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
[ 19, 79, 7, 25 ]
29
[ "19*7=133", "79+25=104", "133-104=29" ]
Current State: 29:[19, 79, 7, 25], Operations: [] Exploring Operation: 19*7=133, Resulting Numbers: [79, 25, 133] Generated Node #2: [79, 25, 133] from Operation: 19*7=133 Current State: 29:[79, 25, 133], Operations: ['19*7=133'] Exploring Operation: 79+25=104, Resulting Numbers: [133, 104] Generated Node #3: [133, 104] from Operation: 79+25=104 Current State: 29:[133, 104], Operations: ['19*7=133', '79+25=104'] Exploring Operation: 133-104=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[19, 79, 7, 25], Operations: [] Exploring Operation: 19+7=26, Resulting Numbers: [79, 25, 26] Generated Node #0,0: 29:[79, 25, 26] Operation: 19+7=26 Exploring Operation: 79-19=60, Resulting Numbers: [7, 25, 60] Generated Node #0,1: 29:[7, 25, 60] Operation: 79-19=60 Exploring Operation: 79-7=72, Resulting Numbers: [19, 25, 72] Generated Node #0,2: 29:[19, 25, 72] Operation: 79-7=72 Moving to Node #0,0 Current State: 29:[79, 25, 26], Operations: ['19+7=26'] Exploring Operation: 79-25=54, Resulting Numbers: [26, 54] Generated Node #0,0,0: 29:[26, 54] Operation: 79-25=54 Exploring Operation: 25+26=51, Resulting Numbers: [79, 51] Generated Node #0,0,1: 29:[79, 51] Operation: 25+26=51 Exploring Operation: 79-26=53, Resulting Numbers: [25, 53] Generated Node #0,0,2: 29:[25, 53] Operation: 79-26=53 Moving to Node #0,1 Current State: 29:[7, 25, 60], Operations: ['79-19=60'] Exploring Operation: 60-25=35, Resulting Numbers: [7, 35] Generated Node #0,1,0: 29:[7, 35] Operation: 60-25=35 Exploring Operation: 60-7=53, Resulting Numbers: [25, 53] Generated Node #0,1,1: 29:[25, 53] Operation: 60-7=53 Exploring Operation: 7+25=32, Resulting Numbers: [60, 32] Generated Node #0,1,2: 29:[60, 32] Operation: 7+25=32 Moving to Node #0,2 Current State: 29:[19, 25, 72], Operations: ['79-7=72'] Exploring Operation: 72-19=53, Resulting Numbers: [25, 53] Generated Node #0,2,0: 29:[25, 53] Operation: 72-19=53 Exploring Operation: 19+25=44, Resulting Numbers: [72, 44] Generated Node #0,2,1: 29:[72, 44] Operation: 19+25=44 Exploring Operation: 72-25=47, Resulting Numbers: [19, 47] Generated Node #0,2,2: 29:[19, 47] Operation: 72-25=47 Moving to Node #0,0,0 Current State: 29:[26, 54], Operations: ['19+7=26', '79-25=54'] Exploring Operation: 26+54=80, Resulting Numbers: [80] 80,29 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 26*54=1404, Resulting Numbers: [1404] 1404,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[25, 53], Operations: ['79-7=72', '72-19=53'] Exploring Operation: 25+53=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 25*53=1325, Resulting Numbers: [1325] 1325,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[25, 53], Operations: ['19+7=26', '79-26=53'] Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 25+53=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 25*53=1325, Resulting Numbers: [1325] 1325,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[25, 53], Operations: ['79-19=60', '60-7=53'] Exploring Operation: 25+53=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 25*53=1325, Resulting Numbers: [1325] 1325,29 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[19, 47], Operations: ['79-7=72', '72-25=47'] Exploring Operation: 19*47=893, Resulting Numbers: [893] 893,29 unequal: No Solution Exploring Operation: 19+47=66, Resulting Numbers: [66] 66,29 unequal: No Solution Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[7, 35], Operations: ['79-19=60', '60-25=35'] Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[60, 32], Operations: ['79-19=60', '7+25=32'] Exploring Operation: 60+32=92, Resulting Numbers: [92] 92,29 unequal: No Solution Exploring Operation: 60*32=1920, Resulting Numbers: [1920] 1920,29 unequal: No Solution Exploring Operation: 60-32=28, Resulting Numbers: [28] 28,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[72, 44], Operations: ['79-7=72', '19+25=44'] Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 72*44=3168, Resulting Numbers: [3168] 3168,29 unequal: No Solution Exploring Operation: 72+44=116, Resulting Numbers: [116] 116,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[79, 51], Operations: ['19+7=26', '25+26=51'] Exploring Operation: 79+51=130, Resulting Numbers: [130] 130,29 unequal: No Solution Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 79*51=4029, Resulting Numbers: [4029] 4029,29 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 40, 5, 25, 62 ]
13
[ "40-25=15", "5*15=75", "75-62=13" ]
Current State: 13:[40, 5, 25, 62], Operations: [] Exploring Operation: 40-25=15, Resulting Numbers: [5, 62, 15] Generated Node #2: [5, 62, 15] from Operation: 40-25=15 Current State: 13:[5, 62, 15], Operations: ['40-25=15'] Exploring Operation: 5*15=75, Resulting Numbers: [62, 75] Generated Node #3: [62, 75] from Operation: 5*15=75 Current State: 13:[62, 75], Operations: ['40-25=15', '5*15=75'] Exploring Operation: 75-62=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[40, 5, 25, 62], Operations: [] Exploring Operation: 62-40=22, Resulting Numbers: [5, 25, 22] Generated Node #0,0: 13:[5, 25, 22] Operation: 62-40=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[5, 25, 22], Operations: ['62-40=22'] Exploring Operation: 25-5=20, Resulting Numbers: [22, 20] Generated Node #0,0,0: 13:[22, 20] Operation: 25-5=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[22, 20], Operations: ['62-40=22', '25-5=20'] Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 9, 51, 94, 27 ]
98
[ "9*27=243", "51+94=145", "243-145=98" ]
Current State: 98:[9, 51, 94, 27], Operations: [] Exploring Operation: 9*27=243, Resulting Numbers: [51, 94, 243] Generated Node #2: [51, 94, 243] from Operation: 9*27=243 Current State: 98:[51, 94, 243], Operations: ['9*27=243'] Exploring Operation: 51+94=145, Resulting Numbers: [243, 145] Generated Node #3: [243, 145] from Operation: 51+94=145 Current State: 98:[243, 145], Operations: ['9*27=243', '51+94=145'] Exploring Operation: 243-145=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[9, 51, 94, 27], Operations: [] Exploring Operation: 27/9=3, Resulting Numbers: [51, 94, 3] Generated Node #0,0: 98:[51, 94, 3] Operation: 27/9=3 Moving to Node #0,0 Current State: 98:[51, 94, 3], Operations: ['27/9=3'] Exploring Operation: 94+3=97, Resulting Numbers: [51, 97] Generated Node #0,0,0: 98:[51, 97] Operation: 94+3=97 Moving to Node #0,0,0 Current State: 98:[51, 97], Operations: ['27/9=3', '94+3=97'] Exploring Operation: 97-51=46, Resulting Numbers: [46] 46,98 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 74, 2, 45, 94 ]
72
[ "74+45=119", "94/2=47", "119-47=72" ]
Current State: 72:[74, 2, 45, 94], Operations: [] Exploring Operation: 74+45=119, Resulting Numbers: [2, 94, 119] Generated Node #2: [2, 94, 119] from Operation: 74+45=119 Current State: 72:[2, 94, 119], Operations: ['74+45=119'] Exploring Operation: 94/2=47, Resulting Numbers: [119, 47] Generated Node #3: [119, 47] from Operation: 94/2=47 Current State: 72:[119, 47], Operations: ['74+45=119', '94/2=47'] Exploring Operation: 119-47=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[74, 2, 45, 94], Operations: [] Exploring Operation: 94-74=20, Resulting Numbers: [2, 45, 20] Generated Node #0,0: 72:[2, 45, 20] Operation: 94-74=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[2, 45, 20], Operations: ['94-74=20'] Exploring Operation: 45-20=25, Resulting Numbers: [2, 25] Generated Node #0,0,0: 72:[2, 25] Operation: 45-20=25 Moving to Node #0,0,0 Current State: 72:[2, 25], Operations: ['94-74=20', '45-20=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,72 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
[ 72, 45, 2, 70 ]
41
[ "72-45=27", "70-2=68", "68-27=41" ]
Current State: 41:[72, 45, 2, 70], Operations: [] Exploring Operation: 72-45=27, Resulting Numbers: [2, 70, 27] Generated Node #2: [2, 70, 27] from Operation: 72-45=27 Current State: 41:[2, 70, 27], Operations: ['72-45=27'] Exploring Operation: 70-2=68, Resulting Numbers: [27, 68] Generated Node #3: [27, 68] from Operation: 70-2=68 Current State: 41:[27, 68], Operations: ['72-45=27', '70-2=68'] Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[72, 45, 2, 70], Operations: [] Exploring Operation: 70-2=68, Resulting Numbers: [72, 45, 68] Generated Node #0,0: 41:[72, 45, 68] Operation: 70-2=68 Exploring Operation: 72/2=36, Resulting Numbers: [45, 70, 36] Generated Node #0,1: 41:[45, 70, 36] Operation: 72/2=36 Exploring Operation: 72-2=70, Resulting Numbers: [45, 70, 70] Generated Node #0,2: 41:[45, 70, 70] Operation: 72-2=70 Exploring Operation: 70/2=35, Resulting Numbers: [72, 45, 35] Generated Node #0,3: 41:[72, 45, 35] Operation: 70/2=35 Exploring Operation: 45-2=43, Resulting Numbers: [72, 70, 43] Generated Node #0,4: 41:[72, 70, 43] Operation: 45-2=43 Moving to Node #0,1 Current State: 41:[45, 70, 36], Operations: ['72/2=36'] Exploring Operation: 70-45=25, Resulting Numbers: [36, 25] Generated Node #0,1,0: 41:[36, 25] Operation: 70-45=25 Exploring Operation: 45-36=9, Resulting Numbers: [70, 9] Generated Node #0,1,1: 41:[70, 9] Operation: 45-36=9 Exploring Operation: 70+36=106, Resulting Numbers: [45, 106] Generated Node #0,1,2: 41:[45, 106] Operation: 70+36=106 Exploring Operation: 70-36=34, Resulting Numbers: [45, 34] Generated Node #0,1,3: 41:[45, 34] Operation: 70-36=34 Exploring Operation: 45+36=81, Resulting Numbers: [70, 81] Generated Node #0,1,4: 41:[70, 81] Operation: 45+36=81 Moving to Node #0,3 Current State: 41:[72, 45, 35], Operations: ['70/2=35'] Exploring Operation: 72-35=37, Resulting Numbers: [45, 37] Generated Node #0,3,0: 41:[45, 37] Operation: 72-35=37 Exploring Operation: 72+35=107, Resulting Numbers: [45, 107] Generated Node #0,3,1: 41:[45, 107] Operation: 72+35=107 Exploring Operation: 45+35=80, Resulting Numbers: [72, 80] Generated Node #0,3,2: 41:[72, 80] Operation: 45+35=80 Exploring Operation: 72-45=27, Resulting Numbers: [35, 27] Generated Node #0,3,3: 41:[35, 27] Operation: 72-45=27 Exploring Operation: 45-35=10, Resulting Numbers: [72, 10] Generated Node #0,3,4: 41:[72, 10] Operation: 45-35=10 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[45, 37], Operations: ['70/2=35', '72-35=37'] Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 45+37=82, Resulting Numbers: [82] 82,41 unequal: No Solution Exploring Operation: 45*37=1665, Resulting Numbers: [1665] 1665,41 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 #0,3,3 Current State: 41:[35, 27], Operations: ['70/2=35', '72-45=27'] 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 Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,41 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:[72, 10], Operations: ['70/2=35', '45-35=10'] Exploring Operation: 72-10=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 72*10=720, Resulting Numbers: [720] 720,41 unequal: No Solution Exploring Operation: 72+10=82, Resulting Numbers: [82] 82,41 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:[45, 107], Operations: ['70/2=35', '72+35=107'] Exploring Operation: 107-45=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 45*107=4815, Resulting Numbers: [4815] 4815,41 unequal: No Solution Exploring Operation: 45+107=152, Resulting Numbers: [152] 152,41 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:[72, 80], Operations: ['70/2=35', '45+35=80'] Exploring Operation: 72*80=5760, Resulting Numbers: [5760] 5760,41 unequal: No Solution Exploring Operation: 72+80=152, Resulting Numbers: [152] 152,41 unequal: No Solution Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,41 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:[72, 45, 68], Operations: ['70-2=68'] Exploring Operation: 68-45=23, Resulting Numbers: [72, 23] Generated Node #0,0,0: 41:[72, 23] Operation: 68-45=23 Exploring Operation: 72-68=4, Resulting Numbers: [45, 4] Generated Node #0,0,1: 41:[45, 4] Operation: 72-68=4 Exploring Operation: 72+68=140, Resulting Numbers: [45, 140] Generated Node #0,0,2: 41:[45, 140] Operation: 72+68=140 Exploring Operation: 72+45=117, Resulting Numbers: [68, 117] Generated Node #0,0,3: 41:[68, 117] Operation: 72+45=117 Exploring Operation: 72-45=27, Resulting Numbers: [68, 27] Generated Node #0,0,4: 41:[68, 27] Operation: 72-45=27 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[45, 4], Operations: ['70-2=68', '72-68=4'] Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,41 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[72, 45, 2, 70], Operations: [] Exploring Operation: 70-2=68, Resulting Numbers: [72, 45, 68] Generated Node #0,0: 41:[72, 45, 68] Operation: 70-2=68 Moving to Node #0,0 Current State: 41:[72, 45, 68], Operations: ['70-2=68'] Exploring Operation: 72-68=4, Resulting Numbers: [45, 4] Generated Node #0,0,1: 41:[45, 4] Operation: 72-68=4 Moving to Node #0,0,1 Current State: 41:[45, 4], Operations: ['70-2=68', '72-68=4'] Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
