Numbers: [2035] 2035,17 unequal: No Solution Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 17:[49, 43], Operations: ['6*2=12', '55-12=43'] Exploring Operation: 49+43=92, Resulting Numbers: [92] 92,17 unequal: No Solution Exploring Operation: 49-43=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 49*43=2107, Resulting Numbers: [2107] 2107,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[49, 67], Operations: ['6*2=12', '55+12=67'] Exploring Operation: 49*67=3283, Resulting Numbers: [3283] 3283,17 unequal: No Solution Exploring Operation: 49+67=116, Resulting Numbers: [116] 116,17 unequal: No Solution Exploring Operation: 67-49=18, Resulting Numbers: [18] 18,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 17:[55, 61], Operations: ['6*2=12', '49+12=61'] Exploring Operation: 55*61=3355, Resulting Numbers: [3355] 3355,17 unequal: No Solution Exploring Operation: 55+61=116, Resulting Numbers: [116] 116,17 unequal: No Solution Exploring Operation: 61-55=6, Resulting Numbers: [6] 6,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[55, 49, 8], Operations: ['6+2=8'] Exploring Operation: 49+8=57, Resulting Numbers: [55, 57] Generated Node #0,1,0: 17:[55, 57] Operation: 49+8=57 Exploring Operation: 55-49=6, Resulting Numbers: [8, 6] Generated Node #0,1,1: 17:[8, 6] Operation: 55-49=6 Exploring Operation: 55+8=63, Resulting Numbers: [49, 63] Generated Node #0,1,2: 17:[49, 63] Operation: 55+8=63 Exploring Operation: 55-8=47, Resulting Numbers: [49, 47] Generated Node #0,1,3: 17:[49, 47] Operation: 55-8=47 Exploring Operation: 49-8=41, Resulting Numbers: [55, 41] Generated Node #0,1,4: 17:[55, 41] Operation: 49-8=41 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 17:[8, 6], Operations: ['6+2=8', '55-49=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 17:[49, 47], Operations: ['6+2=8', '55-8=47'] Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,17 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 17:[55, 41], Operations: ['6+2=8', '49-8=41'] Exploring Operation: 55-41=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 55+41=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 55*41=2255, Resulting Numbers: [2255] 2255,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[55, 57], Operations: ['6+2=8', '49+8=57'] Exploring Operation: 55+57=112, Resulting Numbers: [112] 112,17 unequal: No Solution Exploring Operation: 55*57=3135, Resulting Numbers: [3135] 3135,17 unequal: No Solution Exploring Operation: 57-55=2, Resulting Numbers: [2] 2,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 17:[49, 63], Operations: ['6+2=8', '55+8=63'] Exploring Operation: 49+63=112, Resulting Numbers: [112] 112,17 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 49*63=3087, Resulting Numbers: [3087] 3087,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[55, 2, 43], Operations: ['49-6=43'] Exploring Operation: 2+43=45, Resulting Numbers: [55, 45] Generated Node #0,2,0: 17:[55, 45] Operation: 2+43=45 Exploring Operation: 55+2=57, Resulting Numbers: [43, 57] Generated Node #0,2,1: 17:[43, 57] Operation: 55+2=57 Exploring Operation: 43-2=41, Resulting Numbers: [55, 41] Generated Node #0,2,2: 17:[55, 41] Operation: 43-2=41 Exploring Operation: 55-2=53, Resulting Numbers: [43, 53] Generated Node #0,2,3: 17:[43, 53] Operation: 55-2=53 Exploring Operation: 55-43=12, Resulting Numbers: [2, 12] Generated Node #0,2,4: 17:[2, 12] Operation: 55-43=12 Moving to Node #0,2,4 Current State: 17:[2, 12], Operations: ['49-6=43', '55-43=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[43, 53], Operations: ['49-6=43', '55-2=53'] Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 43*53=2279, Resulting Numbers: [2279] 2279,17 unequal: No Solution Exploring Operation: 43+53=96, Resulting Numbers: [96] 96,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[55, 41], Operations: ['49-6=43', '43-2=41'] Exploring Operation: 55*41=2255, Resulting Numbers: [2255] 2255,17 unequal: No Solution Exploring Operation: 55+41=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 55-41=14, Resulting Numbers: [14] 14,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[55, 45], Operations: ['49-6=43', '2+43=45'] Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,17 unequal: No Solution Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[43, 57], Operations: ['49-6=43', '55+2=57'] Exploring Operation: 43*57=2451, Resulting Numbers: [2451] 2451,17 unequal: No Solution Exploring Operation: 57-43=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 43+57=100, Resulting Numbers: [100] 100,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 17:[49, 2, 49], Operations: ['55-6=49'] Exploring Operation: 49-49=0, Resulting Numbers: [2, 0] Generated Node #0,3,0: 17:[2, 0] Operation: 49-49=0 Exploring Operation: 49-2=47, Resulting Numbers: [49, 47] Generated Node #0,3,1: 17:[49, 47] Operation: 49-2=47 Exploring Operation: 49/49=1, Resulting Numbers: [2, 1] Generated Node #0,3,2: 17:[2, 1] Operation: 49/49=1 Exploring Operation: 49+2=51, Resulting Numbers: [49, 51] Generated Node #0,3,3: 17:[49, 51] Operation: 49+2=51 Exploring Operation: 49-2=47, Resulting Numbers: [49, 47] Generated Node #0,3,4: 17:[49, 47] Operation: 49-2=47 Moving to Node #0,3,2 Current State: 17:[2, 1], Operations: ['55-6=49', '49/49=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,17 unequal: No Solution Moving to Node #0,3,0 Current State: 17:[2, 0], Operations: ['55-6=49', '49-49=0'] Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,17 unequal: No Solution Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,17 unequal: No Solution Moving to Node #0,3,1 Current State: 17:[49, 47], Operations: ['55-6=49', '49-2=47'] Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,17 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,17 unequal: No Solution Moving to Node #0,3,4 Current State: 17:[49, 47], Operations: ['55-6=49', '49-2=47'] Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,17 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,17 unequal: No Solution Moving to Node #0,3,3 Current State: 17:[49, 51], Operations: ['55-6=49', '49+2=51'] Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,17 unequal: No Solution Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 49*51=2499, Resulting Numbers: [2499] 2499,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 35, 63, 8, 45 ]
65
[ "63-35=28", "45-8=37", "28+37=65" ]
Current State: 65:[35, 63, 8, 45], Operations: [] Exploring Operation: 63-35=28, Resulting Numbers: [8, 45, 28] Generated Node #2: [8, 45, 28] from Operation: 63-35=28 Current State: 65:[8, 45, 28], Operations: ['63-35=28'] Exploring Operation: 45-8=37, Resulting Numbers: [28, 37] Generated Node #3: [28, 37] from Operation: 45-8=37 Current State: 65:[28, 37], Operations: ['63-35=28', '45-8=37'] Exploring Operation: 28+37=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[35, 63, 8, 45], Operations: [] Exploring Operation: 45-35=10, Resulting Numbers: [63, 8, 10] Generated Node #0,0: 65:[63, 8, 10] Operation: 45-35=10 Moving to Node #0,0 Current State: 65:[63, 8, 10], Operations: ['45-35=10'] Exploring Operation: 10-8=2, Resulting Numbers: [63, 2] Generated Node #0,0,0: 65:[63, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[63, 2], Operations: ['45-35=10', '10-8=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[35, 63, 8, 45], Operations: [] Exploring Operation: 45-35=10, Resulting Numbers: [63, 8, 10] Generated Node #0,0: 65:[63, 8, 10] Operation: 45-35=10 Moving to Node #0,0 Current State: 65:[63, 8, 10], Operations: ['45-35=10'] Exploring Operation: 10-8=2, Resulting Numbers: [63, 2] Generated Node #0,0,0: 65:[63, 2] Operation: 10-8=2 Moving to Node #0,0,0 Current State: 65:[63, 2], Operations: ['45-35=10', '10-8=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 88, 12, 88, 8 ]
84
[ "88/88=1", "8-1=7", "12*7=84" ]
Current State: 84:[88, 12, 88, 8], Operations: [] Exploring Operation: 88/88=1, Resulting Numbers: [12, 8, 1] Generated Node #2: [12, 8, 1] from Operation: 88/88=1 Current State: 84:[12, 8, 1], Operations: ['88/88=1'] Exploring Operation: 8-1=7, Resulting Numbers: [12, 7] Generated Node #3: [12, 7] from Operation: 8-1=7 Current State: 84:[12, 7], Operations: ['88/88=1', '8-1=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[88, 12, 88, 8], Operations: [] Exploring Operation: 88-88=0, Resulting Numbers: [12, 8, 0] Generated Node #0,0: 84:[12, 8, 0] Operation: 88-88=0 Exploring Operation: 88/88=1, Resulting Numbers: [12, 8, 1] Generated Node #0,1: 84:[12, 8, 1] Operation: 88/88=1 Exploring Operation: 88/8=11, Resulting Numbers: [12, 88, 11] Generated Node #0,2: 84:[12, 88, 11] Operation: 88/8=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[12, 8, 1], Operations: ['88/88=1'] Exploring Operation: 12-8=4, Resulting Numbers: [1, 4] Generated Node #0,1,0: 84:[1, 4] Operation: 12-8=4 Exploring Operation: 12*1=12, Resulting Numbers: [8, 12] Generated Node #0,1,1: 84:[8, 12] Operation: 12*1=12 Exploring Operation: 8-1=7, Resulting Numbers: [12, 7] Generated Node #0,1,2: 84:[12, 7] Operation: 8-1=7 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 84:[12, 7], Operations: ['88/88=1', '8-1=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[88, 12, 88, 8], Operations: [] Exploring Operation: 88/88=1, Resulting Numbers: [12, 8, 1] Generated Node #0,1: 84:[12, 8, 1] Operation: 88/88=1 Moving to Node #0,1 Current State: 84:[12, 8, 1], Operations: ['88/88=1'] Exploring Operation: 8-1=7, Resulting Numbers: [12, 7] Generated Node #0,1,2: 84:[12, 7] Operation: 8-1=7 Moving to Node #0,1,2 Current State: 84:[12, 7], Operations: ['88/88=1', '8-1=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 80, 29, 70, 34 ]
50
[ "80-70=10", "34-29=5", "10*5=50" ]
Current State: 50:[80, 29, 70, 34], Operations: [] Exploring Operation: 80-70=10, Resulting Numbers: [29, 34, 10] Generated Node #2: [29, 34, 10] from Operation: 80-70=10 Current State: 50:[29, 34, 10], Operations: ['80-70=10'] Exploring Operation: 34-29=5, Resulting Numbers: [10, 5] Generated Node #3: [10, 5] from Operation: 34-29=5 Current State: 50:[10, 5], Operations: ['80-70=10', '34-29=5'] Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[80, 29, 70, 34], Operations: [] Exploring Operation: 80-29=51, Resulting Numbers: [70, 34, 51] Generated Node #0,0: 50:[70, 34, 51] Operation: 80-29=51 Exploring Operation: 80-70=10, Resulting Numbers: [29, 34, 10] Generated Node #0,1: 50:[29, 34, 10] Operation: 80-70=10 Exploring Operation: 80-34=46, Resulting Numbers: [29, 70, 46] Generated Node #0,2: 50:[29, 70, 46] Operation: 80-34=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[29, 34, 10], Operations: ['80-70=10'] Exploring Operation: 34-29=5, Resulting Numbers: [10, 5] Generated Node #0,1,0: 50:[10, 5] Operation: 34-29=5 Exploring Operation: 34-10=24, Resulting Numbers: [29, 24] Generated Node #0,1,1: 50:[29, 24] Operation: 34-10=24 Exploring Operation: 34+10=44, Resulting Numbers: [29, 44] Generated Node #0,1,2: 50:[29, 44] Operation: 34+10=44 Moving to Node #0,1,0 Current State: 50:[10, 5], Operations: ['80-70=10', '34-29=5'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[80, 29, 70, 34], Operations: [] Exploring Operation: 80-70=10, Resulting Numbers: [29, 34, 10] Generated Node #0,1: 50:[29, 34, 10] Operation: 80-70=10 Moving to Node #0,1 Current State: 50:[29, 34, 10], Operations: ['80-70=10'] Exploring Operation: 34-29=5, Resulting Numbers: [10, 5] Generated Node #0,1,0: 50:[10, 5] Operation: 34-29=5 Moving to Node #0,1,0 Current State: 50:[10, 5], Operations: ['80-70=10', '34-29=5'] Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 13, 16, 88, 53 ]
67
[ "13*16=208", "88+53=141", "208-141=67" ]
Current State: 67:[13, 16, 88, 53], Operations: [] Exploring Operation: 13*16=208, Resulting Numbers: [88, 53, 208] Generated Node #2: [88, 53, 208] from Operation: 13*16=208 Current State: 67:[88, 53, 208], Operations: ['13*16=208'] Exploring Operation: 88+53=141, Resulting Numbers: [208, 141] Generated Node #3: [208, 141] from Operation: 88+53=141 Current State: 67:[208, 141], Operations: ['13*16=208', '88+53=141'] Exploring Operation: 208-141=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[13, 16, 88, 53], Operations: [] Exploring Operation: 88-16=72, Resulting Numbers: [13, 53, 72] Generated Node #0,0: 67:[13, 53, 72] Operation: 88-16=72 Exploring Operation: 13+16=29, Resulting Numbers: [88, 53, 29] Generated Node #0,1: 67:[88, 53, 29] Operation: 13+16=29 Exploring Operation: 13+53=66, Resulting Numbers: [16, 88, 66] Generated Node #0,2: 67:[16, 88, 66] Operation: 13+53=66 Exploring Operation: 16+53=69, Resulting Numbers: [13, 88, 69] Generated Node #0,3: 67:[13, 88, 69] Operation: 16+53=69 Exploring Operation: 88-13=75, Resulting Numbers: [16, 53, 75] Generated Node #0,4: 67:[16, 53, 75] Operation: 88-13=75 Moving to Node #0,0 Current State: 67:[13, 53, 72], Operations: ['88-16=72'] Exploring Operation: 53-13=40, Resulting Numbers: [72, 40] Generated Node #0,0,0: 67:[72, 40] Operation: 53-13=40 Exploring Operation: 13+53=66, Resulting Numbers: [72, 66] Generated Node #0,0,1: 67:[72, 66] Operation: 13+53=66 Exploring Operation: 13+72=85, Resulting Numbers: [53, 85] Generated Node #0,0,2: 67:[53, 85] Operation: 13+72=85 Exploring Operation: 72-53=19, Resulting Numbers: [13, 19] Generated Node #0,0,3: 67:[13, 19] Operation: 72-53=19 Exploring Operation: 72-13=59, Resulting Numbers: [53, 59] Generated Node #0,0,4: 67:[53, 59] Operation: 72-13=59 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[72, 66], Operations: ['88-16=72', '13+53=66'] Exploring Operation: 72*66=4752, Resulting Numbers: [4752] 4752,67 unequal: No Solution Exploring Operation: 72-66=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 72+66=138, Resulting Numbers: [138] 138,67 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 #0,0,4 Current State: 67:[53, 59], Operations: ['88-16=72', '72-13=59'] Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,67 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,67 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 #0,0,0 Current State: 67:[72, 40], Operations: ['88-16=72', '53-13=40'] Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 72*40=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,67 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 #0,0,2 Current State: 67:[53, 85], Operations: ['88-16=72', '13+72=85'] Exploring Operation: 53*85=4505, Resulting Numbers: [4505] 4505,67 unequal: No Solution Exploring Operation: 53+85=138, Resulting Numbers: [138] 138,67 unequal: No Solution Exploring Operation: 85-53=32, Resulting Numbers: [32] 32,67 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 #0,0,3 Current State: 67:[13, 19], Operations: ['88-16=72', '72-53=19'] Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 13*19=247, Resulting Numbers: [247] 247,67 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,67 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: 67:[16, 88, 66], Operations: ['13+53=66'] Exploring Operation: 88-16=72, Resulting Numbers: [66, 72] Generated Node #0,2,0: 67:[66, 72] Operation: 88-16=72 Exploring Operation: 88-66=22, Resulting Numbers: [16, 22] Generated Node #0,2,1: 67:[16, 22] Operation: 88-66=22 Exploring Operation: 16+88=104, Resulting Numbers: [66, 104] Generated Node #0,2,2: 67:[66, 104] Operation: 16+88=104 Exploring Operation: 16+66=82, Resulting Numbers: [88, 82] Generated Node #0,2,3: 67:[88, 82] Operation: 16+66=82 Exploring Operation: 66-16=50, Resulting Numbers: [88, 50] Generated Node #0,2,4: 67:[88, 50] Operation: 66-16=50 Moving to Node #0,1 Current State: 67:[88, 53, 29], Operations: ['13+16=29'] Exploring Operation: 88-29=59, Resulting Numbers: [53, 59] Generated Node #0,1,0: 67:[53, 59] Operation: 88-29=59 Exploring Operation: 88+29=117, Resulting Numbers: [53, 117] Generated Node #0,1,1: 67:[53, 117] Operation: 88+29=117 Exploring Operation: 53-29=24, Resulting Numbers: [88, 24] Generated Node #0,1,2: 67:[88, 24] Operation: 53-29=24 Exploring Operation: 88-53=35, Resulting Numbers: [29, 35] Generated Node #0,1,3: 67:[29, 35] Operation: 88-53=35 Exploring Operation: 53+29=82, Resulting Numbers: [88, 82] Generated Node #0,1,4: 67:[88, 82] Operation: 53+29=82 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[53, 59], Operations: ['13+16=29', '88-29=59'] Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,67 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,67 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 #0,1,4 Current State: 67:[88, 82], Operations: ['13+16=29', '53+29=82'] Exploring Operation: 88+82=170, Resulting Numbers: [170] 170,67 unequal: No Solution Exploring Operation: 88*82=7216, Resulting Numbers: [7216] 7216,67 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,67 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 #0,1,1 Current State: 67:[53, 117], Operations: ['13+16=29', '88+29=117'] Exploring Operation: 117-53=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 53*117=6201, Resulting Numbers: [6201] 6201,67 unequal: No Solution Exploring Operation: 53+117=170, Resulting Numbers: [170] 170,67 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 #0,1,2 Current State: 67:[88, 24], Operations: ['13+16=29', '53-29=24'] Exploring Operation: 88-24=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 88*24=2112, Resulting Numbers: [2112] 2112,67 unequal: No Solution Exploring Operation: 88+24=112, Resulting Numbers: [112] 112,67 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 #0,1,3 Current State: 67:[29, 35], Operations: ['13+16=29', '88-53=35'] Exploring Operation: 29*35=1015, Resulting Numbers: [1015] 1015,67 unequal: No Solution Exploring Operation: 29+35=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,67 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: 67:[16, 53, 75], Operations: ['88-13=75'] Exploring Operation: 75-53=22, Resulting Numbers: [16, 22] Generated Node #0,4,0: 67:[16, 22] Operation: 75-53=22 Exploring Operation: 75-16=59, Resulting Numbers: [53, 59] Generated Node #0,4,1: 67:[53, 59] Operation: 75-16=59 Exploring Operation: 16+75=91, Resulting Numbers: [53, 91] Generated Node #0,4,2: 67:[53, 91] Operation: 16+75=91 Exploring Operation: 16+53=69, Resulting Numbers: [75, 69] Generated Node #0,4,3: 67:[75, 69] Operation: 16+53=69 Exploring Operation: 53-16=37, Resulting Numbers: [75, 37] Generated Node #0,4,4: 67:[75, 37] Operation: 53-16=37 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 67:[75, 69], Operations: ['88-13=75', '16+53=69'] Exploring Operation: 75*69=5175, Resulting Numbers: [5175] 5175,67 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,67 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 #0,4,1 Current State: 67:[53, 59], Operations: ['88-13=75', '75-16=59'] Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,67 unequal: No Solution Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,67 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 #0,4,2 Current State: 67:[53, 91], Operations: ['88-13=75', '16+75=91'] Exploring Operation: 53*91=4823, Resulting Numbers: [4823] 4823,67 unequal: No Solution Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 53+91=144, Resulting Numbers: [144] 144,67 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 #0,4,4 Current State: 67:[75, 37], Operations: ['88-13=75', '53-16=37'] Exploring Operation: 75*37=2775, Resulting Numbers: [2775] 2775,67 unequal: No Solution Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 75+37=112, Resulting Numbers: [112] 112,67 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 #0,4,0 Current State: 67:[16, 22], Operations: ['88-13=75', '75-53=22'] Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,67 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: 67:[13, 88, 69], Operations: ['16+53=69'] Exploring Operation: 13+69=82, Resulting Numbers: [88, 82] Generated Node #0,3,0: 67:[88, 82] Operation: 13+69=82 Exploring Operation: 88-13=75, Resulting Numbers: [69, 75] Generated Node #0,3,1: 67:[69, 75] Operation: 88-13=75 Exploring Operation: 13+88=101, Resulting Numbers: [69, 101] Generated Node #0,3,2: 67:[69, 101] Operation: 13+88=101 Exploring Operation: 88-69=19, Resulting Numbers: [13, 19] Generated Node #0,3,3: 67:[13, 19] Operation: 88-69=19 Exploring Operation: 69-13=56, Resulting Numbers: [88, 56] Generated Node #0,3,4: 67:[88, 56] Operation: 69-13=56 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 67:[69, 75], Operations: ['16+53=69', '88-13=75'] Exploring Operation: 69+75=144, Resulting Numbers: [144] 144,67 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 69*75=5175, Resulting Numbers: [5175] 5175,67 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 #0,3,4 Current State: 67:[88, 56], Operations: ['16+53=69', '69-13=56'] Exploring Operation: 88*56=4928, Resulting Numbers: [4928] 4928,67 unequal: No Solution Exploring Operation: 88-56=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 88+56=144, Resulting Numbers: [144] 144,67 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 #0,3,0 Current State: 67:[88, 82], Operations: ['16+53=69', '13+69=82'] Exploring Operation: 88+82=170, Resulting Numbers: [170] 170,67 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 88*82=7216, Resulting Numbers: [7216] 7216,67 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 #0,3,2 Current State: 67:[69, 101], Operations: ['16+53=69', '13+88=101'] Exploring Operation: 69*101=6969, Resulting Numbers: [6969] 6969,67 unequal: No Solution Exploring Operation: 69+101=170, Resulting Numbers: [170] 170,67 unequal: No Solution Exploring Operation: 101-69=32, Resulting Numbers: [32] 32,67 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 #0,3,3 Current State: 67:[13, 19], Operations: ['16+53=69', '88-69=19'] Exploring Operation: 13*19=247, Resulting Numbers: [247] 247,67 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,67 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: 67:[66, 72], Operations: ['13+53=66', '88-16=72'] Exploring Operation: 66*72=4752, Resulting Numbers: [4752] 4752,67 unequal: No Solution Exploring Operation: 72-66=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 66+72=138, Resulting Numbers: [138] 138,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[88, 82], Operations: ['13+53=66', '16+66=82'] Exploring Operation: 88+82=170, Resulting Numbers: [170] 170,67 unequal: No Solution Exploring Operation: 88*82=7216, Resulting Numbers: [7216] 7216,67 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[66, 104], Operations: ['13+53=66', '16+88=104'] Exploring Operation: 66+104=170, Resulting Numbers: [170] 170,67 unequal: No Solution Exploring Operation: 66*104=6864, Resulting Numbers: [6864] 6864,67 unequal: No Solution Exploring Operation: 104-66=38, Resulting Numbers: [38] 38,67 unequal: No Solution Moving to Node #0,2,4 Current State: 67:[88, 50], Operations: ['13+53=66', '66-16=50'] Exploring Operation: 88*50=4400, Resulting Numbers: [4400] 4400,67 unequal: No Solution Exploring Operation: 88+50=138, Resulting Numbers: [138] 138,67 unequal: No Solution Exploring Operation: 88-50=38, Resulting Numbers: [38] 38,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[16, 22], Operations: ['13+53=66', '88-66=22'] Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,67 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 34, 70, 36, 82 ]
76
[ "36-34=2", "70+82=152", "152/2=76" ]
Current State: 76:[34, 70, 36, 82], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [70, 82, 2] Generated Node #2: [70, 82, 2] from Operation: 36-34=2 Current State: 76:[70, 82, 2], Operations: ['36-34=2'] Exploring Operation: 70+82=152, Resulting Numbers: [2, 152] Generated Node #3: [2, 152] from Operation: 70+82=152 Current State: 76:[2, 152], Operations: ['36-34=2', '70+82=152'] Exploring Operation: 152/2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[34, 70, 36, 82], Operations: [] Exploring Operation: 70-34=36, Resulting Numbers: [36, 82, 36] Generated Node #0,0: 76:[36, 82, 36] Operation: 70-34=36 Exploring Operation: 36-34=2, Resulting Numbers: [70, 82, 2] Generated Node #0,1: 76:[70, 82, 2] Operation: 36-34=2 Exploring Operation: 82-70=12, Resulting Numbers: [34, 36, 12] Generated Node #0,2: 76:[34, 36, 12] Operation: 82-70=12 Moving to Node #0,0 Current State: 76:[36, 82, 36], Operations: ['70-34=36'] Exploring Operation: 36-36=0, Resulting Numbers: [82, 0] Generated Node #0,0,0: 76:[82, 0] Operation: 36-36=0 Exploring Operation: 82-36=46, Resulting Numbers: [36, 46] Generated Node #0,0,1: 76:[36, 46] Operation: 82-36=46 Exploring Operation: 36/36=1, Resulting Numbers: [82, 1] Generated Node #0,0,2: 76:[82, 1] Operation: 36/36=1 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[82, 1], Operations: ['70-34=36', '36/36=1'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,76 unequal: No Solution Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 82*1=82, Resulting Numbers: [82] 82,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[82, 0], Operations: ['70-34=36', '36-36=0'] Exploring Operation: 82*0=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 82-0=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 82+0=82, Resulting Numbers: [82] 82,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[36, 46], Operations: ['70-34=36', '82-36=46'] Exploring Operation: 36+46=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 36*46=1656, Resulting Numbers: [1656] 1656,76 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: 76:[70, 82, 2], Operations: ['36-34=2'] Exploring Operation: 82-70=12, Resulting Numbers: [2, 12] Generated Node #0,1,0: 76:[2, 12] Operation: 82-70=12 Exploring Operation: 70/2=35, Resulting Numbers: [82, 35] Generated Node #0,1,1: 76:[82, 35] Operation: 70/2=35 Exploring Operation: 82/2=41, Resulting Numbers: [70, 41] Generated Node #0,1,2: 76:[70, 41] Operation: 82/2=41 Moving to Node #0,2 Current State: 76:[34, 36, 12], Operations: ['82-70=12'] Exploring Operation: 36-34=2, Resulting Numbers: [12, 2] Generated Node #0,2,0: 76:[12, 2] Operation: 36-34=2 Exploring Operation: 36/12=3, Resulting Numbers: [34, 3] Generated Node #0,2,1: 76:[34, 3] Operation: 36/12=3 Exploring Operation: 34-12=22, Resulting Numbers: [36, 22] Generated Node #0,2,2: 76:[36, 22] Operation: 34-12=22 Moving to Node #0,2,1 Current State: 76:[34, 3], Operations: ['82-70=12', '36/12=3'] Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,76 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,76 unequal: No Solution Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[36, 22], Operations: ['82-70=12', '34-12=22'] Exploring Operation: 36*22=792, Resulting Numbers: [792] 792,76 unequal: No Solution Exploring Operation: 36+22=58, Resulting Numbers: [58] 58,76 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[12, 2], Operations: ['82-70=12', '36-34=2'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[2, 12], Operations: ['36-34=2', '82-70=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[82, 35], Operations: ['36-34=2', '70/2=35'] Exploring Operation: 82+35=117, Resulting Numbers: [117] 117,76 unequal: No Solution Exploring Operation: 82-35=47, Resulting Numbers: [47] 47,76 unequal: No Solution Exploring Operation: 82*35=2870, Resulting Numbers: [2870] 2870,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[70, 41], Operations: ['36-34=2', '82/2=41'] Exploring Operation: 70*41=2870, Resulting Numbers: [2870] 2870,76 unequal: No Solution Exploring Operation: 70-41=29, Resulting Numbers: [29] 29,76 unequal: No Solution Exploring Operation: 70+41=111, Resulting Numbers: [111] 111,76 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 40, 7, 89, 48 ]
74
[ "40-7=33", "89-48=41", "33+41=74" ]
Current State: 74:[40, 7, 89, 48], Operations: [] Exploring Operation: 40-7=33, Resulting Numbers: [89, 48, 33] Generated Node #2: [89, 48, 33] from Operation: 40-7=33 Current State: 74:[89, 48, 33], Operations: ['40-7=33'] Exploring Operation: 89-48=41, Resulting Numbers: [33, 41] Generated Node #3: [33, 41] from Operation: 89-48=41 Current State: 74:[33, 41], Operations: ['40-7=33', '89-48=41'] Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[40, 7, 89, 48], Operations: [] Exploring Operation: 89-7=82, Resulting Numbers: [40, 48, 82] Generated Node #0,0: 74:[40, 48, 82] Operation: 89-7=82 Exploring Operation: 89-48=41, Resulting Numbers: [40, 7, 41] Generated Node #0,1: 74:[40, 7, 41] Operation: 89-48=41 Moving to Node #0,1 Current State: 74:[40, 7, 41], Operations: ['89-48=41'] Exploring Operation: 41-7=34, Resulting Numbers: [40, 34] Generated Node #0,1,0: 74:[40, 34] Operation: 41-7=34 Exploring Operation: 41-40=1, Resulting Numbers: [7, 1] Generated Node #0,1,1: 74:[7, 1] Operation: 41-40=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[40, 34], Operations: ['89-48=41', '41-7=34'] Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[40, 7, 89, 48], Operations: [] Exploring Operation: 89-48=41, Resulting Numbers: [40, 7, 41] Generated Node #0,1: 74:[40, 7, 41] Operation: 89-48=41 Moving to Node #0,1 Current State: 74:[40, 7, 41], Operations: ['89-48=41'] Exploring Operation: 41-7=34, Resulting Numbers: [40, 34] Generated Node #0,1,0: 74:[40, 34] Operation: 41-7=34 Moving to Node #0,1,0 Current State: 74:[40, 34], Operations: ['89-48=41', '41-7=34'] Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 10, 64, 8, 60 ]
28
[ "10-8=2", "64/2=32", "60-32=28" ]
Current State: 28:[10, 64, 8, 60], Operations: [] Exploring Operation: 10-8=2, Resulting Numbers: [64, 60, 2] Generated Node #2: [64, 60, 2] from Operation: 10-8=2 Current State: 28:[64, 60, 2], Operations: ['10-8=2'] Exploring Operation: 64/2=32, Resulting Numbers: [60, 32] Generated Node #3: [60, 32] from Operation: 64/2=32 Current State: 28:[60, 32], Operations: ['10-8=2', '64/2=32'] Exploring Operation: 60-32=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[10, 64, 8, 60], Operations: [] Exploring Operation: 64/8=8, Resulting Numbers: [10, 60, 8] Generated Node #0,0: 28:[10, 60, 8] Operation: 64/8=8 Exploring Operation: 64-60=4, Resulting Numbers: [10, 8, 4] Generated Node #0,1: 28:[10, 8, 4] Operation: 64-60=4 Moving to Node #0,1 Current State: 28:[10, 8, 4], Operations: ['64-60=4'] Exploring Operation: 10+4=14, Resulting Numbers: [8, 14] Generated Node #0,1,0: 28:[8, 14] Operation: 10+4=14 Exploring Operation: 10-8=2, Resulting Numbers: [4, 2] Generated Node #0,1,1: 28:[4, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[4, 2], Operations: ['64-60=4', '10-8=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[8, 14], Operations: ['64-60=4', '10+4=14'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,28 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: 28:[10, 60, 8], Operations: ['64/8=8'] Exploring Operation: 60-10=50, Resulting Numbers: [8, 50] Generated Node #0,0,0: 28:[8, 50] Operation: 60-10=50 Exploring Operation: 60/10=6, Resulting Numbers: [8, 6] Generated Node #0,0,1: 28:[8, 6] Operation: 60/10=6 Moving to Node #0,0,1 Current State: 28:[8, 6], Operations: ['64/8=8', '60/10=6'] Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[8, 50], Operations: ['64/8=8', '60-10=50'] Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,28 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 58, 88, 38, 52 ]
44
[ "88-58=30", "52-38=14", "30+14=44" ]
Current State: 44:[58, 88, 38, 52], Operations: [] Exploring Operation: 88-58=30, Resulting Numbers: [38, 52, 30] Generated Node #2: [38, 52, 30] from Operation: 88-58=30 Current State: 44:[38, 52, 30], Operations: ['88-58=30'] Exploring Operation: 52-38=14, Resulting Numbers: [30, 14] Generated Node #3: [30, 14] from Operation: 52-38=14 Current State: 44:[30, 14], Operations: ['88-58=30', '52-38=14'] Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[58, 88, 38, 52], Operations: [] Exploring Operation: 88-38=50, Resulting Numbers: [58, 52, 50] Generated Node #0,0: 44:[58, 52, 50] Operation: 88-38=50 Exploring Operation: 88-52=36, Resulting Numbers: [58, 38, 36] Generated Node #0,1: 44:[58, 38, 36] Operation: 88-52=36 Exploring Operation: 88-58=30, Resulting Numbers: [38, 52, 30] Generated Node #0,2: 44:[38, 52, 30] Operation: 88-58=30 Exploring Operation: 58-38=20, Resulting Numbers: [88, 52, 20] Generated Node #0,3: 44:[88, 52, 20] Operation: 58-38=20 Exploring Operation: 58-52=6, Resulting Numbers: [88, 38, 6] Generated Node #0,4: 44:[88, 38, 6] Operation: 58-52=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[38, 52, 30], Operations: ['88-58=30'] Exploring Operation: 52-38=14, Resulting Numbers: [30, 14] Generated Node #0,2,0: 44:[30, 14] Operation: 52-38=14 Exploring Operation: 38-30=8, Resulting Numbers: [52, 8] Generated Node #0,2,1: 44:[52, 8] Operation: 38-30=8 Exploring Operation: 52-30=22, Resulting Numbers: [38, 22] Generated Node #0,2,2: 44:[38, 22] Operation: 52-30=22 Exploring Operation: 38+30=68, Resulting Numbers: [52, 68] Generated Node #0,2,3: 44:[52, 68] Operation: 38+30=68 Exploring Operation: 52+30=82, Resulting Numbers: [38, 82] Generated Node #0,2,4: 44:[38, 82] Operation: 52+30=82 Moving to Node #0,2,2 Current State: 44:[38, 22], Operations: ['88-58=30', '52-30=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 38*22=836, Resulting Numbers: [836] 836,44 unequal: No Solution Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[52, 8], Operations: ['88-58=30', '38-30=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[58, 88, 38, 52], Operations: [] Exploring Operation: 88-58=30, Resulting Numbers: [38, 52, 30] Generated Node #0,2: 44:[38, 52, 30] Operation: 88-58=30 Moving to Node #0,2 Current State: 44:[38, 52, 30], Operations: ['88-58=30'] Exploring Operation: 38-30=8, Resulting Numbers: [52, 8] Generated Node #0,2,1: 44:[52, 8] Operation: 38-30=8 Moving to Node #0,2,1 Current State: 44:[52, 8], Operations: ['88-58=30', '38-30=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 84, 95, 51, 70 ]