sum_heuristic
[ 18, 68, 25, 78 ]
45
[ "18*25=450", "78-68=10", "450/10=45" ]
Current State: 45:[18, 68, 25, 78], Operations: [] Exploring Operation: 18*25=450, Resulting Numbers: [68, 78, 450] Generated Node #2: [68, 78, 450] from Operation: 18*25=450 Current State: 45:[68, 78, 450], Operations: ['18*25=450'] Exploring Operation: 78-68=10, Resulting Numbers: [450, 10] Generated Node #3: [450, 10] from Operation: 78-68=10 Current State: 45:[450, 10], Operations: ['18*25=450', '78-68=10'] Exploring Operation: 450/10=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[18, 68, 25, 78], Operations: [] Exploring Operation: 68-25=43, Resulting Numbers: [18, 78, 43] Generated Node #0,0: 45:[18, 78, 43] Operation: 68-25=43 Exploring Operation: 68-18=50, Resulting Numbers: [25, 78, 50] Generated Node #0,1: 45:[25, 78, 50] Operation: 68-18=50 Exploring Operation: 78-25=53, Resulting Numbers: [18, 68, 53] Generated Node #0,2: 45:[18, 68, 53] Operation: 78-25=53 Exploring Operation: 78-68=10, Resulting Numbers: [18, 25, 10] Generated Node #0,3: 45:[18, 25, 10] Operation: 78-68=10 Moving to Node #0,3 Current State: 45:[18, 25, 10], Operations: ['78-68=10'] Exploring Operation: 18+25=43, Resulting Numbers: [10, 43] Generated Node #0,3,0: 45:[10, 43] Operation: 18+25=43 Exploring Operation: 25-10=15, Resulting Numbers: [18, 15] Generated Node #0,3,1: 45:[18, 15] Operation: 25-10=15 Exploring Operation: 18-10=8, Resulting Numbers: [25, 8] Generated Node #0,3,2: 45:[25, 8] Operation: 18-10=8 Exploring Operation: 25-18=7, Resulting Numbers: [10, 7] Generated Node #0,3,3: 45:[10, 7] Operation: 25-18=7 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 45:[10, 43], Operations: ['78-68=10', '18+25=43'] Exploring Operation: 10+43=53, Resulting Numbers: [53] 53,45 unequal: No Solution Exploring Operation: 43-10=33, Resulting Numbers: [33] 33,45 unequal: No Solution Exploring Operation: 10*43=430, Resulting Numbers: [430] 430,45 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 #0,3,1 Current State: 45:[18, 15], Operations: ['78-68=10', '25-10=15'] Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,45 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,45 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 #0,3,3 Current State: 45:[10, 7], Operations: ['78-68=10', '25-18=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,45 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,45 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 #0,3,2 Current State: 45:[25, 8], Operations: ['78-68=10', '18-10=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,45 unequal: No Solution Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,45 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,45 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: 45:[18, 68, 53], Operations: ['78-25=53'] Exploring Operation: 18+68=86, Resulting Numbers: [53, 86] Generated Node #0,2,0: 45:[53, 86] Operation: 18+68=86 Exploring Operation: 68-53=15, Resulting Numbers: [18, 15] Generated Node #0,2,1: 45:[18, 15] Operation: 68-53=15 Exploring Operation: 68-18=50, Resulting Numbers: [53, 50] Generated Node #0,2,2: 45:[53, 50] Operation: 68-18=50 Exploring Operation: 53-18=35, Resulting Numbers: [68, 35] Generated Node #0,2,3: 45:[68, 35] Operation: 53-18=35 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[18, 15], Operations: ['78-25=53', '68-53=15'] Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,45 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,45 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:[53, 50], Operations: ['78-25=53', '68-18=50'] Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,45 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,45 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 #0,2,3 Current State: 45:[68, 35], Operations: ['78-25=53', '53-18=35'] Exploring Operation: 68*35=2380, Resulting Numbers: [2380] 2380,45 unequal: No Solution Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,45 unequal: No Solution Exploring Operation: 68+35=103, Resulting Numbers: [103] 103,45 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:[53, 86], Operations: ['78-25=53', '18+68=86'] Exploring Operation: 53*86=4558, Resulting Numbers: [4558] 4558,45 unequal: No Solution Exploring Operation: 53+86=139, Resulting Numbers: [139] 139,45 unequal: No Solution Exploring Operation: 86-53=33, Resulting Numbers: [33] 33,45 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: 45:[18, 78, 43], Operations: ['68-25=43'] Exploring Operation: 43-18=25, Resulting Numbers: [78, 25] Generated Node #0,0,0: 45:[78, 25] Operation: 43-18=25 Exploring Operation: 78-43=35, Resulting Numbers: [18, 35] Generated Node #0,0,1: 45:[18, 35] Operation: 78-43=35 Exploring Operation: 18+43=61, Resulting Numbers: [78, 61] Generated Node #0,0,2: 45:[78, 61] Operation: 18+43=61 Exploring Operation: 78-18=60, Resulting Numbers: [43, 60] Generated Node #0,0,3: 45:[43, 60] Operation: 78-18=60 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[18, 35], Operations: ['68-25=43', '78-43=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,45 unequal: No Solution Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,45 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,45 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:[43, 60], Operations: ['68-25=43', '78-18=60'] Exploring Operation: 43*60=2580, Resulting Numbers: [2580] 2580,45 unequal: No Solution Exploring Operation: 60-43=17, Resulting Numbers: [17] 17,45 unequal: No Solution Exploring Operation: 43+60=103, Resulting Numbers: [103] 103,45 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:[78, 25], Operations: ['68-25=43', '43-18=25'] Exploring Operation: 78-25=53, Resulting Numbers: [53] 53,45 unequal: No Solution Exploring Operation: 78*25=1950, Resulting Numbers: [1950] 1950,45 unequal: No Solution Exploring Operation: 78+25=103, Resulting Numbers: [103] 103,45 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:[78, 61], Operations: ['68-25=43', '18+43=61'] Exploring Operation: 78*61=4758, Resulting Numbers: [4758] 4758,45 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,45 unequal: No Solution Exploring Operation: 78+61=139, Resulting Numbers: [139] 139,45 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:[25, 78, 50], Operations: ['68-18=50'] Exploring Operation: 78-50=28, Resulting Numbers: [25, 28] Generated Node #0,1,0: 45:[25, 28] Operation: 78-50=28 Exploring Operation: 50-25=25, Resulting Numbers: [78, 25] Generated Node #0,1,1: 45:[78, 25] Operation: 50-25=25 Exploring Operation: 78-25=53, Resulting Numbers: [50, 53] Generated Node #0,1,2: 45:[50, 53] Operation: 78-25=53 Exploring Operation: 50/25=2, Resulting Numbers: [78, 2] Generated Node #0,1,3: 45:[78, 2] Operation: 50/25=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[50, 53], Operations: ['68-18=50', '78-25=53'] Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,45 unequal: No Solution Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[25, 28], Operations: ['68-18=50', '78-50=28'] Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,45 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 45:[78, 2], Operations: ['68-18=50', '50/25=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,45 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[78, 25], Operations: ['68-18=50', '50-25=25'] Exploring Operation: 78*25=1950, Resulting Numbers: [1950] 1950,45 unequal: No Solution Exploring Operation: 78-25=53, Resulting Numbers: [53] 53,45 unequal: No Solution Exploring Operation: 78+25=103, Resulting Numbers: [103] 103,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 15, 29, 17, 13 ]
55
[ "17-15=2", "13*2=26", "29+26=55" ]
Current State: 55:[15, 29, 17, 13], Operations: [] Exploring Operation: 17-15=2, Resulting Numbers: [29, 13, 2] Generated Node #2: [29, 13, 2] from Operation: 17-15=2 Current State: 55:[29, 13, 2], Operations: ['17-15=2'] Exploring Operation: 13*2=26, Resulting Numbers: [29, 26] Generated Node #3: [29, 26] from Operation: 13*2=26 Current State: 55:[29, 26], Operations: ['17-15=2', '13*2=26'] Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[15, 29, 17, 13], Operations: [] Exploring Operation: 29-15=14, Resulting Numbers: [17, 13, 14] Generated Node #0,0: 55:[17, 13, 14] Operation: 29-15=14 Exploring Operation: 29+17=46, Resulting Numbers: [15, 13, 46] Generated Node #0,1: 55:[15, 13, 46] Operation: 29+17=46 Exploring Operation: 29-17=12, Resulting Numbers: [15, 13, 12] Generated Node #0,2: 55:[15, 13, 12] Operation: 29-17=12 Moving to Node #0,2 Current State: 55:[15, 13, 12], Operations: ['29-17=12'] Exploring Operation: 15-12=3, Resulting Numbers: [13, 3] Generated Node #0,2,0: 55:[13, 3] Operation: 15-12=3 Exploring Operation: 15-13=2, Resulting Numbers: [12, 2] Generated Node #0,2,1: 55:[12, 2] Operation: 15-13=2 Exploring Operation: 13-12=1, Resulting Numbers: [15, 1] Generated Node #0,2,2: 55:[15, 1] Operation: 13-12=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 55:[13, 3], Operations: ['29-17=12', '15-12=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,55 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 55:[12, 2], Operations: ['29-17=12', '15-13=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 55:[15, 1], Operations: ['29-17=12', '13-12=1'] Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,55 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: 55:[17, 13, 14], Operations: ['29-15=14'] Exploring Operation: 17-14=3, Resulting Numbers: [13, 3] Generated Node #0,0,0: 55:[13, 3] Operation: 17-14=3 Exploring Operation: 14-13=1, Resulting Numbers: [17, 1] Generated Node #0,0,1: 55:[17, 1] Operation: 14-13=1 Exploring Operation: 17-13=4, Resulting Numbers: [14, 4] Generated Node #0,0,2: 55:[14, 4] Operation: 17-13=4 Moving to Node #0,1 Current State: 55:[15, 13, 46], Operations: ['29+17=46'] Exploring Operation: 13+46=59, Resulting Numbers: [15, 59] Generated Node #0,1,0: 55:[15, 59] Operation: 13+46=59 Exploring Operation: 15-13=2, Resulting Numbers: [46, 2] Generated Node #0,1,1: 55:[46, 2] Operation: 15-13=2 Exploring Operation: 15+46=61, Resulting Numbers: [13, 61] Generated Node #0,1,2: 55:[13, 61] Operation: 15+46=61 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[15, 59], Operations: ['29+17=46', '13+46=59'] Exploring Operation: 15*59=885, Resulting Numbers: [885] 885,55 unequal: No Solution Exploring Operation: 15+59=74, Resulting Numbers: [74] 74,55 unequal: No Solution Exploring Operation: 59-15=44, Resulting Numbers: [44] 44,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 55:[13, 61], Operations: ['29+17=46', '15+46=61'] Exploring Operation: 13*61=793, Resulting Numbers: [793] 793,55 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,55 unequal: No Solution Exploring Operation: 13+61=74, Resulting Numbers: [74] 74,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 55:[46, 2], Operations: ['29+17=46', '15-13=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,55 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: 55:[13, 3], Operations: ['29-15=14', '17-14=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,55 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[14, 4], Operations: ['29-15=14', '17-13=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,55 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[17, 1], Operations: ['29-15=14', '14-13=1'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,55 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 93, 7, 16, 18 ]
43
[ "93-7=86", "18-16=2", "86/2=43" ]