63
[ "84*95=7980", "7980/70=114", "114-51=63" ]
Current State: 63:[84, 95, 51, 70], Operations: [] Exploring Operation: 84*95=7980, Resulting Numbers: [51, 70, 7980] Generated Node #2: [51, 70, 7980] from Operation: 84*95=7980 Current State: 63:[51, 70, 7980], Operations: ['84*95=7980'] Exploring Operation: 7980/70=114, Resulting Numbers: [51, 114] Generated Node #3: [51, 114] from Operation: 7980/70=114 Current State: 63:[51, 114], Operations: ['84*95=7980', '7980/70=114'] Exploring Operation: 114-51=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[84, 95, 51, 70], Operations: [] Exploring Operation: 95-84=11, Resulting Numbers: [51, 70, 11] Generated Node #0,0: 63:[51, 70, 11] Operation: 95-84=11 Exploring Operation: 95-51=44, Resulting Numbers: [84, 70, 44] Generated Node #0,1: 63:[84, 70, 44] Operation: 95-51=44 Exploring Operation: 95-70=25, Resulting Numbers: [84, 51, 25] Generated Node #0,2: 63:[84, 51, 25] Operation: 95-70=25 Moving to Node #0,0 Current State: 63:[51, 70, 11], Operations: ['95-84=11'] Exploring Operation: 70-51=19, Resulting Numbers: [11, 19] Generated Node #0,0,0: 63:[11, 19] Operation: 70-51=19 Exploring Operation: 70-11=59, Resulting Numbers: [51, 59] Generated Node #0,0,1: 63:[51, 59] Operation: 70-11=59 Exploring Operation: 51+11=62, Resulting Numbers: [70, 62] Generated Node #0,0,2: 63:[70, 62] Operation: 51+11=62 Moving to Node #0,2 Current State: 63:[84, 51, 25], Operations: ['95-70=25'] Exploring Operation: 84-25=59, Resulting Numbers: [51, 59] Generated Node #0,2,0: 63:[51, 59] Operation: 84-25=59 Exploring Operation: 84-51=33, Resulting Numbers: [25, 33] Generated Node #0,2,1: 63:[25, 33] Operation: 84-51=33 Exploring Operation: 51-25=26, Resulting Numbers: [84, 26] Generated Node #0,2,2: 63:[84, 26] Operation: 51-25=26 Moving to Node #0,1 Current State: 63:[84, 70, 44], Operations: ['95-51=44'] Exploring Operation: 84-70=14, Resulting Numbers: [44, 14] Generated Node #0,1,0: 63:[44, 14] Operation: 84-70=14 Exploring Operation: 70-44=26, Resulting Numbers: [84, 26] Generated Node #0,1,1: 63:[84, 26] Operation: 70-44=26 Exploring Operation: 84-44=40, Resulting Numbers: [70, 40] Generated Node #0,1,2: 63:[70, 40] Operation: 84-44=40 Moving to Node #0,0,0 Current State: 63:[11, 19], Operations: ['95-84=11', '70-51=19'] Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,63 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[70, 62], Operations: ['95-84=11', '51+11=62'] Exploring Operation: 70+62=132, Resulting Numbers: [132] 132,63 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 70*62=4340, Resulting Numbers: [4340] 4340,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[51, 59], Operations: ['95-84=11', '70-11=59'] Exploring Operation: 51+59=110, Resulting Numbers: [110] 110,63 unequal: No Solution Exploring Operation: 51*59=3009, Resulting Numbers: [3009] 3009,63 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[25, 33], Operations: ['95-70=25', '84-51=33'] Exploring Operation: 25*33=825, Resulting Numbers: [825] 825,63 unequal: No Solution Exploring Operation: 25+33=58, Resulting Numbers: [58] 58,63 unequal: No Solution Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[51, 59], Operations: ['95-70=25', '84-25=59'] Exploring Operation: 51*59=3009, Resulting Numbers: [3009] 3009,63 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 51+59=110, Resulting Numbers: [110] 110,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[44, 14], Operations: ['95-51=44', '84-70=14'] Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,63 unequal: No Solution Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[84, 26], Operations: ['95-70=25', '51-25=26'] Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,63 unequal: No Solution Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,63 unequal: No Solution Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[70, 40], Operations: ['95-51=44', '84-44=40'] Exploring Operation: 70-40=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 70*40=2800, Resulting Numbers: [2800] 2800,63 unequal: No Solution Exploring Operation: 70+40=110, Resulting Numbers: [110] 110,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[84, 26], Operations: ['95-51=44', '70-44=26'] Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,63 unequal: No Solution Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,63 unequal: No Solution Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,63 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 57, 26, 38, 33 ]
19
[ "57-26=31", "33-31=2", "38/2=19" ]
Current State: 19:[57, 26, 38, 33], Operations: [] Exploring Operation: 57-26=31, Resulting Numbers: [38, 33, 31] Generated Node #2: [38, 33, 31] from Operation: 57-26=31 Current State: 19:[38, 33, 31], Operations: ['57-26=31'] Exploring Operation: 33-31=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 33-31=2 Current State: 19:[38, 2], Operations: ['57-26=31', '33-31=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[57, 26, 38, 33], Operations: [] Exploring Operation: 57-33=24, Resulting Numbers: [26, 38, 24] Generated Node #0,0: 19:[26, 38, 24] Operation: 57-33=24 Exploring Operation: 57-38=19, Resulting Numbers: [26, 33, 19] Generated Node #0,1: 19:[26, 33, 19] Operation: 57-38=19 Exploring Operation: 57-26=31, Resulting Numbers: [38, 33, 31] Generated Node #0,2: 19:[38, 33, 31] Operation: 57-26=31 Exploring Operation: 38-26=12, Resulting Numbers: [57, 33, 12] Generated Node #0,3: 19:[57, 33, 12] Operation: 38-26=12 Exploring Operation: 38-33=5, Resulting Numbers: [57, 26, 5] Generated Node #0,4: 19:[57, 26, 5] Operation: 38-33=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[26, 33, 19], Operations: ['57-38=19'] Exploring Operation: 26+33=59, Resulting Numbers: [19, 59] Generated Node #0,1,0: 19:[19, 59] Operation: 26+33=59 Exploring Operation: 33-26=7, Resulting Numbers: [19, 7] Generated Node #0,1,1: 19:[19, 7] Operation: 33-26=7 Exploring Operation: 26+19=45, Resulting Numbers: [33, 45] Generated Node #0,1,2: 19:[33, 45] Operation: 26+19=45 Exploring Operation: 33-19=14, Resulting Numbers: [26, 14] Generated Node #0,1,3: 19:[26, 14] Operation: 33-19=14 Exploring Operation: 26-19=7, Resulting Numbers: [33, 7] Generated Node #0,1,4: 19:[33, 7] Operation: 26-19=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[19, 7], Operations: ['57-38=19', '33-26=7'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,19 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,19 unequal: No Solution No 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: 19:[26, 14], Operations: ['57-38=19', '33-19=14'] Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,19 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 19:[33, 7], Operations: ['57-38=19', '26-19=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,19 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,19 unequal: No Solution No 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: 19:[19, 59], Operations: ['57-38=19', '26+33=59'] Exploring Operation: 59-19=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 19+59=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 19*59=1121, Resulting Numbers: [1121] 1121,19 unequal: No Solution No 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: 19:[33, 45], Operations: ['57-38=19', '26+19=45'] Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 33*45=1485, Resulting Numbers: [1485] 1485,19 unequal: No Solution Exploring Operation: 33+45=78, Resulting Numbers: [78] 78,19 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[26, 38, 24], Operations: ['57-33=24'] Exploring Operation: 38-26=12, Resulting Numbers: [24, 12] Generated Node #0,0,0: 19:[24, 12] Operation: 38-26=12 Exploring Operation: 26-24=2, Resulting Numbers: [38, 2] Generated Node #0,0,1: 19:[38, 2] Operation: 26-24=2 Exploring Operation: 38-24=14, Resulting Numbers: [26, 14] Generated Node #0,0,2: 19:[26, 14] Operation: 38-24=14 Exploring Operation: 26+38=64, Resulting Numbers: [24, 64] Generated Node #0,0,3: 19:[24, 64] Operation: 26+38=64 Exploring Operation: 26+24=50, Resulting Numbers: [38, 50] Generated Node #0,0,4: 19:[38, 50] Operation: 26+24=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[24, 12], Operations: ['57-33=24', '38-26=12'] Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 24*12=288, Resulting Numbers: [288] 288,19 unequal: No Solution Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,19 unequal: No Solution No 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: 19:[26, 14], Operations: ['57-33=24', '38-24=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,19 unequal: No Solution No 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: 19:[38, 2], Operations: ['57-33=24', '26-24=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[57, 26, 38, 33], Operations: [] Exploring Operation: 57-33=24, Resulting Numbers: [26, 38, 24] Generated Node #0,0: 19:[26, 38, 24] Operation: 57-33=24 Moving to Node #0,0 Current State: 19:[26, 38, 24], Operations: ['57-33=24'] Exploring Operation: 26-24=2, Resulting Numbers: [38, 2] Generated Node #0,0,1: 19:[38, 2] Operation: 26-24=2 Moving to Node #0,0,1 Current State: 19:[38, 2], Operations: ['57-33=24', '26-24=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic
[ 66, 16, 96, 95 ]
83
[ "66+16=82", "96-95=1", "82+1=83" ]
Current State: 83:[66, 16, 96, 95], Operations: [] Exploring Operation: 66+16=82, Resulting Numbers: [96, 95, 82] Generated Node #2: [96, 95, 82] from Operation: 66+16=82 Current State: 83:[96, 95, 82], Operations: ['66+16=82'] Exploring Operation: 96-95=1, Resulting Numbers: [82, 1] Generated Node #3: [82, 1] from Operation: 96-95=1 Current State: 83:[82, 1], Operations: ['66+16=82', '96-95=1'] Exploring Operation: 82+1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[66, 16, 96, 95], Operations: [] Exploring Operation: 66+16=82, Resulting Numbers: [96, 95, 82] Generated Node #0,0: 83:[96, 95, 82] Operation: 66+16=82 Exploring Operation: 96-16=80, Resulting Numbers: [66, 95, 80] Generated Node #0,1: 83:[66, 95, 80] Operation: 96-16=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[96, 95, 82], Operations: ['66+16=82'] Exploring Operation: 96-95=1, Resulting Numbers: [82, 1] Generated Node #0,0,0: 83:[82, 1] Operation: 96-95=1 Exploring Operation: 96-82=14, Resulting Numbers: [95, 14] Generated Node #0,0,1: 83:[95, 14] Operation: 96-82=14 Moving to Node #0,0,1 Current State: 83:[95, 14], Operations: ['66+16=82', '96-82=14'] Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,83 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[82, 1], Operations: ['66+16=82', '96-95=1'] Exploring Operation: 82+1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[66, 16, 96, 95], Operations: [] Exploring Operation: 66+16=82, Resulting Numbers: [96, 95, 82] Generated Node #0,0: 83:[96, 95, 82] Operation: 66+16=82 Moving to Node #0,0 Current State: 83:[96, 95, 82], Operations: ['66+16=82'] Exploring Operation: 96-95=1, Resulting Numbers: [82, 1] Generated Node #0,0,0: 83:[82, 1] Operation: 96-95=1 Moving to Node #0,0,0 Current State: 83:[82, 1], Operations: ['66+16=82', '96-95=1'] Exploring Operation: 82+1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 86, 60, 45, 64 ]
45
[ "86-60=26", "64-45=19", "26+19=45" ]
Current State: 45:[86, 60, 45, 64], Operations: [] Exploring Operation: 86-60=26, Resulting Numbers: [45, 64, 26] Generated Node #2: [45, 64, 26] from Operation: 86-60=26 Current State: 45:[45, 64, 26], Operations: ['86-60=26'] Exploring Operation: 64-45=19, Resulting Numbers: [26, 19] Generated Node #3: [26, 19] from Operation: 64-45=19 Current State: 45:[26, 19], Operations: ['86-60=26', '64-45=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[86, 60, 45, 64], Operations: [] Exploring Operation: 86-60=26, Resulting Numbers: [45, 64, 26] Generated Node #0,0: 45:[45, 64, 26] Operation: 86-60=26 Exploring Operation: 86-64=22, Resulting Numbers: [60, 45, 22] Generated Node #0,1: 45:[60, 45, 22] Operation: 86-64=22 Exploring Operation: 86-45=41, Resulting Numbers: [60, 64, 41] Generated Node #0,2: 45:[60, 64, 41] Operation: 86-45=41 Exploring Operation: 64-60=4, Resulting Numbers: [86, 45, 4] Generated Node #0,3: 45:[86, 45, 4] Operation: 64-60=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[60, 45, 22], Operations: ['86-64=22'] Exploring Operation: 60-45=15, Resulting Numbers: [22, 15] Generated Node #0,1,0: 45:[22, 15] Operation: 60-45=15 Exploring Operation: 60+22=82, Resulting Numbers: [45, 82] Generated Node #0,1,1: 45:[45, 82] Operation: 60+22=82 Exploring Operation: 45-22=23, Resulting Numbers: [60, 23] Generated Node #0,1,2: 45:[60, 23] Operation: 45-22=23 Exploring Operation: 60-22=38, Resulting Numbers: [45, 38] Generated Node #0,1,3: 45:[45, 38] Operation: 60-22=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[22, 15], Operations: ['86-64=22', '60-45=15'] Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,45 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 45:[45, 38], Operations: ['86-64=22', '60-22=38'] Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,45 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 45:[60, 23], Operations: ['86-64=22', '45-22=23'] Exploring Operation: 60+23=83, Resulting Numbers: [83] 83,45 unequal: No Solution Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,45 unequal: No Solution Exploring Operation: 60*23=1380, Resulting Numbers: [1380] 1380,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[45, 82], Operations: ['86-64=22', '60+22=82'] Exploring Operation: 45*82=3690, Resulting Numbers: [3690] 3690,45 unequal: No Solution Exploring Operation: 45+82=127, Resulting Numbers: [127] 127,45 unequal: No Solution Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[45, 64, 26], Operations: ['86-60=26'] Exploring Operation: 64-45=19, Resulting Numbers: [26, 19] Generated Node #0,0,0: 45:[26, 19] Operation: 64-45=19 Exploring Operation: 64-26=38, Resulting Numbers: [45, 38] Generated Node #0,0,1: 45:[45, 38] Operation: 64-26=38 Exploring Operation: 45+26=71, Resulting Numbers: [64, 71] Generated Node #0,0,2: 45:[64, 71] Operation: 45+26=71 Exploring Operation: 45-26=19, Resulting Numbers: [64, 19] Generated Node #0,0,3: 45:[64, 19] Operation: 45-26=19 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[45, 38], Operations: ['86-60=26', '64-26=38'] Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,45 unequal: No Solution Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,45 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[26, 19], Operations: ['86-60=26', '64-45=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[86, 60, 45, 64], Operations: [] Exploring Operation: 86-60=26, Resulting Numbers: [45, 64, 26] Generated Node #0,0: 45:[45, 64, 26] Operation: 86-60=26 Moving to Node #0,0 Current State: 45:[45, 64, 26], Operations: ['86-60=26'] Exploring Operation: 64-45=19, Resulting Numbers: [26, 19] Generated Node #0,0,0: 45:[26, 19] Operation: 64-45=19 Moving to Node #0,0,0 Current State: 45:[26, 19], Operations: ['86-60=26', '64-45=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 73, 92, 35, 32 ]
98
[ "73+92=165", "35+32=67", "165-67=98" ]
Current State: 98:[73, 92, 35, 32], Operations: [] Exploring Operation: 73+92=165, Resulting Numbers: [35, 32, 165] Generated Node #2: [35, 32, 165] from Operation: 73+92=165 Current State: 98:[35, 32, 165], Operations: ['73+92=165'] Exploring Operation: 35+32=67, Resulting Numbers: [165, 67] Generated Node #3: [165, 67] from Operation: 35+32=67 Current State: 98:[165, 67], Operations: ['73+92=165', '35+32=67'] Exploring Operation: 165-67=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[73, 92, 35, 32], Operations: [] Exploring Operation: 73-32=41, Resulting Numbers: [92, 35, 41] Generated Node #0,0: 98:[92, 35, 41] Operation: 73-32=41 Exploring Operation: 73+32=105, Resulting Numbers: [92, 35, 105] Generated Node #0,1: 98:[92, 35, 105] Operation: 73+32=105 Exploring Operation: 35-32=3, Resulting Numbers: [73, 92, 3] Generated Node #0,2: 98:[73, 92, 3] Operation: 35-32=3 Moving to Node #0,1 Current State: 98:[92, 35, 105], Operations: ['73+32=105'] Exploring Operation: 105-92=13, Resulting Numbers: [35, 13] Generated Node #0,1,0: 98:[35, 13] Operation: 105-92=13 Exploring Operation: 105/35=3, Resulting Numbers: [92, 3] Generated Node #0,1,1: 98:[92, 3] Operation: 105/35=3 Exploring Operation: 92-35=57, Resulting Numbers: [105, 57] Generated Node #0,1,2: 98:[105, 57] Operation: 92-35=57 Moving to Node #0,0 Current State: 98:[92, 35, 41], Operations: ['73-32=41'] Exploring Operation: 92-35=57, Resulting Numbers: [41, 57] Generated Node #0,0,0: 98:[41, 57] Operation: 92-35=57 Exploring Operation: 41-35=6, Resulting Numbers: [92, 6] Generated Node #0,0,1: 98:[92, 6] Operation: 41-35=6 Exploring Operation: 92-41=51, Resulting Numbers: [35, 51] Generated Node #0,0,2: 98:[35, 51] Operation: 92-41=51 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 98:[92, 6], Operations: ['73-32=41', '41-35=6'] Exploring Operation: 92*6=552, Resulting Numbers: [552] 552,98 unequal: No Solution Exploring Operation: 92+6=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[73, 92, 35, 32], Operations: [] Exploring Operation: 73-32=41, Resulting Numbers: [92, 35, 41] Generated Node #0,0: 98:[92, 35, 41] Operation: 73-32=41 Moving to Node #0,0 Current State: 98:[92, 35, 41], Operations: ['73-32=41'] Exploring Operation: 41-35=6, Resulting Numbers: [92, 6] Generated Node #0,0,1: 98:[92, 6] Operation: 41-35=6 Moving to Node #0,0,1 Current State: 98:[92, 6], Operations: ['73-32=41', '41-35=6'] Exploring Operation: 92+6=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 41, 23, 43, 50 ]
96
[ "43-41=2", "23*2=46", "50+46=96" ]
Current State: 96:[41, 23, 43, 50], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [23, 50, 2] Generated Node #2: [23, 50, 2] from Operation: 43-41=2 Current State: 96:[23, 50, 2], Operations: ['43-41=2'] Exploring Operation: 23*2=46, Resulting Numbers: [50, 46] Generated Node #3: [50, 46] from Operation: 23*2=46 Current State: 96:[50, 46], Operations: ['43-41=2', '23*2=46'] Exploring Operation: 50+46=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[41, 23, 43, 50], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [23, 50, 2] Generated Node #0,0: 96:[23, 50, 2] Operation: 43-41=2 Exploring Operation: 50-41=9, Resulting Numbers: [23, 43, 9] Generated Node #0,1: 96:[23, 43, 9] Operation: 50-41=9 Moving to Node #0,0 Current State: 96:[23, 50, 2], Operations: ['43-41=2'] Exploring Operation: 50-2=48, Resulting Numbers: [23, 48] Generated Node #0,0,0: 96:[23, 48] Operation: 50-2=48 Exploring Operation: 50/2=25, Resulting Numbers: [23, 25] Generated Node #0,0,1: 96:[23, 25] Operation: 50/2=25 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[23, 48], Operations: ['43-41=2', '50-2=48'] Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 23+48=71, Resulting Numbers: [71] 71,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 96:[23, 25], Operations: ['43-41=2', '50/2=25'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,96 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: 96:[23, 43, 9], Operations: ['50-41=9'] Exploring Operation: 43-9=34, Resulting Numbers: [23, 34] Generated Node #0,1,0: 96:[23, 34] Operation: 43-9=34 Exploring Operation: 43-23=20, Resulting Numbers: [9, 20] Generated Node #0,1,1: 96:[9, 20] Operation: 43-23=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[23, 34], Operations: ['50-41=9', '43-9=34'] Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[9, 20], Operations: ['50-41=9', '43-23=20'] Exploring Operation: 9+20=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,96 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
[ 16, 79, 66, 84 ]
10
[ "66-16=50", "84-79=5", "50/5=10" ]
Current State: 10:[16, 79, 66, 84], Operations: [] Exploring Operation: 66-16=50, Resulting Numbers: [79, 84, 50] Generated Node #2: [79, 84, 50] from Operation: 66-16=50 Current State: 10:[79, 84, 50], Operations: ['66-16=50'] Exploring Operation: 84-79=5, Resulting Numbers: [50, 5] Generated Node #3: [50, 5] from Operation: 84-79=5 Current State: 10:[50, 5], Operations: ['66-16=50', '84-79=5'] Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[16, 79, 66, 84], Operations: [] Exploring Operation: 84-66=18, Resulting Numbers: [16, 79, 18] Generated Node #0,0: 10:[16, 79, 18] Operation: 84-66=18 Exploring Operation: 84-79=5, Resulting Numbers: [16, 66, 5] Generated Node #0,1: 10:[16, 66, 5] Operation: 84-79=5 Exploring Operation: 79-66=13, Resulting Numbers: [16, 84, 13] Generated Node #0,2: 10:[16, 84, 13] Operation: 79-66=13 Moving to Node #0,1 Current State: 10:[16, 66, 5], Operations: ['84-79=5'] Exploring Operation: 66-5=61, Resulting Numbers: [16, 61] Generated Node #0,1,0: 10:[16, 61] Operation: 66-5=61 Exploring Operation: 16-5=11, Resulting Numbers: [66, 11] Generated Node #0,1,1: 10:[66, 11] Operation: 16-5=11 Exploring Operation: 66-16=50, Resulting Numbers: [5, 50] Generated Node #0,1,2: 10:[5, 50] Operation: 66-16=50 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[5, 50], Operations: ['84-79=5', '66-16=50'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,10 unequal: No Solution Exploring Operation: 5+50=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[16, 79, 66, 84], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [16, 66, 5] Generated Node #0,1: 10:[16, 66, 5] Operation: 84-79=5 Moving to Node #0,1 Current State: 10:[16, 66, 5], Operations: ['84-79=5'] Exploring Operation: 66-16=50, Resulting Numbers: [5, 50] Generated Node #0,1,2: 10:[5, 50] Operation: 66-16=50 Moving to Node #0,1,2 Current State: 10:[5, 50], Operations: ['84-79=5', '66-16=50'] Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 9, 59, 11, 9 ]
52
[ "59-9=50", "11-9=2", "50+2=52" ]
Current State: 52:[9, 59, 11, 9], Operations: [] Exploring Operation: 59-9=50, Resulting Numbers: [11, 50] Generated Node #2: [11, 50] from Operation: 59-9=50 Current State: 52:[11, 50], Operations: ['59-9=50'] Exploring Operation: 11-9=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 11-9=2 Current State: 52:[50, 2], Operations: ['59-9=50', '11-9=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[9, 59, 11, 9], Operations: [] Exploring Operation: 11-9=2, Resulting Numbers: [59, 9, 2] Generated Node #0,0: 52:[59, 9, 2] Operation: 11-9=2 Exploring Operation: 9/9=1, Resulting Numbers: [59, 11, 1] Generated Node #0,1: 52:[59, 11, 1] Operation: 9/9=1 Exploring Operation: 59-9=50, Resulting Numbers: [9, 11, 50] Generated Node #0,2: 52:[9, 11, 50] Operation: 59-9=50 Exploring Operation: 9-9=0, Resulting Numbers: [59, 11, 0] Generated Node #0,3: 52:[59, 11, 0] Operation: 9-9=0 Exploring Operation: 59-9=50, Resulting Numbers: [11, 9, 50] Generated Node #0,4: 52:[11, 9, 50] Operation: 59-9=50 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[9, 11, 50], Operations: ['59-9=50'] Exploring Operation: 11-9=2, Resulting Numbers: [50, 2] Generated Node #0,2,0: 52:[50, 2] Operation: 11-9=2 Exploring Operation: 50-9=41, Resulting Numbers: [11, 41] Generated Node #0,2,1: 52:[11, 41] Operation: 50-9=41 Exploring Operation: 11+50=61, Resulting Numbers: [9, 61] Generated Node #0,2,2: 52:[9, 61] Operation: 11+50=61 Exploring Operation: 9+11=20, Resulting Numbers: [50, 20] Generated Node #0,2,3: 52:[50, 20] Operation: 9+11=20 Exploring Operation: 9+50=59, Resulting Numbers: [11, 59] Generated Node #0,2,4: 52:[11, 59] Operation: 9+50=59 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[50, 2], Operations: ['59-9=50', '11-9=2'] Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[9, 59, 11, 9], Operations: [] Exploring Operation: 59-9=50, Resulting Numbers: [9, 11, 50] Generated Node #0,2: 52:[9, 11, 50] Operation: 59-9=50 Moving to Node #0,2 Current State: 52:[9, 11, 50], Operations: ['59-9=50'] Exploring Operation: 11-9=2, Resulting Numbers: [50, 2] Generated Node #0,2,0: 52:[50, 2] Operation: 11-9=2 Moving to Node #0,2,0 Current State: 52:[50, 2], Operations: ['59-9=50', '11-9=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 38, 66, 51, 52 ]
27
[ "66-38=28", "52-51=1", "28-1=27" ]
Current State: 27:[38, 66, 51, 52], Operations: [] Exploring Operation: 66-38=28, Resulting Numbers: [51, 52, 28] Generated Node #2: [51, 52, 28] from Operation: 66-38=28 Current State: 27:[51, 52, 28], Operations: ['66-38=28'] Exploring Operation: 52-51=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 52-51=1 Current State: 27:[28, 1], Operations: ['66-38=28', '52-51=1'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[38, 66, 51, 52], Operations: [] Exploring Operation: 66-52=14, Resulting Numbers: [38, 51, 14] Generated Node #0,0: 27:[38, 51, 14] Operation: 66-52=14 Exploring Operation: 66-51=15, Resulting Numbers: [38, 52, 15] Generated Node #0,1: 27:[38, 52, 15] Operation: 66-51=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[38, 51, 14], Operations: ['66-52=14'] Exploring Operation: 51-14=37, Resulting Numbers: [38, 37] Generated Node #0,0,0: 27:[38, 37] Operation: 51-14=37 Exploring Operation: 51-38=13, Resulting Numbers: [14, 13] Generated Node #0,0,1: 27:[14, 13] Operation: 51-38=13 Moving to Node #0,0,1 Current State: 27:[14, 13], Operations: ['66-52=14', '51-38=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[38, 66, 51, 52], Operations: [] Exploring Operation: 66-52=14, Resulting Numbers: [38, 51, 14] Generated Node #0,0: 27:[38, 51, 14] Operation: 66-52=14 Moving to Node #0,0 Current State: 27:[38, 51, 14], Operations: ['66-52=14'] Exploring Operation: 51-38=13, Resulting Numbers: [14, 13] Generated Node #0,0,1: 27:[14, 13] Operation: 51-38=13 Moving to Node #0,0,1 Current State: 27:[14, 13], Operations: ['66-52=14', '51-38=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 37, 23, 28, 81 ]
14
[ "37-28=9", "81/9=9", "23-9=14" ]
Current State: 14:[37, 23, 28, 81], Operations: [] Exploring Operation: 37-28=9, Resulting Numbers: [23, 81, 9] Generated Node #2: [23, 81, 9] from Operation: 37-28=9 Current State: 14:[23, 81, 9], Operations: ['37-28=9'] Exploring Operation: 81/9=9, Resulting Numbers: [23, 9] Generated Node #3: [23, 9] from Operation: 81/9=9 Current State: 14:[23, 9], Operations: ['37-28=9', '81/9=9'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[37, 23, 28, 81], Operations: [] Exploring Operation: 81-37=44, Resulting Numbers: [23, 28, 44] Generated Node #0,0: 14:[23, 28, 44] Operation: 81-37=44 Exploring Operation: 81-28=53, Resulting Numbers: [37, 23, 53] Generated Node #0,1: 14:[37, 23, 53] Operation: 81-28=53 Moving to Node #0,0 Current State: 14:[23, 28, 44], Operations: ['81-37=44'] Exploring Operation: 44-28=16, Resulting Numbers: [23, 16] Generated Node #0,0,0: 14:[23, 16] Operation: 44-28=16 Exploring Operation: 44-23=21, Resulting Numbers: [28, 21] Generated Node #0,0,1: 14:[28, 21] Operation: 44-23=21 Moving to Node #0,1 Current State: 14:[37, 23, 53], Operations: ['81-28=53'] Exploring Operation: 53-37=16, Resulting Numbers: [23, 16] Generated Node #0,1,0: 14:[23, 16] Operation: 53-37=16 Exploring Operation: 37-23=14, Resulting Numbers: [53, 14] Generated Node #0,1,1: 14:[53, 14] Operation: 37-23=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[23, 16], Operations: ['81-28=53', '53-37=16'] Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,14 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,14 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:[53, 14], Operations: ['81-28=53', '37-23=14'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,14 unequal: No Solution Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,14 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: 14:[23, 16], Operations: ['81-37=44', '44-28=16'] Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[28, 21], Operations: ['81-37=44', '44-23=21'] Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,14 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,14 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 92, 95, 95, 94 ]
94
[ "95-95=0", "92*0=0", "94+0=94" ]
Current State: 94:[92, 95, 95, 94], Operations: [] Exploring Operation: 95-95=0, Resulting Numbers: [92, 94, 0] Generated Node #2: [92, 94, 0] from Operation: 95-95=0 Current State: 94:[92, 94, 0], Operations: ['95-95=0'] Exploring Operation: 92*0=0, Resulting Numbers: [94, 0] Generated Node #3: [94, 0] from Operation: 92*0=0 Current State: 94:[94, 0], Operations: ['95-95=0', '92*0=0'] Exploring Operation: 94+0=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[92, 95, 95, 94], Operations: [] Exploring Operation: 95/95=1, Resulting Numbers: [92, 94, 1] Generated Node #0,0: 94:[92, 94, 1] Operation: 95/95=1 Exploring Operation: 95-92=3, Resulting Numbers: [95, 94, 3] Generated Node #0,1: 94:[95, 94, 3] Operation: 95-92=3 Exploring Operation: 95-92=3, Resulting Numbers: [95, 94, 3] Generated Node #0,2: 94:[95, 94, 3] Operation: 95-92=3 Exploring Operation: 94-92=2, Resulting Numbers: [95, 95, 2] Generated Node #0,3: 94:[95, 95, 2] Operation: 94-92=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[95, 94, 3], Operations: ['95-92=3'] Exploring Operation: 95-94=1, Resulting Numbers: [3, 1] Generated Node #0,1,0: 94:[3, 1] Operation: 95-94=1 Exploring Operation: 95+3=98, Resulting Numbers: [94, 98] Generated Node #0,1,1: 94:[94, 98] Operation: 95+3=98 Exploring Operation: 95-3=92, Resulting Numbers: [94, 92] Generated Node #0,1,2: 94:[94, 92] Operation: 95-3=92 Exploring Operation: 94+3=97, Resulting Numbers: [95, 97] Generated Node #0,1,3: 94:[95, 97] Operation: 94+3=97 Moving to Node #0,1,0 Current State: 94:[3, 1], Operations: ['95-92=3', '95-94=1'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[94, 92], Operations: ['95-92=3', '95-3=92'] Exploring Operation: 94+92=186, Resulting Numbers: [186] 186,94 unequal: No Solution Exploring Operation: 94*92=8648, Resulting Numbers: [8648] 8648,94 unequal: No Solution Exploring Operation: 94-92=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[95, 97], Operations: ['95-92=3', '94+3=97'] Exploring Operation: 95+97=192, Resulting Numbers: [192] 192,94 unequal: No Solution Exploring Operation: 95*97=9215, Resulting Numbers: [9215] 9215,94 unequal: No Solution Exploring Operation: 97-95=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[94, 98], Operations: ['95-92=3', '95+3=98'] Exploring Operation: 94+98=192, Resulting Numbers: [192] 192,94 unequal: No Solution Exploring Operation: 94*98=9212, Resulting Numbers: [9212] 9212,94 unequal: No Solution Exploring Operation: 98-94=4, Resulting Numbers: [4] 4,94 unequal: No Solution No 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: 94:[95, 94, 3], Operations: ['95-92=3'] Exploring Operation: 95-94=1, Resulting Numbers: [3, 1] Generated Node #0,2,0: 94:[3, 1] Operation: 95-94=1 Exploring Operation: 94+3=97, Resulting Numbers: [95, 97] Generated Node #0,2,1: 94:[95, 97] Operation: 94+3=97 Exploring Operation: 95+3=98, Resulting Numbers: [94, 98] Generated Node #0,2,2: 94:[94, 98] Operation: 95+3=98 Exploring Operation: 95-3=92, Resulting Numbers: [94, 92] Generated Node #0,2,3: 94:[94, 92] Operation: 95-3=92 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[3, 1], Operations: ['95-92=3', '95-94=1'] Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,94 unequal: No Solution No 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: 94:[94, 92], Operations: ['95-92=3', '95-3=92'] Exploring Operation: 94-92=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 94+92=186, Resulting Numbers: [186] 186,94 unequal: No Solution Exploring Operation: 94*92=8648, Resulting Numbers: [8648] 8648,94 unequal: No Solution No 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: 94:[95, 97], Operations: ['95-92=3', '94+3=97'] Exploring Operation: 95+97=192, Resulting Numbers: [192] 192,94 unequal: No Solution Exploring Operation: 97-95=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 95*97=9215, Resulting Numbers: [9215] 9215,94 unequal: No Solution No 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: 94:[94, 98], Operations: ['95-92=3', '95+3=98'] Exploring Operation: 94*98=9212, Resulting Numbers: [9212] 9212,94 unequal: No Solution Exploring Operation: 98-94=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 94+98=192, Resulting Numbers: [192] 192,94 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: 94:[95, 95, 2], Operations: ['94-92=2'] Exploring Operation: 95-95=0, Resulting Numbers: [2, 0] Generated Node #0,3,0: 94:[2, 0] Operation: 95-95=0 Exploring Operation: 95/95=1, Resulting Numbers: [2, 1] Generated Node #0,3,1: 94:[2, 1] Operation: 95/95=1 Exploring Operation: 95-2=93, Resulting Numbers: [95, 93] Generated Node #0,3,2: 94:[95, 93] Operation: 95-2=93 Exploring Operation: 95-2=93, Resulting Numbers: [95, 93] Generated Node #0,3,3: 94:[95, 93] Operation: 95-2=93 Moving to Node #0,3,1 Current State: 94:[2, 1], Operations: ['94-92=2', '95/95=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,3,2 Current State: 94:[95, 93], Operations: ['94-92=2', '95-2=93'] Exploring Operation: 95*93=8835, Resulting Numbers: [8835] 8835,94 unequal: No Solution Exploring Operation: 95-93=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 95+93=188, Resulting Numbers: [188] 188,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[2, 0], Operations: ['94-92=2', '95-95=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,94 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[95, 93], Operations: ['94-92=2', '95-2=93'] Exploring Operation: 95*93=8835, Resulting Numbers: [8835] 8835,94 unequal: No Solution Exploring Operation: 95+93=188, Resulting Numbers: [188] 188,94 unequal: No Solution Exploring Operation: 95-93=2, Resulting Numbers: [2] 2,94 unequal: No Solution No 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: 94:[92, 94, 1], Operations: ['95/95=1'] Exploring Operation: 92/1=92, Resulting Numbers: [94, 92] Generated Node #0,0,0: 94:[94, 92] Operation: 92/1=92 Exploring Operation: 92*1=92, Resulting Numbers: [94, 92] Generated Node #0,0,1: 94:[94, 92] Operation: 92*1=92 Exploring Operation: 94-92=2, Resulting Numbers: [1, 2] Generated Node #0,0,2: 94:[1, 2] Operation: 94-92=2 Exploring Operation: 92+1=93, Resulting Numbers: [94, 93] Generated Node #0,0,3: 94:[94, 93] Operation: 92+1=93 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[1, 2], Operations: ['95/95=1', '94-92=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,94 unequal: No Solution No 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: 94:[94, 93], Operations: ['95/95=1', '92+1=93'] Exploring Operation: 94*93=8742, Resulting Numbers: [8742] 8742,94 unequal: No Solution Exploring Operation: 94+93=187, Resulting Numbers: [187] 187,94 unequal: No Solution Exploring Operation: 94-93=1, Resulting Numbers: [1] 1,94 unequal: No Solution No 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: 94:[94, 92], Operations: ['95/95=1', '92/1=92'] Exploring Operation: 94+92=186, Resulting Numbers: [186] 186,94 unequal: No Solution Exploring Operation: 94*92=8648, Resulting Numbers: [8648] 8648,94 unequal: No Solution Exploring Operation: 94-92=2, Resulting Numbers: [2] 2,94 unequal: No Solution No 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: 94:[94, 92], Operations: ['95/95=1', '92*1=92'] Exploring Operation: 94-92=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 94*92=8648, Resulting Numbers: [8648] 8648,94 unequal: No Solution Exploring Operation: 94+92=186, Resulting Numbers: [186] 186,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 71, 66, 13, 65 ]