Current State: 43:[93, 7, 16, 18], Operations: [] Exploring Operation: 93-7=86, Resulting Numbers: [16, 18, 86] Generated Node #2: [16, 18, 86] from Operation: 93-7=86 Current State: 43:[16, 18, 86], Operations: ['93-7=86'] Exploring Operation: 18-16=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 18-16=2 Current State: 43:[86, 2], Operations: ['93-7=86', '18-16=2'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[93, 7, 16, 18], Operations: [] Exploring Operation: 93-18=75, Resulting Numbers: [7, 16, 75] Generated Node #0,0: 43:[7, 16, 75] Operation: 93-18=75 Exploring Operation: 7+16=23, Resulting Numbers: [93, 18, 23] Generated Node #0,1: 43:[93, 18, 23] Operation: 7+16=23 Exploring Operation: 93-16=77, Resulting Numbers: [7, 18, 77] Generated Node #0,2: 43:[7, 18, 77] Operation: 93-16=77 Exploring Operation: 93-7=86, Resulting Numbers: [16, 18, 86] Generated Node #0,3: 43:[16, 18, 86] Operation: 93-7=86 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[7, 16, 75], Operations: ['93-18=75'] Exploring Operation: 75-16=59, Resulting Numbers: [7, 59] Generated Node #0,0,0: 43:[7, 59] Operation: 75-16=59 Exploring Operation: 7+16=23, Resulting Numbers: [75, 23] Generated Node #0,0,1: 43:[75, 23] Operation: 7+16=23 Exploring Operation: 75-7=68, Resulting Numbers: [16, 68] Generated Node #0,0,2: 43:[16, 68] Operation: 75-7=68 Exploring Operation: 16-7=9, Resulting Numbers: [75, 9] Generated Node #0,0,3: 43:[75, 9] Operation: 16-7=9 Moving to Node #0,0,0 Current State: 43:[7, 59], Operations: ['93-18=75', '75-16=59'] Exploring Operation: 7+59=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 7*59=413, Resulting Numbers: [413] 413,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[16, 68], Operations: ['93-18=75', '75-7=68'] Exploring Operation: 16*68=1088, Resulting Numbers: [1088] 1088,43 unequal: No Solution Exploring Operation: 16+68=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 68-16=52, Resulting Numbers: [52] 52,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[75, 23], Operations: ['93-18=75', '7+16=23'] Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,43 unequal: No Solution Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[75, 9], Operations: ['93-18=75', '16-7=9'] Exploring Operation: 75*9=675, Resulting Numbers: [675] 675,43 unequal: No Solution Exploring Operation: 75-9=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 75+9=84, Resulting Numbers: [84] 84,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[93, 18, 23], Operations: ['7+16=23'] Exploring Operation: 93-23=70, Resulting Numbers: [18, 70] Generated Node #0,1,0: 43:[18, 70] Operation: 93-23=70 Exploring Operation: 93-18=75, Resulting Numbers: [23, 75] Generated Node #0,1,1: 43:[23, 75] Operation: 93-18=75 Exploring Operation: 93+18=111, Resulting Numbers: [23, 111] Generated Node #0,1,2: 43:[23, 111] Operation: 93+18=111 Exploring Operation: 18+23=41, Resulting Numbers: [93, 41] Generated Node #0,1,3: 43:[93, 41] Operation: 18+23=41 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[18, 70], Operations: ['7+16=23', '93-23=70'] Exploring Operation: 18+70=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 18*70=1260, Resulting Numbers: [1260] 1260,43 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:[23, 75], Operations: ['7+16=23', '93-18=75'] Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 23*75=1725, Resulting Numbers: [1725] 1725,43 unequal: No Solution Exploring Operation: 23+75=98, Resulting Numbers: [98] 98,43 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 #0,1,3 Current State: 43:[93, 41], Operations: ['7+16=23', '18+23=41'] Exploring Operation: 93*41=3813, Resulting Numbers: [3813] 3813,43 unequal: No Solution Exploring Operation: 93-41=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 93+41=134, Resulting Numbers: [134] 134,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 43:[23, 111], Operations: ['7+16=23', '93+18=111'] Exploring Operation: 111-23=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 23+111=134, Resulting Numbers: [134] 134,43 unequal: No Solution Exploring Operation: 23*111=2553, Resulting Numbers: [2553] 2553,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[7, 18, 77], Operations: ['93-16=77'] Exploring Operation: 77-18=59, Resulting Numbers: [7, 59] Generated Node #0,2,0: 43:[7, 59] Operation: 77-18=59 Exploring Operation: 77-7=70, Resulting Numbers: [18, 70] Generated Node #0,2,1: 43:[18, 70] Operation: 77-7=70 Exploring Operation: 77/7=11, Resulting Numbers: [18, 11] Generated Node #0,2,2: 43:[18, 11] Operation: 77/7=11 Exploring Operation: 7+18=25, Resulting Numbers: [77, 25] Generated Node #0,2,3: 43:[77, 25] Operation: 7+18=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 43:[7, 59], Operations: ['93-16=77', '77-18=59'] Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 7*59=413, Resulting Numbers: [413] 413,43 unequal: No Solution Exploring Operation: 7+59=66, Resulting Numbers: [66] 66,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 43:[18, 70], Operations: ['93-16=77', '77-7=70'] Exploring Operation: 18+70=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 18*70=1260, Resulting Numbers: [1260] 1260,43 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,43 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:[77, 25], Operations: ['93-16=77', '7+18=25'] Exploring Operation: 77*25=1925, Resulting Numbers: [1925] 1925,43 unequal: No Solution Exploring Operation: 77-25=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 77+25=102, Resulting Numbers: [102] 102,43 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:[18, 11], Operations: ['93-16=77', '77/7=11'] Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,43 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,43 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 #0,3 Current State: 43:[16, 18, 86], Operations: ['93-7=86'] Exploring Operation: 86-18=68, Resulting Numbers: [16, 68] Generated Node #0,3,0: 43:[16, 68] Operation: 86-18=68 Exploring Operation: 86-16=70, Resulting Numbers: [18, 70] Generated Node #0,3,1: 43:[18, 70] Operation: 86-16=70 Exploring Operation: 18-16=2, Resulting Numbers: [86, 2] Generated Node #0,3,2: 43:[86, 2] Operation: 18-16=2 Exploring Operation: 16+18=34, Resulting Numbers: [86, 34] Generated Node #0,3,3: 43:[86, 34] Operation: 16+18=34 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 43:[16, 68], Operations: ['93-7=86', '86-18=68'] Exploring Operation: 68-16=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 16*68=1088, Resulting Numbers: [1088] 1088,43 unequal: No Solution Exploring Operation: 16+68=84, Resulting Numbers: [84] 84,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 43:[18, 70], Operations: ['93-7=86', '86-16=70'] Exploring Operation: 18*70=1260, Resulting Numbers: [1260] 1260,43 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 18+70=88, Resulting Numbers: [88] 88,43 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:[86, 34], Operations: ['93-7=86', '16+18=34'] Exploring Operation: 86+34=120, Resulting Numbers: [120] 120,43 unequal: No Solution Exploring Operation: 86*34=2924, Resulting Numbers: [2924] 2924,43 unequal: No Solution Exploring Operation: 86-34=52, Resulting Numbers: [52] 52,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 43:[86, 2], Operations: ['93-7=86', '18-16=2'] Exploring Operation: 86*2=172, Resulting Numbers: [172] 172,43 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 86+2=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[93, 7, 16, 18], Operations: [] Exploring Operation: 93-7=86, Resulting Numbers: [16, 18, 86] Generated Node #0,3: 43:[16, 18, 86] Operation: 93-7=86 Moving to Node #0,3 Current State: 43:[16, 18, 86], Operations: ['93-7=86'] Exploring Operation: 18-16=2, Resulting Numbers: [86, 2] Generated Node #0,3,2: 43:[86, 2] Operation: 18-16=2 Moving to Node #0,3,2 Current State: 43:[86, 2], Operations: ['93-7=86', '18-16=2'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.936632
hs_4
sum_heuristic
[ 87, 70, 93, 5 ]
59
[ "87+70=157", "93+5=98", "157-98=59" ]
Current State: 59:[87, 70, 93, 5], Operations: [] Exploring Operation: 87+70=157, Resulting Numbers: [93, 5, 157] Generated Node #2: [93, 5, 157] from Operation: 87+70=157 Current State: 59:[93, 5, 157], Operations: ['87+70=157'] Exploring Operation: 93+5=98, Resulting Numbers: [157, 98] Generated Node #3: [157, 98] from Operation: 93+5=98 Current State: 59:[157, 98], Operations: ['87+70=157', '93+5=98'] Exploring Operation: 157-98=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[87, 70, 93, 5], Operations: [] Exploring Operation: 70-5=65, Resulting Numbers: [87, 93, 65] Generated Node #0,0: 59:[87, 93, 65] Operation: 70-5=65 Exploring Operation: 87-5=82, Resulting Numbers: [70, 93, 82] Generated Node #0,1: 59:[70, 93, 82] Operation: 87-5=82 Exploring Operation: 93-5=88, Resulting Numbers: [87, 70, 88] Generated Node #0,2: 59:[87, 70, 88] Operation: 93-5=88 Exploring Operation: 87+5=92, Resulting Numbers: [70, 93, 92] Generated Node #0,3: 59:[70, 93, 92] Operation: 87+5=92 Moving to Node #0,0 Current State: 59:[87, 93, 65], Operations: ['70-5=65'] Exploring Operation: 87+93=180, Resulting Numbers: [65, 180] Generated Node #0,0,0: 59:[65, 180] Operation: 87+93=180 Exploring Operation: 93-87=6, Resulting Numbers: [65, 6] Generated Node #0,0,1: 59:[65, 6] Operation: 93-87=6 Exploring Operation: 93-65=28, Resulting Numbers: [87, 28] Generated Node #0,0,2: 59:[87, 28] Operation: 93-65=28 Exploring Operation: 87-65=22, Resulting Numbers: [93, 22] Generated Node #0,0,3: 59:[93, 22] Operation: 87-65=22 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[65, 6], Operations: ['70-5=65', '93-87=6'] Exploring Operation: 65*6=390, Resulting Numbers: [390] 390,59 unequal: No Solution Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[87, 70, 93, 5], Operations: [] Exploring Operation: 70-5=65, Resulting Numbers: [87, 93, 65] Generated Node #0,0: 59:[87, 93, 65] Operation: 70-5=65 Moving to Node #0,0 Current State: 59:[87, 93, 65], Operations: ['70-5=65'] Exploring Operation: 93-87=6, Resulting Numbers: [65, 6] Generated Node #0,0,1: 59:[65, 6] Operation: 93-87=6 Moving to Node #0,0,1 Current State: 59:[65, 6], Operations: ['70-5=65', '93-87=6'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 60, 38, 10, 12 ]
36
[ "60/10=6", "12/6=2", "38-2=36" ]
Current State: 36:[60, 38, 10, 12], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [38, 12, 6] Generated Node #2: [38, 12, 6] from Operation: 60/10=6 Current State: 36:[38, 12, 6], Operations: ['60/10=6'] Exploring Operation: 12/6=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 12/6=2 Current State: 36:[38, 2], Operations: ['60/10=6', '12/6=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[60, 38, 10, 12], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [38, 12, 6] Generated Node #0,0: 36:[38, 12, 6] Operation: 60/10=6 Exploring Operation: 60/12=5, Resulting Numbers: [38, 10, 5] Generated Node #0,1: 36:[38, 10, 5] Operation: 60/12=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[38, 12, 6], Operations: ['60/10=6'] Exploring Operation: 12+6=18, Resulting Numbers: [38, 18] Generated Node #0,0,0: 36:[38, 18] Operation: 12+6=18 Exploring Operation: 12-6=6, Resulting Numbers: [38, 6] Generated Node #0,0,1: 36:[38, 6] Operation: 12-6=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[38, 18], Operations: ['60/10=6', '12+6=18'] Exploring Operation: 38+18=56, Resulting Numbers: [56] 56,36 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,36 unequal: No Solution No 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: 36:[38, 6], Operations: ['60/10=6', '12-6=6'] Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,36 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,36 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: 36:[38, 10, 5], Operations: ['60/12=5'] Exploring Operation: 10/5=2, Resulting Numbers: [38, 2] Generated Node #0,1,0: 36:[38, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [38, 5] Generated Node #0,1,1: 36:[38, 5] Operation: 10-5=5 Moving to Node #0,1,0 Current State: 36:[38, 2], Operations: ['60/12=5', '10/5=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[60, 38, 10, 12], Operations: [] Exploring Operation: 60/12=5, Resulting Numbers: [38, 10, 5] Generated Node #0,1: 36:[38, 10, 5] Operation: 60/12=5 Moving to Node #0,1 Current State: 36:[38, 10, 5], Operations: ['60/12=5'] Exploring Operation: 10/5=2, Resulting Numbers: [38, 2] Generated Node #0,1,0: 36:[38, 2] Operation: 10/5=2 Moving to Node #0,1,0 Current State: 36:[38, 2], Operations: ['60/12=5', '10/5=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 43, 3, 3, 2 ]