58
[ "71-13=58", "66-65=1", "58*1=58" ]
Current State: 58:[71, 66, 13, 65], Operations: [] Exploring Operation: 71-13=58, Resulting Numbers: [66, 65, 58] Generated Node #2: [66, 65, 58] from Operation: 71-13=58 Current State: 58:[66, 65, 58], Operations: ['71-13=58'] Exploring Operation: 66-65=1, Resulting Numbers: [58, 1] Generated Node #3: [58, 1] from Operation: 66-65=1 Current State: 58:[58, 1], Operations: ['71-13=58', '66-65=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[71, 66, 13, 65], Operations: [] Exploring Operation: 71-13=58, Resulting Numbers: [66, 65, 58] Generated Node #0,0: 58:[66, 65, 58] Operation: 71-13=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[66, 65, 58], Operations: ['71-13=58'] Exploring Operation: 66-65=1, Resulting Numbers: [58, 1] Generated Node #0,0,0: 58:[58, 1] Operation: 66-65=1 Moving to Node #0,0,0 Current State: 58:[58, 1], Operations: ['71-13=58', '66-65=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[71, 66, 13, 65], Operations: [] Exploring Operation: 71-13=58, Resulting Numbers: [66, 65, 58] Generated Node #0,0: 58:[66, 65, 58] Operation: 71-13=58 Moving to Node #0,0 Current State: 58:[66, 65, 58], Operations: ['71-13=58'] Exploring Operation: 66-65=1, Resulting Numbers: [58, 1] Generated Node #0,0,0: 58:[58, 1] Operation: 66-65=1 Moving to Node #0,0,0 Current State: 58:[58, 1], Operations: ['71-13=58', '66-65=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 36, 66, 9, 24 ]
54
[ "66-36=30", "30-24=6", "9*6=54" ]
Current State: 54:[36, 66, 9, 24], Operations: [] Exploring Operation: 66-36=30, Resulting Numbers: [9, 24, 30] Generated Node #2: [9, 24, 30] from Operation: 66-36=30 Current State: 54:[9, 24, 30], Operations: ['66-36=30'] Exploring Operation: 30-24=6, Resulting Numbers: [9, 6] Generated Node #3: [9, 6] from Operation: 30-24=6 Current State: 54:[9, 6], Operations: ['66-36=30', '30-24=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[36, 66, 9, 24], Operations: [] Exploring Operation: 66-36=30, Resulting Numbers: [9, 24, 30] Generated Node #0,0: 54:[9, 24, 30] Operation: 66-36=30 Exploring Operation: 66-9=57, Resulting Numbers: [36, 24, 57] Generated Node #0,1: 54:[36, 24, 57] Operation: 66-9=57 Exploring Operation: 36-9=27, Resulting Numbers: [66, 24, 27] Generated Node #0,2: 54:[66, 24, 27] Operation: 36-9=27 Exploring Operation: 36-24=12, Resulting Numbers: [66, 9, 12] Generated Node #0,3: 54:[66, 9, 12] Operation: 36-24=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[9, 24, 30], Operations: ['66-36=30'] Exploring Operation: 24+30=54, Resulting Numbers: [9, 54] Generated Node #0,0,0: 54:[9, 54] Operation: 24+30=54 Exploring Operation: 24-9=15, Resulting Numbers: [30, 15] Generated Node #0,0,1: 54:[30, 15] Operation: 24-9=15 Exploring Operation: 30-9=21, Resulting Numbers: [24, 21] Generated Node #0,0,2: 54:[24, 21] Operation: 30-9=21 Exploring Operation: 30-24=6, Resulting Numbers: [9, 6] Generated Node #0,0,3: 54:[9, 6] Operation: 30-24=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[9, 54], Operations: ['66-36=30', '24+30=54'] Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 9+54=63, Resulting Numbers: [63] 63,54 unequal: No Solution Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,54 unequal: No Solution Exploring Operation: 9*54=486, Resulting Numbers: [486] 486,54 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 #0,0,3 Current State: 54:[9, 6], Operations: ['66-36=30', '30-24=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[36, 66, 9, 24], Operations: [] Exploring Operation: 66-36=30, Resulting Numbers: [9, 24, 30] Generated Node #0,0: 54:[9, 24, 30] Operation: 66-36=30 Moving to Node #0,0 Current State: 54:[9, 24, 30], Operations: ['66-36=30'] Exploring Operation: 30-24=6, Resulting Numbers: [9, 6] Generated Node #0,0,3: 54:[9, 6] Operation: 30-24=6 Moving to Node #0,0,3 Current State: 54:[9, 6], Operations: ['66-36=30', '30-24=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 58, 65, 76, 69 ]
49
[ "65-58=7", "76-69=7", "7*7=49" ]
Current State: 49:[58, 65, 76, 69], Operations: [] Exploring Operation: 65-58=7, Resulting Numbers: [76, 69, 7] Generated Node #2: [76, 69, 7] from Operation: 65-58=7 Current State: 49:[76, 69, 7], Operations: ['65-58=7'] Exploring Operation: 76-69=7, Resulting Numbers: [7, 7] Generated Node #3: [7, 7] from Operation: 76-69=7 Current State: 49:[7, 7], Operations: ['65-58=7', '76-69=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[58, 65, 76, 69], Operations: [] Exploring Operation: 76-58=18, Resulting Numbers: [65, 69, 18] Generated Node #0,0: 49:[65, 69, 18] Operation: 76-58=18 Exploring Operation: 65-58=7, Resulting Numbers: [76, 69, 7] Generated Node #0,1: 49:[76, 69, 7] Operation: 65-58=7 Exploring Operation: 69-65=4, Resulting Numbers: [58, 76, 4] Generated Node #0,2: 49:[58, 76, 4] Operation: 69-65=4 Exploring Operation: 76-65=11, Resulting Numbers: [58, 69, 11] Generated Node #0,3: 49:[58, 69, 11] Operation: 76-65=11 Exploring Operation: 76-69=7, Resulting Numbers: [58, 65, 7] Generated Node #0,4: 49:[58, 65, 7] Operation: 76-69=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[58, 65, 7], Operations: ['76-69=7'] Exploring Operation: 58-7=51, Resulting Numbers: [65, 51] Generated Node #0,4,0: 49:[65, 51] Operation: 58-7=51 Exploring Operation: 65+7=72, Resulting Numbers: [58, 72] Generated Node #0,4,1: 49:[58, 72] Operation: 65+7=72 Exploring Operation: 65-7=58, Resulting Numbers: [58, 58] Generated Node #0,4,2: 49:[58, 58] Operation: 65-7=58 Exploring Operation: 65-58=7, Resulting Numbers: [7, 7] Generated Node #0,4,3: 49:[7, 7] Operation: 65-58=7 Exploring Operation: 58+7=65, Resulting Numbers: [65, 65] Generated Node #0,4,4: 49:[65, 65] Operation: 58+7=65 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 49:[7, 7], Operations: ['76-69=7', '65-58=7'] Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,49 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[58, 65, 76, 69], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [58, 65, 7] Generated Node #0,4: 49:[58, 65, 7] Operation: 76-69=7 Moving to Node #0,4 Current State: 49:[58, 65, 7], Operations: ['76-69=7'] Exploring Operation: 65-58=7, Resulting Numbers: [7, 7] Generated Node #0,4,3: 49:[7, 7] Operation: 65-58=7 Moving to Node #0,4,3 Current State: 49:[7, 7], Operations: ['76-69=7', '65-58=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 45, 55, 56, 30 ]
14
[ "45+55=100", "56+30=86", "100-86=14" ]
Current State: 14:[45, 55, 56, 30], Operations: [] Exploring Operation: 45+55=100, Resulting Numbers: [56, 30, 100] Generated Node #2: [56, 30, 100] from Operation: 45+55=100 Current State: 14:[56, 30, 100], Operations: ['45+55=100'] Exploring Operation: 56+30=86, Resulting Numbers: [100, 86] Generated Node #3: [100, 86] from Operation: 56+30=86 Current State: 14:[100, 86], Operations: ['45+55=100', '56+30=86'] Exploring Operation: 100-86=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[45, 55, 56, 30], Operations: [] Exploring Operation: 56-55=1, Resulting Numbers: [45, 30, 1] Generated Node #0,0: 14:[45, 30, 1] Operation: 56-55=1 Exploring Operation: 56-45=11, Resulting Numbers: [55, 30, 11] Generated Node #0,1: 14:[55, 30, 11] Operation: 56-45=11 Exploring Operation: 55-45=10, Resulting Numbers: [56, 30, 10] Generated Node #0,2: 14:[56, 30, 10] Operation: 55-45=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[45, 30, 1], Operations: ['56-55=1'] Exploring Operation: 45-1=44, Resulting Numbers: [30, 44] Generated Node #0,0,0: 14:[30, 44] Operation: 45-1=44 Exploring Operation: 30-1=29, Resulting Numbers: [45, 29] Generated Node #0,0,1: 14:[45, 29] Operation: 30-1=29 Exploring Operation: 45-30=15, Resulting Numbers: [1, 15] Generated Node #0,0,2: 14:[1, 15] Operation: 45-30=15 Moving to Node #0,0,2 Current State: 14:[1, 15], Operations: ['56-55=1', '45-30=15'] Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[45, 55, 56, 30], Operations: [] Exploring Operation: 56-55=1, Resulting Numbers: [45, 30, 1] Generated Node #0,0: 14:[45, 30, 1] Operation: 56-55=1 Moving to Node #0,0 Current State: 14:[45, 30, 1], Operations: ['56-55=1'] Exploring Operation: 45-30=15, Resulting Numbers: [1, 15] Generated Node #0,0,2: 14:[1, 15] Operation: 45-30=15 Moving to Node #0,0,2 Current State: 14:[1, 15], Operations: ['56-55=1', '45-30=15'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 79, 36, 21, 48 ]
70
[ "79-36=43", "48-21=27", "43+27=70" ]
Current State: 70:[79, 36, 21, 48], Operations: [] Exploring Operation: 79-36=43, Resulting Numbers: [21, 48, 43] Generated Node #2: [21, 48, 43] from Operation: 79-36=43 Current State: 70:[21, 48, 43], Operations: ['79-36=43'] Exploring Operation: 48-21=27, Resulting Numbers: [43, 27] Generated Node #3: [43, 27] from Operation: 48-21=27 Current State: 70:[43, 27], Operations: ['79-36=43', '48-21=27'] Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[79, 36, 21, 48], Operations: [] Exploring Operation: 21+48=69, Resulting Numbers: [79, 36, 69] Generated Node #0,0: 70:[79, 36, 69] Operation: 21+48=69 Exploring Operation: 48-36=12, Resulting Numbers: [79, 21, 12] Generated Node #0,1: 70:[79, 21, 12] Operation: 48-36=12 Exploring Operation: 79-48=31, Resulting Numbers: [36, 21, 31] Generated Node #0,2: 70:[36, 21, 31] Operation: 79-48=31 Exploring Operation: 48-21=27, Resulting Numbers: [79, 36, 27] Generated Node #0,3: 70:[79, 36, 27] Operation: 48-21=27 Exploring Operation: 36-21=15, Resulting Numbers: [79, 48, 15] Generated Node #0,4: 70:[79, 48, 15] Operation: 36-21=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[79, 36, 69], Operations: ['21+48=69'] Exploring Operation: 79-69=10, Resulting Numbers: [36, 10] Generated Node #0,0,0: 70:[36, 10] Operation: 79-69=10 Exploring Operation: 69-36=33, Resulting Numbers: [79, 33] Generated Node #0,0,1: 70:[79, 33] Operation: 69-36=33 Exploring Operation: 36+69=105, Resulting Numbers: [79, 105] Generated Node #0,0,2: 70:[79, 105] Operation: 36+69=105 Exploring Operation: 79-36=43, Resulting Numbers: [69, 43] Generated Node #0,0,3: 70:[69, 43] Operation: 79-36=43 Exploring Operation: 79+36=115, Resulting Numbers: [69, 115] Generated Node #0,0,4: 70:[69, 115] Operation: 79+36=115 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[36, 10], Operations: ['21+48=69', '79-69=10'] Exploring Operation: 36*10=360, Resulting Numbers: [360] 360,70 unequal: No Solution Exploring Operation: 36+10=46, Resulting Numbers: [46] 46,70 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 70:[69, 43], Operations: ['21+48=69', '79-36=43'] Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 69+43=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 69*43=2967, Resulting Numbers: [2967] 2967,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 70:[79, 33], Operations: ['21+48=69', '69-36=33'] Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,70 unequal: No Solution Exploring Operation: 79*33=2607, Resulting Numbers: [2607] 2607,70 unequal: No Solution Exploring Operation: 79+33=112, Resulting Numbers: [112] 112,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 70:[79, 105], Operations: ['21+48=69', '36+69=105'] Exploring Operation: 79*105=8295, Resulting Numbers: [8295] 8295,70 unequal: No Solution Exploring Operation: 105-79=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 79+105=184, Resulting Numbers: [184] 184,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 70:[69, 115], Operations: ['21+48=69', '79+36=115'] Exploring Operation: 69+115=184, Resulting Numbers: [184] 184,70 unequal: No Solution Exploring Operation: 69*115=7935, Resulting Numbers: [7935] 7935,70 unequal: No Solution Exploring Operation: 115-69=46, Resulting Numbers: [46] 46,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[36, 21, 31], Operations: ['79-48=31'] Exploring Operation: 36-21=15, Resulting Numbers: [31, 15] Generated Node #0,2,0: 70:[31, 15] Operation: 36-21=15 Exploring Operation: 36+21=57, Resulting Numbers: [31, 57] Generated Node #0,2,1: 70:[31, 57] Operation: 36+21=57 Exploring Operation: 36+31=67, Resulting Numbers: [21, 67] Generated Node #0,2,2: 70:[21, 67] Operation: 36+31=67 Exploring Operation: 36-31=5, Resulting Numbers: [21, 5] Generated Node #0,2,3: 70:[21, 5] Operation: 36-31=5 Exploring Operation: 31-21=10, Resulting Numbers: [36, 10] Generated Node #0,2,4: 70:[36, 10] Operation: 31-21=10 Moving to Node #0,2,4 Current State: 70:[36, 10], Operations: ['79-48=31', '31-21=10'] Exploring Operation: 36*10=360, Resulting Numbers: [360] 360,70 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 36+10=46, Resulting Numbers: [46] 46,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[31, 15], Operations: ['79-48=31', '36-21=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,70 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,70 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,70 unequal: No Solution Moving to Node #0,2,3 Current State: 70:[21, 5], Operations: ['79-48=31', '36-31=5'] Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,70 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,70 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[21, 67], Operations: ['79-48=31', '36+31=67'] Exploring Operation: 21+67=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 21*67=1407, Resulting Numbers: [1407] 1407,70 unequal: No Solution Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[31, 57], Operations: ['79-48=31', '36+21=57'] Exploring Operation: 57-31=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 31+57=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 31*57=1767, Resulting Numbers: [1767] 1767,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[79, 21, 12], Operations: ['48-36=12'] Exploring Operation: 79+12=91, Resulting Numbers: [21, 91] Generated Node #0,1,0: 70:[21, 91] Operation: 79+12=91 Exploring Operation: 21+12=33, Resulting Numbers: [79, 33] Generated Node #0,1,1: 70:[79, 33] Operation: 21+12=33 Exploring Operation: 79-12=67, Resulting Numbers: [21, 67] Generated Node #0,1,2: 70:[21, 67] Operation: 79-12=67 Exploring Operation: 79-21=58, Resulting Numbers: [12, 58] Generated Node #0,1,3: 70:[12, 58] Operation: 79-21=58 Exploring Operation: 21-12=9, Resulting Numbers: [79, 9] Generated Node #0,1,4: 70:[79, 9] Operation: 21-12=9 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 70:[21, 67], Operations: ['48-36=12', '79-12=67'] Exploring Operation: 21+67=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 21*67=1407, Resulting Numbers: [1407] 1407,70 unequal: No Solution Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 70:[79, 9], Operations: ['48-36=12', '21-12=9'] Exploring Operation: 79*9=711, Resulting Numbers: [711] 711,70 unequal: No Solution Exploring Operation: 79+9=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[79, 36, 21, 48], Operations: [] Exploring Operation: 48-36=12, Resulting Numbers: [79, 21, 12] Generated Node #0,1: 70:[79, 21, 12] Operation: 48-36=12 Moving to Node #0,1 Current State: 70:[79, 21, 12], Operations: ['48-36=12'] Exploring Operation: 21-12=9, Resulting Numbers: [79, 9] Generated Node #0,1,4: 70:[79, 9] Operation: 21-12=9 Moving to Node #0,1,4 Current State: 70:[79, 9], Operations: ['48-36=12', '21-12=9'] Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.947917
hs_5
mult_heuristic
[ 45, 28, 18, 62 ]
63
[ "45-28=17", "18+62=80", "80-17=63" ]
Current State: 63:[45, 28, 18, 62], Operations: [] Exploring Operation: 45-28=17, Resulting Numbers: [18, 62, 17] Generated Node #2: [18, 62, 17] from Operation: 45-28=17 Current State: 63:[18, 62, 17], Operations: ['45-28=17'] Exploring Operation: 18+62=80, Resulting Numbers: [17, 80] Generated Node #3: [17, 80] from Operation: 18+62=80 Current State: 63:[17, 80], Operations: ['45-28=17', '18+62=80'] Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[45, 28, 18, 62], Operations: [] Exploring Operation: 45-28=17, Resulting Numbers: [18, 62, 17] Generated Node #0,0: 63:[18, 62, 17] Operation: 45-28=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[18, 62, 17], Operations: ['45-28=17'] Exploring Operation: 18-17=1, Resulting Numbers: [62, 1] Generated Node #0,0,0: 63:[62, 1] Operation: 18-17=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[62, 1], Operations: ['45-28=17', '18-17=1'] Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[45, 28, 18, 62], Operations: [] Exploring Operation: 45-28=17, Resulting Numbers: [18, 62, 17] Generated Node #0,0: 63:[18, 62, 17] Operation: 45-28=17 Moving to Node #0,0 Current State: 63:[18, 62, 17], Operations: ['45-28=17'] Exploring Operation: 18-17=1, Resulting Numbers: [62, 1] Generated Node #0,0,0: 63:[62, 1] Operation: 18-17=1 Moving to Node #0,0,0 Current State: 63:[62, 1], Operations: ['45-28=17', '18-17=1'] Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 10, 46, 98, 5 ]
47
[ "10+46=56", "98+5=103", "103-56=47" ]
Current State: 47:[10, 46, 98, 5], Operations: [] Exploring Operation: 10+46=56, Resulting Numbers: [98, 5, 56] Generated Node #2: [98, 5, 56] from Operation: 10+46=56 Current State: 47:[98, 5, 56], Operations: ['10+46=56'] Exploring Operation: 98+5=103, Resulting Numbers: [56, 103] Generated Node #3: [56, 103] from Operation: 98+5=103 Current State: 47:[56, 103], Operations: ['10+46=56', '98+5=103'] Exploring Operation: 103-56=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[10, 46, 98, 5], Operations: [] Exploring Operation: 10+5=15, Resulting Numbers: [46, 98, 15] Generated Node #0,0: 47:[46, 98, 15] Operation: 10+5=15 Exploring Operation: 10*5=50, Resulting Numbers: [46, 98, 50] Generated Node #0,1: 47:[46, 98, 50] Operation: 10*5=50 Exploring Operation: 98-5=93, Resulting Numbers: [10, 46, 93] Generated Node #0,2: 47:[10, 46, 93] Operation: 98-5=93 Exploring Operation: 98-46=52, Resulting Numbers: [10, 5, 52] Generated Node #0,3: 47:[10, 5, 52] Operation: 98-46=52 Exploring Operation: 98-10=88, Resulting Numbers: [46, 5, 88] Generated Node #0,4: 47:[46, 5, 88] Operation: 98-10=88 Moving to Node #0,1 Current State: 47:[46, 98, 50], Operations: ['10*5=50'] Exploring Operation: 46+98=144, Resulting Numbers: [50, 144] Generated Node #0,1,0: 47:[50, 144] Operation: 46+98=144 Exploring Operation: 50-46=4, Resulting Numbers: [98, 4] Generated Node #0,1,1: 47:[98, 4] Operation: 50-46=4 Exploring Operation: 46+50=96, Resulting Numbers: [98, 96] Generated Node #0,1,2: 47:[98, 96] Operation: 46+50=96 Exploring Operation: 98-50=48, Resulting Numbers: [46, 48] Generated Node #0,1,3: 47:[46, 48] Operation: 98-50=48 Exploring Operation: 98-46=52, Resulting Numbers: [50, 52] Generated Node #0,1,4: 47:[50, 52] Operation: 98-46=52 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 47:[46, 48], Operations: ['10*5=50', '98-50=48'] Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,47 unequal: No Solution Exploring Operation: 46*48=2208, Resulting Numbers: [2208] 2208,47 unequal: No Solution Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,47 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 #0,1,4 Current State: 47:[50, 52], Operations: ['10*5=50', '98-46=52'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,47 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,47 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:[98, 4], Operations: ['10*5=50', '50-46=4'] Exploring Operation: 98-4=94, Resulting Numbers: [94] 94,47 unequal: No Solution Exploring Operation: 98+4=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 98*4=392, Resulting Numbers: [392] 392,47 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:[50, 144], Operations: ['10*5=50', '46+98=144'] Exploring Operation: 50*144=7200, Resulting Numbers: [7200] 7200,47 unequal: No Solution Exploring Operation: 50+144=194, Resulting Numbers: [194] 194,47 unequal: No Solution Exploring Operation: 144-50=94, Resulting Numbers: [94] 94,47 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 #0,1,2 Current State: 47:[98, 96], Operations: ['10*5=50', '46+50=96'] Exploring Operation: 98+96=194, Resulting Numbers: [194] 194,47 unequal: No Solution Exploring Operation: 98-96=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 98*96=9408, Resulting Numbers: [9408] 9408,47 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:[10, 46, 93], Operations: ['98-5=93'] Exploring Operation: 93-10=83, Resulting Numbers: [46, 83] Generated Node #0,2,0: 47:[46, 83] Operation: 93-10=83 Exploring Operation: 46-10=36, Resulting Numbers: [93, 36] Generated Node #0,2,1: 47:[93, 36] Operation: 46-10=36 Exploring Operation: 93-46=47, Resulting Numbers: [10, 47] Generated Node #0,2,2: 47:[10, 47] Operation: 93-46=47 Exploring Operation: 10+46=56, Resulting Numbers: [93, 56] Generated Node #0,2,3: 47:[93, 56] Operation: 10+46=56 Exploring Operation: 10+93=103, Resulting Numbers: [46, 103] Generated Node #0,2,4: 47:[46, 103] Operation: 10+93=103 Moving to Node #0,4 Current State: 47:[46, 5, 88], Operations: ['98-10=88'] Exploring Operation: 88-46=42, Resulting Numbers: [5, 42] Generated Node #0,4,0: 47:[5, 42] Operation: 88-46=42 Exploring Operation: 46-5=41, Resulting Numbers: [88, 41] Generated Node #0,4,1: 47:[88, 41] Operation: 46-5=41 Exploring Operation: 88-5=83, Resulting Numbers: [46, 83] Generated Node #0,4,2: 47:[46, 83] Operation: 88-5=83 Exploring Operation: 5+88=93, Resulting Numbers: [46, 93] Generated Node #0,4,3: 47:[46, 93] Operation: 5+88=93 Exploring Operation: 46+5=51, Resulting Numbers: [88, 51] Generated Node #0,4,4: 47:[88, 51] Operation: 46+5=51 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 47:[46, 83], Operations: ['98-10=88', '88-5=83'] Exploring Operation: 46+83=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 83-46=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 46*83=3818, Resulting Numbers: [3818] 3818,47 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 #0,4,4 Current State: 47:[88, 51], Operations: ['98-10=88', '46+5=51'] Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,47 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,47 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 #0,4,0 Current State: 47:[5, 42], Operations: ['98-10=88', '88-46=42'] Exploring Operation: 5*42=210, Resulting Numbers: [210] 210,47 unequal: No Solution Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[10, 46, 98, 5], Operations: [] Exploring Operation: 98-10=88, Resulting Numbers: [46, 5, 88] Generated Node #0,4: 47:[46, 5, 88] Operation: 98-10=88 Moving to Node #0,4 Current State: 47:[46, 5, 88], Operations: ['98-10=88'] Exploring Operation: 88-46=42, Resulting Numbers: [5, 42] Generated Node #0,4,0: 47:[5, 42] Operation: 88-46=42 Moving to Node #0,4,0 Current State: 47:[5, 42], Operations: ['98-10=88', '88-46=42'] Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 87, 19, 16, 18 ]
23
[ "87-18=69", "19-16=3", "69/3=23" ]
Current State: 23:[87, 19, 16, 18], Operations: [] Exploring Operation: 87-18=69, Resulting Numbers: [19, 16, 69] Generated Node #2: [19, 16, 69] from Operation: 87-18=69 Current State: 23:[19, 16, 69], Operations: ['87-18=69'] Exploring Operation: 19-16=3, Resulting Numbers: [69, 3] Generated Node #3: [69, 3] from Operation: 19-16=3 Current State: 23:[69, 3], Operations: ['87-18=69', '19-16=3'] Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[87, 19, 16, 18], Operations: [] Exploring Operation: 87-16=71, Resulting Numbers: [19, 18, 71] Generated Node #0,0: 23:[19, 18, 71] Operation: 87-16=71 Exploring Operation: 87-19=68, Resulting Numbers: [16, 18, 68] Generated Node #0,1: 23:[16, 18, 68] Operation: 87-19=68 Exploring Operation: 87-18=69, Resulting Numbers: [19, 16, 69] Generated Node #0,2: 23:[19, 16, 69] Operation: 87-18=69 Moving to Node #0,0 Current State: 23:[19, 18, 71], Operations: ['87-16=71'] Exploring Operation: 19+18=37, Resulting Numbers: [71, 37] Generated Node #0,0,0: 23:[71, 37] Operation: 19+18=37 Exploring Operation: 71-18=53, Resulting Numbers: [19, 53] Generated Node #0,0,1: 23:[19, 53] Operation: 71-18=53 Exploring Operation: 71-19=52, Resulting Numbers: [18, 52] Generated Node #0,0,2: 23:[18, 52] Operation: 71-19=52 Moving to Node #0,1 Current State: 23:[16, 18, 68], Operations: ['87-19=68'] Exploring Operation: 68-18=50, Resulting Numbers: [16, 50] Generated Node #0,1,0: 23:[16, 50] Operation: 68-18=50 Exploring Operation: 68-16=52, Resulting Numbers: [18, 52] Generated Node #0,1,1: 23:[18, 52] Operation: 68-16=52 Exploring Operation: 16+18=34, Resulting Numbers: [68, 34] Generated Node #0,1,2: 23:[68, 34] Operation: 16+18=34 Moving to Node #0,2 Current State: 23:[19, 16, 69], Operations: ['87-18=69'] Exploring Operation: 69-16=53, Resulting Numbers: [19, 53] Generated Node #0,2,0: 23:[19, 53] Operation: 69-16=53 Exploring Operation: 69-19=50, Resulting Numbers: [16, 50] Generated Node #0,2,1: 23:[16, 50] Operation: 69-19=50 Exploring Operation: 19+16=35, Resulting Numbers: [69, 35] Generated Node #0,2,2: 23:[69, 35] Operation: 19+16=35 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[19, 53], Operations: ['87-18=69', '69-16=53'] Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,23 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,23 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[16, 50], Operations: ['87-18=69', '69-19=50'] Exploring Operation: 16*50=800, Resulting Numbers: [800] 800,23 unequal: No Solution Exploring Operation: 16+50=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[69, 35], Operations: ['87-18=69', '19+16=35'] Exploring Operation: 69+35=104, Resulting Numbers: [104] 104,23 unequal: No Solution Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 69*35=2415, Resulting Numbers: [2415] 2415,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 23:[19, 53], Operations: ['87-16=71', '71-18=53'] Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,23 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[18, 52], Operations: ['87-16=71', '71-19=52'] Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 18+52=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 18*52=936, Resulting Numbers: [936] 936,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[18, 52], Operations: ['87-19=68', '68-16=52'] Exploring Operation: 18+52=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 18*52=936, Resulting Numbers: [936] 936,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[16, 50], Operations: ['87-19=68', '68-18=50'] Exploring Operation: 16*50=800, Resulting Numbers: [800] 800,23 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 16+50=66, Resulting Numbers: [66] 66,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[68, 34], Operations: ['87-19=68', '16+18=34'] Exploring Operation: 68-34=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 68/34=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 68+34=102, Resulting Numbers: [102] 102,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[71, 37], Operations: ['87-16=71', '19+18=37'] Exploring Operation: 71*37=2627, Resulting Numbers: [2627] 2627,23 unequal: No Solution Exploring Operation: 71+37=108, Resulting Numbers: [108] 108,23 unequal: No Solution Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,23 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 30, 34, 77, 4 ]
89
[ "77-30=47", "34*4=136", "136-47=89" ]
Current State: 89:[30, 34, 77, 4], Operations: [] Exploring Operation: 77-30=47, Resulting Numbers: [34, 4, 47] Generated Node #2: [34, 4, 47] from Operation: 77-30=47 Current State: 89:[34, 4, 47], Operations: ['77-30=47'] Exploring Operation: 34*4=136, Resulting Numbers: [47, 136] Generated Node #3: [47, 136] from Operation: 34*4=136 Current State: 89:[47, 136], Operations: ['77-30=47', '34*4=136'] Exploring Operation: 136-47=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[30, 34, 77, 4], Operations: [] Exploring Operation: 34*4=136, Resulting Numbers: [30, 77, 136] Generated Node #0,0: 89:[30, 77, 136] Operation: 34*4=136 Exploring Operation: 30*4=120, Resulting Numbers: [34, 77, 120] Generated Node #0,1: 89:[34, 77, 120] Operation: 30*4=120 Moving to Node #0,1 Current State: 89:[34, 77, 120], Operations: ['30*4=120'] Exploring Operation: 34+77=111, Resulting Numbers: [120, 111] Generated Node #0,1,0: 89:[120, 111] Operation: 34+77=111 Exploring Operation: 120-34=86, Resulting Numbers: [77, 86] Generated Node #0,1,1: 89:[77, 86] Operation: 120-34=86 Moving to Node #0,0 Current State: 89:[30, 77, 136], Operations: ['34*4=136'] Exploring Operation: 30+77=107, Resulting Numbers: [136, 107] Generated Node #0,0,0: 89:[136, 107] Operation: 30+77=107 Exploring Operation: 136-30=106, Resulting Numbers: [77, 106] Generated Node #0,0,1: 89:[77, 106] Operation: 136-30=106 Moving to Node #0,1,1 Current State: 89:[77, 86], Operations: ['30*4=120', '120-34=86'] Exploring Operation: 77+86=163, Resulting Numbers: [163] 163,89 unequal: No Solution Exploring Operation: 86-77=9, Resulting Numbers: [9] 9,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[77, 106], Operations: ['34*4=136', '136-30=106'] Exploring Operation: 77+106=183, Resulting Numbers: [183] 183,89 unequal: No Solution Exploring Operation: 106-77=29, Resulting Numbers: [29] 29,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[120, 111], Operations: ['30*4=120', '34+77=111'] Exploring Operation: 120-111=9, Resulting Numbers: [9] 9,89 unequal: No Solution Exploring Operation: 120+111=231, Resulting Numbers: [231] 231,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[136, 107], Operations: ['34*4=136', '30+77=107'] Exploring Operation: 136+107=243, Resulting Numbers: [243] 243,89 unequal: No Solution Exploring Operation: 136-107=29, Resulting Numbers: [29] 29,89 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 52, 96, 87, 63 ]
45
[ "96-87=9", "63/9=7", "52-7=45" ]