26
[ "43+3=46", "46/2=23", "3+23=26" ]
Current State: 26:[43, 3, 3, 2], Operations: [] Exploring Operation: 43+3=46, Resulting Numbers: [2, 46] Generated Node #2: [2, 46] from Operation: 43+3=46 Current State: 26:[2, 46], Operations: ['43+3=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,26 equal: Goal Reached Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[43, 3, 3, 2], Operations: [] Exploring Operation: 43-3=40, Resulting Numbers: [3, 2, 40] Generated Node #0,0: 26:[3, 2, 40] Operation: 43-3=40 Exploring Operation: 43-3=40, Resulting Numbers: [3, 2, 40] Generated Node #0,1: 26:[3, 2, 40] Operation: 43-3=40 Exploring Operation: 43-2=41, Resulting Numbers: [3, 3, 41] Generated Node #0,2: 26:[3, 3, 41] Operation: 43-2=41 Exploring Operation: 3/3=1, Resulting Numbers: [43, 2, 1] Generated Node #0,3: 26:[43, 2, 1] Operation: 3/3=1 Moving to Node #0,0 Current State: 26:[3, 2, 40], Operations: ['43-3=40'] Exploring Operation: 3-2=1, Resulting Numbers: [40, 1] Generated Node #0,0,0: 26:[40, 1] Operation: 3-2=1 Exploring Operation: 40-3=37, Resulting Numbers: [2, 37] Generated Node #0,0,1: 26:[2, 37] Operation: 40-3=37 Exploring Operation: 40/2=20, Resulting Numbers: [3, 20] Generated Node #0,0,2: 26:[3, 20] Operation: 40/2=20 Exploring Operation: 40-2=38, Resulting Numbers: [3, 38] Generated Node #0,0,3: 26:[3, 38] Operation: 40-2=38 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[3, 20], Operations: ['43-3=40', '40/2=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,26 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[2, 37], Operations: ['43-3=40', '40-3=37'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,26 unequal: No Solution Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,26 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 #0,0,3 Current State: 26:[3, 38], Operations: ['43-3=40', '40-2=38'] Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,26 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,26 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[40, 1], Operations: ['43-3=40', '3-2=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 26:[3, 2, 40], Operations: ['43-3=40'] Exploring Operation: 3-2=1, Resulting Numbers: [40, 1] Generated Node #0,1,0: 26:[40, 1] Operation: 3-2=1 Exploring Operation: 40-2=38, Resulting Numbers: [3, 38] Generated Node #0,1,1: 26:[3, 38] Operation: 40-2=38 Exploring Operation: 40-3=37, Resulting Numbers: [2, 37] Generated Node #0,1,2: 26:[2, 37] Operation: 40-3=37 Exploring Operation: 40/2=20, Resulting Numbers: [3, 20] Generated Node #0,1,3: 26:[3, 20] Operation: 40/2=20 Moving to Node #0,2 Current State: 26:[3, 3, 41], Operations: ['43-2=41'] Exploring Operation: 41-3=38, Resulting Numbers: [3, 38] Generated Node #0,2,0: 26:[3, 38] Operation: 41-3=38 Exploring Operation: 41-3=38, Resulting Numbers: [3, 38] Generated Node #0,2,1: 26:[3, 38] Operation: 41-3=38 Exploring Operation: 3/3=1, Resulting Numbers: [41, 1] Generated Node #0,2,2: 26:[41, 1] Operation: 3/3=1 Exploring Operation: 3-3=0, Resulting Numbers: [41, 0] Generated Node #0,2,3: 26:[41, 0] Operation: 3-3=0 Moving to Node #0,3 Current State: 26:[43, 2, 1], Operations: ['3/3=1'] Exploring Operation: 43*1=43, Resulting Numbers: [2, 43] Generated Node #0,3,0: 26:[2, 43] Operation: 43*1=43 Exploring Operation: 43-2=41, Resulting Numbers: [1, 41] Generated Node #0,3,1: 26:[1, 41] Operation: 43-2=41 Exploring Operation: 43/1=43, Resulting Numbers: [2, 43] Generated Node #0,3,2: 26:[2, 43] Operation: 43/1=43 Exploring Operation: 43-1=42, Resulting Numbers: [2, 42] Generated Node #0,3,3: 26:[2, 42] Operation: 43-1=42 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 26:[1, 41], Operations: ['3/3=1', '43-2=41'] Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,26 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 #0,3,3 Current State: 26:[2, 42], Operations: ['3/3=1', '43-1=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,26 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,26 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,26 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 #0,3,0 Current State: 26:[2, 43], Operations: ['3/3=1', '43*1=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,26 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,26 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,26 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 #0,3,2 Current State: 26:[2, 43], Operations: ['3/3=1', '43/1=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,26 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 26:[3, 20], Operations: ['43-3=40', '40/2=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,26 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[2, 37], Operations: ['43-3=40', '40-3=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,26 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,26 unequal: No Solution Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[3, 38], Operations: ['43-3=40', '40-2=38'] Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,26 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,26 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[3, 38], Operations: ['43-2=41', '41-3=38'] Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,26 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[3, 38], Operations: ['43-2=41', '41-3=38'] Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,26 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[40, 1], Operations: ['43-3=40', '3-2=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[41, 1], Operations: ['43-2=41', '3/3=1'] Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[41, 0], Operations: ['43-2=41', '3-3=0'] Exploring Operation: 41*0=0, Resulting Numbers: [0] 0,26 unequal: No Solution Exploring Operation: 41-0=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 41+0=41, Resulting Numbers: [41] 41,26 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 92, 21, 19, 77 ]
10
[ "92+21=113", "77+113=190", "190/19=10" ]
Current State: 10:[92, 21, 19, 77], Operations: [] Exploring Operation: 92+21=113, Resulting Numbers: [19, 77, 113] Generated Node #2: [19, 77, 113] from Operation: 92+21=113 Current State: 10:[19, 77, 113], Operations: ['92+21=113'] Exploring Operation: 77+113=190, Resulting Numbers: [19, 190] Generated Node #3: [19, 190] from Operation: 77+113=190 Current State: 10:[19, 190], Operations: ['92+21=113', '77+113=190'] Exploring Operation: 190/19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[92, 21, 19, 77], Operations: [] Exploring Operation: 92-19=73, Resulting Numbers: [21, 77, 73] Generated Node #0,0: 10:[21, 77, 73] Operation: 92-19=73 Exploring Operation: 92-77=15, Resulting Numbers: [21, 19, 15] Generated Node #0,1: 10:[21, 19, 15] Operation: 92-77=15 Exploring Operation: 92-21=71, Resulting Numbers: [19, 77, 71] Generated Node #0,2: 10:[19, 77, 71] Operation: 92-21=71 Exploring Operation: 77-21=56, Resulting Numbers: [92, 19, 56] Generated Node #0,3: 10:[92, 19, 56] Operation: 77-21=56 Moving to Node #0,1 Current State: 10:[21, 19, 15], Operations: ['92-77=15'] Exploring Operation: 21-15=6, Resulting Numbers: [19, 6] Generated Node #0,1,0: 10:[19, 6] Operation: 21-15=6 Exploring Operation: 21-19=2, Resulting Numbers: [15, 2] Generated Node #0,1,1: 10:[15, 2] Operation: 21-19=2 Exploring Operation: 21+19=40, Resulting Numbers: [15, 40] Generated Node #0,1,2: 10:[15, 40] Operation: 21+19=40 Exploring Operation: 19-15=4, Resulting Numbers: [21, 4] Generated Node #0,1,3: 10:[21, 4] Operation: 19-15=4 Moving to Node #0,3 Current State: 10:[92, 19, 56], Operations: ['77-21=56'] Exploring Operation: 92+19=111, Resulting Numbers: [56, 111] Generated Node #0,3,0: 10:[56, 111] Operation: 92+19=111 Exploring Operation: 56-19=37, Resulting Numbers: [92, 37] Generated Node #0,3,1: 10:[92, 37] Operation: 56-19=37 Exploring Operation: 92-56=36, Resulting Numbers: [19, 36] Generated Node #0,3,2: 10:[19, 36] Operation: 92-56=36 Exploring Operation: 92-19=73, Resulting Numbers: [56, 73] Generated Node #0,3,3: 10:[56, 73] Operation: 92-19=73 Moving to Node #0,2 Current State: 10:[19, 77, 71], Operations: ['92-21=71'] Exploring Operation: 19+77=96, Resulting Numbers: [71, 96] Generated Node #0,2,0: 10:[71, 96] Operation: 19+77=96 Exploring Operation: 77-71=6, Resulting Numbers: [19, 6] Generated Node #0,2,1: 10:[19, 6] Operation: 77-71=6 Exploring Operation: 77-19=58, Resulting Numbers: [71, 58] Generated Node #0,2,2: 10:[71, 58] Operation: 77-19=58 Exploring Operation: 71-19=52, Resulting Numbers: [77, 52] Generated Node #0,2,3: 10:[77, 52] Operation: 71-19=52 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 10:[19, 6], Operations: ['92-21=71', '77-71=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,10 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,10 unequal: No Solution No 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: 10:[71, 58], Operations: ['92-21=71', '77-19=58'] Exploring Operation: 71*58=4118, Resulting Numbers: [4118] 4118,10 unequal: No Solution Exploring Operation: 71-58=13, Resulting Numbers: [13] 13,10 unequal: No Solution Exploring Operation: 71+58=129, Resulting Numbers: [129] 129,10 unequal: No Solution No 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: 10:[77, 52], Operations: ['92-21=71', '71-19=52'] Exploring Operation: 77*52=4004, Resulting Numbers: [4004] 4004,10 unequal: No Solution Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 77+52=129, Resulting Numbers: [129] 129,10 unequal: No Solution No 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: 10:[71, 96], Operations: ['92-21=71', '19+77=96'] Exploring Operation: 96-71=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 71*96=6816, Resulting Numbers: [6816] 6816,10 unequal: No Solution Exploring Operation: 71+96=167, Resulting Numbers: [167] 167,10 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: 10:[21, 77, 73], Operations: ['92-19=73'] Exploring Operation: 77-21=56, Resulting Numbers: [73, 56] Generated Node #0,0,0: 10:[73, 56] Operation: 77-21=56 Exploring Operation: 77-73=4, Resulting Numbers: [21, 4] Generated Node #0,0,1: 10:[21, 4] Operation: 77-73=4 Exploring Operation: 73-21=52, Resulting Numbers: [77, 52] Generated Node #0,0,2: 10:[77, 52] Operation: 73-21=52 Exploring Operation: 21+77=98, Resulting Numbers: [73, 98] Generated Node #0,0,3: 10:[73, 98] Operation: 21+77=98 Moving to Node #0,1,1 Current State: 10:[15, 2], Operations: ['92-77=15', '21-19=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,10 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,10 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[19, 6], Operations: ['92-77=15', '21-15=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,10 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,10 unequal: No Solution Moving to Node #0,1,3 Current State: 10:[21, 4], Operations: ['92-77=15', '19-15=4'] Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,10 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[21, 4], Operations: ['92-19=73', '77-73=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,10 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,10 unequal: No Solution Moving to Node #0,3,2 Current State: 10:[19, 36], Operations: ['77-21=56', '92-56=36'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,10 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,10 unequal: No Solution Moving to Node #0,1,2 Current State: 10:[15, 40], Operations: ['92-77=15', '21+19=40'] Exploring Operation: 40-15=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 15*40=600, Resulting Numbers: [600] 600,10 unequal: No Solution Exploring Operation: 15+40=55, Resulting Numbers: [55] 55,10 unequal: No Solution Moving to Node #0,3,3 Current State: 10:[56, 73], Operations: ['77-21=56', '92-19=73'] Exploring Operation: 56*73=4088, Resulting Numbers: [4088] 4088,10 unequal: No Solution Exploring Operation: 56+73=129, Resulting Numbers: [129] 129,10 unequal: No Solution Exploring Operation: 73-56=17, Resulting Numbers: [17] 17,10 unequal: No Solution Moving to Node #0,3,1 Current State: 10:[92, 37], Operations: ['77-21=56', '56-19=37'] Exploring Operation: 92-37=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 92*37=3404, Resulting Numbers: [3404] 3404,10 unequal: No Solution Exploring Operation: 92+37=129, Resulting Numbers: [129] 129,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[77, 52], Operations: ['92-19=73', '73-21=52'] Exploring Operation: 77+52=129, Resulting Numbers: [129] 129,10 unequal: No Solution Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 77*52=4004, Resulting Numbers: [4004] 4004,10 unequal: No Solution Moving to Node #0,0,0 Current State: 10:[73, 56], Operations: ['92-19=73', '77-21=56'] Exploring Operation: 73-56=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 73*56=4088, Resulting Numbers: [4088] 4088,10 unequal: No Solution Exploring Operation: 73+56=129, Resulting Numbers: [129] 129,10 unequal: No Solution Moving to Node #0,3,0 Current State: 10:[56, 111], Operations: ['77-21=56', '92+19=111'] Exploring Operation: 56*111=6216, Resulting Numbers: [6216] 6216,10 unequal: No Solution Exploring Operation: 56+111=167, Resulting Numbers: [167] 167,10 unequal: No Solution Exploring Operation: 111-56=55, Resulting Numbers: [55] 55,10 unequal: No Solution Moving to Node #0,0,3 Current State: 10:[73, 98], Operations: ['92-19=73', '21+77=98'] Exploring Operation: 73*98=7154, Resulting Numbers: [7154] 7154,10 unequal: No Solution Exploring Operation: 73+98=171, Resulting Numbers: [171] 171,10 unequal: No Solution Exploring Operation: 98-73=25, Resulting Numbers: [25] 25,10 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 92, 74, 3, 67 ]
13
[ "92-74=18", "3*18=54", "67-54=13" ]
Current State: 13:[92, 74, 3, 67], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [3, 67, 18] Generated Node #2: [3, 67, 18] from Operation: 92-74=18 Current State: 13:[3, 67, 18], Operations: ['92-74=18'] Exploring Operation: 3*18=54, Resulting Numbers: [67, 54] Generated Node #3: [67, 54] from Operation: 3*18=54 Current State: 13:[67, 54], Operations: ['92-74=18', '3*18=54'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[92, 74, 3, 67], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [3, 67, 18] Generated Node #0,0: 13:[3, 67, 18] Operation: 92-74=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[3, 67, 18], Operations: ['92-74=18'] Exploring Operation: 67-18=49, Resulting Numbers: [3, 49] Generated Node #0,0,0: 13:[3, 49] Operation: 67-18=49 Moving to Node #0,0,0 Current State: 13:[3, 49], Operations: ['92-74=18', '67-18=49'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,13 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
[ 33, 46, 73, 59 ]
71
[ "33+59=92", "92/46=2", "73-2=71" ]
Current State: 71:[33, 46, 73, 59], Operations: [] Exploring Operation: 33+59=92, Resulting Numbers: [46, 73, 92] Generated Node #2: [46, 73, 92] from Operation: 33+59=92 Current State: 71:[46, 73, 92], Operations: ['33+59=92'] Exploring Operation: 92/46=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 92/46=2 Current State: 71:[73, 2], Operations: ['33+59=92', '92/46=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[33, 46, 73, 59], Operations: [] Exploring Operation: 33+59=92, Resulting Numbers: [46, 73, 92] Generated Node #0,0: 71:[46, 73, 92] Operation: 33+59=92 Exploring Operation: 73-33=40, Resulting Numbers: [46, 59, 40] Generated Node #0,1: 71:[46, 59, 40] Operation: 73-33=40 Exploring Operation: 33+46=79, Resulting Numbers: [73, 59, 79] Generated Node #0,2: 71:[73, 59, 79] Operation: 33+46=79 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[73, 59, 79], Operations: ['33+46=79'] Exploring Operation: 79-59=20, Resulting Numbers: [73, 20] Generated Node #0,2,0: 71:[73, 20] Operation: 79-59=20 Exploring Operation: 73-59=14, Resulting Numbers: [79, 14] Generated Node #0,2,1: 71:[79, 14] Operation: 73-59=14 Exploring Operation: 73+59=132, Resulting Numbers: [79, 132] Generated Node #0,2,2: 71:[79, 132] Operation: 73+59=132 Moving to Node #0,2,0 Current State: 71:[73, 20], Operations: ['33+46=79', '79-59=20'] Exploring Operation: 73*20=1460, Resulting Numbers: [1460] 1460,71 unequal: No Solution Exploring Operation: 73+20=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[79, 14], Operations: ['33+46=79', '73-59=14'] Exploring Operation: 79*14=1106, Resulting Numbers: [1106] 1106,71 unequal: No Solution Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,71 unequal: No Solution Exploring Operation: 79+14=93, Resulting Numbers: [93] 93,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[79, 132], Operations: ['33+46=79', '73+59=132'] Exploring Operation: 79+132=211, Resulting Numbers: [211] 211,71 unequal: No Solution Exploring Operation: 132-79=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 79*132=10428, Resulting Numbers: [10428] 10428,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[46, 73, 92], Operations: ['33+59=92'] Exploring Operation: 73-46=27, Resulting Numbers: [92, 27] Generated Node #0,0,0: 71:[92, 27] Operation: 73-46=27 Exploring Operation: 92-46=46, Resulting Numbers: [73, 46] Generated Node #0,0,1: 71:[73, 46] Operation: 92-46=46 Exploring Operation: 46+73=119, Resulting Numbers: [92, 119] Generated Node #0,0,2: 71:[92, 119] Operation: 46+73=119 Moving to Node #0,0,1 Current State: 71:[73, 46], Operations: ['33+59=92', '92-46=46'] Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,71 unequal: No Solution Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,71 unequal: No Solution Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[92, 27], Operations: ['33+59=92', '73-46=27'] Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,71 unequal: No Solution Exploring Operation: 92+27=119, Resulting Numbers: [119] 119,71 unequal: No Solution Exploring Operation: 92*27=2484, Resulting Numbers: [2484] 2484,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[92, 119], Operations: ['33+59=92', '46+73=119'] Exploring Operation: 92*119=10948, Resulting Numbers: [10948] 10948,71 unequal: No Solution Exploring Operation: 119-92=27, Resulting Numbers: [27] 27,71 unequal: No Solution Exploring Operation: 92+119=211, Resulting Numbers: [211] 211,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[46, 59, 40], Operations: ['73-33=40'] Exploring Operation: 59+40=99, Resulting Numbers: [46, 99] Generated Node #0,1,0: 71:[46, 99] Operation: 59+40=99 Exploring Operation: 46+59=105, Resulting Numbers: [40, 105] Generated Node #0,1,1: 71:[40, 105] Operation: 46+59=105 Exploring Operation: 46+40=86, Resulting Numbers: [59, 86] Generated Node #0,1,2: 71:[59, 86] Operation: 46+40=86 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 71:[59, 86], Operations: ['73-33=40', '46+40=86'] Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,71 unequal: No Solution Exploring Operation: 59+86=145, Resulting Numbers: [145] 145,71 unequal: No Solution Exploring Operation: 59*86=5074, Resulting Numbers: [5074] 5074,71 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 #0,1,0 Current State: 71:[46, 99], Operations: ['73-33=40', '59+40=99'] Exploring Operation: 46*99=4554, Resulting Numbers: [4554] 4554,71 unequal: No Solution Exploring Operation: 99-46=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 46+99=145, Resulting Numbers: [145] 145,71 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:[40, 105], Operations: ['73-33=40', '46+59=105'] Exploring Operation: 40+105=145, Resulting Numbers: [145] 145,71 unequal: No Solution Exploring Operation: 40*105=4200, Resulting Numbers: [4200] 4200,71 unequal: No Solution Exploring Operation: 105-40=65, Resulting Numbers: [65] 65,71 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 No solution found.
0
hs_3
sum_heuristic
[ 26, 22, 69, 25 ]
98
[ "26-22=4", "69+25=94", "4+94=98" ]
Current State: 98:[26, 22, 69, 25], Operations: [] Exploring Operation: 26-22=4, Resulting Numbers: [69, 25, 4] Generated Node #2: [69, 25, 4] from Operation: 26-22=4 Current State: 98:[69, 25, 4], Operations: ['26-22=4'] Exploring Operation: 69+25=94, Resulting Numbers: [4, 94] Generated Node #3: [4, 94] from Operation: 69+25=94 Current State: 98:[4, 94], Operations: ['26-22=4', '69+25=94'] Exploring Operation: 4+94=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[26, 22, 69, 25], Operations: [] Exploring Operation: 69+25=94, Resulting Numbers: [26, 22, 94] Generated Node #0,0: 98:[26, 22, 94] Operation: 69+25=94 Exploring Operation: 26+69=95, Resulting Numbers: [22, 25, 95] Generated Node #0,1: 98:[22, 25, 95] Operation: 26+69=95 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[22, 25, 95], Operations: ['26+69=95'] Exploring Operation: 25-22=3, Resulting Numbers: [95, 3] Generated Node #0,1,0: 98:[95, 3] Operation: 25-22=3 Exploring Operation: 22+25=47, Resulting Numbers: [95, 47] Generated Node #0,1,1: 98:[95, 47] Operation: 22+25=47 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[95, 3], Operations: ['26+69=95', '25-22=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[26, 22, 69, 25], Operations: [] Exploring Operation: 26+69=95, Resulting Numbers: [22, 25, 95] Generated Node #0,1: 98:[22, 25, 95] Operation: 26+69=95 Moving to Node #0,1 Current State: 98:[22, 25, 95], Operations: ['26+69=95'] Exploring Operation: 25-22=3, Resulting Numbers: [95, 3] Generated Node #0,1,0: 98:[95, 3] Operation: 25-22=3 Moving to Node #0,1,0 Current State: 98:[95, 3], Operations: ['26+69=95', '25-22=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 54, 33, 17, 3 ]
68
[ "54/3=18", "33+17=50", "18+50=68" ]
Current State: 68:[54, 33, 17, 3], Operations: [] Exploring Operation: 54/3=18, Resulting Numbers: [33, 17, 18] Generated Node #2: [33, 17, 18] from Operation: 54/3=18 Current State: 68:[33, 17, 18], Operations: ['54/3=18'] Exploring Operation: 33+17=50, Resulting Numbers: [18, 50] Generated Node #3: [18, 50] from Operation: 33+17=50 Current State: 68:[18, 50], Operations: ['54/3=18', '33+17=50'] Exploring Operation: 18+50=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[54, 33, 17, 3], Operations: [] Exploring Operation: 54/3=18, Resulting Numbers: [33, 17, 18] Generated Node #0,0: 68:[33, 17, 18] Operation: 54/3=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[33, 17, 18], Operations: ['54/3=18'] Exploring Operation: 33-17=16, Resulting Numbers: [18, 16] Generated Node #0,0,0: 68:[18, 16] Operation: 33-17=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[18, 16], Operations: ['54/3=18', '33-17=16'] Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 25, 45, 12, 60 ]
36
[ "45-25=20", "12*60=720", "720/20=36" ]
Current State: 36:[25, 45, 12, 60], Operations: [] Exploring Operation: 45-25=20, Resulting Numbers: [12, 60, 20] Generated Node #2: [12, 60, 20] from Operation: 45-25=20 Current State: 36:[12, 60, 20], Operations: ['45-25=20'] Exploring Operation: 12*60=720, Resulting Numbers: [20, 720] Generated Node #3: [20, 720] from Operation: 12*60=720 Current State: 36:[20, 720], Operations: ['45-25=20', '12*60=720'] Exploring Operation: 720/20=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[25, 45, 12, 60], Operations: [] Exploring Operation: 60-25=35, Resulting Numbers: [45, 12, 35] Generated Node #0,0: 36:[45, 12, 35] Operation: 60-25=35 Exploring Operation: 60/12=5, Resulting Numbers: [25, 45, 5] Generated Node #0,1: 36:[25, 45, 5] Operation: 60/12=5 Exploring Operation: 45-25=20, Resulting Numbers: [12, 60, 20] Generated Node #0,2: 36:[12, 60, 20] Operation: 45-25=20 Exploring Operation: 60-45=15, Resulting Numbers: [25, 12, 15] Generated Node #0,3: 36:[25, 12, 15] Operation: 60-45=15 Moving to Node #0,0 Current State: 36:[45, 12, 35], Operations: ['60-25=35'] Exploring Operation: 12+35=47, Resulting Numbers: [45, 47] Generated Node #0,0,0: 36:[45, 47] Operation: 12+35=47 Exploring Operation: 45-35=10, Resulting Numbers: [12, 10] Generated Node #0,0,1: 36:[12, 10] Operation: 45-35=10 Exploring Operation: 35-12=23, Resulting Numbers: [45, 23] Generated Node #0,0,2: 36:[45, 23] Operation: 35-12=23 Exploring Operation: 45-12=33, Resulting Numbers: [35, 33] Generated Node #0,0,3: 36:[35, 33] Operation: 45-12=33 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[12, 10], Operations: ['60-25=35', '45-35=10'] Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,36 unequal: No Solution Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,36 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,36 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 #0,0,3 Current State: 36:[35, 33], Operations: ['60-25=35', '45-12=33'] Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,36 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,36 