Current State: 45:[52, 96, 87, 63], Operations: [] Exploring Operation: 96-87=9, Resulting Numbers: [52, 63, 9] Generated Node #2: [52, 63, 9] from Operation: 96-87=9 Current State: 45:[52, 63, 9], Operations: ['96-87=9'] Exploring Operation: 63/9=7, Resulting Numbers: [52, 7] Generated Node #3: [52, 7] from Operation: 63/9=7 Current State: 45:[52, 7], Operations: ['96-87=9', '63/9=7'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[52, 96, 87, 63], Operations: [] Exploring Operation: 96-52=44, Resulting Numbers: [87, 63, 44] Generated Node #0,0: 45:[87, 63, 44] Operation: 96-52=44 Exploring Operation: 87-63=24, Resulting Numbers: [52, 96, 24] Generated Node #0,1: 45:[52, 96, 24] Operation: 87-63=24 Exploring Operation: 96-63=33, Resulting Numbers: [52, 87, 33] Generated Node #0,2: 45:[52, 87, 33] Operation: 96-63=33 Exploring Operation: 96-87=9, Resulting Numbers: [52, 63, 9] Generated Node #0,3: 45:[52, 63, 9] Operation: 96-87=9 Moving to Node #0,3 Current State: 45:[52, 63, 9], Operations: ['96-87=9'] Exploring Operation: 63-52=11, Resulting Numbers: [9, 11] Generated Node #0,3,0: 45:[9, 11] Operation: 63-52=11 Exploring Operation: 63-9=54, Resulting Numbers: [52, 54] Generated Node #0,3,1: 45:[52, 54] Operation: 63-9=54 Exploring Operation: 63/9=7, Resulting Numbers: [52, 7] Generated Node #0,3,2: 45:[52, 7] Operation: 63/9=7 Exploring Operation: 52-9=43, Resulting Numbers: [63, 43] Generated Node #0,3,3: 45:[63, 43] Operation: 52-9=43 Moving to Node #0,2 Current State: 45:[52, 87, 33], Operations: ['96-63=33'] Exploring Operation: 52+33=85, Resulting Numbers: [87, 85] Generated Node #0,2,0: 45:[87, 85] Operation: 52+33=85 Exploring Operation: 52-33=19, Resulting Numbers: [87, 19] Generated Node #0,2,1: 45:[87, 19] Operation: 52-33=19 Exploring Operation: 87-52=35, Resulting Numbers: [33, 35] Generated Node #0,2,2: 45:[33, 35] Operation: 87-52=35 Exploring Operation: 87-33=54, Resulting Numbers: [52, 54] Generated Node #0,2,3: 45:[52, 54] Operation: 87-33=54 Moving to Node #0,0 Current State: 45:[87, 63, 44], Operations: ['96-52=44'] Exploring Operation: 87-63=24, Resulting Numbers: [44, 24] Generated Node #0,0,0: 45:[44, 24] Operation: 87-63=24 Exploring Operation: 63-44=19, Resulting Numbers: [87, 19] Generated Node #0,0,1: 45:[87, 19] Operation: 63-44=19 Exploring Operation: 87-44=43, Resulting Numbers: [63, 43] Generated Node #0,0,2: 45:[63, 43] Operation: 87-44=43 Exploring Operation: 87+44=131, Resulting Numbers: [63, 131] Generated Node #0,0,3: 45:[63, 131] Operation: 87+44=131 Moving to Node #0,1 Current State: 45:[52, 96, 24], Operations: ['87-63=24'] Exploring Operation: 96-24=72, Resulting Numbers: [52, 72] Generated Node #0,1,0: 45:[52, 72] Operation: 96-24=72 Exploring Operation: 96/24=4, Resulting Numbers: [52, 4] Generated Node #0,1,1: 45:[52, 4] Operation: 96/24=4 Exploring Operation: 52-24=28, Resulting Numbers: [96, 28] Generated Node #0,1,2: 45:[96, 28] Operation: 52-24=28 Exploring Operation: 96-52=44, Resulting Numbers: [24, 44] Generated Node #0,1,3: 45:[24, 44] Operation: 96-52=44 Moving to Node #0,3,0 Current State: 45:[9, 11], Operations: ['96-87=9', '63-52=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,45 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[52, 4], Operations: ['87-63=24', '96/24=4'] Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,45 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 52*4=208, Resulting Numbers: [208] 208,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[52, 7], Operations: ['96-87=9', '63/9=7'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[52, 96, 87, 63], Operations: [] Exploring Operation: 96-87=9, Resulting Numbers: [52, 63, 9] Generated Node #0,3: 45:[52, 63, 9] Operation: 96-87=9 Moving to Node #0,3 Current State: 45:[52, 63, 9], Operations: ['96-87=9'] Exploring Operation: 63/9=7, Resulting Numbers: [52, 7] Generated Node #0,3,2: 45:[52, 7] Operation: 63/9=7 Moving to Node #0,3,2 Current State: 45:[52, 7], Operations: ['96-87=9', '63/9=7'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.972222
hs_4
mult_heuristic
[ 22, 17, 23, 19 ]
86
[ "22-19=3", "23*3=69", "17+69=86" ]
Current State: 86:[22, 17, 23, 19], Operations: [] Exploring Operation: 22-19=3, Resulting Numbers: [17, 23, 3] Generated Node #2: [17, 23, 3] from Operation: 22-19=3 Current State: 86:[17, 23, 3], Operations: ['22-19=3'] Exploring Operation: 23*3=69, Resulting Numbers: [17, 69] Generated Node #3: [17, 69] from Operation: 23*3=69 Current State: 86:[17, 69], Operations: ['22-19=3', '23*3=69'] Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[22, 17, 23, 19], Operations: [] Exploring Operation: 22+19=41, Resulting Numbers: [17, 23, 41] Generated Node #0,0: 86:[17, 23, 41] Operation: 22+19=41 Exploring Operation: 23-22=1, Resulting Numbers: [17, 19, 1] Generated Node #0,1: 86:[17, 19, 1] Operation: 23-22=1 Exploring Operation: 22+23=45, Resulting Numbers: [17, 19, 45] Generated Node #0,2: 86:[17, 19, 45] Operation: 22+23=45 Exploring Operation: 23+19=42, Resulting Numbers: [22, 17, 42] Generated Node #0,3: 86:[22, 17, 42] Operation: 23+19=42 Exploring Operation: 22-19=3, Resulting Numbers: [17, 23, 3] Generated Node #0,4: 86:[17, 23, 3] Operation: 22-19=3 Moving to Node #0,1 Current State: 86:[17, 19, 1], Operations: ['23-22=1'] Exploring Operation: 17+19=36, Resulting Numbers: [1, 36] Generated Node #0,1,0: 86:[1, 36] Operation: 17+19=36 Exploring Operation: 19-1=18, Resulting Numbers: [17, 18] Generated Node #0,1,1: 86:[17, 18] Operation: 19-1=18 Exploring Operation: 17*1=17, Resulting Numbers: [19, 17] Generated Node #0,1,2: 86:[19, 17] Operation: 17*1=17 Exploring Operation: 19-17=2, Resulting Numbers: [1, 2] Generated Node #0,1,3: 86:[1, 2] Operation: 19-17=2 Exploring Operation: 17-1=16, Resulting Numbers: [19, 16] Generated Node #0,1,4: 86:[19, 16] Operation: 17-1=16 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 86:[1, 2], Operations: ['23-22=1', '19-17=2'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[1, 36], Operations: ['23-22=1', '17+19=36'] Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 1*36=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[17, 18], Operations: ['23-22=1', '19-1=18'] Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,86 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 86:[19, 16], Operations: ['23-22=1', '17-1=16'] Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,86 unequal: No Solution Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[19, 17], Operations: ['23-22=1', '17*1=17'] Exploring Operation: 19*17=323, Resulting Numbers: [323] 323,86 unequal: No Solution Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 86:[17, 19, 45], Operations: ['22+23=45'] Exploring Operation: 19-17=2, Resulting Numbers: [45, 2] Generated Node #0,2,0: 86:[45, 2] Operation: 19-17=2 Exploring Operation: 17+19=36, Resulting Numbers: [45, 36] Generated Node #0,2,1: 86:[45, 36] Operation: 17+19=36 Exploring Operation: 45-19=26, Resulting Numbers: [17, 26] Generated Node #0,2,2: 86:[17, 26] Operation: 45-19=26 Exploring Operation: 17+45=62, Resulting Numbers: [19, 62] Generated Node #0,2,3: 86:[19, 62] Operation: 17+45=62 Exploring Operation: 45-17=28, Resulting Numbers: [19, 28] Generated Node #0,2,4: 86:[19, 28] Operation: 45-17=28 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 86:[45, 2], Operations: ['22+23=45', '19-17=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,86 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 #0,2,1 Current State: 86:[45, 36], Operations: ['22+23=45', '17+19=36'] Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 45*36=1620, Resulting Numbers: [1620] 1620,86 unequal: No Solution Exploring Operation: 45+36=81, Resulting Numbers: [81] 81,86 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 #0,2,2 Current State: 86:[17, 26], Operations: ['22+23=45', '45-19=26'] Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,86 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,86 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 #0,2,4 Current State: 86:[19, 28], Operations: ['22+23=45', '45-17=28'] Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 19*28=532, Resulting Numbers: [532] 532,86 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 #0,2,3 Current State: 86:[19, 62], Operations: ['22+23=45', '17+45=62'] Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 19+62=81, Resulting Numbers: [81] 81,86 unequal: No Solution Exploring Operation: 19*62=1178, Resulting Numbers: [1178] 1178,86 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: 86:[22, 17, 42], Operations: ['23+19=42'] Exploring Operation: 22+17=39, Resulting Numbers: [42, 39] Generated Node #0,3,0: 86:[42, 39] Operation: 22+17=39 Exploring Operation: 42-22=20, Resulting Numbers: [17, 20] Generated Node #0,3,1: 86:[17, 20] Operation: 42-22=20 Exploring Operation: 22-17=5, Resulting Numbers: [42, 5] Generated Node #0,3,2: 86:[42, 5] Operation: 22-17=5 Exploring Operation: 22+42=64, Resulting Numbers: [17, 64] Generated Node #0,3,3: 86:[17, 64] Operation: 22+42=64 Exploring Operation: 17+42=59, Resulting Numbers: [22, 59] Generated Node #0,3,4: 86:[22, 59] Operation: 17+42=59 Moving to Node #0,4 Current State: 86:[17, 23, 3], Operations: ['22-19=3'] Exploring Operation: 17+23=40, Resulting Numbers: [3, 40] Generated Node #0,4,0: 86:[3, 40] Operation: 17+23=40 Exploring Operation: 17*3=51, Resulting Numbers: [23, 51] Generated Node #0,4,1: 86:[23, 51] Operation: 17*3=51 Exploring Operation: 23+3=26, Resulting Numbers: [17, 26] Generated Node #0,4,2: 86:[17, 26] Operation: 23+3=26 Exploring Operation: 17-3=14, Resulting Numbers: [23, 14] Generated Node #0,4,3: 86:[23, 14] Operation: 17-3=14 Exploring Operation: 23-17=6, Resulting Numbers: [3, 6] Generated Node #0,4,4: 86:[3, 6] Operation: 23-17=6 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 86:[3, 40], Operations: ['22-19=3', '17+23=40'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 86:[3, 6], Operations: ['22-19=3', '23-17=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 86:[23, 51], Operations: ['22-19=3', '17*3=51'] Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,86 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 86:[17, 26], Operations: ['22-19=3', '23+3=26'] Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 86:[23, 14], Operations: ['22-19=3', '17-3=14'] Exploring Operation: 23+14=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 23*14=322, Resulting Numbers: [322] 322,86 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: 86:[17, 23, 41], Operations: ['22+19=41'] Exploring Operation: 23-17=6, Resulting Numbers: [41, 6] Generated Node #0,0,0: 86:[41, 6] Operation: 23-17=6 Exploring Operation: 41-23=18, Resulting Numbers: [17, 18] Generated Node #0,0,1: 86:[17, 18] Operation: 41-23=18 Exploring Operation: 17+23=40, Resulting Numbers: [41, 40] Generated Node #0,0,2: 86:[41, 40] Operation: 17+23=40 Exploring Operation: 17+41=58, Resulting Numbers: [23, 58] Generated Node #0,0,3: 86:[23, 58] Operation: 17+41=58 Exploring Operation: 23+41=64, Resulting Numbers: [17, 64] Generated Node #0,0,4: 86:[17, 64] Operation: 23+41=64 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[41, 40], Operations: ['22+19=41', '17+23=40'] Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,86 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,86 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,86 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:[41, 6], Operations: ['22+19=41', '23-17=6'] Exploring Operation: 41*6=246, Resulting Numbers: [246] 246,86 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 41+6=47, Resulting Numbers: [47] 47,86 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 #0,0,1 Current State: 86:[17, 18], Operations: ['22+19=41', '41-23=18'] Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,86 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,86 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 #0,0,3 Current State: 86:[23, 58], Operations: ['22+19=41', '17+41=58'] Exploring Operation: 58-23=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 23*58=1334, Resulting Numbers: [1334] 1334,86 unequal: No Solution Exploring Operation: 23+58=81, Resulting Numbers: [81] 81,86 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 #0,0,4 Current State: 86:[17, 64], Operations: ['22+19=41', '23+41=64'] Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,86 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 86:[42, 5], Operations: ['23+19=42', '22-17=5'] Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 42*5=210, Resulting Numbers: [210] 210,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[42, 39], Operations: ['23+19=42', '22+17=39'] Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,86 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 42*39=1638, Resulting Numbers: [1638] 1638,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[17, 20], Operations: ['23+19=42', '42-22=20'] Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,86 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[17, 64], Operations: ['23+19=42', '22+42=64'] Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,86 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,86 unequal: No Solution Moving to Node #0,3,4 Current State: 86:[22, 59], Operations: ['23+19=42', '17+42=59'] Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,86 unequal: No Solution Exploring Operation: 22*59=1298, Resulting Numbers: [1298] 1298,86 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,86 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 35, 70, 75, 54 ]
95
[ "54-35=19", "75-70=5", "19*5=95" ]
Current State: 95:[35, 70, 75, 54], Operations: [] Exploring Operation: 54-35=19, Resulting Numbers: [70, 75, 19] Generated Node #2: [70, 75, 19] from Operation: 54-35=19 Current State: 95:[70, 75, 19], Operations: ['54-35=19'] Exploring Operation: 75-70=5, Resulting Numbers: [19, 5] Generated Node #3: [19, 5] from Operation: 75-70=5 Current State: 95:[19, 5], Operations: ['54-35=19', '75-70=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[35, 70, 75, 54], Operations: [] Exploring Operation: 70-54=16, Resulting Numbers: [35, 75, 16] Generated Node #0,0: 95:[35, 75, 16] Operation: 70-54=16 Exploring Operation: 54-35=19, Resulting Numbers: [70, 75, 19] Generated Node #0,1: 95:[70, 75, 19] Operation: 54-35=19 Exploring Operation: 75-54=21, Resulting Numbers: [35, 70, 21] Generated Node #0,2: 95:[35, 70, 21] Operation: 75-54=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[35, 75, 16], Operations: ['70-54=16'] Exploring Operation: 35-16=19, Resulting Numbers: [75, 19] Generated Node #0,0,0: 95:[75, 19] Operation: 35-16=19 Exploring Operation: 35+75=110, Resulting Numbers: [16, 110] Generated Node #0,0,1: 95:[16, 110] Operation: 35+75=110 Exploring Operation: 75+16=91, Resulting Numbers: [35, 91] Generated Node #0,0,2: 95:[35, 91] Operation: 75+16=91 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 95:[16, 110], Operations: ['70-54=16', '35+75=110'] Exploring Operation: 16*110=1760, Resulting Numbers: [1760] 1760,95 unequal: No Solution Exploring Operation: 16+110=126, Resulting Numbers: [126] 126,95 unequal: No Solution Exploring Operation: 110-16=94, Resulting Numbers: [94] 94,95 unequal: No Solution No 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: 95:[75, 19], Operations: ['70-54=16', '35-16=19'] Exploring Operation: 75-19=56, Resulting Numbers: [56] 56,95 unequal: No Solution Exploring Operation: 75*19=1425, Resulting Numbers: [1425] 1425,95 unequal: No Solution Exploring Operation: 75+19=94, Resulting Numbers: [94] 94,95 unequal: No Solution No 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: 95:[35, 91], Operations: ['70-54=16', '75+16=91'] Exploring Operation: 35+91=126, Resulting Numbers: [126] 126,95 unequal: No Solution Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,95 unequal: No Solution Exploring Operation: 35*91=3185, Resulting Numbers: [3185] 3185,95 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: 95:[35, 70, 21], Operations: ['75-54=21'] Exploring Operation: 70/35=2, Resulting Numbers: [21, 2] Generated Node #0,2,0: 95:[21, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [21, 35] Generated Node #0,2,1: 95:[21, 35] Operation: 70-35=35 Exploring Operation: 35+70=105, Resulting Numbers: [21, 105] Generated Node #0,2,2: 95:[21, 105] Operation: 35+70=105 Moving to Node #0,2,0 Current State: 95:[21, 2], Operations: ['75-54=21', '70/35=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,95 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,95 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[21, 105], Operations: ['75-54=21', '35+70=105'] Exploring Operation: 105/21=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 105-21=84, Resulting Numbers: [84] 84,95 unequal: No Solution Exploring Operation: 21+105=126, Resulting Numbers: [126] 126,95 unequal: No Solution Moving to Node #0,2,1 Current State: 95:[21, 35], Operations: ['75-54=21', '70-35=35'] Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,95 unequal: No Solution Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,95 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,95 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 #0,1 Current State: 95:[70, 75, 19], Operations: ['54-35=19'] Exploring Operation: 75-70=5, Resulting Numbers: [19, 5] Generated Node #0,1,0: 95:[19, 5] Operation: 75-70=5 Exploring Operation: 75+19=94, Resulting Numbers: [70, 94] Generated Node #0,1,1: 95:[70, 94] Operation: 75+19=94 Exploring Operation: 70+19=89, Resulting Numbers: [75, 89] Generated Node #0,1,2: 95:[75, 89] Operation: 70+19=89 Moving to Node #0,1,0 Current State: 95:[19, 5], Operations: ['54-35=19', '75-70=5'] Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[35, 70, 75, 54], Operations: [] Exploring Operation: 54-35=19, Resulting Numbers: [70, 75, 19] Generated Node #0,1: 95:[70, 75, 19] Operation: 54-35=19 Moving to Node #0,1 Current State: 95:[70, 75, 19], Operations: ['54-35=19'] Exploring Operation: 75-70=5, Resulting Numbers: [19, 5] Generated Node #0,1,0: 95:[19, 5] Operation: 75-70=5 Moving to Node #0,1,0 Current State: 95:[19, 5], Operations: ['54-35=19', '75-70=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 71, 4, 25, 65 ]
61
[ "65-25=40", "40/4=10", "71-10=61" ]
Current State: 61:[71, 4, 25, 65], Operations: [] Exploring Operation: 65-25=40, Resulting Numbers: [71, 4, 40] Generated Node #2: [71, 4, 40] from Operation: 65-25=40 Current State: 61:[71, 4, 40], Operations: ['65-25=40'] Exploring Operation: 40/4=10, Resulting Numbers: [71, 10] Generated Node #3: [71, 10] from Operation: 40/4=10 Current State: 61:[71, 10], Operations: ['65-25=40', '40/4=10'] Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[71, 4, 25, 65], Operations: [] Exploring Operation: 71-4=67, Resulting Numbers: [25, 65, 67] Generated Node #0,0: 61:[25, 65, 67] Operation: 71-4=67 Exploring Operation: 65-4=61, Resulting Numbers: [71, 25, 61] Generated Node #0,1: 61:[71, 25, 61] Operation: 65-4=61 Exploring Operation: 4+25=29, Resulting Numbers: [71, 65, 29] Generated Node #0,2: 61:[71, 65, 29] Operation: 4+25=29 Moving to Node #0,0 Current State: 61:[25, 65, 67], Operations: ['71-4=67'] Exploring Operation: 67-25=42, Resulting Numbers: [65, 42] Generated Node #0,0,0: 61:[65, 42] Operation: 67-25=42 Exploring Operation: 65-25=40, Resulting Numbers: [67, 40] Generated Node #0,0,1: 61:[67, 40] Operation: 65-25=40 Exploring Operation: 25+65=90, Resulting Numbers: [67, 90] Generated Node #0,0,2: 61:[67, 90] Operation: 25+65=90 Moving to Node #0,1 Current State: 61:[71, 25, 61], Operations: ['65-4=61'] Exploring Operation: 25+61=86, Resulting Numbers: [71, 86] Generated Node #0,1,0: 61:[71, 86] Operation: 25+61=86 Exploring Operation: 71-25=46, Resulting Numbers: [61, 46] Generated Node #0,1,1: 61:[61, 46] Operation: 71-25=46 Exploring Operation: 71+25=96, Resulting Numbers: [61, 96] Generated Node #0,1,2: 61:[61, 96] Operation: 71+25=96 Moving to Node #0,2 Current State: 61:[71, 65, 29], Operations: ['4+25=29'] Exploring Operation: 71+29=100, Resulting Numbers: [65, 100] Generated Node #0,2,0: 61:[65, 100] Operation: 71+29=100 Exploring Operation: 71-29=42, Resulting Numbers: [65, 42] Generated Node #0,2,1: 61:[65, 42] Operation: 71-29=42 Exploring Operation: 65-29=36, Resulting Numbers: [71, 36] Generated Node #0,2,2: 61:[71, 36] Operation: 65-29=36 Moving to Node #0,1,1 Current State: 61:[61, 46], Operations: ['65-4=61', '71-25=46'] Exploring Operation: 61-46=15, Resulting Numbers: [15] 15,61 unequal: No Solution Exploring Operation: 61+46=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 61*46=2806, Resulting Numbers: [2806] 2806,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[65, 42], Operations: ['4+25=29', '71-29=42'] Exploring Operation: 65+42=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 65-42=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 65*42=2730, Resulting Numbers: [2730] 2730,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[65, 42], Operations: ['71-4=67', '67-25=42'] Exploring Operation: 65-42=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 65*42=2730, Resulting Numbers: [2730] 2730,61 unequal: No Solution Exploring Operation: 65+42=107, Resulting Numbers: [107] 107,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[67, 40], Operations: ['71-4=67', '65-25=40'] Exploring Operation: 67+40=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 67-40=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 67*40=2680, Resulting Numbers: [2680] 2680,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[67, 90], Operations: ['71-4=67', '25+65=90'] Exploring Operation: 90-67=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 67+90=157, Resulting Numbers: [157] 157,61 unequal: No Solution Exploring Operation: 67*90=6030, Resulting Numbers: [6030] 6030,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[61, 96], Operations: ['65-4=61', '71+25=96'] Exploring Operation: 96-61=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 61+96=157, Resulting Numbers: [157] 157,61 unequal: No Solution Exploring Operation: 61*96=5856, Resulting Numbers: [5856] 5856,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[71, 86], Operations: ['65-4=61', '25+61=86'] Exploring Operation: 86-71=15, Resulting Numbers: [15] 15,61 unequal: No Solution Exploring Operation: 71*86=6106, Resulting Numbers: [6106] 6106,61 unequal: No Solution Exploring Operation: 71+86=157, Resulting Numbers: [157] 157,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[71, 36], Operations: ['4+25=29', '65-29=36'] Exploring Operation: 71+36=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 71-36=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 71*36=2556, Resulting Numbers: [2556] 2556,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[65, 100], Operations: ['4+25=29', '71+29=100'] Exploring Operation: 65+100=165, Resulting Numbers: [165] 165,61 unequal: No Solution Exploring Operation: 100-65=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 65*100=6500, Resulting Numbers: [6500] 6500,61 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 26, 78, 85, 8 ]
98
[ "26+78=104", "104/8=13", "85+13=98" ]
Current State: 98:[26, 78, 85, 8], Operations: [] Exploring Operation: 26+78=104, Resulting Numbers: [85, 8, 104] Generated Node #2: [85, 8, 104] from Operation: 26+78=104 Current State: 98:[85, 8, 104], Operations: ['26+78=104'] Exploring Operation: 104/8=13, Resulting Numbers: [85, 13] Generated Node #3: [85, 13] from Operation: 104/8=13 Current State: 98:[85, 13], Operations: ['26+78=104', '104/8=13'] Exploring Operation: 85+13=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[26, 78, 85, 8], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [26, 8, 7] Generated Node #0,0: 98:[26, 8, 7] Operation: 85-78=7 Exploring Operation: 78/26=3, Resulting Numbers: [85, 8, 3] Generated Node #0,1: 98:[85, 8, 3] Operation: 78/26=3 Exploring Operation: 78-26=52, Resulting Numbers: [85, 8, 52] Generated Node #0,2: 98:[85, 8, 52] Operation: 78-26=52 Moving to Node #0,0 Current State: 98:[26, 8, 7], Operations: ['85-78=7'] Exploring Operation: 26-8=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 98:[7, 18] Operation: 26-8=18 Exploring Operation: 26-7=19, Resulting Numbers: [8, 19] Generated Node #0,0,1: 98:[8, 19] Operation: 26-7=19 Exploring Operation: 8+7=15, Resulting Numbers: [26, 15] Generated Node #0,0,2: 98:[26, 15] Operation: 8+7=15 Moving to Node #0,1 Current State: 98:[85, 8, 3], Operations: ['78/26=3'] Exploring Operation: 85+8=93, Resulting Numbers: [3, 93] Generated Node #0,1,0: 98:[3, 93] Operation: 85+8=93 Exploring Operation: 85+3=88, Resulting Numbers: [8, 88] Generated Node #0,1,1: 98:[8, 88] Operation: 85+3=88 Exploring Operation: 8-3=5, Resulting Numbers: [85, 5] Generated Node #0,1,2: 98:[85, 5] Operation: 8-3=5 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 98:[3, 93], Operations: ['78/26=3', '85+8=93'] Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,98 unequal: No Solution Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,98 unequal: No Solution Exploring Operation: 3+93=96, Resulting Numbers: [96] 96,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 98:[8, 88], Operations: ['78/26=3', '85+3=88'] Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,98 unequal: No Solution Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,98 unequal: No Solution Exploring Operation: 8+88=96, Resulting Numbers: [96] 96,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 98:[85, 5], Operations: ['78/26=3', '8-3=5'] Exploring Operation: 85-5=80, Resulting Numbers: [80] 80,98 unequal: No Solution Exploring Operation: 85+5=90, Resulting Numbers: [90] 90,98 unequal: No Solution Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,98 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: 98:[85, 8, 52], Operations: ['78-26=52'] Exploring Operation: 85-52=33, Resulting Numbers: [8, 33] Generated Node #0,2,0: 98:[8, 33] Operation: 85-52=33 Exploring Operation: 85+8=93, Resulting Numbers: [52, 93] Generated Node #0,2,1: 98:[52, 93] Operation: 85+8=93 Exploring Operation: 52-8=44, Resulting Numbers: [85, 44] Generated Node #0,2,2: 98:[85, 44] Operation: 52-8=44 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 98:[52, 93], Operations: ['78-26=52', '85+8=93'] Exploring Operation: 52*93=4836, Resulting Numbers: [4836] 4836,98 unequal: No Solution Exploring Operation: 93-52=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 52+93=145, Resulting Numbers: [145] 145,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 98:[8, 33], Operations: ['78-26=52', '85-52=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,98 unequal: No Solution Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 98:[85, 44], Operations: ['78-26=52', '52-8=44'] Exploring Operation: 85+44=129, Resulting Numbers: [129] 129,98 unequal: No Solution Exploring Operation: 85*44=3740, Resulting Numbers: [3740] 3740,98 unequal: No Solution Exploring Operation: 85-44=41, Resulting Numbers: [41] 41,98 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: 98:[7, 18], Operations: ['85-78=7', '26-8=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,98 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,98 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[8, 19], Operations: ['85-78=7', '26-7=19'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,98 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,98 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[26, 15], Operations: ['85-78=7', '8+7=15'] Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,98 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,98 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 3, 28, 14, 58 ]
64
[ "3*28=84", "84/14=6", "58+6=64" ]
Current State: 64:[3, 28, 14, 58], Operations: [] Exploring Operation: 3*28=84, Resulting Numbers: [14, 58, 84] Generated Node #2: [14, 58, 84] from Operation: 3*28=84 Current State: 64:[14, 58, 84], Operations: ['3*28=84'] Exploring Operation: 84/14=6, Resulting Numbers: [58, 6] Generated Node #3: [58, 6] from Operation: 84/14=6 Current State: 64:[58, 6], Operations: ['3*28=84', '84/14=6'] Exploring Operation: 58+6=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[3, 28, 14, 58], Operations: [] Exploring Operation: 3+28=31, Resulting Numbers: [14, 58, 31] Generated Node #0,0: 64:[14, 58, 31] Operation: 3+28=31 Exploring Operation: 58-28=30, Resulting Numbers: [3, 14, 30] Generated Node #0,1: 64:[3, 14, 30] Operation: 58-28=30 Exploring Operation: 28/14=2, Resulting Numbers: [3, 58, 2] Generated Node #0,2: 64:[3, 58, 2] Operation: 28/14=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[3, 14, 30], Operations: ['58-28=30'] Exploring Operation: 30-14=16, Resulting Numbers: [3, 16] Generated Node #0,1,0: 64:[3, 16] Operation: 30-14=16 Exploring Operation: 3+30=33, Resulting Numbers: [14, 33] Generated Node #0,1,1: 64:[14, 33] Operation: 3+30=33 Exploring Operation: 3+14=17, Resulting Numbers: [30, 17] Generated Node #0,1,2: 64:[30, 17] Operation: 3+14=17 Moving to Node #0,1,0 Current State: 64:[3, 16], Operations: ['58-28=30', '30-14=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,64 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,64 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[14, 33], Operations: ['58-28=30', '3+30=33'] Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,64 unequal: No Solution Exploring Operation: 14*33=462, Resulting Numbers: [462] 462,64 unequal: No Solution Exploring Operation: 14+33=47, Resulting Numbers: [47] 47,64 unequal: No Solution Moving to Node #0,1,2 Current State: 64:[30, 17], Operations: ['58-28=30', '3+14=17'] Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,64 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,64 unequal: No Solution Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[3, 58, 2], Operations: ['28/14=2'] Exploring Operation: 58/2=29, Resulting Numbers: [3, 29] Generated Node #0,2,0: 64:[3, 29] Operation: 58/2=29 Exploring Operation: 58+2=60, Resulting Numbers: [3, 60] Generated Node #0,2,1: 64:[3, 60] Operation: 58+2=60 Exploring Operation: 3+58=61, Resulting Numbers: [2, 61] Generated Node #0,2,2: 64:[2, 61] Operation: 3+58=61 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 64:[2, 61], Operations: ['28/14=2', '3+58=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,64 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,64 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 64:[3, 29], Operations: ['28/14=2', '58/2=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,64 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,64 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 64:[3, 60], Operations: ['28/14=2', '58+2=60'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,64 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[14, 58, 31], Operations: ['3+28=31'] Exploring Operation: 14+58=72, Resulting Numbers: [31, 72] Generated Node #0,0,0: 64:[31, 72] Operation: 14+58=72 Exploring Operation: 31-14=17, Resulting Numbers: [58, 17] Generated Node #0,0,1: 64:[58, 17] Operation: 31-14=17 Exploring Operation: 58-31=27, Resulting Numbers: [14, 27] Generated Node #0,0,2: 64:[14, 27] Operation: 58-31=27 Moving to Node #0,0,1 Current State: 64:[58, 17], Operations: ['3+28=31', '31-14=17'] Exploring Operation: 58-17=41, Resulting Numbers: [41] 41,64 unequal: No Solution Exploring Operation: 58+17=75, Resulting Numbers: [75] 75,64 unequal: No Solution Exploring Operation: 58*17=986, Resulting Numbers: [986] 986,64 unequal: No Solution Moving to Node #0,0,2 Current State: 64:[14, 27], Operations: ['3+28=31', '58-31=27'] Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,64 unequal: No Solution Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,64 unequal: No Solution Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[31, 72], Operations: ['3+28=31', '14+58=72'] Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,64 unequal: No Solution Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,64 unequal: No Solution Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 28, 22, 5, 30 ]
41
[ "28-22=6", "5+30=35", "6+35=41" ]
Current State: 41:[28, 22, 5, 30], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [5, 30, 6] Generated Node #2: [5, 30, 6] from Operation: 28-22=6 Current State: 41:[5, 30, 6], Operations: ['28-22=6'] Exploring Operation: 5+30=35, Resulting Numbers: [6, 35] Generated Node #3: [6, 35] from Operation: 5+30=35 Current State: 41:[6, 35], Operations: ['28-22=6', '5+30=35'] Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[28, 22, 5, 30], Operations: [] Exploring Operation: 5+30=35, Resulting Numbers: [28, 22, 35] Generated Node #0,0: 41:[28, 22, 35] Operation: 5+30=35 Exploring Operation: 22+5=27, Resulting Numbers: [28, 30, 27] Generated Node #0,1: 41:[28, 30, 27] Operation: 22+5=27 Exploring Operation: 28+5=33, Resulting Numbers: [22, 30, 33] Generated Node #0,2: 41:[22, 30, 33] Operation: 28+5=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[28, 22, 35], Operations: ['5+30=35'] Exploring Operation: 22+35=57, Resulting Numbers: [28, 57] Generated Node #0,0,0: 41:[28, 57] Operation: 22+35=57 Exploring Operation: 28-22=6, Resulting Numbers: [35, 6] Generated Node #0,0,1: 41:[35, 6] Operation: 28-22=6 Exploring Operation: 28+22=50, Resulting Numbers: [35, 50] Generated Node #0,0,2: 41:[35, 50] Operation: 28+22=50 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[35, 50], Operations: ['5+30=35', '28+22=50'] Exploring Operation: 35*50=1750, Resulting Numbers: [1750] 1750,41 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 35+50=85, Resulting Numbers: [85] 85,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[28, 57], Operations: ['5+30=35', '22+35=57'] Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 28+57=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 28*57=1596, Resulting Numbers: [1596] 1596,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[35, 6], Operations: ['5+30=35', '28-22=6'] Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[28, 22, 5, 30], Operations: [] Exploring Operation: 5+30=35, Resulting Numbers: [28, 22, 35] Generated Node #0,0: 41:[28, 22, 35] Operation: 5+30=35 Moving to Node #0,0 Current State: 41:[28, 22, 35], Operations: ['5+30=35'] Exploring Operation: 28-22=6, Resulting Numbers: [35, 6] Generated Node #0,0,1: 41:[35, 6] Operation: 28-22=6 Moving to Node #0,0,1 Current State: 41:[35, 6], Operations: ['5+30=35', '28-22=6'] Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 57, 38, 9, 60 ]
81
[ "57*60=3420", "3420/38=90", "90-9=81" ]