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 #0,0,2 Current State: 36:[45, 23], Operations: ['60-25=35', '35-12=23'] Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,36 unequal: No Solution Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,36 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,36 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 #0,0,0 Current State: 36:[45, 47], Operations: ['60-25=35', '12+35=47'] Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,36 unequal: No Solution Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,36 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,36 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: 36:[25, 12, 15], Operations: ['60-45=15'] Exploring Operation: 25+12=37, Resulting Numbers: [15, 37] Generated Node #0,3,0: 36:[15, 37] Operation: 25+12=37 Exploring Operation: 25-12=13, Resulting Numbers: [15, 13] Generated Node #0,3,1: 36:[15, 13] Operation: 25-12=13 Exploring Operation: 25-15=10, Resulting Numbers: [12, 10] Generated Node #0,3,2: 36:[12, 10] Operation: 25-15=10 Exploring Operation: 25+15=40, Resulting Numbers: [12, 40] Generated Node #0,3,3: 36:[12, 40] Operation: 25+15=40 Moving to Node #0,1 Current State: 36:[25, 45, 5], Operations: ['60/12=5'] Exploring Operation: 45-25=20, Resulting Numbers: [5, 20] Generated Node #0,1,0: 36:[5, 20] Operation: 45-25=20 Exploring Operation: 25/5=5, Resulting Numbers: [45, 5] Generated Node #0,1,1: 36:[45, 5] Operation: 25/5=5 Exploring Operation: 25-5=20, Resulting Numbers: [45, 20] Generated Node #0,1,2: 36:[45, 20] Operation: 25-5=20 Exploring Operation: 45/5=9, Resulting Numbers: [25, 9] Generated Node #0,1,3: 36:[25, 9] Operation: 45/5=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[5, 20], Operations: ['60/12=5', '45-25=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,36 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,36 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:[25, 9], Operations: ['60/12=5', '45/5=9'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,36 unequal: No Solution Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,36 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,36 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:[45, 5], Operations: ['60/12=5', '25/5=5'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 45*5=225, Resulting Numbers: [225] 225,36 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,36 unequal: No Solution Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,36 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 #0,1,2 Current State: 36:[45, 20], Operations: ['60/12=5', '25-5=20'] Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,36 unequal: No Solution Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,36 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,36 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:[12, 60, 20], Operations: ['45-25=20'] Exploring Operation: 60-20=40, Resulting Numbers: [12, 40] Generated Node #0,2,0: 36:[12, 40] Operation: 60-20=40 Exploring Operation: 60/20=3, Resulting Numbers: [12, 3] Generated Node #0,2,1: 36:[12, 3] Operation: 60/20=3 Exploring Operation: 60/12=5, Resulting Numbers: [20, 5] Generated Node #0,2,2: 36:[20, 5] Operation: 60/12=5 Exploring Operation: 60-12=48, Resulting Numbers: [20, 48] Generated Node #0,2,3: 36:[20, 48] Operation: 60-12=48 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 36:[12, 3], Operations: ['45-25=20', '60/20=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,36 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[25, 45, 12, 60], Operations: [] Exploring Operation: 45-25=20, Resulting Numbers: [12, 60, 20] Generated Node #0,2: 36:[12, 60, 20] Operation: 45-25=20 Moving to Node #0,2 Current State: 36:[12, 60, 20], Operations: ['45-25=20'] Exploring Operation: 60/20=3, Resulting Numbers: [12, 3] Generated Node #0,2,1: 36:[12, 3] Operation: 60/20=3 Moving to Node #0,2,1 Current State: 36:[12, 3], Operations: ['45-25=20', '60/20=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
sum_heuristic
[ 4, 78, 17, 39 ]
88
[ "78-17=61", "61-39=22", "4*22=88" ]
Current State: 88:[4, 78, 17, 39], Operations: [] Exploring Operation: 78-17=61, Resulting Numbers: [4, 39, 61] Generated Node #2: [4, 39, 61] from Operation: 78-17=61 Current State: 88:[4, 39, 61], Operations: ['78-17=61'] Exploring Operation: 61-39=22, Resulting Numbers: [4, 22] Generated Node #3: [4, 22] from Operation: 61-39=22 Current State: 88:[4, 22], Operations: ['78-17=61', '61-39=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[4, 78, 17, 39], Operations: [] Exploring Operation: 78+17=95, Resulting Numbers: [4, 39, 95] Generated Node #0,0: 88:[4, 39, 95] Operation: 78+17=95 Exploring Operation: 4+78=82, Resulting Numbers: [17, 39, 82] Generated Node #0,1: 88:[17, 39, 82] Operation: 4+78=82 Exploring Operation: 78-39=39, Resulting Numbers: [4, 17, 39] Generated Node #0,2: 88:[4, 17, 39] Operation: 78-39=39 Exploring Operation: 39-17=22, Resulting Numbers: [4, 78, 22] Generated Node #0,3: 88:[4, 78, 22] Operation: 39-17=22 Exploring Operation: 78/39=2, Resulting Numbers: [4, 17, 2] Generated Node #0,4: 88:[4, 17, 2] Operation: 78/39=2 Moving to Node #0,4 Current State: 88:[4, 17, 2], Operations: ['78/39=2'] Exploring Operation: 4*2=8, Resulting Numbers: [17, 8] Generated Node #0,4,0: 88:[17, 8] Operation: 4*2=8 Exploring Operation: 17+2=19, Resulting Numbers: [4, 19] Generated Node #0,4,1: 88:[4, 19] Operation: 17+2=19 Exploring Operation: 17-4=13, Resulting Numbers: [2, 13] Generated Node #0,4,2: 88:[2, 13] Operation: 17-4=13 Exploring Operation: 4+17=21, Resulting Numbers: [2, 21] Generated Node #0,4,3: 88:[2, 21] Operation: 4+17=21 Exploring Operation: 17-2=15, Resulting Numbers: [4, 15] Generated Node #0,4,4: 88:[4, 15] Operation: 17-2=15 Moving to Node #0,3 Current State: 88:[4, 78, 22], Operations: ['39-17=22'] Exploring Operation: 4+78=82, Resulting Numbers: [22, 82] Generated Node #0,3,0: 88:[22, 82] Operation: 4+78=82 Exploring Operation: 78+22=100, Resulting Numbers: [4, 100] Generated Node #0,3,1: 88:[4, 100] Operation: 78+22=100 Exploring Operation: 78-4=74, Resulting Numbers: [22, 74] Generated Node #0,3,2: 88:[22, 74] Operation: 78-4=74 Exploring Operation: 4*22=88, Resulting Numbers: [78, 88] Generated Node #0,3,3: 88:[78, 88] Operation: 4*22=88 Exploring Operation: 78-22=56, Resulting Numbers: [4, 56] Generated Node #0,3,4: 88:[4, 56] Operation: 78-22=56 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 88:[22, 82], Operations: ['39-17=22', '4+78=82'] Exploring Operation: 22*82=1804, Resulting Numbers: [1804] 1804,88 unequal: No Solution Exploring Operation: 22+82=104, Resulting Numbers: [104] 104,88 unequal: No Solution Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 88:[78, 88], Operations: ['39-17=22', '4*22=88'] Exploring Operation: 88-78=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 78*88=6864, Resulting Numbers: [6864] 6864,88 unequal: No Solution Exploring Operation: 78+88=166, Resulting Numbers: [166] 166,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 88:[4, 100], Operations: ['39-17=22', '78+22=100'] Exploring Operation: 4*100=400, Resulting Numbers: [400] 400,88 unequal: No Solution Exploring Operation: 100/4=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 4+100=104, Resulting Numbers: [104] 104,88 unequal: No Solution Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 88:[4, 56], Operations: ['39-17=22', '78-22=56'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 4*56=224, Resulting Numbers: [224] 224,88 unequal: No Solution Exploring Operation: 4+56=60, Resulting Numbers: [60] 60,88 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 88:[22, 74], Operations: ['39-17=22', '78-4=74'] Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,88 unequal: No Solution Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,88 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: 88:[4, 17, 39], Operations: ['78-39=39'] Exploring Operation: 17-4=13, Resulting Numbers: [39, 13] Generated Node #0,2,0: 88:[39, 13] Operation: 17-4=13 Exploring Operation: 4+39=43, Resulting Numbers: [17, 43] Generated Node #0,2,1: 88:[17, 43] Operation: 4+39=43 Exploring Operation: 17+39=56, Resulting Numbers: [4, 56] Generated Node #0,2,2: 88:[4, 56] Operation: 17+39=56 Exploring Operation: 4+17=21, Resulting Numbers: [39, 21] Generated Node #0,2,3: 88:[39, 21] Operation: 4+17=21 Exploring Operation: 39-17=22, Resulting Numbers: [4, 22] Generated Node #0,2,4: 88:[4, 22] Operation: 39-17=22 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 88:[4, 22], Operations: ['78-39=39', '39-17=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[4, 78, 17, 39], Operations: [] Exploring Operation: 78-39=39, Resulting Numbers: [4, 17, 39] Generated Node #0,2: 88:[4, 17, 39] Operation: 78-39=39 Moving to Node #0,2 Current State: 88:[4, 17, 39], Operations: ['78-39=39'] Exploring Operation: 39-17=22, Resulting Numbers: [4, 22] Generated Node #0,2,4: 88:[4, 22] Operation: 39-17=22 Moving to Node #0,2,4 Current State: 88:[4, 22], Operations: ['78-39=39', '39-17=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic
[ 98, 41, 10, 55 ]
94
[ "98+41=139", "55-10=45", "139-45=94" ]
Current State: 94:[98, 41, 10, 55], Operations: [] Exploring Operation: 98+41=139, Resulting Numbers: [10, 55, 139] Generated Node #2: [10, 55, 139] from Operation: 98+41=139 Current State: 94:[10, 55, 139], Operations: ['98+41=139'] Exploring Operation: 55-10=45, Resulting Numbers: [139, 45] Generated Node #3: [139, 45] from Operation: 55-10=45 Current State: 94:[139, 45], Operations: ['98+41=139', '55-10=45'] Exploring Operation: 139-45=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[98, 41, 10, 55], Operations: [] Exploring Operation: 55-10=45, Resulting Numbers: [98, 41, 45] Generated Node #0,0: 94:[98, 41, 45] Operation: 55-10=45 Exploring Operation: 41+10=51, Resulting Numbers: [98, 55, 51] Generated Node #0,1: 94:[98, 55, 51] Operation: 41+10=51 Exploring Operation: 41+55=96, Resulting Numbers: [98, 10, 96] Generated Node #0,2: 94:[98, 10, 96] Operation: 41+55=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[98, 41, 45], Operations: ['55-10=45'] Exploring Operation: 98-45=53, Resulting Numbers: [41, 53] Generated Node #0,0,0: 94:[41, 53] Operation: 98-45=53 Exploring Operation: 98-41=57, Resulting Numbers: [45, 57] Generated Node #0,0,1: 94:[45, 57] Operation: 98-41=57 Exploring Operation: 45-41=4, Resulting Numbers: [98, 4] Generated Node #0,0,2: 94:[98, 4] Operation: 45-41=4 Moving to Node #0,0,2 Current State: 94:[98, 4], Operations: ['55-10=45', '45-41=4'] Exploring Operation: 98*4=392, Resulting Numbers: [392] 392,94 unequal: No Solution Exploring Operation: 98+4=102, Resulting Numbers: [102] 102,94 unequal: No Solution Exploring Operation: 98-4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[98, 41, 10, 55], Operations: [] Exploring Operation: 55-10=45, Resulting Numbers: [98, 41, 45] Generated Node #0,0: 94:[98, 41, 45] Operation: 55-10=45 Moving to Node #0,0 Current State: 94:[98, 41, 45], Operations: ['55-10=45'] Exploring Operation: 45-41=4, Resulting Numbers: [98, 4] Generated Node #0,0,2: 94:[98, 4] Operation: 45-41=4 Moving to Node #0,0,2 Current State: 94:[98, 4], Operations: ['55-10=45', '45-41=4'] Exploring Operation: 98-4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 51, 3, 83, 56 ]
16
[ "56-51=5", "83-3=80", "80/5=16" ]