Current State: 81:[57, 38, 9, 60], Operations: [] Exploring Operation: 57*60=3420, Resulting Numbers: [38, 9, 3420] Generated Node #2: [38, 9, 3420] from Operation: 57*60=3420 Current State: 81:[38, 9, 3420], Operations: ['57*60=3420'] Exploring Operation: 3420/38=90, Resulting Numbers: [9, 90] Generated Node #3: [9, 90] from Operation: 3420/38=90 Current State: 81:[9, 90], Operations: ['57*60=3420', '3420/38=90'] Exploring Operation: 90-9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[57, 38, 9, 60], Operations: [] Exploring Operation: 60-57=3, Resulting Numbers: [38, 9, 3] Generated Node #0,0: 81:[38, 9, 3] Operation: 60-57=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[38, 9, 3], Operations: ['60-57=3'] Exploring Operation: 38-9=29, Resulting Numbers: [3, 29] Generated Node #0,0,0: 81:[3, 29] Operation: 38-9=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[3, 29], Operations: ['60-57=3', '38-9=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 91, 89, 80 ]
34
[ "44+91=135", "89+80=169", "169-135=34" ]
Current State: 34:[44, 91, 89, 80], Operations: [] Exploring Operation: 44+91=135, Resulting Numbers: [89, 80, 135] Generated Node #2: [89, 80, 135] from Operation: 44+91=135 Current State: 34:[89, 80, 135], Operations: ['44+91=135'] Exploring Operation: 89+80=169, Resulting Numbers: [135, 169] Generated Node #3: [135, 169] from Operation: 89+80=169 Current State: 34:[135, 169], Operations: ['44+91=135', '89+80=169'] Exploring Operation: 169-135=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[44, 91, 89, 80], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [44, 89, 11] Generated Node #0,0: 34:[44, 89, 11] Operation: 91-80=11 Exploring Operation: 91-89=2, Resulting Numbers: [44, 80, 2] Generated Node #0,1: 34:[44, 80, 2] Operation: 91-89=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[44, 80, 2], Operations: ['91-89=2'] Exploring Operation: 80-44=36, Resulting Numbers: [2, 36] Generated Node #0,1,0: 34:[2, 36] Operation: 80-44=36 Exploring Operation: 80/2=40, Resulting Numbers: [44, 40] Generated Node #0,1,1: 34:[44, 40] Operation: 80/2=40 Moving to Node #0,1,0 Current State: 34:[2, 36], Operations: ['91-89=2', '80-44=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[44, 91, 89, 80], Operations: [] Exploring Operation: 91-89=2, Resulting Numbers: [44, 80, 2] Generated Node #0,1: 34:[44, 80, 2] Operation: 91-89=2 Moving to Node #0,1 Current State: 34:[44, 80, 2], Operations: ['91-89=2'] Exploring Operation: 80-44=36, Resulting Numbers: [2, 36] Generated Node #0,1,0: 34:[2, 36] Operation: 80-44=36 Moving to Node #0,1,0 Current State: 34:[2, 36], Operations: ['91-89=2', '80-44=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 52, 14, 16, 9 ]
45
[ "52-14=38", "16-9=7", "38+7=45" ]
Current State: 45:[52, 14, 16, 9], Operations: [] Exploring Operation: 52-14=38, Resulting Numbers: [16, 9, 38] Generated Node #2: [16, 9, 38] from Operation: 52-14=38 Current State: 45:[16, 9, 38], Operations: ['52-14=38'] Exploring Operation: 16-9=7, Resulting Numbers: [38, 7] Generated Node #3: [38, 7] from Operation: 16-9=7 Current State: 45:[38, 7], Operations: ['52-14=38', '16-9=7'] Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[52, 14, 16, 9], Operations: [] Exploring Operation: 52-9=43, Resulting Numbers: [14, 16, 43] Generated Node #0,0: 45:[14, 16, 43] Operation: 52-9=43 Exploring Operation: 14-9=5, Resulting Numbers: [52, 16, 5] Generated Node #0,1: 45:[52, 16, 5] Operation: 14-9=5 Exploring Operation: 16-14=2, Resulting Numbers: [52, 9, 2] Generated Node #0,2: 45:[52, 9, 2] Operation: 16-14=2 Exploring Operation: 52-14=38, Resulting Numbers: [16, 9, 38] Generated Node #0,3: 45:[16, 9, 38] Operation: 52-14=38 Exploring Operation: 52-16=36, Resulting Numbers: [14, 9, 36] Generated Node #0,4: 45:[14, 9, 36] Operation: 52-16=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[14, 16, 43], Operations: ['52-9=43'] Exploring Operation: 16+43=59, Resulting Numbers: [14, 59] Generated Node #0,0,0: 45:[14, 59] Operation: 16+43=59 Exploring Operation: 16-14=2, Resulting Numbers: [43, 2] Generated Node #0,0,1: 45:[43, 2] Operation: 16-14=2 Exploring Operation: 43-14=29, Resulting Numbers: [16, 29] Generated Node #0,0,2: 45:[16, 29] Operation: 43-14=29 Exploring Operation: 14+43=57, Resulting Numbers: [16, 57] Generated Node #0,0,3: 45:[16, 57] Operation: 14+43=57 Exploring Operation: 43-16=27, Resulting Numbers: [14, 27] Generated Node #0,0,4: 45:[14, 27] Operation: 43-16=27 Moving to Node #0,0,1 Current State: 45:[43, 2], Operations: ['52-9=43', '16-14=2'] Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,45 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,45 unequal: No Solution Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[52, 14, 16, 9], Operations: [] Exploring Operation: 52-9=43, Resulting Numbers: [14, 16, 43] Generated Node #0,0: 45:[14, 16, 43] Operation: 52-9=43 Moving to Node #0,0 Current State: 45:[14, 16, 43], Operations: ['52-9=43'] Exploring Operation: 16-14=2, Resulting Numbers: [43, 2] Generated Node #0,0,1: 45:[43, 2] Operation: 16-14=2 Moving to Node #0,0,1 Current State: 45:[43, 2], Operations: ['52-9=43', '16-14=2'] Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 4, 31, 28, 55 ]
41
[ "4*31=124", "28+55=83", "124-83=41" ]
Current State: 41:[4, 31, 28, 55], Operations: [] Exploring Operation: 4*31=124, Resulting Numbers: [28, 55, 124] Generated Node #2: [28, 55, 124] from Operation: 4*31=124 Current State: 41:[28, 55, 124], Operations: ['4*31=124'] Exploring Operation: 28+55=83, Resulting Numbers: [124, 83] Generated Node #3: [124, 83] from Operation: 28+55=83 Current State: 41:[124, 83], Operations: ['4*31=124', '28+55=83'] Exploring Operation: 124-83=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[4, 31, 28, 55], Operations: [] Exploring Operation: 28-4=24, Resulting Numbers: [31, 55, 24] Generated Node #0,0: 41:[31, 55, 24] Operation: 28-4=24 Exploring Operation: 31-4=27, Resulting Numbers: [28, 55, 27] Generated Node #0,1: 41:[28, 55, 27] Operation: 31-4=27 Exploring Operation: 55-4=51, Resulting Numbers: [31, 28, 51] Generated Node #0,2: 41:[31, 28, 51] Operation: 55-4=51 Exploring Operation: 4+28=32, Resulting Numbers: [31, 55, 32] Generated Node #0,3: 41:[31, 55, 32] Operation: 4+28=32 Exploring Operation: 4+31=35, Resulting Numbers: [28, 55, 35] Generated Node #0,4: 41:[28, 55, 35] Operation: 4+31=35 Moving to Node #0,2 Current State: 41:[31, 28, 51], Operations: ['55-4=51'] Exploring Operation: 31-28=3, Resulting Numbers: [51, 3] Generated Node #0,2,0: 41:[51, 3] Operation: 31-28=3 Exploring Operation: 31+28=59, Resulting Numbers: [51, 59] Generated Node #0,2,1: 41:[51, 59] Operation: 31+28=59 Exploring Operation: 28+51=79, Resulting Numbers: [31, 79] Generated Node #0,2,2: 41:[31, 79] Operation: 28+51=79 Exploring Operation: 51-28=23, Resulting Numbers: [31, 23] Generated Node #0,2,3: 41:[31, 23] Operation: 51-28=23 Exploring Operation: 51-31=20, Resulting Numbers: [28, 20] Generated Node #0,2,4: 41:[28, 20] Operation: 51-31=20 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 41:[51, 59], Operations: ['55-4=51', '31+28=59'] Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 51+59=110, Resulting Numbers: [110] 110,41 unequal: No Solution Exploring Operation: 51*59=3009, Resulting Numbers: [3009] 3009,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 41:[31, 23], Operations: ['55-4=51', '51-28=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 41:[28, 20], Operations: ['55-4=51', '51-31=20'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 28*20=560, Resulting Numbers: [560] 560,41 unequal: No Solution Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[51, 3], Operations: ['55-4=51', '31-28=3'] Exploring Operation: 51*3=153, Resulting Numbers: [153] 153,41 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 41:[31, 79], Operations: ['55-4=51', '28+51=79'] Exploring Operation: 79-31=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 31+79=110, Resulting Numbers: [110] 110,41 unequal: No Solution Exploring Operation: 31*79=2449, Resulting Numbers: [2449] 2449,41 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: 41:[28, 55, 35], Operations: ['4+31=35'] Exploring Operation: 55-28=27, Resulting Numbers: [35, 27] Generated Node #0,4,0: 41:[35, 27] Operation: 55-28=27 Exploring Operation: 55-35=20, Resulting Numbers: [28, 20] Generated Node #0,4,1: 41:[28, 20] Operation: 55-35=20 Exploring Operation: 35-28=7, Resulting Numbers: [55, 7] Generated Node #0,4,2: 41:[55, 7] Operation: 35-28=7 Exploring Operation: 28+55=83, Resulting Numbers: [35, 83] Generated Node #0,4,3: 41:[35, 83] Operation: 28+55=83 Exploring Operation: 28+35=63, Resulting Numbers: [55, 63] Generated Node #0,4,4: 41:[55, 63] Operation: 28+35=63 Moving to Node #0,3 Current State: 41:[31, 55, 32], Operations: ['4+28=32'] Exploring Operation: 55-32=23, Resulting Numbers: [31, 23] Generated Node #0,3,0: 41:[31, 23] Operation: 55-32=23 Exploring Operation: 32-31=1, Resulting Numbers: [55, 1] Generated Node #0,3,1: 41:[55, 1] Operation: 32-31=1 Exploring Operation: 31+32=63, Resulting Numbers: [55, 63] Generated Node #0,3,2: 41:[55, 63] Operation: 31+32=63 Exploring Operation: 55-31=24, Resulting Numbers: [32, 24] Generated Node #0,3,3: 41:[32, 24] Operation: 55-31=24 Exploring Operation: 31+55=86, Resulting Numbers: [32, 86] Generated Node #0,3,4: 41:[32, 86] Operation: 31+55=86 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 41:[32, 24], Operations: ['4+28=32', '55-31=24'] Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,41 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[31, 23], Operations: ['4+28=32', '55-32=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 41:[55, 63], Operations: ['4+28=32', '31+32=63'] Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,41 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 41:[55, 1], Operations: ['4+28=32', '32-31=1'] Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,41 unequal: No Solution Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 41:[32, 86], Operations: ['4+28=32', '31+55=86'] Exploring Operation: 86-32=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 32+86=118, Resulting Numbers: [118] 118,41 unequal: No Solution Exploring Operation: 32*86=2752, Resulting Numbers: [2752] 2752,41 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: 41:[31, 55, 24], Operations: ['28-4=24'] Exploring Operation: 31-24=7, Resulting Numbers: [55, 7] Generated Node #0,0,0: 41:[55, 7] Operation: 31-24=7 Exploring Operation: 31+24=55, Resulting Numbers: [55, 55] Generated Node #0,0,1: 41:[55, 55] Operation: 31+24=55 Exploring Operation: 55-24=31, Resulting Numbers: [31, 31] Generated Node #0,0,2: 41:[31, 31] Operation: 55-24=31 Exploring Operation: 55+24=79, Resulting Numbers: [31, 79] Generated Node #0,0,3: 41:[31, 79] Operation: 55+24=79 Exploring Operation: 55-31=24, Resulting Numbers: [24, 24] Generated Node #0,0,4: 41:[24, 24] Operation: 55-31=24 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[31, 31], Operations: ['28-4=24', '55-24=31'] Exploring Operation: 31*31=961, Resulting Numbers: [961] 961,41 unequal: No Solution Exploring Operation: 31-31=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 31+31=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 31/31=1, Resulting Numbers: [1] 1,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[55, 55], Operations: ['28-4=24', '31+24=55'] Exploring Operation: 55/55=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 55-55=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 55*55=3025, Resulting Numbers: [3025] 3025,41 unequal: No Solution Exploring Operation: 55+55=110, Resulting Numbers: [110] 110,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 41:[24, 24], Operations: ['28-4=24', '55-31=24'] Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,41 unequal: No Solution Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[55, 7], Operations: ['28-4=24', '31-24=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 41:[31, 79], Operations: ['28-4=24', '55+24=79'] Exploring Operation: 31*79=2449, Resulting Numbers: [2449] 2449,41 unequal: No Solution Exploring Operation: 31+79=110, Resulting Numbers: [110] 110,41 unequal: No Solution Exploring Operation: 79-31=48, Resulting Numbers: [48] 48,41 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: 41:[28, 55, 27], Operations: ['31-4=27'] Exploring Operation: 55-27=28, Resulting Numbers: [28, 28] Generated Node #0,1,0: 41:[28, 28] Operation: 55-27=28 Exploring Operation: 55+27=82, Resulting Numbers: [28, 82] Generated Node #0,1,1: 41:[28, 82] Operation: 55+27=82 Exploring Operation: 28-27=1, Resulting Numbers: [55, 1] Generated Node #0,1,2: 41:[55, 1] Operation: 28-27=1 Exploring Operation: 55-28=27, Resulting Numbers: [27, 27] Generated Node #0,1,3: 41:[27, 27] Operation: 55-28=27 Exploring Operation: 28+27=55, Resulting Numbers: [55, 55] Generated Node #0,1,4: 41:[55, 55] Operation: 28+27=55 Moving to Node #0,4,0 Current State: 41:[35, 27], Operations: ['4+31=35', '55-28=27'] Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 35*27=945, Resulting Numbers: [945] 945,41 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[28, 28], Operations: ['31-4=27', '55-27=28'] Exploring Operation: 28*28=784, Resulting Numbers: [784] 784,41 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,41 unequal: No Solution Moving to Node #0,1,3 Current State: 41:[27, 27], Operations: ['31-4=27', '55-28=27'] Exploring Operation: 27-27=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 27+27=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 27*27=729, Resulting Numbers: [729] 729,41 unequal: No Solution Exploring Operation: 27/27=1, Resulting Numbers: [1] 1,41 unequal: No Solution Moving to Node #0,1,4 Current State: 41:[55, 55], Operations: ['31-4=27', '28+27=55'] Exploring Operation: 55*55=3025, Resulting Numbers: [3025] 3025,41 unequal: No Solution Exploring Operation: 55-55=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 55/55=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 55+55=110, Resulting Numbers: [110] 110,41 unequal: No Solution Moving to Node #0,4,1 Current State: 41:[28, 20], Operations: ['4+31=35', '55-35=20'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 28*20=560, Resulting Numbers: [560] 560,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[55, 63], Operations: ['4+31=35', '28+35=63'] Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,41 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,41 unequal: No Solution Moving to Node #0,4,3 Current State: 41:[35, 83], Operations: ['4+31=35', '28+55=83'] Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 35+83=118, Resulting Numbers: [118] 118,41 unequal: No Solution Exploring Operation: 35*83=2905, Resulting Numbers: [2905] 2905,41 unequal: No Solution Moving to Node #0,4,2 Current State: 41:[55, 7], Operations: ['4+31=35', '35-28=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,41 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[55, 1], Operations: ['31-4=27', '28-27=1'] Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,41 unequal: No Solution Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[28, 82], Operations: ['31-4=27', '55+27=82'] Exploring Operation: 28*82=2296, Resulting Numbers: [2296] 2296,41 unequal: No Solution Exploring Operation: 28+82=110, Resulting Numbers: [110] 110,41 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,41 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 47, 5, 18, 22 ]
82
[ "47-5=42", "18+22=40", "42+40=82" ]
Current State: 82:[47, 5, 18, 22], Operations: [] Exploring Operation: 47-5=42, Resulting Numbers: [18, 22, 42] Generated Node #2: [18, 22, 42] from Operation: 47-5=42 Current State: 82:[18, 22, 42], Operations: ['47-5=42'] Exploring Operation: 18+22=40, Resulting Numbers: [42, 40] Generated Node #3: [42, 40] from Operation: 18+22=40 Current State: 82:[42, 40], Operations: ['47-5=42', '18+22=40'] Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[47, 5, 18, 22], Operations: [] Exploring Operation: 18+22=40, Resulting Numbers: [47, 5, 40] Generated Node #0,0: 82:[47, 5, 40] Operation: 18+22=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[47, 5, 40], Operations: ['18+22=40'] Exploring Operation: 47-5=42, Resulting Numbers: [40, 42] Generated Node #0,0,0: 82:[40, 42] Operation: 47-5=42 Moving to Node #0,0,0 Current State: 82:[40, 42], Operations: ['18+22=40', '47-5=42'] Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[47, 5, 18, 22], Operations: [] Exploring Operation: 18+22=40, Resulting Numbers: [47, 5, 40] Generated Node #0,0: 82:[47, 5, 40] Operation: 18+22=40 Moving to Node #0,0 Current State: 82:[47, 5, 40], Operations: ['18+22=40'] Exploring Operation: 47-5=42, Resulting Numbers: [40, 42] Generated Node #0,0,0: 82:[40, 42] Operation: 47-5=42 Moving to Node #0,0,0 Current State: 82:[40, 42], Operations: ['18+22=40', '47-5=42'] Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 28, 22, 3, 81 ]
78
[ "28-22=6", "3+81=84", "84-6=78" ]
Current State: 78:[28, 22, 3, 81], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [3, 81, 6] Generated Node #2: [3, 81, 6] from Operation: 28-22=6 Current State: 78:[3, 81, 6], Operations: ['28-22=6'] Exploring Operation: 3+81=84, Resulting Numbers: [6, 84] Generated Node #3: [6, 84] from Operation: 3+81=84 Current State: 78:[6, 84], Operations: ['28-22=6', '3+81=84'] Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[28, 22, 3, 81], Operations: [] Exploring Operation: 28-3=25, Resulting Numbers: [22, 81, 25] Generated Node #0,0: 78:[22, 81, 25] Operation: 28-3=25 Exploring Operation: 81-3=78, Resulting Numbers: [28, 22, 78] Generated Node #0,1: 78:[28, 22, 78] Operation: 81-3=78 Exploring Operation: 28-22=6, Resulting Numbers: [3, 81, 6] Generated Node #0,2: 78:[3, 81, 6] Operation: 28-22=6 Exploring Operation: 81/3=27, Resulting Numbers: [28, 22, 27] Generated Node #0,3: 78:[28, 22, 27] Operation: 81/3=27 Exploring Operation: 22+3=25, Resulting Numbers: [28, 81, 25] Generated Node #0,4: 78:[28, 81, 25] Operation: 22+3=25 Moving to Node #0,2 Current State: 78:[3, 81, 6], Operations: ['28-22=6'] Exploring Operation: 6/3=2, Resulting Numbers: [81, 2] Generated Node #0,2,0: 78:[81, 2] Operation: 6/3=2 Exploring Operation: 81-6=75, Resulting Numbers: [3, 75] Generated Node #0,2,1: 78:[3, 75] Operation: 81-6=75 Exploring Operation: 81/3=27, Resulting Numbers: [6, 27] Generated Node #0,2,2: 78:[6, 27] Operation: 81/3=27 Exploring Operation: 6-3=3, Resulting Numbers: [81, 3] Generated Node #0,2,3: 78:[81, 3] Operation: 6-3=3 Exploring Operation: 81-3=78, Resulting Numbers: [6, 78] Generated Node #0,2,4: 78:[6, 78] Operation: 81-3=78 Moving to Node #0,4 Current State: 78:[28, 81, 25], Operations: ['22+3=25'] Exploring Operation: 81-28=53, Resulting Numbers: [25, 53] Generated Node #0,4,0: 78:[25, 53] Operation: 81-28=53 Exploring Operation: 28+25=53, Resulting Numbers: [81, 53] Generated Node #0,4,1: 78:[81, 53] Operation: 28+25=53 Exploring Operation: 28-25=3, Resulting Numbers: [81, 3] Generated Node #0,4,2: 78:[81, 3] Operation: 28-25=3 Exploring Operation: 81-25=56, Resulting Numbers: [28, 56] Generated Node #0,4,3: 78:[28, 56] Operation: 81-25=56 Exploring Operation: 81+25=106, Resulting Numbers: [28, 106] Generated Node #0,4,4: 78:[28, 106] Operation: 81+25=106 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 78:[81, 3], Operations: ['22+3=25', '28-25=3'] Exploring Operation: 81*3=243, Resulting Numbers: [243] 243,78 unequal: No Solution Exploring Operation: 81+3=84, Resulting Numbers: [84] 84,78 unequal: No Solution Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[28, 22, 3, 81], Operations: [] Exploring Operation: 22+3=25, Resulting Numbers: [28, 81, 25] Generated Node #0,4: 78:[28, 81, 25] Operation: 22+3=25 Moving to Node #0,4 Current State: 78:[28, 81, 25], Operations: ['22+3=25'] Exploring Operation: 28-25=3, Resulting Numbers: [81, 3] Generated Node #0,4,2: 78:[81, 3] Operation: 28-25=3 Moving to Node #0,4,2 Current State: 78:[81, 3], Operations: ['22+3=25', '28-25=3'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 57, 54, 13, 2 ]
71
[ "57-13=44", "54/2=27", "44+27=71" ]
Current State: 71:[57, 54, 13, 2], Operations: [] Exploring Operation: 57-13=44, Resulting Numbers: [54, 2, 44] Generated Node #2: [54, 2, 44] from Operation: 57-13=44 Current State: 71:[54, 2, 44], Operations: ['57-13=44'] Exploring Operation: 54/2=27, Resulting Numbers: [44, 27] Generated Node #3: [44, 27] from Operation: 54/2=27 Current State: 71:[44, 27], Operations: ['57-13=44', '54/2=27'] Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[57, 54, 13, 2], Operations: [] Exploring Operation: 57+13=70, Resulting Numbers: [54, 2, 70] Generated Node #0,0: 71:[54, 2, 70] Operation: 57+13=70 Exploring Operation: 13*2=26, Resulting Numbers: [57, 54, 26] Generated Node #0,1: 71:[57, 54, 26] Operation: 13*2=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[57, 54, 26], Operations: ['13*2=26'] Exploring Operation: 54+26=80, Resulting Numbers: [57, 80] Generated Node #0,1,0: 71:[57, 80] Operation: 54+26=80 Exploring Operation: 57+26=83, Resulting Numbers: [54, 83] Generated Node #0,1,1: 71:[54, 83] Operation: 57+26=83 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[57, 80], Operations: ['13*2=26', '54+26=80'] Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 57+80=137, Resulting Numbers: [137] 137,71 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 #0,1,1 Current State: 71:[54, 83], Operations: ['13*2=26', '57+26=83'] Exploring Operation: 54+83=137, Resulting Numbers: [137] 137,71 unequal: No Solution Exploring Operation: 83-54=29, Resulting Numbers: [29] 29,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[54, 2, 70], Operations: ['57+13=70'] Exploring Operation: 2+70=72, Resulting Numbers: [54, 72] Generated Node #0,0,0: 71:[54, 72] Operation: 2+70=72 Exploring Operation: 54+2=56, Resulting Numbers: [70, 56] Generated Node #0,0,1: 71:[70, 56] Operation: 54+2=56 Moving to Node #0,0,1 Current State: 71:[70, 56], Operations: ['57+13=70', '54+2=56'] Exploring Operation: 70-56=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 70+56=126, Resulting Numbers: [126] 126,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[54, 72], Operations: ['57+13=70', '2+70=72'] Exploring Operation: 72-54=18, Resulting Numbers: [18] 18,71 unequal: No Solution Exploring Operation: 54+72=126, Resulting Numbers: [126] 126,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 53, 26, 39 ]
72
[ "6+53=59", "39-26=13", "59+13=72" ]
Current State: 72:[6, 53, 26, 39], Operations: [] Exploring Operation: 6+53=59, Resulting Numbers: [26, 39, 59] Generated Node #2: [26, 39, 59] from Operation: 6+53=59 Current State: 72:[26, 39, 59], Operations: ['6+53=59'] Exploring Operation: 39-26=13, Resulting Numbers: [59, 13] Generated Node #3: [59, 13] from Operation: 39-26=13 Current State: 72:[59, 13], Operations: ['6+53=59', '39-26=13'] Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[6, 53, 26, 39], Operations: [] Exploring Operation: 53-39=14, Resulting Numbers: [6, 26, 14] Generated Node #0,0: 72:[6, 26, 14] Operation: 53-39=14 Exploring Operation: 53-26=27, Resulting Numbers: [6, 39, 27] Generated Node #0,1: 72:[6, 39, 27] Operation: 53-26=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[6, 26, 14], Operations: ['53-39=14'] Exploring Operation: 26-14=12, Resulting Numbers: [6, 12] Generated Node #0,0,0: 72:[6, 12] Operation: 26-14=12 Exploring Operation: 14-6=8, Resulting Numbers: [26, 8] Generated Node #0,0,1: 72:[26, 8] Operation: 14-6=8 Moving to Node #0,0,0 Current State: 72:[6, 12], Operations: ['53-39=14', '26-14=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[6, 53, 26, 39], Operations: [] Exploring Operation: 53-39=14, Resulting Numbers: [6, 26, 14] Generated Node #0,0: 72:[6, 26, 14] Operation: 53-39=14 Moving to Node #0,0 Current State: 72:[6, 26, 14], Operations: ['53-39=14'] Exploring Operation: 26-14=12, Resulting Numbers: [6, 12] Generated Node #0,0,0: 72:[6, 12] Operation: 26-14=12 Moving to Node #0,0,0 Current State: 72:[6, 12], Operations: ['53-39=14', '26-14=12'] Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 23, 20, 36, 21 ]
28
[ "23+20=43", "36-21=15", "43-15=28" ]
Current State: 28:[23, 20, 36, 21], Operations: [] Exploring Operation: 23+20=43, Resulting Numbers: [36, 21, 43] Generated Node #2: [36, 21, 43] from Operation: 23+20=43 Current State: 28:[36, 21, 43], Operations: ['23+20=43'] Exploring Operation: 36-21=15, Resulting Numbers: [43, 15] Generated Node #3: [43, 15] from Operation: 36-21=15 Current State: 28:[43, 15], Operations: ['23+20=43', '36-21=15'] Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[23, 20, 36, 21], Operations: [] Exploring Operation: 36-21=15, Resulting Numbers: [23, 20, 15] Generated Node #0,0: 28:[23, 20, 15] Operation: 36-21=15 Exploring Operation: 36-23=13, Resulting Numbers: [20, 21, 13] Generated Node #0,1: 28:[20, 21, 13] Operation: 36-23=13 Exploring Operation: 23-21=2, Resulting Numbers: [20, 36, 2] Generated Node #0,2: 28:[20, 36, 2] Operation: 23-21=2 Moving to Node #0,0 Current State: 28:[23, 20, 15], Operations: ['36-21=15'] Exploring Operation: 23-15=8, Resulting Numbers: [20, 8] Generated Node #0,0,0: 28:[20, 8] Operation: 23-15=8 Exploring Operation: 20-15=5, Resulting Numbers: [23, 5] Generated Node #0,0,1: 28:[23, 5] Operation: 20-15=5 Exploring Operation: 23-20=3, Resulting Numbers: [15, 3] Generated Node #0,0,2: 28:[15, 3] Operation: 23-20=3 Moving to Node #0,1 Current State: 28:[20, 21, 13], Operations: ['36-23=13'] Exploring Operation: 21-13=8, Resulting Numbers: [20, 8] Generated Node #0,1,0: 28:[20, 8] Operation: 21-13=8 Exploring Operation: 20-13=7, Resulting Numbers: [21, 7] Generated Node #0,1,1: 28:[21, 7] Operation: 20-13=7 Exploring Operation: 21-20=1, Resulting Numbers: [13, 1] Generated Node #0,1,2: 28:[13, 1] Operation: 21-20=1 Moving to Node #0,2 Current State: 28:[20, 36, 2], Operations: ['23-21=2'] Exploring Operation: 20/2=10, Resulting Numbers: [36, 10] Generated Node #0,2,0: 28:[36, 10] Operation: 20/2=10 Exploring Operation: 36/2=18, Resulting Numbers: [20, 18] Generated Node #0,2,1: 28:[20, 18] Operation: 36/2=18 Exploring Operation: 36-20=16, Resulting Numbers: [2, 16] Generated Node #0,2,2: 28:[2, 16] Operation: 36-20=16 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 28:[2, 16], Operations: ['23-21=2', '36-20=16'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,28 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 28:[20, 18], Operations: ['23-21=2', '36/2=18'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 28:[36, 10], Operations: ['23-21=2', '20/2=10'] Exploring Operation: 36*10=360, Resulting Numbers: [360] 360,28 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,28 unequal: No Solution Exploring Operation: 36+10=46, Resulting Numbers: [46] 46,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 28:[15, 3], Operations: ['36-21=15', '23-20=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,28 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,28 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,28 unequal: No Solution Moving to Node #0,1,2 Current State: 28:[13, 1], Operations: ['36-23=13', '21-20=1'] Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[23, 5], Operations: ['36-21=15', '20-15=5'] Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[23, 20, 36, 21], Operations: [] Exploring Operation: 36-21=15, Resulting Numbers: [23, 20, 15] Generated Node #0,0: 28:[23, 20, 15] Operation: 36-21=15 Moving to Node #0,0 Current State: 28:[23, 20, 15], Operations: ['36-21=15'] Exploring Operation: 20-15=5, Resulting Numbers: [23, 5] Generated Node #0,0,1: 28:[23, 5] Operation: 20-15=5 Moving to Node #0,0,1 Current State: 28:[23, 5], Operations: ['36-21=15', '20-15=5'] Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
0.972222
hs_3
sum_heuristic
[ 13, 34, 2, 69 ]
83
[ "69-34=35", "2*35=70", "13+70=83" ]
Current State: 83:[13, 34, 2, 69], Operations: [] Exploring Operation: 69-34=35, Resulting Numbers: [13, 2, 35] Generated Node #2: [13, 2, 35] from Operation: 69-34=35 Current State: 83:[13, 2, 35], Operations: ['69-34=35'] Exploring Operation: 2*35=70, Resulting Numbers: [13, 70] Generated Node #3: [13, 70] from Operation: 2*35=70 Current State: 83:[13, 70], Operations: ['69-34=35', '2*35=70'] Exploring Operation: 13+70=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[13, 34, 2, 69], Operations: [] Exploring Operation: 13*2=26, Resulting Numbers: [34, 69, 26] Generated Node #0,0: 83:[34, 69, 26] Operation: 13*2=26 Exploring Operation: 34*2=68, Resulting Numbers: [13, 69, 68] Generated Node #0,1: 83:[13, 69, 68] Operation: 34*2=68 Exploring Operation: 13+2=15, Resulting Numbers: [34, 69, 15] Generated Node #0,2: 83:[34, 69, 15] Operation: 13+2=15 Exploring Operation: 13+34=47, Resulting Numbers: [2, 69, 47] Generated Node #0,3: 83:[2, 69, 47] Operation: 13+34=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[13, 69, 68], Operations: ['34*2=68'] Exploring Operation: 68-13=55, Resulting Numbers: [69, 55] Generated Node #0,1,0: 83:[69, 55] Operation: 68-13=55 Exploring Operation: 13+68=81, Resulting Numbers: [69, 81] Generated Node #0,1,1: 83:[69, 81] Operation: 13+68=81 Exploring Operation: 69-13=56, Resulting Numbers: [68, 56] Generated Node #0,1,2: 83:[68, 56] Operation: 69-13=56 Exploring Operation: 13+69=82, Resulting Numbers: [68, 82] Generated Node #0,1,3: 83:[68, 82] Operation: 13+69=82 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[69, 81], Operations: ['34*2=68', '13+68=81'] Exploring Operation: 81-69=12, Resulting Numbers: [12] 12,83 unequal: No Solution Exploring Operation: 69+81=150, Resulting Numbers: [150] 150,83 unequal: No Solution Exploring Operation: 69*81=5589, Resulting Numbers: [5589] 5589,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 83:[68, 82], Operations: ['34*2=68', '13+69=82'] Exploring Operation: 68*82=5576, Resulting Numbers: [5576] 5576,83 unequal: No Solution Exploring Operation: 82-68=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 68+82=150, Resulting Numbers: [150] 150,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[69, 55], Operations: ['34*2=68', '68-13=55'] Exploring Operation: 69+55=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 69-55=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 69*55=3795, Resulting Numbers: [3795] 3795,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 83:[68, 56], Operations: ['34*2=68', '69-13=56'] Exploring Operation: 68*56=3808, Resulting Numbers: [3808] 3808,83 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,83 unequal: No Solution Exploring Operation: 68+56=124, Resulting Numbers: [124] 124,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[34, 69, 26], Operations: ['13*2=26'] Exploring Operation: 34+26=60, Resulting Numbers: [69, 60] Generated Node #0,0,0: 83:[69, 60] Operation: 34+26=60 Exploring Operation: 69+26=95, Resulting Numbers: [34, 95] Generated Node #0,0,1: 83:[34, 95] Operation: 69+26=95 Exploring Operation: 34+69=103, Resulting Numbers: [26, 103] Generated Node #0,0,2: 83:[26, 103] Operation: 34+69=103 Exploring Operation: 34-26=8, Resulting Numbers: [69, 8] Generated Node #0,0,3: 83:[69, 8] Operation: 34-26=8 Moving to Node #0,0,0 Current State: 83:[69, 60], Operations: ['13*2=26', '34+26=60'] Exploring Operation: 69-60=9, Resulting Numbers: [9] 9,83 unequal: No Solution Exploring Operation: 69*60=4140, Resulting Numbers: [4140] 4140,83 unequal: No Solution Exploring Operation: 69+60=129, Resulting Numbers: [129] 129,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[34, 95], Operations: ['13*2=26', '69+26=95'] Exploring Operation: 95-34=61, Resulting Numbers: [61] 61,83 unequal: No Solution Exploring Operation: 34*95=3230, Resulting Numbers: [3230] 3230,83 unequal: No Solution Exploring Operation: 34+95=129, Resulting Numbers: [129] 129,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[26, 103], Operations: ['13*2=26', '34+69=103'] Exploring Operation: 26*103=2678, Resulting Numbers: [2678] 2678,83 unequal: No Solution Exploring Operation: 26+103=129, Resulting Numbers: [129] 129,83 unequal: No Solution Exploring Operation: 103-26=77, Resulting Numbers: [77] 77,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[69, 8], Operations: ['13*2=26', '34-26=8'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,83 unequal: No Solution Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,83 unequal: No Solution Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,83 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 #0,2 Current State: 83:[34, 69, 15], Operations: ['13+2=15'] Exploring Operation: 69+15=84, Resulting Numbers: [34, 84] Generated Node #0,2,0: 83:[34, 84] Operation: 69+15=84 Exploring Operation: 34+15=49, Resulting Numbers: [69, 49] Generated Node #0,2,1: 83:[69, 49] Operation: 34+15=49 Exploring Operation: 69-15=54, Resulting Numbers: [34, 54] Generated Node #0,2,2: 83:[34, 54] Operation: 69-15=54 Exploring Operation: 34-15=19, Resulting Numbers: [69, 19] Generated Node #0,2,3: 83:[69, 19] Operation: 34-15=19 Moving to Node #0,2,1 Current State: 83:[69, 49], Operations: ['13+2=15', '34+15=49'] Exploring Operation: 69+49=118, Resulting Numbers: [118] 118,83 unequal: No Solution Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,83 unequal: No Solution Exploring Operation: 69*49=3381, Resulting Numbers: [3381] 3381,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[34, 84], Operations: ['13+2=15', '69+15=84'] Exploring Operation: 34*84=2856, Resulting Numbers: [2856] 2856,83 unequal: No Solution Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,83 unequal: No Solution Exploring Operation: 34+84=118, Resulting Numbers: [118] 118,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[69, 19], Operations: ['13+2=15', '34-15=19'] Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,83 unequal: No Solution Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[34, 54], Operations: ['13+2=15', '69-15=54'] Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,83 unequal: No Solution Exploring Operation: 34+54=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 34*54=1836, Resulting Numbers: [1836] 1836,83 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 #0,3 Current State: 83:[2, 69, 47], Operations: ['13+34=47'] Exploring Operation: 2*47=94, Resulting Numbers: [69, 94] Generated Node #0,3,0: 83:[69, 94] Operation: 2*47=94 Exploring Operation: 2+69=71, Resulting Numbers: [47, 71] Generated Node #0,3,1: 83:[47, 71] Operation: 2+69=71 Exploring Operation: 2+47=49, Resulting Numbers: [69, 49] Generated Node #0,3,2: 83:[69, 49] Operation: 2+47=49 Exploring Operation: 69-2=67, Resulting Numbers: [47, 67] Generated Node #0,3,3: 83:[47, 67] Operation: 69-2=67 Moving to Node #0,3,0 Current State: 83:[69, 94], Operations: ['13+34=47', '2*47=94'] Exploring Operation: 94-69=25, Resulting Numbers: [25] 25,83 unequal: No Solution Exploring Operation: 69*94=6486, Resulting Numbers: [6486] 6486,83 unequal: No Solution Exploring Operation: 69+94=163, Resulting Numbers: [163] 163,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[69, 49], Operations: ['13+34=47', '2+47=49'] Exploring Operation: 69+49=118, Resulting Numbers: [118] 118,83 unequal: No Solution Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,83 unequal: No Solution Exploring Operation: 69*49=3381, Resulting Numbers: [3381] 3381,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[47, 71], Operations: ['13+34=47', '2+69=71'] Exploring Operation: 47*71=3337, Resulting Numbers: [3337] 3337,83 unequal: No Solution Exploring Operation: 47+71=118, Resulting Numbers: [118] 118,83 unequal: No Solution Exploring Operation: 71-47=24, Resulting Numbers: [24] 24,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[47, 67], Operations: ['13+34=47', '69-2=67'] Exploring Operation: 47+67=114, Resulting Numbers: [114] 114,83 unequal: No Solution Exploring Operation: 67-47=20, Resulting Numbers: [20] 20,83 unequal: No Solution Exploring Operation: 47*67=3149, Resulting Numbers: [3149] 3149,83 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
[ 21, 35, 50, 41 ]
35
[ "21+35=56", "50+41=91", "91-56=35" ]
Current State: 35:[21, 35, 50, 41], Operations: [] Exploring Operation: 21+35=56, Resulting Numbers: [50, 41, 56] Generated Node #2: [50, 41, 56] from Operation: 21+35=56 Current State: 35:[50, 41, 56], Operations: ['21+35=56'] Exploring Operation: 50+41=91, Resulting Numbers: [56, 91] Generated Node #3: [56, 91] from Operation: 50+41=91 Current State: 35:[56, 91], Operations: ['21+35=56', '50+41=91'] Exploring Operation: 91-56=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[21, 35, 50, 41], Operations: [] Exploring Operation: 50-41=9, Resulting Numbers: [21, 35, 9] Generated Node #0,0: 35:[21, 35, 9] Operation: 50-41=9 Exploring Operation: 50-21=29, Resulting Numbers: [35, 41, 29] Generated Node #0,1: 35:[35, 41, 29] Operation: 50-21=29 Moving to Node #0,1 Current State: 35:[35, 41, 29], Operations: ['50-21=29'] Exploring Operation: 41-29=12, Resulting Numbers: [35, 12] Generated Node #0,1,0: 35:[35, 12] Operation: 41-29=12 Exploring Operation: 41-35=6, Resulting Numbers: [29, 6] Generated Node #0,1,1: 35:[29, 6] Operation: 41-35=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[35, 12], Operations: ['50-21=29', '41-29=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[29, 6], Operations: ['50-21=29', '41-35=6'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,35 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[21, 35, 50, 41], Operations: [] Exploring Operation: 50-21=29, Resulting Numbers: [35, 41, 29] Generated Node #0,1: 35:[35, 41, 29] Operation: 50-21=29 Moving to Node #0,1 Current State: 35:[35, 41, 29], Operations: ['50-21=29'] Exploring Operation: 41-35=6, Resulting Numbers: [29, 6] Generated Node #0,1,1: 35:[29, 6] Operation: 41-35=6 Moving to Node #0,1,1 Current State: 35:[29, 6], Operations: ['50-21=29', '41-35=6'] Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 23, 73, 79, 10 ]
76
[ "79-10=69", "69/23=3", "73+3=76" ]
Current State: 76:[23, 73, 79, 10], Operations: [] Exploring Operation: 79-10=69, Resulting Numbers: [23, 73, 69] Generated Node #2: [23, 73, 69] from Operation: 79-10=69 Current State: 76:[23, 73, 69], Operations: ['79-10=69'] Exploring Operation: 69/23=3, Resulting Numbers: [73, 3] Generated Node #3: [73, 3] from Operation: 69/23=3 Current State: 76:[73, 3], Operations: ['79-10=69', '69/23=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[23, 73, 79, 10], Operations: [] Exploring Operation: 23-10=13, Resulting Numbers: [73, 79, 13] Generated Node #0,0: 76:[73, 79, 13] Operation: 23-10=13 Exploring Operation: 23+10=33, Resulting Numbers: [73, 79, 33] Generated Node #0,1: 76:[73, 79, 33] Operation: 23+10=33 Moving to Node #0,1 Current State: 76:[73, 79, 33], Operations: ['23+10=33'] Exploring Operation: 79-73=6, Resulting Numbers: [33, 6] Generated Node #0,1,0: 76:[33, 6] Operation: 79-73=6 Exploring Operation: 73-33=40, Resulting Numbers: [79, 40] Generated Node #0,1,1: 76:[79, 40] Operation: 73-33=40 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[79, 40], Operations: ['23+10=33', '73-33=40'] Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 79+40=119, Resulting Numbers: [119] 119,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[33, 6], Operations: ['23+10=33', '79-73=6'] Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,76 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: 76:[73, 79, 13], Operations: ['23-10=13'] Exploring Operation: 73+13=86, Resulting Numbers: [79, 86] Generated Node #0,0,0: 76:[79, 86] Operation: 73+13=86 Exploring Operation: 79-73=6, Resulting Numbers: [13, 6] Generated Node #0,0,1: 76:[13, 6] Operation: 79-73=6 Moving to Node #0,0,1 Current State: 76:[13, 6], Operations: ['23-10=13', '79-73=6'] Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,76 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[79, 86], Operations: ['23-10=13', '73+13=86'] Exploring Operation: 86-79=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 79+86=165, Resulting Numbers: [165] 165,76 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 75, 11, 3, 49 ]
95
[ "11+49=60", "60/3=20", "75+20=95" ]
Current State: 95:[75, 11, 3, 49], Operations: [] Exploring Operation: 11+49=60, Resulting Numbers: [75, 3, 60] Generated Node #2: [75, 3, 60] from Operation: 11+49=60 Current State: 95:[75, 3, 60], Operations: ['11+49=60'] Exploring Operation: 60/3=20, Resulting Numbers: [75, 20] Generated Node #3: [75, 20] from Operation: 60/3=20 Current State: 95:[75, 20], Operations: ['11+49=60', '60/3=20'] Exploring Operation: 75+20=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[75, 11, 3, 49], Operations: [] Exploring Operation: 75+11=86, Resulting Numbers: [3, 49, 86] Generated Node #0,0: 95:[3, 49, 86] Operation: 75+11=86 Exploring Operation: 75-49=26, Resulting Numbers: [11, 3, 26] Generated Node #0,1: 95:[11, 3, 26] Operation: 75-49=26 Exploring Operation: 49-11=38, Resulting Numbers: [75, 3, 38] Generated Node #0,2: 95:[75, 3, 38] Operation: 49-11=38 Exploring Operation: 75+49=124, Resulting Numbers: [11, 3, 124] Generated Node #0,3: 95:[11, 3, 124] Operation: 75+49=124 Moving to Node #0,1 Current State: 95:[11, 3, 26], Operations: ['75-49=26'] Exploring Operation: 26-3=23, Resulting Numbers: [11, 23] Generated Node #0,1,0: 95:[11, 23] Operation: 26-3=23 Exploring Operation: 26-11=15, Resulting Numbers: [3, 15] Generated Node #0,1,1: 95:[3, 15] Operation: 26-11=15 Exploring Operation: 11-3=8, Resulting Numbers: [26, 8] Generated Node #0,1,2: 95:[26, 8] Operation: 11-3=8 Exploring Operation: 11+3=14, Resulting Numbers: [26, 14] Generated Node #0,1,3: 95:[26, 14] Operation: 11+3=14 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[3, 15], Operations: ['75-49=26', '26-11=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,95 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,95 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,95 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,95 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 #0,1,0 Current State: 95:[11, 23], Operations: ['75-49=26', '26-3=23'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,95 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,95 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 #0,1,2 Current State: 95:[26, 8], Operations: ['75-49=26', '11-3=8'] Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,95 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,95 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 #0,1,3 Current State: 95:[26, 14], Operations: ['75-49=26', '11+3=14'] Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,95 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,95 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: 95:[11, 3, 124], Operations: ['75+49=124'] Exploring Operation: 124-3=121, Resulting Numbers: [11, 121] Generated Node #0,3,0: 95:[11, 121] Operation: 124-3=121 Exploring Operation: 11-3=8, Resulting Numbers: [124, 8] Generated Node #0,3,1: 95:[124, 8] Operation: 11-3=8 Exploring Operation: 124-11=113, Resulting Numbers: [3, 113] Generated Node #0,3,2: 95:[3, 113] Operation: 124-11=113 Exploring Operation: 11+3=14, Resulting Numbers: [124, 14] Generated Node #0,3,3: 95:[124, 14] Operation: 11+3=14 Moving to Node #0,2 Current State: 95:[75, 3, 38], Operations: ['49-11=38'] Exploring Operation: 75+38=113, Resulting Numbers: [3, 113] Generated Node #0,2,0: 95:[3, 113] Operation: 75+38=113 Exploring Operation: 75+3=78, Resulting Numbers: [38, 78] Generated Node #0,2,1: 95:[38, 78] Operation: 75+3=78 Exploring Operation: 75-38=37, Resulting Numbers: [3, 37] Generated Node #0,2,2: 95:[3, 37] Operation: 75-38=37 Exploring Operation: 75/3=25, Resulting Numbers: [38, 25] Generated Node #0,2,3: 95:[38, 25] Operation: 75/3=25 Moving to Node #0,0 Current State: 95:[3, 49, 86], Operations: ['75+11=86'] Exploring Operation: 86-49=37, Resulting Numbers: [3, 37] Generated Node #0,0,0: 95:[3, 37] Operation: 86-49=37 Exploring Operation: 49-3=46, Resulting Numbers: [86, 46] Generated Node #0,0,1: 95:[86, 46] Operation: 49-3=46 Exploring Operation: 3+49=52, Resulting Numbers: [86, 52] Generated Node #0,0,2: 95:[86, 52] Operation: 3+49=52 Exploring Operation: 3+86=89, Resulting Numbers: [49, 89] Generated Node #0,0,3: 95:[49, 89] Operation: 3+86=89 Moving to Node #0,3,2 Current State: 95:[3, 113], Operations: ['75+49=124', '124-11=113'] Exploring Operation: 3*113=339, Resulting Numbers: [339] 339,95 unequal: No Solution Exploring Operation: 113-3=110, Resulting Numbers: [110] 110,95 unequal: No Solution Exploring Operation: 3+113=116, Resulting Numbers: [116] 116,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[3, 37], Operations: ['49-11=38', '75-38=37'] Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,95 unequal: No Solution Moving to Node #0,2,0 Current State: 95:[3, 113], Operations: ['49-11=38', '75+38=113'] Exploring Operation: 113-3=110, Resulting Numbers: [110] 110,95 unequal: No Solution Exploring Operation: 3*113=339, Resulting Numbers: [339] 339,95 unequal: No Solution Exploring Operation: 3+113=116, Resulting Numbers: [116] 116,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[3, 37], Operations: ['75+11=86', '86-49=37'] Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,95 unequal: No Solution Moving to Node #0,2,3 Current State: 95:[38, 25], Operations: ['49-11=38', '75/3=25'] Exploring Operation: 38-25=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 38*25=950, Resulting Numbers: [950] 950,95 unequal: No Solution Exploring Operation: 38+25=63, Resulting Numbers: [63] 63,95 unequal: No Solution Moving to Node #0,3,1 Current State: 95:[124, 8], Operations: ['75+49=124', '11-3=8'] Exploring Operation: 124+8=132, Resulting Numbers: [132] 132,95 unequal: No Solution Exploring Operation: 124*8=992, Resulting Numbers: [992] 992,95 unequal: No Solution Exploring Operation: 124-8=116, Resulting Numbers: [116] 116,95 unequal: No Solution Moving to Node #0,3,0 Current State: 95:[11, 121], Operations: ['75+49=124', '124-3=121'] Exploring Operation: 121/11=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 121-11=110, Resulting Numbers: [110] 110,95 unequal: No Solution Exploring Operation: 11+121=132, Resulting Numbers: [132] 132,95 unequal: No Solution Exploring Operation: 11*121=1331, Resulting Numbers: [1331] 1331,95 unequal: No Solution Moving to Node #0,3,3 Current State: 95:[124, 14], Operations: ['75+49=124', '11+3=14'] Exploring Operation: 124*14=1736, Resulting Numbers: [1736] 1736,95 unequal: No Solution Exploring Operation: 124+14=138, Resulting Numbers: [138] 138,95 unequal: No Solution Exploring Operation: 124-14=110, Resulting Numbers: [110] 110,95 unequal: No Solution Moving to Node #0,0,3 Current State: 95:[49, 89], Operations: ['75+11=86', '3+86=89'] Exploring Operation: 89-49=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 49+89=138, Resulting Numbers: [138] 138,95 unequal: No Solution Exploring Operation: 49*89=4361, Resulting Numbers: [4361] 4361,95 unequal: No Solution Moving to Node #0,2,1 Current State: 95:[38, 78], Operations: ['49-11=38', '75+3=78'] Exploring Operation: 38+78=116, Resulting Numbers: [116] 116,95 unequal: No Solution Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 38*78=2964, Resulting Numbers: [2964] 2964,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[86, 46], Operations: ['75+11=86', '49-3=46'] Exploring Operation: 86-46=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 86+46=132, Resulting Numbers: [132] 132,95 unequal: No Solution Exploring Operation: 86*46=3956, Resulting Numbers: [3956] 3956,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[86, 52], Operations: ['75+11=86', '3+49=52'] Exploring Operation: 86-52=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 86+52=138, Resulting Numbers: [138] 138,95 unequal: No Solution Exploring Operation: 86*52=4472, Resulting Numbers: [4472] 4472,95 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 18, 70, 64, 10 ]
98
[ "70-64=6", "18*6=108", "108-10=98" ]
Current State: 98:[18, 70, 64, 10], Operations: [] Exploring Operation: 70-64=6, Resulting Numbers: [18, 10, 6] Generated Node #2: [18, 10, 6] from Operation: 70-64=6 Current State: 98:[18, 10, 6], Operations: ['70-64=6'] Exploring Operation: 18*6=108, Resulting Numbers: [10, 108] Generated Node #3: [10, 108] from Operation: 18*6=108 Current State: 98:[10, 108], Operations: ['70-64=6', '18*6=108'] Exploring Operation: 108-10=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[18, 70, 64, 10], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [18, 64, 7] Generated Node #0,0: 98:[18, 64, 7] Operation: 70/10=7 Exploring Operation: 70-18=52, Resulting Numbers: [64, 10, 52] Generated Node #0,1: 98:[64, 10, 52] Operation: 70-18=52 Exploring Operation: 70-64=6, Resulting Numbers: [18, 10, 6] Generated Node #0,2: 98:[18, 10, 6] Operation: 70-64=6 Exploring Operation: 64-18=46, Resulting Numbers: [70, 10, 46] Generated Node #0,3: 98:[70, 10, 46] Operation: 64-18=46 Moving to Node #0,2 Current State: 98:[18, 10, 6], Operations: ['70-64=6'] Exploring Operation: 10+6=16, Resulting Numbers: [18, 16] Generated Node #0,2,0: 98:[18, 16] Operation: 10+6=16 Exploring Operation: 18-10=8, Resulting Numbers: [6, 8] Generated Node #0,2,1: 98:[6, 8] Operation: 18-10=8 Exploring Operation: 18-6=12, Resulting Numbers: [10, 12] Generated Node #0,2,2: 98:[10, 12] Operation: 18-6=12 Exploring Operation: 18/6=3, Resulting Numbers: [10, 3] Generated Node #0,2,3: 98:[10, 3] Operation: 18/6=3 Moving to Node #0,0 Current State: 98:[18, 64, 7], Operations: ['70/10=7'] Exploring Operation: 18-7=11, Resulting Numbers: [64, 11] Generated Node #0,0,0: 98:[64, 11] Operation: 18-7=11 Exploring Operation: 18+64=82, Resulting Numbers: [7, 82] Generated Node #0,0,1: 98:[7, 82] Operation: 18+64=82 Exploring Operation: 64-18=46, Resulting Numbers: [7, 46] Generated Node #0,0,2: 98:[7, 46] Operation: 64-18=46 Exploring Operation: 64-7=57, Resulting Numbers: [18, 57] Generated Node #0,0,3: 98:[18, 57] Operation: 64-7=57 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[7, 46], Operations: ['70/10=7', '64-18=46'] Exploring Operation: 7+46=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,98 unequal: No Solution Exploring Operation: 7*46=322, Resulting Numbers: [322] 322,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 98:[18, 57], Operations: ['70/10=7', '64-7=57'] Exploring Operation: 18*57=1026, Resulting Numbers: [1026] 1026,98 unequal: No Solution Exploring Operation: 18+57=75, Resulting Numbers: [75] 75,98 unequal: No Solution Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 98:[7, 82], Operations: ['70/10=7', '18+64=82'] Exploring Operation: 7*82=574, Resulting Numbers: [574] 574,98 unequal: No Solution Exploring Operation: 7+82=89, Resulting Numbers: [89] 89,98 unequal: No Solution Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[64, 11], Operations: ['70/10=7', '18-7=11'] Exploring Operation: 64-11=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 64*11=704, Resulting Numbers: [704] 704,98 unequal: No Solution Exploring Operation: 64+11=75, Resulting Numbers: [75] 75,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 98:[64, 10, 52], Operations: ['70-18=52'] Exploring Operation: 64-10=54, Resulting Numbers: [52, 54] Generated Node #0,1,0: 98:[52, 54] Operation: 64-10=54 Exploring Operation: 64+52=116, Resulting Numbers: [10, 116] Generated Node #0,1,1: 98:[10, 116] Operation: 64+52=116 Exploring Operation: 52-10=42, Resulting Numbers: [64, 42] Generated Node #0,1,2: 98:[64, 42] Operation: 52-10=42 Exploring Operation: 64-52=12, Resulting Numbers: [10, 12] Generated Node #0,1,3: 98:[10, 12] Operation: 64-52=12 Moving to Node #0,3 Current State: 98:[70, 10, 46], Operations: ['64-18=46'] Exploring Operation: 70/10=7, Resulting Numbers: [46, 7] Generated Node #0,3,0: 98:[46, 7] Operation: 70/10=7 Exploring Operation: 70+10=80, Resulting Numbers: [46, 80] Generated Node #0,3,1: 98:[46, 80] Operation: 70+10=80 Exploring Operation: 70-46=24, Resulting Numbers: [10, 24] Generated Node #0,3,2: 98:[10, 24] Operation: 70-46=24 Exploring Operation: 70-10=60, Resulting Numbers: [46, 60] Generated Node #0,3,3: 98:[46, 60] Operation: 70-10=60 Moving to Node #0,2,1 Current State: 98:[6, 8], Operations: ['70-64=6', '18-10=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,98 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,98 unequal: No Solution Moving to Node #0,3,0 Current State: 98:[46, 7], Operations: ['64-18=46', '70/10=7'] Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,98 unequal: No Solution Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 46*7=322, Resulting Numbers: [322] 322,98 unequal: No Solution Moving to Node #0,2,3 Current State: 98:[10, 3], Operations: ['70-64=6', '18/6=3'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[10, 12], Operations: ['70-64=6', '18-6=12'] Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,98 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[10, 12], Operations: ['70-18=52', '64-52=12'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[18, 16], Operations: ['70-64=6', '10+6=16'] Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,98 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[52, 54], Operations: ['70-18=52', '64-10=54'] Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 52*54=2808, Resulting Numbers: [2808] 2808,98 unequal: No Solution Exploring Operation: 52+54=106, Resulting Numbers: [106] 106,98 unequal: No Solution Moving to Node #0,3,2 Current State: 98:[10, 24], Operations: ['64-18=46', '70-46=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,98 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,98 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,98 unequal: No Solution Moving to Node #0,3,3 Current State: 98:[46, 60], Operations: ['64-18=46', '70-10=60'] Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,98 unequal: No Solution Exploring Operation: 46*60=2760, Resulting Numbers: [2760] 2760,98 unequal: No Solution Exploring Operation: 46+60=106, Resulting Numbers: [106] 106,98 unequal: No Solution Moving to Node #0,3,1 Current State: 98:[46, 80], Operations: ['64-18=46', '70+10=80'] Exploring Operation: 80-46=34, Resulting Numbers: [34] 34,98 unequal: No Solution Exploring Operation: 46+80=126, Resulting Numbers: [126] 126,98 unequal: No Solution Exploring Operation: 46*80=3680, Resulting Numbers: [3680] 3680,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[10, 116], Operations: ['70-18=52', '64+52=116'] Exploring Operation: 116-10=106, Resulting Numbers: [106] 106,98 unequal: No Solution Exploring Operation: 10+116=126, Resulting Numbers: [126] 126,98 unequal: No Solution Exploring Operation: 10*116=1160, Resulting Numbers: [1160] 1160,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[64, 42], Operations: ['70-18=52', '52-10=42'] Exploring Operation: 64*42=2688, Resulting Numbers: [2688] 2688,98 unequal: No Solution Exploring Operation: 64+42=106, Resulting Numbers: [106] 106,98 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,98 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 69, 67, 50, 68 ]
100
[ "69+67=136", "50*136=6800", "6800/68=100" ]
Current State: 100:[69, 67, 50, 68], Operations: [] Exploring Operation: 69+67=136, Resulting Numbers: [50, 68, 136] Generated Node #2: [50, 68, 136] from Operation: 69+67=136 Current State: 100:[50, 68, 136], Operations: ['69+67=136'] Exploring Operation: 50*136=6800, Resulting Numbers: [68, 6800] Generated Node #3: [68, 6800] from Operation: 50*136=6800 Current State: 100:[68, 6800], Operations: ['69+67=136', '50*136=6800'] Exploring Operation: 6800/68=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[69, 67, 50, 68], Operations: [] Exploring Operation: 69-67=2, Resulting Numbers: [50, 68, 2] Generated Node #0,0: 100:[50, 68, 2] Operation: 69-67=2 Moving to Node #0,0 Current State: 100:[50, 68, 2], Operations: ['69-67=2'] Exploring Operation: 68-50=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 100:[2, 18] Operation: 68-50=18 Moving to Node #0,0,0 Current State: 100:[2, 18], Operations: ['69-67=2', '68-50=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 93, 33, 87, 2 ]
36
[ "93-87=6", "6/2=3", "33+3=36" ]
Current State: 36:[93, 33, 87, 2], Operations: [] Exploring Operation: 93-87=6, Resulting Numbers: [33, 2, 6] Generated Node #2: [33, 2, 6] from Operation: 93-87=6 Current State: 36:[33, 2, 6], Operations: ['93-87=6'] Exploring Operation: 6/2=3, Resulting Numbers: [33, 3] Generated Node #3: [33, 3] from Operation: 6/2=3 Current State: 36:[33, 3], Operations: ['93-87=6', '6/2=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[93, 33, 87, 2], Operations: [] Exploring Operation: 93-87=6, Resulting Numbers: [33, 2, 6] Generated Node #0,0: 36:[33, 2, 6] Operation: 93-87=6 Exploring Operation: 93-33=60, Resulting Numbers: [87, 2, 60] Generated Node #0,1: 36:[87, 2, 60] Operation: 93-33=60 Exploring Operation: 93-2=91, Resulting Numbers: [33, 87, 91] Generated Node #0,2: 36:[33, 87, 91] Operation: 93-2=91 Exploring Operation: 87-33=54, Resulting Numbers: [93, 2, 54] Generated Node #0,3: 36:[93, 2, 54] Operation: 87-33=54 Exploring Operation: 33+2=35, Resulting Numbers: [93, 87, 35] Generated Node #0,4: 36:[93, 87, 35] Operation: 33+2=35 Moving to Node #0,0 Current State: 36:[33, 2, 6], Operations: ['93-87=6'] Exploring Operation: 6-2=4, Resulting Numbers: [33, 4] Generated Node #0,0,0: 36:[33, 4] Operation: 6-2=4 Exploring Operation: 33+6=39, Resulting Numbers: [2, 39] Generated Node #0,0,1: 36:[2, 39] Operation: 33+6=39 Exploring Operation: 33+2=35, Resulting Numbers: [6, 35] Generated Node #0,0,2: 36:[6, 35] Operation: 33+2=35 Exploring Operation: 2*6=12, Resulting Numbers: [33, 12] Generated Node #0,0,3: 36:[33, 12] Operation: 2*6=12 Exploring Operation: 6/2=3, Resulting Numbers: [33, 3] Generated Node #0,0,4: 36:[33, 3] Operation: 6/2=3 Moving to Node #0,3 Current State: 36:[93, 2, 54], Operations: ['87-33=54'] Exploring Operation: 93+2=95, Resulting Numbers: [54, 95] Generated Node #0,3,0: 36:[54, 95] Operation: 93+2=95 Exploring Operation: 93-2=91, Resulting Numbers: [54, 91] Generated Node #0,3,1: 36:[54, 91] Operation: 93-2=91 Exploring Operation: 54-2=52, Resulting Numbers: [93, 52] Generated Node #0,3,2: 36:[93, 52] Operation: 54-2=52 Exploring Operation: 93-54=39, Resulting Numbers: [2, 39] Generated Node #0,3,3: 36:[2, 39] Operation: 93-54=39 Exploring Operation: 54/2=27, Resulting Numbers: [93, 27] Generated Node #0,3,4: 36:[93, 27] Operation: 54/2=27 Moving to Node #0,1 Current State: 36:[87, 2, 60], Operations: ['93-33=60'] Exploring Operation: 60/2=30, Resulting Numbers: [87, 30] Generated Node #0,1,0: 36:[87, 30] Operation: 60/2=30 Exploring Operation: 87-2=85, Resulting Numbers: [60, 85] Generated Node #0,1,1: 36:[60, 85] Operation: 87-2=85 Exploring Operation: 87-60=27, Resulting Numbers: [2, 27] Generated Node #0,1,2: 36:[2, 27] Operation: 87-60=27 Exploring Operation: 87+2=89, Resulting Numbers: [60, 89] Generated Node #0,1,3: 36:[60, 89] Operation: 87+2=89 Exploring Operation: 60-2=58, Resulting Numbers: [87, 58] Generated Node #0,1,4: 36:[87, 58] Operation: 60-2=58 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 36:[2, 27], Operations: ['93-33=60', '87-60=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[87, 30], Operations: ['93-33=60', '60/2=30'] Exploring Operation: 87+30=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 87*30=2610, Resulting Numbers: [2610] 2610,36 unequal: No Solution Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 36:[60, 85], Operations: ['93-33=60', '87-2=85'] Exploring Operation: 60*85=5100, Resulting Numbers: [5100] 5100,36 unequal: No Solution Exploring Operation: 60+85=145, Resulting Numbers: [145] 145,36 unequal: No Solution Exploring Operation: 85-60=25, Resulting Numbers: [25] 25,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 36:[87, 58], Operations: ['93-33=60', '60-2=58'] Exploring Operation: 87-58=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 87*58=5046, Resulting Numbers: [5046] 5046,36 unequal: No Solution Exploring Operation: 87+58=145, Resulting Numbers: [145] 145,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 36:[60, 89], Operations: ['93-33=60', '87+2=89'] Exploring Operation: 89-60=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 60+89=149, Resulting Numbers: [149] 149,36 unequal: No Solution Exploring Operation: 60*89=5340, Resulting Numbers: [5340] 5340,36 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: 36:[33, 87, 91], Operations: ['93-2=91'] Exploring Operation: 91-33=58, Resulting Numbers: [87, 58] Generated Node #0,2,0: 36:[87, 58] Operation: 91-33=58 Exploring Operation: 33+91=124, Resulting Numbers: [87, 124] Generated Node #0,2,1: 36:[87, 124] Operation: 33+91=124 Exploring Operation: 33+87=120, Resulting Numbers: [91, 120] Generated Node #0,2,2: 36:[91, 120] Operation: 33+87=120 Exploring Operation: 87-33=54, Resulting Numbers: [91, 54] Generated Node #0,2,3: 36:[91, 54] Operation: 87-33=54 Exploring Operation: 91-87=4, Resulting Numbers: [33, 4] Generated Node #0,2,4: 36:[33, 4] Operation: 91-87=4 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 36:[33, 4], Operations: ['93-2=91', '91-87=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 36:[87, 58], Operations: ['93-2=91', '91-33=58'] Exploring Operation: 87+58=145, Resulting Numbers: [145] 145,36 unequal: No Solution Exploring Operation: 87*58=5046, Resulting Numbers: [5046] 5046,36 unequal: No Solution Exploring Operation: 87-58=29, Resulting Numbers: [29] 29,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 36:[91, 54], Operations: ['93-2=91', '87-33=54'] Exploring Operation: 91*54=4914, Resulting Numbers: [4914] 4914,36 unequal: No Solution Exploring Operation: 91-54=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 91+54=145, Resulting Numbers: [145] 145,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 36:[87, 124], Operations: ['93-2=91', '33+91=124'] Exploring Operation: 124-87=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 87+124=211, Resulting Numbers: [211] 211,36 unequal: No Solution Exploring Operation: 87*124=10788, Resulting Numbers: [10788] 10788,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 36:[91, 120], Operations: ['93-2=91', '33+87=120'] Exploring Operation: 91*120=10920, Resulting Numbers: [10920] 10920,36 unequal: No Solution Exploring Operation: 91+120=211, Resulting Numbers: [211] 211,36 unequal: No Solution Exploring Operation: 120-91=29, Resulting Numbers: [29] 29,36 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: 36:[93, 87, 35], Operations: ['33+2=35'] Exploring Operation: 87+35=122, Resulting Numbers: [93, 122] Generated Node #0,4,0: 36:[93, 122] Operation: 87+35=122 Exploring Operation: 93-35=58, Resulting Numbers: [87, 58] Generated Node #0,4,1: 36:[87, 58] Operation: 93-35=58 Exploring Operation: 93-87=6, Resulting Numbers: [35, 6] Generated Node #0,4,2: 36:[35, 6] Operation: 93-87=6 Exploring Operation: 93+35=128, Resulting Numbers: [87, 128] Generated Node #0,4,3: 36:[87, 128] Operation: 93+35=128 Exploring Operation: 87-35=52, Resulting Numbers: [93, 52] Generated Node #0,4,4: 36:[93, 52] Operation: 87-35=52 Moving to Node #0,0,2 Current State: 36:[6, 35], Operations: ['93-87=6', '33+2=35'] Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 6*35=210, Resulting Numbers: [210] 210,36 unequal: No Solution Moving to Node #0,4,2 Current State: 36:[35, 6], Operations: ['33+2=35', '93-87=6'] Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,36 unequal: No Solution Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[2, 39], Operations: ['93-87=6', '33+6=39'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,36 unequal: No Solution Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,36 unequal: No Solution Moving to Node #0,3,3 Current State: 36:[2, 39], Operations: ['87-33=54', '93-54=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,36 unequal: No Solution Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[33, 4], Operations: ['93-87=6', '6-2=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,36 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,0,4 Current State: 36:[33, 3], Operations: ['93-87=6', '6/2=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[93, 33, 87, 2], Operations: [] Exploring Operation: 93-87=6, Resulting Numbers: [33, 2, 6] Generated Node #0,0: 36:[33, 2, 6] Operation: 93-87=6 Moving to Node #0,0 Current State: 36:[33, 2, 6], Operations: ['93-87=6'] Exploring Operation: 6/2=3, Resulting Numbers: [33, 3] Generated Node #0,0,4: 36:[33, 3] Operation: 6/2=3 Moving to Node #0,0,4 Current State: 36:[33, 3], Operations: ['93-87=6', '6/2=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.930556
hs_5
sum_heuristic
[ 84, 53, 82, 95 ]
40
[ "84+53=137", "82+95=177", "177-137=40" ]