Current State: 16:[51, 3, 83, 56], Operations: [] Exploring Operation: 56-51=5, Resulting Numbers: [3, 83, 5] Generated Node #2: [3, 83, 5] from Operation: 56-51=5 Current State: 16:[3, 83, 5], Operations: ['56-51=5'] Exploring Operation: 83-3=80, Resulting Numbers: [5, 80] Generated Node #3: [5, 80] from Operation: 83-3=80 Current State: 16:[5, 80], Operations: ['56-51=5', '83-3=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[51, 3, 83, 56], Operations: [] Exploring Operation: 83-56=27, Resulting Numbers: [51, 3, 27] Generated Node #0,0: 16:[51, 3, 27] Operation: 83-56=27 Exploring Operation: 56-51=5, Resulting Numbers: [3, 83, 5] Generated Node #0,1: 16:[3, 83, 5] Operation: 56-51=5 Exploring Operation: 83-51=32, Resulting Numbers: [3, 56, 32] Generated Node #0,2: 16:[3, 56, 32] Operation: 83-51=32 Exploring Operation: 51/3=17, Resulting Numbers: [83, 56, 17] Generated Node #0,3: 16:[83, 56, 17] Operation: 51/3=17 Moving to Node #0,0 Current State: 16:[51, 3, 27], Operations: ['83-56=27'] Exploring Operation: 51/3=17, Resulting Numbers: [27, 17] Generated Node #0,0,0: 16:[27, 17] Operation: 51/3=17 Exploring Operation: 51-27=24, Resulting Numbers: [3, 24] Generated Node #0,0,1: 16:[3, 24] Operation: 51-27=24 Exploring Operation: 27/3=9, Resulting Numbers: [51, 9] Generated Node #0,0,2: 16:[51, 9] Operation: 27/3=9 Exploring Operation: 51-3=48, Resulting Numbers: [27, 48] Generated Node #0,0,3: 16:[27, 48] Operation: 51-3=48 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[3, 24], Operations: ['83-56=27', '51-27=24'] Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,16 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[27, 17], Operations: ['83-56=27', '51/3=17'] Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 27+17=44, Resulting Numbers: [44] 44,16 unequal: No Solution Exploring Operation: 27*17=459, Resulting Numbers: [459] 459,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[51, 9], Operations: ['83-56=27', '27/3=9'] Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 51*9=459, Resulting Numbers: [459] 459,16 unequal: No Solution Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[27, 48], Operations: ['83-56=27', '51-3=48'] Exploring Operation: 27*48=1296, Resulting Numbers: [1296] 1296,16 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 27+48=75, Resulting Numbers: [75] 75,16 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: 16:[3, 56, 32], Operations: ['83-51=32'] Exploring Operation: 56-32=24, Resulting Numbers: [3, 24] Generated Node #0,2,0: 16:[3, 24] Operation: 56-32=24 Exploring Operation: 32-3=29, Resulting Numbers: [56, 29] Generated Node #0,2,1: 16:[56, 29] Operation: 32-3=29 Exploring Operation: 56-3=53, Resulting Numbers: [32, 53] Generated Node #0,2,2: 16:[32, 53] Operation: 56-3=53 Exploring Operation: 3+56=59, Resulting Numbers: [32, 59] Generated Node #0,2,3: 16:[32, 59] Operation: 3+56=59 Moving to Node #0,1 Current State: 16:[3, 83, 5], Operations: ['56-51=5'] Exploring Operation: 83-3=80, Resulting Numbers: [5, 80] Generated Node #0,1,0: 16:[5, 80] Operation: 83-3=80 Exploring Operation: 3+5=8, Resulting Numbers: [83, 8] Generated Node #0,1,1: 16:[83, 8] Operation: 3+5=8 Exploring Operation: 83-5=78, Resulting Numbers: [3, 78] Generated Node #0,1,2: 16:[3, 78] Operation: 83-5=78 Exploring Operation: 5-3=2, Resulting Numbers: [83, 2] Generated Node #0,1,3: 16:[83, 2] Operation: 5-3=2 Moving to Node #0,3 Current State: 16:[83, 56, 17], Operations: ['51/3=17'] Exploring Operation: 56-17=39, Resulting Numbers: [83, 39] Generated Node #0,3,0: 16:[83, 39] Operation: 56-17=39 Exploring Operation: 83-17=66, Resulting Numbers: [56, 66] Generated Node #0,3,1: 16:[56, 66] Operation: 83-17=66 Exploring Operation: 83-56=27, Resulting Numbers: [17, 27] Generated Node #0,3,2: 16:[17, 27] Operation: 83-56=27 Exploring Operation: 83+56=139, Resulting Numbers: [17, 139] Generated Node #0,3,3: 16:[17, 139] Operation: 83+56=139 Moving to Node #0,2,0 Current State: 16:[3, 24], Operations: ['83-51=32', '56-32=24'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,16 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[17, 27], Operations: ['51/3=17', '83-56=27'] Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,16 unequal: No Solution Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,16 unequal: No Solution Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[32, 53], Operations: ['83-51=32', '56-3=53'] Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 32*53=1696, Resulting Numbers: [1696] 1696,16 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[56, 29], Operations: ['83-51=32', '32-3=29'] Exploring Operation: 56*29=1624, Resulting Numbers: [1624] 1624,16 unequal: No Solution Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 56+29=85, Resulting Numbers: [85] 85,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[32, 59], Operations: ['83-51=32', '3+56=59'] Exploring Operation: 32+59=91, Resulting Numbers: [91] 91,16 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 32*59=1888, Resulting Numbers: [1888] 1888,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[3, 78], Operations: ['56-51=5', '83-5=78'] Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,16 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 3*78=234, Resulting Numbers: [234] 234,16 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[5, 80], Operations: ['56-51=5', '83-3=80'] Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,16 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[51, 3, 83, 56], Operations: [] Exploring Operation: 56-51=5, Resulting Numbers: [3, 83, 5] Generated Node #0,1: 16:[3, 83, 5] Operation: 56-51=5 Moving to Node #0,1 Current State: 16:[3, 83, 5], Operations: ['56-51=5'] Exploring Operation: 83-3=80, Resulting Numbers: [5, 80] Generated Node #0,1,0: 16:[5, 80] Operation: 83-3=80 Moving to Node #0,1,0 Current State: 16:[5, 80], Operations: ['56-51=5', '83-3=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.947917
hs_4
sum_heuristic
[ 16, 3, 87, 21 ]
34
[ "21-16=5", "87/3=29", "5+29=34" ]
Current State: 34:[16, 3, 87, 21], Operations: [] Exploring Operation: 21-16=5, Resulting Numbers: [3, 87, 5] Generated Node #2: [3, 87, 5] from Operation: 21-16=5 Current State: 34:[3, 87, 5], Operations: ['21-16=5'] Exploring Operation: 87/3=29, Resulting Numbers: [5, 29] Generated Node #3: [5, 29] from Operation: 87/3=29 Current State: 34:[5, 29], Operations: ['21-16=5', '87/3=29'] Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[16, 3, 87, 21], Operations: [] Exploring Operation: 87/3=29, Resulting Numbers: [16, 21, 29] Generated Node #0,0: 34:[16, 21, 29] Operation: 87/3=29 Exploring Operation: 87-21=66, Resulting Numbers: [16, 3, 66] Generated Node #0,1: 34:[16, 3, 66] Operation: 87-21=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[16, 21, 29], Operations: ['87/3=29'] Exploring Operation: 16+21=37, Resulting Numbers: [29, 37] Generated Node #0,0,0: 34:[29, 37] Operation: 16+21=37 Exploring Operation: 29-21=8, Resulting Numbers: [16, 8] Generated Node #0,0,1: 34:[16, 8] Operation: 29-21=8 Moving to Node #0,0,1 Current State: 34:[16, 8], Operations: ['87/3=29', '29-21=8'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[29, 37], Operations: ['87/3=29', '16+21=37'] Exploring Operation: 29+37=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 37-29=8, Resulting Numbers: [8] 8,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[16, 3, 66], Operations: ['87-21=66'] Exploring Operation: 66/3=22, Resulting Numbers: [16, 22] Generated Node #0,1,0: 34:[16, 22] Operation: 66/3=22 Exploring Operation: 66-16=50, Resulting Numbers: [3, 50] Generated Node #0,1,1: 34:[3, 50] Operation: 66-16=50 Moving to Node #0,1,0 Current State: 34:[16, 22], Operations: ['87-21=66', '66/3=22'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[3, 50], Operations: ['87-21=66', '66-16=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,34 unequal: No Solution Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,34 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
[ 14, 71, 11, 5 ]
69
[ "14+71=85", "11+5=16", "85-16=69" ]
Current State: 69:[14, 71, 11, 5], Operations: [] Exploring Operation: 14+71=85, Resulting Numbers: [11, 5, 85] Generated Node #2: [11, 5, 85] from Operation: 14+71=85 Current State: 69:[11, 5, 85], Operations: ['14+71=85'] Exploring Operation: 11+5=16, Resulting Numbers: [85, 16] Generated Node #3: [85, 16] from Operation: 11+5=16 Current State: 69:[85, 16], Operations: ['14+71=85', '11+5=16'] Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[14, 71, 11, 5], Operations: [] Exploring Operation: 14+11=25, Resulting Numbers: [71, 5, 25] Generated Node #0,0: 69:[71, 5, 25] Operation: 14+11=25 Exploring Operation: 14-11=3, Resulting Numbers: [71, 5, 3] Generated Node #0,1: 69:[71, 5, 3] Operation: 14-11=3 Exploring Operation: 14+5=19, Resulting Numbers: [71, 11, 19] Generated Node #0,2: 69:[71, 11, 19] Operation: 14+5=19 Exploring Operation: 11-5=6, Resulting Numbers: [14, 71, 6] Generated Node #0,3: 69:[14, 71, 6] Operation: 11-5=6 Exploring Operation: 14*5=70, Resulting Numbers: [71, 11, 70] Generated Node #0,4: 69:[71, 11, 70] Operation: 14*5=70 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[71, 5, 3], Operations: ['14-11=3'] Exploring Operation: 5-3=2, Resulting Numbers: [71, 2] Generated Node #0,1,0: 69:[71, 2] Operation: 5-3=2 Exploring Operation: 71+5=76, Resulting Numbers: [3, 76] Generated Node #0,1,1: 69:[3, 76] Operation: 71+5=76 Exploring Operation: 71+3=74, Resulting Numbers: [5, 74] Generated Node #0,1,2: 69:[5, 74] Operation: 71+3=74 Exploring Operation: 71-3=68, Resulting Numbers: [5, 68] Generated Node #0,1,3: 69:[5, 68] Operation: 71-3=68 Exploring Operation: 71-5=66, Resulting Numbers: [3, 66] Generated Node #0,1,4: 69:[3, 66] Operation: 71-5=66 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[71, 2], Operations: ['14-11=3', '5-3=2'] Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,69 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,69 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[14, 71, 11, 5], Operations: [] Exploring Operation: 14-11=3, Resulting Numbers: [71, 5, 3] Generated Node #0,1: 69:[71, 5, 3] Operation: 14-11=3 Moving to Node #0,1 Current State: 69:[71, 5, 3], Operations: ['14-11=3'] Exploring Operation: 5-3=2, Resulting Numbers: [71, 2] Generated Node #0,1,0: 69:[71, 2] Operation: 5-3=2 Moving to Node #0,1,0 Current State: 69:[71, 2], Operations: ['14-11=3', '5-3=2'] Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 5, 40, 5, 53 ]
23
[ "40-5=35", "5+53=58", "58-35=23" ]
Current State: 23:[5, 40, 5, 53], Operations: [] Exploring Operation: 40-5=35, Resulting Numbers: [53, 35] Generated Node #2: [53, 35] from Operation: 40-5=35 Current State: 23:[53, 35], Operations: ['40-5=35'] Exploring Operation: 5+53=58, Resulting Numbers: [35, 58] Generated Node #3: [35, 58] from Operation: 5+53=58 Current State: 23:[35, 58], Operations: ['40-5=35', '5+53=58'] Exploring Operation: 58-35=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[5, 40, 5, 53], Operations: [] Exploring Operation: 40-5=35, Resulting Numbers: [5, 53, 35] Generated Node #0,0: 23:[5, 53, 35] Operation: 40-5=35 Exploring Operation: 5*5=25, Resulting Numbers: [40, 53, 25] Generated Node #0,1: 23:[40, 53, 25] Operation: 5*5=25 Exploring Operation: 5+5=10, Resulting Numbers: [40, 53, 10] Generated Node #0,2: 23:[40, 53, 10] Operation: 5+5=10 Exploring Operation: 53-40=13, Resulting Numbers: [5, 5, 13] Generated Node #0,3: 23:[5, 5, 13] Operation: 53-40=13 Moving to Node #0,3 Current State: 23:[5, 5, 13], Operations: ['53-40=13'] Exploring Operation: 5+5=10, Resulting Numbers: [13, 10] Generated Node #0,3,0: 23:[13, 10] Operation: 5+5=10 Exploring Operation: 5*5=25, Resulting Numbers: [13, 25] Generated Node #0,3,1: 23:[13, 25] Operation: 5*5=25 Exploring Operation: 5+13=18, Resulting Numbers: [5, 18] Generated Node #0,3,2: 23:[5, 18] Operation: 5+13=18 Exploring Operation: 5+13=18, Resulting Numbers: [5, 18] Generated Node #0,3,3: 23:[5, 18] Operation: 5+13=18 Moving to Node #0,1 Current State: 23:[40, 53, 25], Operations: ['5*5=25'] Exploring Operation: 40+53=93, Resulting Numbers: [25, 93] Generated Node #0,1,0: 23:[25, 93] Operation: 40+53=93 Exploring Operation: 53-40=13, Resulting Numbers: [25, 13] Generated Node #0,1,1: 23:[25, 13] Operation: 53-40=13 Exploring Operation: 53-25=28, Resulting Numbers: [40, 28] Generated Node #0,1,2: 23:[40, 28] Operation: 53-25=28 Exploring Operation: 40-25=15, Resulting Numbers: [53, 15] Generated Node #0,1,3: 23:[53, 15] Operation: 40-25=15 Moving to Node #0,2 Current State: 23:[40, 53, 10], Operations: ['5+5=10'] Exploring Operation: 40-10=30, Resulting Numbers: [53, 30] Generated Node #0,2,0: 23:[53, 30] Operation: 40-10=30 Exploring Operation: 53-40=13, Resulting Numbers: [10, 13] Generated Node #0,2,1: 23:[10, 13] Operation: 53-40=13 Exploring Operation: 53-10=43, Resulting Numbers: [40, 43] Generated Node #0,2,2: 23:[40, 43] Operation: 53-10=43 Exploring Operation: 40/10=4, Resulting Numbers: [53, 4] Generated Node #0,2,3: 23:[53, 4] Operation: 40/10=4 Moving to Node #0,0 Current State: 23:[5, 53, 35], Operations: ['40-5=35'] Exploring Operation: 53-35=18, Resulting Numbers: [5, 18] Generated Node #0,0,0: 23:[5, 18] Operation: 53-35=18 Exploring Operation: 35-5=30, Resulting Numbers: [53, 30] Generated Node #0,0,1: 23:[53, 30] Operation: 35-5=30 Exploring Operation: 53-5=48, Resulting Numbers: [35, 48] Generated Node #0,0,2: 23:[35, 48] Operation: 53-5=48 Exploring Operation: 35/5=7, Resulting Numbers: [53, 7] Generated Node #0,0,3: 23:[53, 7] Operation: 35/5=7 Moving to Node #0,3,1 Current State: 23:[13, 25], Operations: ['53-40=13', '5*5=25'] Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,23 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 13*25=325, Resulting Numbers: [325] 325,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[25, 13], Operations: ['5*5=25', '53-40=13'] Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,23 unequal: No Solution Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,23 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[40, 28], Operations: ['5*5=25', '53-25=28'] Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,23 unequal: No Solution Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[5, 18], Operations: ['53-40=13', '5+13=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,23 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[5, 40, 5, 53], Operations: [] Exploring Operation: 53-40=13, Resulting Numbers: [5, 5, 13] Generated Node #0,3: 23:[5, 5, 13] Operation: 53-40=13 Moving to Node #0,3 Current State: 23:[5, 5, 13], Operations: ['53-40=13'] Exploring Operation: 5+13=18, Resulting Numbers: [5, 18] Generated Node #0,3,2: 23:[5, 18] Operation: 5+13=18 Moving to Node #0,3,2 Current State: 23:[5, 18], Operations: ['53-40=13', '5+13=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.969618