Current State: 40:[84, 53, 82, 95], Operations: [] Exploring Operation: 84+53=137, Resulting Numbers: [82, 95, 137] Generated Node #2: [82, 95, 137] from Operation: 84+53=137 Current State: 40:[82, 95, 137], Operations: ['84+53=137'] Exploring Operation: 82+95=177, Resulting Numbers: [137, 177] Generated Node #3: [137, 177] from Operation: 82+95=177 Current State: 40:[137, 177], Operations: ['84+53=137', '82+95=177'] Exploring Operation: 177-137=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[84, 53, 82, 95], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [84, 82, 42] Generated Node #0,0: 40:[84, 82, 42] Operation: 95-53=42 Exploring Operation: 95-82=13, Resulting Numbers: [84, 53, 13] Generated Node #0,1: 40:[84, 53, 13] Operation: 95-82=13 Exploring Operation: 84-53=31, Resulting Numbers: [82, 95, 31] Generated Node #0,2: 40:[82, 95, 31] Operation: 84-53=31 Exploring Operation: 95-84=11, Resulting Numbers: [53, 82, 11] Generated Node #0,3: 40:[53, 82, 11] Operation: 95-84=11 Exploring Operation: 84-82=2, Resulting Numbers: [53, 95, 2] Generated Node #0,4: 40:[53, 95, 2] Operation: 84-82=2 Moving to Node #0,3 Current State: 40:[53, 82, 11], Operations: ['95-84=11'] Exploring Operation: 82-11=71, Resulting Numbers: [53, 71] Generated Node #0,3,0: 40:[53, 71] Operation: 82-11=71 Exploring Operation: 82+11=93, Resulting Numbers: [53, 93] Generated Node #0,3,1: 40:[53, 93] Operation: 82+11=93 Exploring Operation: 53-11=42, Resulting Numbers: [82, 42] Generated Node #0,3,2: 40:[82, 42] Operation: 53-11=42 Exploring Operation: 53+11=64, Resulting Numbers: [82, 64] Generated Node #0,3,3: 40:[82, 64] Operation: 53+11=64 Exploring Operation: 82-53=29, Resulting Numbers: [11, 29] Generated Node #0,3,4: 40:[11, 29] Operation: 82-53=29 Moving to Node #0,1 Current State: 40:[84, 53, 13], Operations: ['95-82=13'] Exploring Operation: 53+13=66, Resulting Numbers: [84, 66] Generated Node #0,1,0: 40:[84, 66] Operation: 53+13=66 Exploring Operation: 84+13=97, Resulting Numbers: [53, 97] Generated Node #0,1,1: 40:[53, 97] Operation: 84+13=97 Exploring Operation: 53-13=40, Resulting Numbers: [84, 40] Generated Node #0,1,2: 40:[84, 40] Operation: 53-13=40 Exploring Operation: 84-13=71, Resulting Numbers: [53, 71] Generated Node #0,1,3: 40:[53, 71] Operation: 84-13=71 Exploring Operation: 84-53=31, Resulting Numbers: [13, 31] Generated Node #0,1,4: 40:[13, 31] Operation: 84-53=31 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 40:[13, 31], Operations: ['95-82=13', '84-53=31'] Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 13*31=403, Resulting Numbers: [403] 403,40 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 40:[84, 40], Operations: ['95-82=13', '53-13=40'] Exploring Operation: 84+40=124, Resulting Numbers: [124] 124,40 unequal: No Solution Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 84*40=3360, Resulting Numbers: [3360] 3360,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 40:[53, 71], Operations: ['95-82=13', '84-13=71'] Exploring Operation: 53+71=124, Resulting Numbers: [124] 124,40 unequal: No Solution Exploring Operation: 53*71=3763, Resulting Numbers: [3763] 3763,40 unequal: No Solution Exploring Operation: 71-53=18, Resulting Numbers: [18] 18,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[84, 66], Operations: ['95-82=13', '53+13=66'] Exploring Operation: 84*66=5544, Resulting Numbers: [5544] 5544,40 unequal: No Solution Exploring Operation: 84-66=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 84+66=150, Resulting Numbers: [150] 150,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[53, 97], Operations: ['95-82=13', '84+13=97'] Exploring Operation: 97-53=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 53+97=150, Resulting Numbers: [150] 150,40 unequal: No Solution Exploring Operation: 53*97=5141, Resulting Numbers: [5141] 5141,40 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: 40:[53, 95, 2], Operations: ['84-82=2'] Exploring Operation: 95-53=42, Resulting Numbers: [2, 42] Generated Node #0,4,0: 40:[2, 42] Operation: 95-53=42 Exploring Operation: 95+2=97, Resulting Numbers: [53, 97] Generated Node #0,4,1: 40:[53, 97] Operation: 95+2=97 Exploring Operation: 95-2=93, Resulting Numbers: [53, 93] Generated Node #0,4,2: 40:[53, 93] Operation: 95-2=93 Exploring Operation: 53+2=55, Resulting Numbers: [95, 55] Generated Node #0,4,3: 40:[95, 55] Operation: 53+2=55 Exploring Operation: 53-2=51, Resulting Numbers: [95, 51] Generated Node #0,4,4: 40:[95, 51] Operation: 53-2=51 Moving to Node #0,0 Current State: 40:[84, 82, 42], Operations: ['95-53=42'] Exploring Operation: 84/42=2, Resulting Numbers: [82, 2] Generated Node #0,0,0: 40:[82, 2] Operation: 84/42=2 Exploring Operation: 84+82=166, Resulting Numbers: [42, 166] Generated Node #0,0,1: 40:[42, 166] Operation: 84+82=166 Exploring Operation: 84-82=2, Resulting Numbers: [42, 2] Generated Node #0,0,2: 40:[42, 2] Operation: 84-82=2 Exploring Operation: 84-42=42, Resulting Numbers: [82, 42] Generated Node #0,0,3: 40:[82, 42] Operation: 84-42=42 Exploring Operation: 82-42=40, Resulting Numbers: [84, 40] Generated Node #0,0,4: 40:[84, 40] Operation: 82-42=40 Moving to Node #0,2 Current State: 40:[82, 95, 31], Operations: ['84-53=31'] Exploring Operation: 95+31=126, Resulting Numbers: [82, 126] Generated Node #0,2,0: 40:[82, 126] Operation: 95+31=126 Exploring Operation: 82+31=113, Resulting Numbers: [95, 113] Generated Node #0,2,1: 40:[95, 113] Operation: 82+31=113 Exploring Operation: 95-82=13, Resulting Numbers: [31, 13] Generated Node #0,2,2: 40:[31, 13] Operation: 95-82=13 Exploring Operation: 82-31=51, Resulting Numbers: [95, 51] Generated Node #0,2,3: 40:[95, 51] Operation: 82-31=51 Exploring Operation: 95-31=64, Resulting Numbers: [82, 64] Generated Node #0,2,4: 40:[82, 64] Operation: 95-31=64 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 40:[31, 13], Operations: ['84-53=31', '95-82=13'] Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,40 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 40:[95, 51], Operations: ['84-53=31', '82-31=51'] Exploring Operation: 95-51=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 95+51=146, Resulting Numbers: [146] 146,40 unequal: No Solution Exploring Operation: 95*51=4845, Resulting Numbers: [4845] 4845,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 40:[82, 64], Operations: ['84-53=31', '95-31=64'] Exploring Operation: 82*64=5248, Resulting Numbers: [5248] 5248,40 unequal: No Solution Exploring Operation: 82+64=146, Resulting Numbers: [146] 146,40 unequal: No Solution Exploring Operation: 82-64=18, Resulting Numbers: [18] 18,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[82, 126], Operations: ['84-53=31', '95+31=126'] Exploring Operation: 82*126=10332, Resulting Numbers: [10332] 10332,40 unequal: No Solution Exploring Operation: 126-82=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 82+126=208, Resulting Numbers: [208] 208,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 40:[95, 113], Operations: ['84-53=31', '82+31=113'] Exploring Operation: 113-95=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 95+113=208, Resulting Numbers: [208] 208,40 unequal: No Solution Exploring Operation: 95*113=10735, Resulting Numbers: [10735] 10735,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 40:[2, 42], Operations: ['84-82=2', '95-53=42'] Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[84, 53, 82, 95], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [53, 95, 2] Generated Node #0,4: 40:[53, 95, 2] Operation: 84-82=2 Moving to Node #0,4 Current State: 40:[53, 95, 2], Operations: ['84-82=2'] Exploring Operation: 95-53=42, Resulting Numbers: [2, 42] Generated Node #0,4,0: 40:[2, 42] Operation: 95-53=42 Moving to Node #0,4,0 Current State: 40:[2, 42], Operations: ['84-82=2', '95-53=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
0.94184
hs_5
sum_heuristic
[ 50, 21, 56, 62 ]
47
[ "50+21=71", "56+62=118", "118-71=47" ]
Current State: 47:[50, 21, 56, 62], Operations: [] Exploring Operation: 50+21=71, Resulting Numbers: [56, 62, 71] Generated Node #2: [56, 62, 71] from Operation: 50+21=71 Current State: 47:[56, 62, 71], Operations: ['50+21=71'] Exploring Operation: 56+62=118, Resulting Numbers: [71, 118] Generated Node #3: [71, 118] from Operation: 56+62=118 Current State: 47:[71, 118], Operations: ['50+21=71', '56+62=118'] Exploring Operation: 118-71=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[50, 21, 56, 62], Operations: [] Exploring Operation: 62-21=41, Resulting Numbers: [50, 56, 41] Generated Node #0,0: 47:[50, 56, 41] Operation: 62-21=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[50, 56, 41], Operations: ['62-21=41'] Exploring Operation: 56-41=15, Resulting Numbers: [50, 15] Generated Node #0,0,0: 47:[50, 15] Operation: 56-41=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[50, 15], Operations: ['62-21=41', '56-41=15'] Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 2, 41, 9, 55 ]
19
[ "55-41=14", "2*14=28", "28-9=19" ]
Current State: 19:[2, 41, 9, 55], Operations: [] Exploring Operation: 55-41=14, Resulting Numbers: [2, 9, 14] Generated Node #2: [2, 9, 14] from Operation: 55-41=14 Current State: 19:[2, 9, 14], Operations: ['55-41=14'] Exploring Operation: 2*14=28, Resulting Numbers: [9, 28] Generated Node #3: [9, 28] from Operation: 2*14=28 Current State: 19:[9, 28], Operations: ['55-41=14', '2*14=28'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[2, 41, 9, 55], Operations: [] Exploring Operation: 55-41=14, Resulting Numbers: [2, 9, 14] Generated Node #0,0: 19:[2, 9, 14] Operation: 55-41=14 Exploring Operation: 2*9=18, Resulting Numbers: [41, 55, 18] Generated Node #0,1: 19:[41, 55, 18] Operation: 2*9=18 Exploring Operation: 55-2=53, Resulting Numbers: [41, 9, 53] Generated Node #0,2: 19:[41, 9, 53] Operation: 55-2=53 Exploring Operation: 41-2=39, Resulting Numbers: [9, 55, 39] Generated Node #0,3: 19:[9, 55, 39] Operation: 41-2=39 Exploring Operation: 2+9=11, Resulting Numbers: [41, 55, 11] Generated Node #0,4: 19:[41, 55, 11] Operation: 2+9=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[2, 9, 14], Operations: ['55-41=14'] Exploring Operation: 2+9=11, Resulting Numbers: [14, 11] Generated Node #0,0,0: 19:[14, 11] Operation: 2+9=11 Exploring Operation: 14-2=12, Resulting Numbers: [9, 12] Generated Node #0,0,1: 19:[9, 12] Operation: 14-2=12 Exploring Operation: 2*9=18, Resulting Numbers: [14, 18] Generated Node #0,0,2: 19:[14, 18] Operation: 2*9=18 Exploring Operation: 9-2=7, Resulting Numbers: [14, 7] Generated Node #0,0,3: 19:[14, 7] Operation: 9-2=7 Exploring Operation: 2+14=16, Resulting Numbers: [9, 16] Generated Node #0,0,4: 19:[9, 16] Operation: 2+14=16 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 19:[14, 18], Operations: ['55-41=14', '2*9=18'] Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 14+18=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 14*18=252, Resulting Numbers: [252] 252,19 unequal: No Solution No 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: 19:[14, 11], Operations: ['55-41=14', '2+9=11'] Exploring Operation: 14*11=154, Resulting Numbers: [154] 154,19 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,19 unequal: No Solution No 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: 19:[9, 16], Operations: ['55-41=14', '2+14=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,19 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,19 unequal: No Solution No 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: 19:[9, 12], Operations: ['55-41=14', '14-2=12'] Exploring Operation: 9*12=108, Resulting Numbers: [108] 108,19 unequal: No Solution Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,19 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,19 unequal: No Solution No 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: 19:[14, 7], Operations: ['55-41=14', '9-2=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,19 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 14+7=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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[41, 55, 18], Operations: ['2*9=18'] Exploring Operation: 41+18=59, Resulting Numbers: [55, 59] Generated Node #0,1,0: 19:[55, 59] Operation: 41+18=59 Exploring Operation: 55+18=73, Resulting Numbers: [41, 73] Generated Node #0,1,1: 19:[41, 73] Operation: 55+18=73 Exploring Operation: 55-18=37, Resulting Numbers: [41, 37] Generated Node #0,1,2: 19:[41, 37] Operation: 55-18=37 Exploring Operation: 55-41=14, Resulting Numbers: [18, 14] Generated Node #0,1,3: 19:[18, 14] Operation: 55-41=14 Exploring Operation: 41-18=23, Resulting Numbers: [55, 23] Generated Node #0,1,4: 19:[55, 23] Operation: 41-18=23 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 19:[18, 14], Operations: ['2*9=18', '55-41=14'] Exploring Operation: 18*14=252, Resulting Numbers: [252] 252,19 unequal: No Solution Exploring Operation: 18+14=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,19 unequal: No Solution No 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: 19:[41, 37], Operations: ['2*9=18', '55-18=37'] Exploring Operation: 41*37=1517, Resulting Numbers: [1517] 1517,19 unequal: No Solution Exploring Operation: 41-37=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 41+37=78, Resulting Numbers: [78] 78,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 19:[55, 23], Operations: ['2*9=18', '41-18=23'] Exploring Operation: 55+23=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 55*23=1265, Resulting Numbers: [1265] 1265,19 unequal: No Solution Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,19 unequal: No Solution No 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: 19:[55, 59], Operations: ['2*9=18', '41+18=59'] Exploring Operation: 55+59=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 59-55=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 55*59=3245, Resulting Numbers: [3245] 3245,19 unequal: No Solution No 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: 19:[41, 73], Operations: ['2*9=18', '55+18=73'] Exploring Operation: 41*73=2993, Resulting Numbers: [2993] 2993,19 unequal: No Solution Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 41+73=114, Resulting Numbers: [114] 114,19 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[41, 9, 53], Operations: ['55-2=53'] Exploring Operation: 41+9=50, Resulting Numbers: [53, 50] Generated Node #0,2,0: 19:[53, 50] Operation: 41+9=50 Exploring Operation: 9+53=62, Resulting Numbers: [41, 62] Generated Node #0,2,1: 19:[41, 62] Operation: 9+53=62 Exploring Operation: 53-41=12, Resulting Numbers: [9, 12] Generated Node #0,2,2: 19:[9, 12] Operation: 53-41=12 Exploring Operation: 41-9=32, Resulting Numbers: [53, 32] Generated Node #0,2,3: 19:[53, 32] Operation: 41-9=32 Exploring Operation: 53-9=44, Resulting Numbers: [41, 44] Generated Node #0,2,4: 19:[41, 44] Operation: 53-9=44 Moving to Node #0,2,2 Current State: 19:[9, 12], Operations: ['55-2=53', '53-41=12'] Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,19 unequal: No Solution Exploring Operation: 9*12=108, Resulting Numbers: [108] 108,19 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,19 unequal: No Solution Moving to Node #0,2,4 Current State: 19:[41, 44], Operations: ['55-2=53', '53-9=44'] Exploring Operation: 41+44=85, Resulting Numbers: [85] 85,19 unequal: No Solution Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 41*44=1804, Resulting Numbers: [1804] 1804,19 unequal: No Solution Moving to Node #0,2,3 Current State: 19:[53, 32], Operations: ['55-2=53', '41-9=32'] Exploring Operation: 53*32=1696, Resulting Numbers: [1696] 1696,19 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,19 unequal: No Solution Exploring Operation: 53+32=85, Resulting Numbers: [85] 85,19 unequal: No Solution Moving to Node #0,2,0 Current State: 19:[53, 50], Operations: ['55-2=53', '41+9=50'] Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,19 unequal: No Solution Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,19 unequal: No Solution Moving to Node #0,2,1 Current State: 19:[41, 62], Operations: ['55-2=53', '9+53=62'] Exploring Operation: 41*62=2542, Resulting Numbers: [2542] 2542,19 unequal: No Solution Exploring Operation: 41+62=103, Resulting Numbers: [103] 103,19 unequal: No Solution Exploring Operation: 62-41=21, Resulting Numbers: [21] 21,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[9, 55, 39], Operations: ['41-2=39'] Exploring Operation: 39-9=30, Resulting Numbers: [55, 30] Generated Node #0,3,0: 19:[55, 30] Operation: 39-9=30 Exploring Operation: 9+55=64, Resulting Numbers: [39, 64] Generated Node #0,3,1: 19:[39, 64] Operation: 9+55=64 Exploring Operation: 9+39=48, Resulting Numbers: [55, 48] Generated Node #0,3,2: 19:[55, 48] Operation: 9+39=48 Exploring Operation: 55-9=46, Resulting Numbers: [39, 46] Generated Node #0,3,3: 19:[39, 46] Operation: 55-9=46 Exploring Operation: 55-39=16, Resulting Numbers: [9, 16] Generated Node #0,3,4: 19:[9, 16] Operation: 55-39=16 Moving to Node #0,3,4 Current State: 19:[9, 16], Operations: ['41-2=39', '55-39=16'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,19 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[39, 46], Operations: ['41-2=39', '55-9=46'] Exploring Operation: 39*46=1794, Resulting Numbers: [1794] 1794,19 unequal: No Solution Exploring Operation: 39+46=85, Resulting Numbers: [85] 85,19 unequal: No Solution Exploring Operation: 46-39=7, Resulting Numbers: [7] 7,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[55, 30], Operations: ['41-2=39', '39-9=30'] Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,19 unequal: No Solution Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,19 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[39, 64], Operations: ['41-2=39', '9+55=64'] Exploring Operation: 39+64=103, Resulting Numbers: [103] 103,19 unequal: No Solution Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 39*64=2496, Resulting Numbers: [2496] 2496,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[55, 48], Operations: ['41-2=39', '9+39=48'] Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,19 unequal: No Solution Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 19:[41, 55, 11], Operations: ['2+9=11'] Exploring Operation: 41+11=52, Resulting Numbers: [55, 52] Generated Node #0,4,0: 19:[55, 52] Operation: 41+11=52 Exploring Operation: 55-41=14, Resulting Numbers: [11, 14] Generated Node #0,4,1: 19:[11, 14] Operation: 55-41=14 Exploring Operation: 55/11=5, Resulting Numbers: [41, 5] Generated Node #0,4,2: 19:[41, 5] Operation: 55/11=5 Exploring Operation: 41-11=30, Resulting Numbers: [55, 30] Generated Node #0,4,3: 19:[55, 30] Operation: 41-11=30 Exploring Operation: 55-11=44, Resulting Numbers: [41, 44] Generated Node #0,4,4: 19:[41, 44] Operation: 55-11=44 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 19:[11, 14], Operations: ['2+9=11', '55-41=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,19 unequal: No Solution No 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: 19:[41, 5], Operations: ['2+9=11', '55/11=5'] Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,19 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 19:[55, 30], Operations: ['2+9=11', '41-11=30'] Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,19 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 19:[41, 44], Operations: ['2+9=11', '55-11=44'] Exploring Operation: 41+44=85, Resulting Numbers: [85] 85,19 unequal: No Solution Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 41*44=1804, Resulting Numbers: [1804] 1804,19 unequal: No Solution No 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: 19:[55, 52], Operations: ['2+9=11', '41+11=52'] Exploring Operation: 55-52=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 55*52=2860, Resulting Numbers: [2860] 2860,19 unequal: No Solution Exploring Operation: 55+52=107, Resulting Numbers: [107] 107,19 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_5
sum_heuristic
[ 2, 18, 90, 59 ]
47
[ "18-2=16", "90-59=31", "16+31=47" ]
Current State: 47:[2, 18, 90, 59], Operations: [] Exploring Operation: 18-2=16, Resulting Numbers: [90, 59, 16] Generated Node #2: [90, 59, 16] from Operation: 18-2=16 Current State: 47:[90, 59, 16], Operations: ['18-2=16'] Exploring Operation: 90-59=31, Resulting Numbers: [16, 31] Generated Node #3: [16, 31] from Operation: 90-59=31 Current State: 47:[16, 31], Operations: ['18-2=16', '90-59=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[2, 18, 90, 59], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [18, 59, 45] Generated Node #0,0: 47:[18, 59, 45] Operation: 90/2=45 Moving to Node #0,0 Current State: 47:[18, 59, 45], Operations: ['90/2=45'] Exploring Operation: 59-18=41, Resulting Numbers: [45, 41] Generated Node #0,0,0: 47:[45, 41] Operation: 59-18=41 Moving to Node #0,0,0 Current State: 47:[45, 41], Operations: ['90/2=45', '59-18=41'] Exploring Operation: 45+41=86, Resulting Numbers: [86] 86,47 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 72, 76, 31, 48 ]
43
[ "76-72=4", "48/4=12", "31+12=43" ]
Current State: 43:[72, 76, 31, 48], Operations: [] Exploring Operation: 76-72=4, Resulting Numbers: [31, 48, 4] Generated Node #2: [31, 48, 4] from Operation: 76-72=4 Current State: 43:[31, 48, 4], Operations: ['76-72=4'] Exploring Operation: 48/4=12, Resulting Numbers: [31, 12] Generated Node #3: [31, 12] from Operation: 48/4=12 Current State: 43:[31, 12], Operations: ['76-72=4', '48/4=12'] Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[72, 76, 31, 48], Operations: [] Exploring Operation: 76-72=4, Resulting Numbers: [31, 48, 4] Generated Node #0,0: 43:[31, 48, 4] Operation: 76-72=4 Exploring Operation: 76-31=45, Resulting Numbers: [72, 48, 45] Generated Node #0,1: 43:[72, 48, 45] Operation: 76-31=45 Exploring Operation: 76-48=28, Resulting Numbers: [72, 31, 28] Generated Node #0,2: 43:[72, 31, 28] Operation: 76-48=28 Exploring Operation: 72-31=41, Resulting Numbers: [76, 48, 41] Generated Node #0,3: 43:[76, 48, 41] Operation: 72-31=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[72, 48, 45], Operations: ['76-31=45'] Exploring Operation: 48-45=3, Resulting Numbers: [72, 3] Generated Node #0,1,0: 43:[72, 3] Operation: 48-45=3 Exploring Operation: 72-45=27, Resulting Numbers: [48, 27] Generated Node #0,1,1: 43:[48, 27] Operation: 72-45=27 Exploring Operation: 72+48=120, Resulting Numbers: [45, 120] Generated Node #0,1,2: 43:[45, 120] Operation: 72+48=120 Exploring Operation: 72-48=24, Resulting Numbers: [45, 24] Generated Node #0,1,3: 43:[45, 24] Operation: 72-48=24 Moving to Node #0,1,1 Current State: 43:[48, 27], Operations: ['76-31=45', '72-45=27'] Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[45, 24], Operations: ['76-31=45', '72-48=24'] Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 45*24=1080, Resulting Numbers: [1080] 1080,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[72, 3], Operations: ['76-31=45', '48-45=3'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,43 unequal: No Solution Exploring Operation: 72*3=216, Resulting Numbers: [216] 216,43 unequal: No Solution Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[45, 120], Operations: ['76-31=45', '72+48=120'] Exploring Operation: 45*120=5400, Resulting Numbers: [5400] 5400,43 unequal: No Solution Exploring Operation: 45+120=165, Resulting Numbers: [165] 165,43 unequal: No Solution Exploring Operation: 120-45=75, Resulting Numbers: [75] 75,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 43:[76, 48, 41], Operations: ['72-31=41'] Exploring Operation: 76-48=28, Resulting Numbers: [41, 28] Generated Node #0,3,0: 43:[41, 28] Operation: 76-48=28 Exploring Operation: 48-41=7, Resulting Numbers: [76, 7] Generated Node #0,3,1: 43:[76, 7] Operation: 48-41=7 Exploring Operation: 76-41=35, Resulting Numbers: [48, 35] Generated Node #0,3,2: 43:[48, 35] Operation: 76-41=35 Exploring Operation: 76+41=117, Resulting Numbers: [48, 117] Generated Node #0,3,3: 43:[48, 117] Operation: 76+41=117 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 43:[48, 35], Operations: ['72-31=41', '76-41=35'] Exploring Operation: 48+35=83, Resulting Numbers: [83] 83,43 unequal: No Solution Exploring Operation: 48*35=1680, Resulting Numbers: [1680] 1680,43 unequal: No Solution Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 43:[41, 28], Operations: ['72-31=41', '76-48=28'] Exploring Operation: 41+28=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 41*28=1148, Resulting Numbers: [1148] 1148,43 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 43:[76, 7], Operations: ['72-31=41', '48-41=7'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 76*7=532, Resulting Numbers: [532] 532,43 unequal: No Solution Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 43:[48, 117], Operations: ['72-31=41', '76+41=117'] Exploring Operation: 48+117=165, Resulting Numbers: [165] 165,43 unequal: No Solution Exploring Operation: 117-48=69, Resulting Numbers: [69] 69,43 unequal: No Solution Exploring Operation: 48*117=5616, Resulting Numbers: [5616] 5616,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[31, 48, 4], Operations: ['76-72=4'] Exploring Operation: 48-4=44, Resulting Numbers: [31, 44] Generated Node #0,0,0: 43:[31, 44] Operation: 48-4=44 Exploring Operation: 48+4=52, Resulting Numbers: [31, 52] Generated Node #0,0,1: 43:[31, 52] Operation: 48+4=52 Exploring Operation: 31-4=27, Resulting Numbers: [48, 27] Generated Node #0,0,2: 43:[48, 27] Operation: 31-4=27 Exploring Operation: 31+4=35, Resulting Numbers: [48, 35] Generated Node #0,0,3: 43:[48, 35] Operation: 31+4=35 Moving to Node #0,0,0 Current State: 43:[31, 44], Operations: ['76-72=4', '48-4=44'] Exploring Operation: 31*44=1364, Resulting Numbers: [1364] 1364,43 unequal: No Solution Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 31+44=75, Resulting Numbers: [75] 75,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[48, 35], Operations: ['76-72=4', '31+4=35'] Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 48*35=1680, Resulting Numbers: [1680] 1680,43 unequal: No Solution Exploring Operation: 48+35=83, Resulting Numbers: [83] 83,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[48, 27], Operations: ['76-72=4', '31-4=27'] Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,43 unequal: No Solution Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[31, 52], Operations: ['76-72=4', '48+4=52'] Exploring Operation: 31+52=83, Resulting Numbers: [83] 83,43 unequal: No Solution Exploring Operation: 31*52=1612, Resulting Numbers: [1612] 1612,43 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[72, 31, 28], Operations: ['76-48=28'] Exploring Operation: 72-28=44, Resulting Numbers: [31, 44] Generated Node #0,2,0: 43:[31, 44] Operation: 72-28=44 Exploring Operation: 72+28=100, Resulting Numbers: [31, 100] Generated Node #0,2,1: 43:[31, 100] Operation: 72+28=100 Exploring Operation: 31+28=59, Resulting Numbers: [72, 59] Generated Node #0,2,2: 43:[72, 59] Operation: 31+28=59 Exploring Operation: 72-31=41, Resulting Numbers: [28, 41] Generated Node #0,2,3: 43:[28, 41] Operation: 72-31=41 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 43:[31, 44], Operations: ['76-48=28', '72-28=44'] Exploring Operation: 31*44=1364, Resulting Numbers: [1364] 1364,43 unequal: No Solution Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 31+44=75, Resulting Numbers: [75] 75,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 43:[28, 41], Operations: ['76-48=28', '72-31=41'] Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 28*41=1148, Resulting Numbers: [1148] 1148,43 unequal: No Solution Exploring Operation: 28+41=69, Resulting Numbers: [69] 69,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 43:[72, 59], Operations: ['76-48=28', '31+28=59'] Exploring Operation: 72+59=131, Resulting Numbers: [131] 131,43 unequal: No Solution Exploring Operation: 72-59=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 72*59=4248, Resulting Numbers: [4248] 4248,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 43:[31, 100], Operations: ['76-48=28', '72+28=100'] Exploring Operation: 31*100=3100, Resulting Numbers: [3100] 3100,43 unequal: No Solution Exploring Operation: 31+100=131, Resulting Numbers: [131] 131,43 unequal: No Solution Exploring Operation: 100-31=69, Resulting Numbers: [69] 69,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 66, 6, 86, 64 ]
14
[ "86-66=20", "64+20=84", "84/6=14" ]
Current State: 14:[66, 6, 86, 64], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [6, 64, 20] Generated Node #2: [6, 64, 20] from Operation: 86-66=20 Current State: 14:[6, 64, 20], Operations: ['86-66=20'] Exploring Operation: 64+20=84, Resulting Numbers: [6, 84] Generated Node #3: [6, 84] from Operation: 64+20=84 Current State: 14:[6, 84], Operations: ['86-66=20', '64+20=84'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[66, 6, 86, 64], Operations: [] Exploring Operation: 66/6=11, Resulting Numbers: [86, 64, 11] Generated Node #0,0: 14:[86, 64, 11] Operation: 66/6=11 Exploring Operation: 86-64=22, Resulting Numbers: [66, 6, 22] Generated Node #0,1: 14:[66, 6, 22] Operation: 86-64=22 Exploring Operation: 86-66=20, Resulting Numbers: [6, 64, 20] Generated Node #0,2: 14:[6, 64, 20] Operation: 86-66=20 Exploring Operation: 66-64=2, Resulting Numbers: [6, 86, 2] Generated Node #0,3: 14:[6, 86, 2] Operation: 66-64=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[6, 64, 20], Operations: ['86-66=20'] Exploring Operation: 6+64=70, Resulting Numbers: [20, 70] Generated Node #0,2,0: 14:[20, 70] Operation: 6+64=70 Exploring Operation: 20-6=14, Resulting Numbers: [64, 14] Generated Node #0,2,1: 14:[64, 14] Operation: 20-6=14 Exploring Operation: 64-6=58, Resulting Numbers: [20, 58] Generated Node #0,2,2: 14:[20, 58] Operation: 64-6=58 Exploring Operation: 64-20=44, Resulting Numbers: [6, 44] Generated Node #0,2,3: 14:[6, 44] Operation: 64-20=44 Moving to Node #0,2,3 Current State: 14:[6, 44], Operations: ['86-66=20', '64-20=44'] Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,14 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,14 unequal: No Solution Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,14 unequal: No Solution Moving to Node #0,2,2 Current State: 14:[20, 58], Operations: ['86-66=20', '64-6=58'] Exploring Operation: 58-20=38, Resulting Numbers: [38] 38,14 unequal: No Solution Exploring Operation: 20*58=1160, Resulting Numbers: [1160] 1160,14 unequal: No Solution Exploring Operation: 20+58=78, Resulting Numbers: [78] 78,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[64, 14], Operations: ['86-66=20', '20-6=14'] Exploring Operation: 64*14=896, Resulting Numbers: [896] 896,14 unequal: No Solution Exploring Operation: 64+14=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[20, 70], Operations: ['86-66=20', '6+64=70'] Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,14 unequal: No Solution Exploring Operation: 20*70=1400, Resulting Numbers: [1400] 1400,14 unequal: No Solution Exploring Operation: 20+70=90, Resulting Numbers: [90] 90,14 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 Current State: 14:[66, 6, 22], Operations: ['86-64=22'] Exploring Operation: 66-6=60, Resulting Numbers: [22, 60] Generated Node #0,1,0: 14:[22, 60] Operation: 66-6=60 Exploring Operation: 66/22=3, Resulting Numbers: [6, 3] Generated Node #0,1,1: 14:[6, 3] Operation: 66/22=3 Exploring Operation: 66/6=11, Resulting Numbers: [22, 11] Generated Node #0,1,2: 14:[22, 11] Operation: 66/6=11 Exploring Operation: 66-22=44, Resulting Numbers: [6, 44] Generated Node #0,1,3: 14:[6, 44] Operation: 66-22=44 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[6, 3], Operations: ['86-64=22', '66/22=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,14 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,14 unequal: No Solution No 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: 14:[22, 11], Operations: ['86-64=22', '66/6=11'] Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,14 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,14 unequal: No Solution No 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: 14:[6, 44], Operations: ['86-64=22', '66-22=44'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,14 unequal: No Solution Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,14 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,14 unequal: No Solution No 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: 14:[22, 60], Operations: ['86-64=22', '66-6=60'] Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,14 unequal: No Solution Exploring Operation: 22+60=82, Resulting Numbers: [82] 82,14 unequal: No Solution Exploring Operation: 22*60=1320, Resulting Numbers: [1320] 1320,14 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: 14:[6, 86, 2], Operations: ['66-64=2'] Exploring Operation: 86-2=84, Resulting Numbers: [6, 84] Generated Node #0,3,0: 14:[6, 84] Operation: 86-2=84 Exploring Operation: 86/2=43, Resulting Numbers: [6, 43] Generated Node #0,3,1: 14:[6, 43] Operation: 86/2=43 Exploring Operation: 86-6=80, Resulting Numbers: [2, 80] Generated Node #0,3,2: 14:[2, 80] Operation: 86-6=80 Exploring Operation: 6+2=8, Resulting Numbers: [86, 8] Generated Node #0,3,3: 14:[86, 8] Operation: 6+2=8 Moving to Node #0,3,1 Current State: 14:[6, 43], Operations: ['66-64=2', '86/2=43'] Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,14 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 6*43=258, Resulting Numbers: [258] 258,14 unequal: No Solution Moving to Node #0,3,2 Current State: 14:[2, 80], Operations: ['66-64=2', '86-6=80'] Exploring Operation: 2+80=82, Resulting Numbers: [82] 82,14 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 2*80=160, Resulting Numbers: [160] 160,14 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,14 unequal: No Solution Moving to Node #0,3,0 Current State: 14:[6, 84], Operations: ['66-64=2', '86-2=84'] Exploring Operation: 6*84=504, Resulting Numbers: [504] 504,14 unequal: No Solution Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[66, 6, 86, 64], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [6, 86, 2] Generated Node #0,3: 14:[6, 86, 2] Operation: 66-64=2 Moving to Node #0,3 Current State: 14:[6, 86, 2], Operations: ['66-64=2'] Exploring Operation: 86-2=84, Resulting Numbers: [6, 84] Generated Node #0,3,0: 14:[6, 84] Operation: 86-2=84 Moving to Node #0,3,0 Current State: 14:[6, 84], Operations: ['66-64=2', '86-2=84'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_4
sum_heuristic
[ 8, 36, 21, 94 ]
38
[ "8*21=168", "36+94=130", "168-130=38" ]
Current State: 38:[8, 36, 21, 94], Operations: [] Exploring Operation: 8*21=168, Resulting Numbers: [36, 94, 168] Generated Node #2: [36, 94, 168] from Operation: 8*21=168 Current State: 38:[36, 94, 168], Operations: ['8*21=168'] Exploring Operation: 36+94=130, Resulting Numbers: [168, 130] Generated Node #3: [168, 130] from Operation: 36+94=130 Current State: 38:[168, 130], Operations: ['8*21=168', '36+94=130'] Exploring Operation: 168-130=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[8, 36, 21, 94], Operations: [] Exploring Operation: 94-21=73, Resulting Numbers: [8, 36, 73] Generated Node #0,0: 38:[8, 36, 73] Operation: 94-21=73 Exploring Operation: 94-36=58, Resulting Numbers: [8, 21, 58] Generated Node #0,1: 38:[8, 21, 58] Operation: 94-36=58 Exploring Operation: 94-8=86, Resulting Numbers: [36, 21, 86] Generated Node #0,2: 38:[36, 21, 86] Operation: 94-8=86 Exploring Operation: 8+36=44, Resulting Numbers: [21, 94, 44] Generated Node #0,3: 38:[21, 94, 44] Operation: 8+36=44 Moving to Node #0,1 Current State: 38:[8, 21, 58], Operations: ['94-36=58'] Exploring Operation: 58-8=50, Resulting Numbers: [21, 50] Generated Node #0,1,0: 38:[21, 50] Operation: 58-8=50 Exploring Operation: 21-8=13, Resulting Numbers: [58, 13] Generated Node #0,1,1: 38:[58, 13] Operation: 21-8=13 Exploring Operation: 58-21=37, Resulting Numbers: [8, 37] Generated Node #0,1,2: 38:[8, 37] Operation: 58-21=37 Exploring Operation: 8+21=29, Resulting Numbers: [58, 29] Generated Node #0,1,3: 38:[58, 29] Operation: 8+21=29 Moving to Node #0,0 Current State: 38:[8, 36, 73], Operations: ['94-21=73'] Exploring Operation: 8+36=44, Resulting Numbers: [73, 44] Generated Node #0,0,0: 38:[73, 44] Operation: 8+36=44 Exploring Operation: 73-36=37, Resulting Numbers: [8, 37] Generated Node #0,0,1: 38:[8, 37] Operation: 73-36=37 Exploring Operation: 36-8=28, Resulting Numbers: [73, 28] Generated Node #0,0,2: 38:[73, 28] Operation: 36-8=28 Exploring Operation: 73-8=65, Resulting Numbers: [36, 65] Generated Node #0,0,3: 38:[36, 65] Operation: 73-8=65 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 38:[8, 37], Operations: ['94-21=73', '73-36=37'] Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,38 unequal: No Solution Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,38 unequal: No Solution Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 38:[36, 65], Operations: ['94-21=73', '73-8=65'] Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,38 unequal: No Solution Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[73, 44], Operations: ['94-21=73', '8+36=44'] Exploring Operation: 73+44=117, Resulting Numbers: [117] 117,38 unequal: No Solution Exploring Operation: 73-44=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 73*44=3212, Resulting Numbers: [3212] 3212,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 38:[73, 28], Operations: ['94-21=73', '36-8=28'] Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,38 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,38 unequal: No Solution Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,38 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: 38:[36, 21, 86], Operations: ['94-8=86'] Exploring Operation: 86-21=65, Resulting Numbers: [36, 65] Generated Node #0,2,0: 38:[36, 65] Operation: 86-21=65 Exploring Operation: 36+21=57, Resulting Numbers: [86, 57] Generated Node #0,2,1: 38:[86, 57] Operation: 36+21=57 Exploring Operation: 36-21=15, Resulting Numbers: [86, 15] Generated Node #0,2,2: 38:[86, 15] Operation: 36-21=15 Exploring Operation: 86-36=50, Resulting Numbers: [21, 50] Generated Node #0,2,3: 38:[21, 50] Operation: 86-36=50 Moving to Node #0,3 Current State: 38:[21, 94, 44], Operations: ['8+36=44'] Exploring Operation: 94-21=73, Resulting Numbers: [44, 73] Generated Node #0,3,0: 38:[44, 73] Operation: 94-21=73 Exploring Operation: 21+94=115, Resulting Numbers: [44, 115] Generated Node #0,3,1: 38:[44, 115] Operation: 21+94=115 Exploring Operation: 44-21=23, Resulting Numbers: [94, 23] Generated Node #0,3,2: 38:[94, 23] Operation: 44-21=23 Exploring Operation: 94-44=50, Resulting Numbers: [21, 50] Generated Node #0,3,3: 38:[21, 50] Operation: 94-44=50 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 38:[21, 50], Operations: ['8+36=44', '94-44=50'] Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,38 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 #0,3,0 Current State: 38:[44, 73], Operations: ['8+36=44', '94-21=73'] Exploring Operation: 73-44=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 44+73=117, Resulting Numbers: [117] 117,38 unequal: No Solution Exploring Operation: 44*73=3212, Resulting Numbers: [3212] 3212,38 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 #0,3,2 Current State: 38:[94, 23], Operations: ['8+36=44', '44-21=23'] Exploring Operation: 94*23=2162, Resulting Numbers: [2162] 2162,38 unequal: No Solution Exploring Operation: 94+23=117, Resulting Numbers: [117] 117,38 unequal: No Solution Exploring Operation: 94-23=71, Resulting Numbers: [71] 71,38 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 #0,3,1 Current State: 38:[44, 115], Operations: ['8+36=44', '21+94=115'] Exploring Operation: 44*115=5060, Resulting Numbers: [5060] 5060,38 unequal: No Solution Exploring Operation: 44+115=159, Resulting Numbers: [159] 159,38 unequal: No Solution Exploring Operation: 115-44=71, Resulting Numbers: [71] 71,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 38:[8, 37], Operations: ['94-36=58', '58-21=37'] Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,38 unequal: No Solution Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[21, 50], Operations: ['94-36=58', '58-8=50'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[21, 50], Operations: ['94-8=86', '86-36=50'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[58, 13], Operations: ['94-36=58', '21-8=13'] Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,38 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[36, 65], Operations: ['94-8=86', '86-21=65'] Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,38 unequal: No Solution Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,38 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[58, 29], Operations: ['94-36=58', '8+21=29'] Exploring Operation: 58+29=87, Resulting Numbers: [87] 87,38 unequal: No Solution Exploring Operation: 58*29=1682, Resulting Numbers: [1682] 1682,38 unequal: No Solution Exploring Operation: 58-29=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 58/29=2, Resulting Numbers: [2] 2,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[86, 15], Operations: ['94-8=86', '36-21=15'] Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,38 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[86, 57], Operations: ['94-8=86', '36+21=57'] Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 86+57=143, Resulting Numbers: [143] 143,38 unequal: No Solution Exploring Operation: 86*57=4902, Resulting Numbers: [4902] 4902,38 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 87, 22, 25, 25 ]
22
[ "25-25=0", "87*0=0", "22+0=22" ]
Current State: 22:[87, 22, 25, 25], Operations: [] Exploring Operation: 25-25=0, Resulting Numbers: [87, 22, 0] Generated Node #2: [87, 22, 0] from Operation: 25-25=0 Current State: 22:[87, 22, 0], Operations: ['25-25=0'] Exploring Operation: 87*0=0, Resulting Numbers: [22, 0] Generated Node #3: [22, 0] from Operation: 87*0=0 Current State: 22:[22, 0], Operations: ['25-25=0', '87*0=0'] Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[87, 22, 25, 25], Operations: [] Exploring Operation: 87-25=62, Resulting Numbers: [22, 25, 62] Generated Node #0,0: 22:[22, 25, 62] Operation: 87-25=62 Exploring Operation: 87-25=62, Resulting Numbers: [22, 25, 62] Generated Node #0,1: 22:[22, 25, 62] Operation: 87-25=62 Exploring Operation: 25/25=1, Resulting Numbers: [87, 22, 1] Generated Node #0,2: 22:[87, 22, 1] Operation: 25/25=1 Exploring Operation: 87-22=65, Resulting Numbers: [25, 25, 65] Generated Node #0,3: 22:[25, 25, 65] Operation: 87-22=65 Moving to Node #0,0 Current State: 22:[22, 25, 62], Operations: ['87-25=62'] Exploring Operation: 62-22=40, Resulting Numbers: [25, 40] Generated Node #0,0,0: 22:[25, 40] Operation: 62-22=40 Exploring Operation: 62-25=37, Resulting Numbers: [22, 37] Generated Node #0,0,1: 22:[22, 37] Operation: 62-25=37 Exploring Operation: 25-22=3, Resulting Numbers: [62, 3] Generated Node #0,0,2: 22:[62, 3] Operation: 25-22=3 Exploring Operation: 22+25=47, Resulting Numbers: [62, 47] Generated Node #0,0,3: 22:[62, 47] Operation: 22+25=47 Moving to Node #0,1 Current State: 22:[22, 25, 62], Operations: ['87-25=62'] Exploring Operation: 62-22=40, Resulting Numbers: [25, 40] Generated Node #0,1,0: 22:[25, 40] Operation: 62-22=40 Exploring Operation: 22+25=47, Resulting Numbers: [62, 47] Generated Node #0,1,1: 22:[62, 47] Operation: 22+25=47 Exploring Operation: 62-25=37, Resulting Numbers: [22, 37] Generated Node #0,1,2: 22:[22, 37] Operation: 62-25=37 Exploring Operation: 25-22=3, Resulting Numbers: [62, 3] Generated Node #0,1,3: 22:[62, 3] Operation: 25-22=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 22:[22, 37], Operations: ['87-25=62', '62-25=37'] Exploring Operation: 22+37=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 22*37=814, Resulting Numbers: [814] 814,22 unequal: No Solution Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[25, 40], Operations: ['87-25=62', '62-22=40'] Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,22 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 22:[62, 3], Operations: ['87-25=62', '25-22=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[62, 47], Operations: ['87-25=62', '22+25=47'] Exploring Operation: 62*47=2914, Resulting Numbers: [2914] 2914,22 unequal: No Solution Exploring Operation: 62+47=109, Resulting Numbers: [109] 109,22 unequal: No Solution Exploring Operation: 62-47=15, Resulting Numbers: [15] 15,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 22:[25, 25, 65], Operations: ['87-22=65'] Exploring Operation: 25-25=0, Resulting Numbers: [65, 0] Generated Node #0,3,0: 22:[65, 0] Operation: 25-25=0 Exploring Operation: 65-25=40, Resulting Numbers: [25, 40] Generated Node #0,3,1: 22:[25, 40] Operation: 65-25=40 Exploring Operation: 65-25=40, Resulting Numbers: [25, 40] Generated Node #0,3,2: 22:[25, 40] Operation: 65-25=40 Exploring Operation: 25/25=1, Resulting Numbers: [65, 1] Generated Node #0,3,3: 22:[65, 1] Operation: 25/25=1 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 22:[25, 40], Operations: ['87-22=65', '65-25=40'] Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 22:[25, 40], Operations: ['87-22=65', '65-25=40'] Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,22 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 22:[65, 1], Operations: ['87-22=65', '25/25=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 22:[65, 0], Operations: ['87-22=65', '25-25=0'] Exploring Operation: 65+0=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 65*0=0, Resulting Numbers: [0] 0,22 unequal: No Solution Exploring Operation: 65-0=65, Resulting Numbers: [65] 65,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 22:[87, 22, 1], Operations: ['25/25=1'] Exploring Operation: 87*1=87, Resulting Numbers: [22, 87] Generated Node #0,2,0: 22:[22, 87] Operation: 87*1=87 Exploring Operation: 87-1=86, Resulting Numbers: [22, 86] Generated Node #0,2,1: 22:[22, 86] Operation: 87-1=86 Exploring Operation: 87-22=65, Resulting Numbers: [1, 65] Generated Node #0,2,2: 22:[1, 65] Operation: 87-22=65 Exploring Operation: 87/1=87, Resulting Numbers: [22, 87] Generated Node #0,2,3: 22:[22, 87] Operation: 87/1=87 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[1, 65], Operations: ['25/25=1', '87-22=65'] Exploring Operation: 1*65=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,22 unequal: No Solution Exploring Operation: 1+65=66, Resulting Numbers: [66] 66,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[22, 86], Operations: ['25/25=1', '87-1=86'] Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,22 unequal: No Solution Exploring Operation: 22*86=1892, Resulting Numbers: [1892] 1892,22 unequal: No Solution Exploring Operation: 22+86=108, Resulting Numbers: [108] 108,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[22, 87], Operations: ['25/25=1', '87*1=87'] Exploring Operation: 22+87=109, Resulting Numbers: [109] 109,22 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 22*87=1914, Resulting Numbers: [1914] 1914,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 22:[22, 87], Operations: ['25/25=1', '87/1=87'] Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 22+87=109, Resulting Numbers: [109] 109,22 unequal: No Solution Exploring Operation: 22*87=1914, Resulting Numbers: [1914] 1914,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 22:[22, 37], Operations: ['87-25=62', '62-25=37'] Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 22*37=814, Resulting Numbers: [814] 814,22 unequal: No Solution Exploring Operation: 22+37=59, Resulting Numbers: [59] 59,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[25, 40], Operations: ['87-25=62', '62-22=40'] Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,22 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[62, 3], Operations: ['87-25=62', '25-22=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,22 unequal: No Solution Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[62, 47], Operations: ['87-25=62', '22+25=47'] Exploring Operation: 62+47=109, Resulting Numbers: [109] 109,22 unequal: No Solution Exploring Operation: 62*47=2914, Resulting Numbers: [2914] 2914,22 unequal: No Solution Exploring Operation: 62-47=15, Resulting Numbers: [15] 15,22 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 66, 62, 76, 7 ]
73
[ "66-62=4", "76-7=69", "4+69=73" ]
Current State: 73:[66, 62, 76, 7], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [76, 7, 4] Generated Node #2: [76, 7, 4] from Operation: 66-62=4 Current State: 73:[76, 7, 4], Operations: ['66-62=4'] Exploring Operation: 76-7=69, Resulting Numbers: [4, 69] Generated Node #3: [4, 69] from Operation: 76-7=69 Current State: 73:[4, 69], Operations: ['66-62=4', '76-7=69'] Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[66, 62, 76, 7], Operations: [] Exploring Operation: 66-7=59, Resulting Numbers: [62, 76, 59] Generated Node #0,0: 73:[62, 76, 59] Operation: 66-7=59 Exploring Operation: 62+7=69, Resulting Numbers: [66, 76, 69] Generated Node #0,1: 73:[66, 76, 69] Operation: 62+7=69 Exploring Operation: 76-7=69, Resulting Numbers: [66, 62, 69] Generated Node #0,2: 73:[66, 62, 69] Operation: 76-7=69 Exploring Operation: 66+7=73, Resulting Numbers: [62, 76, 73] Generated Node #0,3: 73:[62, 76, 73] Operation: 66+7=73 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[66, 76, 69], Operations: ['62+7=69'] Exploring Operation: 69-66=3, Resulting Numbers: [76, 3] Generated Node #0,1,0: 73:[76, 3] Operation: 69-66=3 Exploring Operation: 66+76=142, Resulting Numbers: [69, 142] Generated Node #0,1,1: 73:[69, 142] Operation: 66+76=142 Exploring Operation: 66+69=135, Resulting Numbers: [76, 135] Generated Node #0,1,2: 73:[76, 135] Operation: 66+69=135 Exploring Operation: 76-66=10, Resulting Numbers: [69, 10] Generated Node #0,1,3: 73:[69, 10] Operation: 76-66=10 Moving to Node #0,1,2 Current State: 73:[76, 135], Operations: ['62+7=69', '66+69=135'] Exploring Operation: 76*135=10260, Resulting Numbers: [10260] 10260,73 unequal: No Solution Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 76+135=211, Resulting Numbers: [211] 211,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[69, 10], Operations: ['62+7=69', '76-66=10'] Exploring Operation: 69+10=79, Resulting Numbers: [79] 79,73 unequal: No Solution Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 69*10=690, Resulting Numbers: [690] 690,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[69, 142], Operations: ['62+7=69', '66+76=142'] Exploring Operation: 69*142=9798, Resulting Numbers: [9798] 9798,73 unequal: No Solution Exploring Operation: 69+142=211, Resulting Numbers: [211] 211,73 unequal: No Solution Exploring Operation: 142-69=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[66, 62, 76, 7], Operations: [] Exploring Operation: 62+7=69, Resulting Numbers: [66, 76, 69] Generated Node #0,1: 73:[66, 76, 69] Operation: 62+7=69 Moving to Node #0,1 Current State: 73:[66, 76, 69], Operations: ['62+7=69'] Exploring Operation: 66+76=142, Resulting Numbers: [69, 142] Generated Node #0,1,1: 73:[69, 142] Operation: 66+76=142 Moving to Node #0,1,1 Current State: 73:[69, 142], Operations: ['62+7=69', '66+76=142'] Exploring Operation: 142-69=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 18, 16, 75, 3 ]
37
[ "18*3=54", "16+75=91", "91-54=37" ]
Current State: 37:[18, 16, 75, 3], Operations: [] Exploring Operation: 18*3=54, Resulting Numbers: [16, 75, 54] Generated Node #2: [16, 75, 54] from Operation: 18*3=54 Current State: 37:[16, 75, 54], Operations: ['18*3=54'] Exploring Operation: 16+75=91, Resulting Numbers: [54, 91] Generated Node #3: [54, 91] from Operation: 16+75=91 Current State: 37:[54, 91], Operations: ['18*3=54', '16+75=91'] Exploring Operation: 91-54=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[18, 16, 75, 3], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [18, 16, 25] Generated Node #0,0: 37:[18, 16, 25] Operation: 75/3=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[18, 16, 25], Operations: ['75/3=25'] Exploring Operation: 18+16=34, Resulting Numbers: [25, 34] Generated Node #0,0,0: 37:[25, 34] Operation: 18+16=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[25, 34], Operations: ['75/3=25', '18+16=34'] Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,37 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
[ 85, 7, 43, 61 ]
74
[ "85+7=92", "61-43=18", "92-18=74" ]
Current State: 74:[85, 7, 43, 61], Operations: [] Exploring Operation: 85+7=92, Resulting Numbers: [43, 61, 92] Generated Node #2: [43, 61, 92] from Operation: 85+7=92 Current State: 74:[43, 61, 92], Operations: ['85+7=92'] Exploring Operation: 61-43=18, Resulting Numbers: [92, 18] Generated Node #3: [92, 18] from Operation: 61-43=18 Current State: 74:[92, 18], Operations: ['85+7=92', '61-43=18'] Exploring Operation: 92-18=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[85, 7, 43, 61], Operations: [] Exploring Operation: 7+61=68, Resulting Numbers: [85, 43, 68] Generated Node #0,0: 74:[85, 43, 68] Operation: 7+61=68 Exploring Operation: 85-61=24, Resulting Numbers: [7, 43, 24] Generated Node #0,1: 74:[7, 43, 24] Operation: 85-61=24 Exploring Operation: 85-7=78, Resulting Numbers: [43, 61, 78] Generated Node #0,2: 74:[43, 61, 78] Operation: 85-7=78 Exploring Operation: 43-7=36, Resulting Numbers: [85, 61, 36] Generated Node #0,3: 74:[85, 61, 36] Operation: 43-7=36 Exploring Operation: 85-43=42, Resulting Numbers: [7, 61, 42] Generated Node #0,4: 74:[7, 61, 42] Operation: 85-43=42 Moving to Node #0,0 Current State: 74:[85, 43, 68], Operations: ['7+61=68'] Exploring Operation: 68-43=25, Resulting Numbers: [85, 25] Generated Node #0,0,0: 74:[85, 25] Operation: 68-43=25 Exploring Operation: 43+68=111, Resulting Numbers: [85, 111] Generated Node #0,0,1: 74:[85, 111] Operation: 43+68=111 Exploring Operation: 85-68=17, Resulting Numbers: [43, 17] Generated Node #0,0,2: 74:[43, 17] Operation: 85-68=17 Exploring Operation: 85-43=42, Resulting Numbers: [68, 42] Generated Node #0,0,3: 74:[68, 42] Operation: 85-43=42 Exploring Operation: 85+43=128, Resulting Numbers: [68, 128] Generated Node #0,0,4: 74:[68, 128] Operation: 85+43=128 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 74:[68, 42], Operations: ['7+61=68', '85-43=42'] Exploring Operation: 68*42=2856, Resulting Numbers: [2856] 2856,74 unequal: No Solution Exploring Operation: 68+42=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,74 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 #0,0,2 Current State: 74:[43, 17], Operations: ['7+61=68', '85-68=17'] Exploring Operation: 43+17=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 43*17=731, Resulting Numbers: [731] 731,74 unequal: No Solution Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,74 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 #0,0,0 Current State: 74:[85, 25], Operations: ['7+61=68', '68-43=25'] Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 85+25=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 85*25=2125, Resulting Numbers: [2125] 2125,74 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 #0,0,1 Current State: 74:[85, 111], Operations: ['7+61=68', '43+68=111'] Exploring Operation: 85*111=9435, Resulting Numbers: [9435] 9435,74 unequal: No Solution Exploring Operation: 111-85=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 85+111=196, Resulting Numbers: [196] 196,74 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 #0,0,4 Current State: 74:[68, 128], Operations: ['7+61=68', '85+43=128'] Exploring Operation: 68+128=196, Resulting Numbers: [196] 196,74 unequal: No Solution Exploring Operation: 68*128=8704, Resulting Numbers: [8704] 8704,74 unequal: No Solution Exploring Operation: 128-68=60, Resulting Numbers: [60] 60,74 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: 74:[7, 61, 42], Operations: ['85-43=42'] Exploring Operation: 7+61=68, Resulting Numbers: [42, 68] Generated Node #0,4,0: 74:[42, 68] Operation: 7+61=68 Exploring Operation: 61-7=54, Resulting Numbers: [42, 54] Generated Node #0,4,1: 74:[42, 54] Operation: 61-7=54 Exploring Operation: 42/7=6, Resulting Numbers: [61, 6] Generated Node #0,4,2: 74:[61, 6] Operation: 42/7=6 Exploring Operation: 61-42=19, Resulting Numbers: [7, 19] Generated Node #0,4,3: 74:[7, 19] Operation: 61-42=19 Exploring Operation: 42-7=35, Resulting Numbers: [61, 35] Generated Node #0,4,4: 74:[61, 35] Operation: 42-7=35 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 74:[42, 68], Operations: ['85-43=42', '7+61=68'] Exploring Operation: 42*68=2856, Resulting Numbers: [2856] 2856,74 unequal: No Solution Exploring Operation: 42+68=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,74 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 #0,4,4 Current State: 74:[61, 35], Operations: ['85-43=42', '42-7=35'] Exploring Operation: 61-35=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 61*35=2135, Resulting Numbers: [2135] 2135,74 unequal: No Solution Exploring Operation: 61+35=96, Resulting Numbers: [96] 96,74 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 #0,4,2 Current State: 74:[61, 6], Operations: ['85-43=42', '42/7=6'] Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,74 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,74 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,74 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 #0,4,1 Current State: 74:[42, 54], Operations: ['85-43=42', '61-7=54'] Exploring Operation: 42+54=96, Resulting Numbers: [96] 96,74 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,74 unequal: No Solution Exploring Operation: 42*54=2268, Resulting Numbers: [2268] 2268,74 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 #0,4,3 Current State: 74:[7, 19], Operations: ['85-43=42', '61-42=19'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,74 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,74 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,74 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: 74:[43, 61, 78], Operations: ['85-7=78'] Exploring Operation: 43+61=104, Resulting Numbers: [78, 104] Generated Node #0,2,0: 74:[78, 104] Operation: 43+61=104 Exploring Operation: 43+78=121, Resulting Numbers: [61, 121] Generated Node #0,2,1: 74:[61, 121] Operation: 43+78=121 Exploring Operation: 78-61=17, Resulting Numbers: [43, 17] Generated Node #0,2,2: 74:[43, 17] Operation: 78-61=17 Exploring Operation: 78-43=35, Resulting Numbers: [61, 35] Generated Node #0,2,3: 74:[61, 35] Operation: 78-43=35 Exploring Operation: 61-43=18, Resulting Numbers: [78, 18] Generated Node #0,2,4: 74:[78, 18] Operation: 61-43=18 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 74:[61, 35], Operations: ['85-7=78', '78-43=35'] Exploring Operation: 61-35=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 61+35=96, Resulting Numbers: [96] 96,74 unequal: No Solution Exploring Operation: 61*35=2135, Resulting Numbers: [2135] 2135,74 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 #0,2,4 Current State: 74:[78, 18], Operations: ['85-7=78', '61-43=18'] Exploring Operation: 78+18=96, Resulting Numbers: [96] 96,74 unequal: No Solution Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 78*18=1404, Resulting Numbers: [1404] 1404,74 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 #0,2,2 Current State: 74:[43, 17], Operations: ['85-7=78', '78-61=17'] Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 43*17=731, Resulting Numbers: [731] 731,74 unequal: No Solution Exploring Operation: 43+17=60, Resulting Numbers: [60] 60,74 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 #0,2,0 Current State: 74:[78, 104], Operations: ['85-7=78', '43+61=104'] Exploring Operation: 78+104=182, Resulting Numbers: [182] 182,74 unequal: No Solution Exploring Operation: 78*104=8112, Resulting Numbers: [8112] 8112,74 unequal: No Solution Exploring Operation: 104-78=26, Resulting Numbers: [26] 26,74 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 #0,2,1 Current State: 74:[61, 121], Operations: ['85-7=78', '43+78=121'] Exploring Operation: 61+121=182, Resulting Numbers: [182] 182,74 unequal: No Solution Exploring Operation: 61*121=7381, Resulting Numbers: [7381] 7381,74 unequal: No Solution Exploring Operation: 121-61=60, Resulting Numbers: [60] 60,74 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: 74:[7, 43, 24], Operations: ['85-61=24'] Exploring Operation: 7+24=31, Resulting Numbers: [43, 31] Generated Node #0,1,0: 74:[43, 31] Operation: 7+24=31 Exploring Operation: 43-7=36, Resulting Numbers: [24, 36] Generated Node #0,1,1: 74:[24, 36] Operation: 43-7=36 Exploring Operation: 43+24=67, Resulting Numbers: [7, 67] Generated Node #0,1,2: 74:[7, 67] Operation: 43+24=67 Exploring Operation: 43-24=19, Resulting Numbers: [7, 19] Generated Node #0,1,3: 74:[7, 19] Operation: 43-24=19 Exploring Operation: 24-7=17, Resulting Numbers: [43, 17] Generated Node #0,1,4: 74:[43, 17] Operation: 24-7=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[43, 31], Operations: ['85-61=24', '7+24=31'] Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[85, 7, 43, 61], Operations: [] Exploring Operation: 85-61=24, Resulting Numbers: [7, 43, 24] Generated Node #0,1: 74:[7, 43, 24] Operation: 85-61=24 Moving to Node #0,1 Current State: 74:[7, 43, 24], Operations: ['85-61=24'] Exploring Operation: 7+24=31, Resulting Numbers: [43, 31] Generated Node #0,1,0: 74:[43, 31] Operation: 7+24=31 Moving to Node #0,1,0 Current State: 74:[43, 31], Operations: ['85-61=24', '7+24=31'] Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.934896
hs_5
mult_heuristic
[ 63, 43, 28, 98 ]
25
[ "63*28=1764", "1764/98=18", "43-18=25" ]
Current State: 25:[63, 43, 28, 98], Operations: [] Exploring Operation: 63*28=1764, Resulting Numbers: [43, 98, 1764] Generated Node #2: [43, 98, 1764] from Operation: 63*28=1764 Current State: 25:[43, 98, 1764], Operations: ['63*28=1764'] Exploring Operation: 1764/98=18, Resulting Numbers: [43, 18] Generated Node #3: [43, 18] from Operation: 1764/98=18 Current State: 25:[43, 18], Operations: ['63*28=1764', '1764/98=18'] Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[63, 43, 28, 98], Operations: [] Exploring Operation: 63-28=35, Resulting Numbers: [43, 98, 35] Generated Node #0,0: 25:[43, 98, 35] Operation: 63-28=35 Exploring Operation: 98-63=35, Resulting Numbers: [43, 28, 35] Generated Node #0,1: 25:[43, 28, 35] Operation: 98-63=35 Exploring Operation: 98-43=55, Resulting Numbers: [63, 28, 55] Generated Node #0,2: 25:[63, 28, 55] Operation: 98-43=55 Exploring Operation: 63-43=20, Resulting Numbers: [28, 98, 20] Generated Node #0,3: 25:[28, 98, 20] Operation: 63-43=20 Moving to Node #0,1 Current State: 25:[43, 28, 35], Operations: ['98-63=35'] Exploring Operation: 43+28=71, Resulting Numbers: [35, 71] Generated Node #0,1,0: 25:[35, 71] Operation: 43+28=71 Exploring Operation: 43-28=15, Resulting Numbers: [35, 15] Generated Node #0,1,1: 25:[35, 15] Operation: 43-28=15 Exploring Operation: 35-28=7, Resulting Numbers: [43, 7] Generated Node #0,1,2: 25:[43, 7] Operation: 35-28=7 Exploring Operation: 43-35=8, Resulting Numbers: [28, 8] Generated Node #0,1,3: 25:[28, 8] Operation: 43-35=8 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 25:[28, 8], Operations: ['98-63=35', '43-35=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[35, 15], Operations: ['98-63=35', '43-28=15'] Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,25 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 25:[43, 7], Operations: ['98-63=35', '35-28=7'] Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 43*7=301, Resulting Numbers: [301] 301,25 unequal: No Solution Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 25:[35, 71], Operations: ['98-63=35', '43+28=71'] Exploring Operation: 35+71=106, Resulting Numbers: [106] 106,25 unequal: No Solution Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 35*71=2485, Resulting Numbers: [2485] 2485,25 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: 25:[63, 28, 55], Operations: ['98-43=55'] Exploring Operation: 55-28=27, Resulting Numbers: [63, 27] Generated Node #0,2,0: 25:[63, 27] Operation: 55-28=27 Exploring Operation: 63-28=35, Resulting Numbers: [55, 35] Generated Node #0,2,1: 25:[55, 35] Operation: 63-28=35 Exploring Operation: 63-55=8, Resulting Numbers: [28, 8] Generated Node #0,2,2: 25:[28, 8] Operation: 63-55=8 Exploring Operation: 63+28=91, Resulting Numbers: [55, 91] Generated Node #0,2,3: 25:[55, 91] Operation: 63+28=91 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 25:[28, 8], Operations: ['98-43=55', '63-55=8'] Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,25 unequal: No Solution Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 25:[63, 27], Operations: ['98-43=55', '55-28=27'] Exploring Operation: 63*27=1701, Resulting Numbers: [1701] 1701,25 unequal: No Solution Exploring Operation: 63+27=90, Resulting Numbers: [90] 90,25 unequal: No Solution Exploring Operation: 63-27=36, Resulting Numbers: [36] 36,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 25:[55, 35], Operations: ['98-43=55', '63-28=35'] Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 55+35=90, Resulting Numbers: [90] 90,25 unequal: No Solution Exploring Operation: 55*35=1925, Resulting Numbers: [1925] 1925,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 25:[55, 91], Operations: ['98-43=55', '63+28=91'] Exploring Operation: 55*91=5005, Resulting Numbers: [5005] 5005,25 unequal: No Solution Exploring Operation: 55+91=146, Resulting Numbers: [146] 146,25 unequal: No Solution Exploring Operation: 91-55=36, Resulting Numbers: [36] 36,25 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: 25:[28, 98, 20], Operations: ['63-43=20'] Exploring Operation: 98-28=70, Resulting Numbers: [20, 70] Generated Node #0,3,0: 25:[20, 70] Operation: 98-28=70 Exploring Operation: 98-20=78, Resulting Numbers: [28, 78] Generated Node #0,3,1: 25:[28, 78] Operation: 98-20=78 Exploring Operation: 28+20=48, Resulting Numbers: [98, 48] Generated Node #0,3,2: 25:[98, 48] Operation: 28+20=48 Exploring Operation: 28-20=8, Resulting Numbers: [98, 8] Generated Node #0,3,3: 25:[98, 8] Operation: 28-20=8 Moving to Node #0,0 Current State: 25:[43, 98, 35], Operations: ['63-28=35'] Exploring Operation: 43+98=141, Resulting Numbers: [35, 141] Generated Node #0,0,0: 25:[35, 141] Operation: 43+98=141 Exploring Operation: 98-43=55, Resulting Numbers: [35, 55] Generated Node #0,0,1: 25:[35, 55] Operation: 98-43=55 Exploring Operation: 43-35=8, Resulting Numbers: [98, 8] Generated Node #0,0,2: 25:[98, 8] Operation: 43-35=8 Exploring Operation: 98-35=63, Resulting Numbers: [43, 63] Generated Node #0,0,3: 25:[43, 63] Operation: 98-35=63 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 25:[35, 55], Operations: ['63-28=35', '98-43=55'] Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,25 unequal: No Solution Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 35*55=1925, Resulting Numbers: [1925] 1925,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 25:[43, 63], Operations: ['63-28=35', '98-35=63'] Exploring Operation: 43*63=2709, Resulting Numbers: [2709] 2709,25 unequal: No Solution Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 43+63=106, Resulting Numbers: [106] 106,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 25:[98, 8], Operations: ['63-28=35', '43-35=8'] Exploring Operation: 98+8=106, Resulting Numbers: [106] 106,25 unequal: No Solution Exploring Operation: 98*8=784, Resulting Numbers: [784] 784,25 unequal: No Solution Exploring Operation: 98-8=90, Resulting Numbers: [90] 90,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[35, 141], Operations: ['63-28=35', '43+98=141'] Exploring Operation: 35*141=4935, Resulting Numbers: [4935] 4935,25 unequal: No Solution Exploring Operation: 35+141=176, Resulting Numbers: [176] 176,25 unequal: No Solution Exploring Operation: 141-35=106, Resulting Numbers: [106] 106,25 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: 25:[20, 70], Operations: ['63-43=20', '98-28=70'] Exploring Operation: 20+70=90, Resulting Numbers: [90] 90,25 unequal: No Solution Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 20*70=1400, Resulting Numbers: [1400] 1400,25 unequal: No Solution Moving to Node #0,3,1 Current State: 25:[28, 78], Operations: ['63-43=20', '98-20=78'] Exploring Operation: 28*78=2184, Resulting Numbers: [2184] 2184,25 unequal: No Solution Exploring Operation: 28+78=106, Resulting Numbers: [106] 106,25 unequal: No Solution Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,25 unequal: No Solution Moving to Node #0,3,3 Current State: 25:[98, 8], Operations: ['63-43=20', '28-20=8'] Exploring Operation: 98*8=784, Resulting Numbers: [784] 784,25 unequal: No Solution Exploring Operation: 98+8=106, Resulting Numbers: [106] 106,25 unequal: No Solution Exploring Operation: 98-8=90, Resulting Numbers: [90] 90,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[98, 48], Operations: ['63-43=20', '28+20=48'] Exploring Operation: 98+48=146, Resulting Numbers: [146] 146,25 unequal: No Solution Exploring Operation: 98*48=4704, Resulting Numbers: [4704] 4704,25 unequal: No Solution Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,25 unequal: No Solution No solution found.
0
hs_4
sum_heuristic