hs_4
mult_heuristic
[ 30, 41, 61, 2 ]
35
[ "30/2=15", "61-41=20", "15+20=35" ]
Current State: 35:[30, 41, 61, 2], Operations: [] Exploring Operation: 30/2=15, Resulting Numbers: [41, 61, 15] Generated Node #2: [41, 61, 15] from Operation: 30/2=15 Current State: 35:[41, 61, 15], Operations: ['30/2=15'] Exploring Operation: 61-41=20, Resulting Numbers: [15, 20] Generated Node #3: [15, 20] from Operation: 61-41=20 Current State: 35:[15, 20], Operations: ['30/2=15', '61-41=20'] Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[30, 41, 61, 2], Operations: [] Exploring Operation: 41-30=11, Resulting Numbers: [61, 2, 11] Generated Node #0,0: 35:[61, 2, 11] Operation: 41-30=11 Exploring Operation: 61-30=31, Resulting Numbers: [41, 2, 31] Generated Node #0,1: 35:[41, 2, 31] Operation: 61-30=31 Exploring Operation: 30+2=32, Resulting Numbers: [41, 61, 32] Generated Node #0,2: 35:[41, 61, 32] Operation: 30+2=32 Exploring Operation: 61-41=20, Resulting Numbers: [30, 2, 20] Generated Node #0,3: 35:[30, 2, 20] Operation: 61-41=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[41, 2, 31], Operations: ['61-30=31'] Exploring Operation: 2+31=33, Resulting Numbers: [41, 33] Generated Node #0,1,0: 35:[41, 33] Operation: 2+31=33 Exploring Operation: 41+2=43, Resulting Numbers: [31, 43] Generated Node #0,1,1: 35:[31, 43] Operation: 41+2=43 Exploring Operation: 41-31=10, Resulting Numbers: [2, 10] Generated Node #0,1,2: 35:[2, 10] Operation: 41-31=10 Exploring Operation: 41-2=39, Resulting Numbers: [31, 39] Generated Node #0,1,3: 35:[31, 39] Operation: 41-2=39 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 35:[2, 10], Operations: ['61-30=31', '41-31=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[41, 33], Operations: ['61-30=31', '2+31=33'] Exploring Operation: 41*33=1353, Resulting Numbers: [1353] 1353,35 unequal: No Solution Exploring Operation: 41+33=74, Resulting Numbers: [74] 74,35 unequal: No Solution Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 35:[31, 39], Operations: ['61-30=31', '41-2=39'] Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 31*39=1209, Resulting Numbers: [1209] 1209,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 35:[31, 43], Operations: ['61-30=31', '41+2=43'] Exploring Operation: 31*43=1333, Resulting Numbers: [1333] 1333,35 unequal: No Solution Exploring Operation: 31+43=74, Resulting Numbers: [74] 74,35 unequal: No Solution Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 35:[30, 2, 20], Operations: ['61-41=20'] Exploring Operation: 20/2=10, Resulting Numbers: [30, 10] Generated Node #0,3,0: 35:[30, 10] Operation: 20/2=10 Exploring Operation: 30-20=10, Resulting Numbers: [2, 10] Generated Node #0,3,1: 35:[2, 10] Operation: 30-20=10 Exploring Operation: 30+2=32, Resulting Numbers: [20, 32] Generated Node #0,3,2: 35:[20, 32] Operation: 30+2=32 Exploring Operation: 2*20=40, Resulting Numbers: [30, 40] Generated Node #0,3,3: 35:[30, 40] Operation: 2*20=40 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 35:[2, 10], Operations: ['61-41=20', '30-20=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 35:[30, 10], Operations: ['61-41=20', '20/2=10'] Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,35 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 35:[30, 40], Operations: ['61-41=20', '2*20=40'] Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 35:[20, 32], Operations: ['61-41=20', '30+2=32'] Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,35 unequal: No Solution Exploring Operation: 20*32=640, Resulting Numbers: [640] 640,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[61, 2, 11], Operations: ['41-30=11'] Exploring Operation: 61-11=50, Resulting Numbers: [2, 50] Generated Node #0,0,0: 35:[2, 50] Operation: 61-11=50 Exploring Operation: 61-2=59, Resulting Numbers: [11, 59] Generated Node #0,0,1: 35:[11, 59] Operation: 61-2=59 Exploring Operation: 61+2=63, Resulting Numbers: [11, 63] Generated Node #0,0,2: 35:[11, 63] Operation: 61+2=63 Exploring Operation: 11-2=9, Resulting Numbers: [61, 9] Generated Node #0,0,3: 35:[61, 9] Operation: 11-2=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[2, 50], Operations: ['41-30=11', '61-11=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,35 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,35 unequal: No Solution Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[11, 59], Operations: ['41-30=11', '61-2=59'] Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 11*59=649, Resulting Numbers: [649] 649,35 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 35:[61, 9], Operations: ['41-30=11', '11-2=9'] Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,35 unequal: No Solution Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 35:[11, 63], Operations: ['41-30=11', '61+2=63'] Exploring Operation: 11*63=693, Resulting Numbers: [693] 693,35 unequal: No Solution Exploring Operation: 11+63=74, Resulting Numbers: [74] 74,35 unequal: No Solution Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[41, 61, 32], Operations: ['30+2=32'] Exploring Operation: 61-32=29, Resulting Numbers: [41, 29] Generated Node #0,2,0: 35:[41, 29] Operation: 61-32=29 Exploring Operation: 41+32=73, Resulting Numbers: [61, 73] Generated Node #0,2,1: 35:[61, 73] Operation: 41+32=73 Exploring Operation: 41-32=9, Resulting Numbers: [61, 9] Generated Node #0,2,2: 35:[61, 9] Operation: 41-32=9 Exploring Operation: 61-41=20, Resulting Numbers: [32, 20] Generated Node #0,2,3: 35:[32, 20] Operation: 61-41=20 Moving to Node #0,2,0 Current State: 35:[41, 29], Operations: ['30+2=32', '61-32=29'] Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 41*29=1189, Resulting Numbers: [1189] 1189,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[32, 20], Operations: ['30+2=32', '61-41=20'] Exploring Operation: 32+20=52, Resulting Numbers: [52] 52,35 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 32*20=640, Resulting Numbers: [640] 640,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[61, 9], Operations: ['30+2=32', '41-32=9'] Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,35 unequal: No Solution Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[61, 73], Operations: ['30+2=32', '41+32=73'] Exploring Operation: 61*73=4453, Resulting Numbers: [4453] 4453,35 unequal: No Solution Exploring Operation: 73-61=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 61+73=134, Resulting Numbers: [134] 134,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 44, 72, 9, 36 ]
97
[ "44*72=3168", "3168/36=88", "9+88=97" ]
Current State: 97:[44, 72, 9, 36], Operations: [] Exploring Operation: 44*72=3168, Resulting Numbers: [9, 36, 3168] Generated Node #2: [9, 36, 3168] from Operation: 44*72=3168 Current State: 97:[9, 36, 3168], Operations: ['44*72=3168'] Exploring Operation: 3168/36=88, Resulting Numbers: [9, 88] Generated Node #3: [9, 88] from Operation: 3168/36=88 Current State: 97:[9, 88], Operations: ['44*72=3168', '3168/36=88'] Exploring Operation: 9+88=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[44, 72, 9, 36], Operations: [] Exploring Operation: 44+9=53, Resulting Numbers: [72, 36, 53] Generated Node #0,0: 97:[72, 36, 53] Operation: 44+9=53 Exploring Operation: 72+9=81, Resulting Numbers: [44, 36, 81] Generated Node #0,1: 97:[44, 36, 81] Operation: 72+9=81 Exploring Operation: 9+36=45, Resulting Numbers: [44, 72, 45] Generated Node #0,2: 97:[44, 72, 45] Operation: 9+36=45 Exploring Operation: 44+36=80, Resulting Numbers: [72, 9, 80] Generated Node #0,3: 97:[72, 9, 80] Operation: 44+36=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[72, 36, 53], Operations: ['44+9=53'] Exploring Operation: 36+53=89, Resulting Numbers: [72, 89] Generated Node #0,0,0: 97:[72, 89] Operation: 36+53=89 Exploring Operation: 72+36=108, Resulting Numbers: [53, 108] Generated Node #0,0,1: 97:[53, 108] Operation: 72+36=108 Exploring Operation: 72-36=36, Resulting Numbers: [53, 36] Generated Node #0,0,2: 97:[53, 36] Operation: 72-36=36 Exploring Operation: 72+53=125, Resulting Numbers: [36, 125] Generated Node #0,0,3: 97:[36, 125] Operation: 72+53=125 Moving to Node #0,0,0 Current State: 97:[72, 89], Operations: ['44+9=53', '36+53=89'] Exploring Operation: 72*89=6408, Resulting Numbers: [6408] 6408,97 unequal: No Solution Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,97 unequal: No Solution Exploring Operation: 72+89=161, Resulting Numbers: [161] 161,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[53, 108], Operations: ['44+9=53', '72+36=108'] Exploring Operation: 53+108=161, Resulting Numbers: [161] 161,97 unequal: No Solution Exploring Operation: 108-53=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 53*108=5724, Resulting Numbers: [5724] 5724,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[36, 125], Operations: ['44+9=53', '72+53=125'] Exploring Operation: 36*125=4500, Resulting Numbers: [4500] 4500,97 unequal: No Solution Exploring Operation: 125-36=89, Resulting Numbers: [89] 89,97 unequal: No Solution Exploring Operation: 36+125=161, Resulting Numbers: [161] 161,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[53, 36], Operations: ['44+9=53', '72-36=36'] Exploring Operation: 53*36=1908, Resulting Numbers: [1908] 1908,97 unequal: No Solution Exploring Operation: 53+36=89, Resulting Numbers: [89] 89,97 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[44, 36, 81], Operations: ['72+9=81'] Exploring Operation: 44+81=125, Resulting Numbers: [36, 125] Generated Node #0,1,0: 97:[36, 125] Operation: 44+81=125 Exploring Operation: 36+81=117, Resulting Numbers: [44, 117] Generated Node #0,1,1: 97:[44, 117] Operation: 36+81=117 Exploring Operation: 44+36=80, Resulting Numbers: [81, 80] Generated Node #0,1,2: 97:[81, 80] Operation: 44+36=80 Exploring Operation: 44-36=8, Resulting Numbers: [81, 8] Generated Node #0,1,3: 97:[81, 8] Operation: 44-36=8 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 97:[81, 80], Operations: ['72+9=81', '44+36=80'] Exploring Operation: 81*80=6480, Resulting Numbers: [6480] 6480,97 unequal: No Solution Exploring Operation: 81+80=161, Resulting Numbers: [161] 161,97 unequal: No Solution Exploring Operation: 81-80=1, Resulting Numbers: [1] 1,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 97:[44, 117], Operations: ['72+9=81', '36+81=117'] Exploring Operation: 44*117=5148, Resulting Numbers: [5148] 5148,97 unequal: No Solution Exploring Operation: 117-44=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 44+117=161, Resulting Numbers: [161] 161,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[36, 125], Operations: ['72+9=81', '44+81=125'] Exploring Operation: 36+125=161, Resulting Numbers: [161] 161,97 unequal: No Solution Exploring Operation: 125-36=89, Resulting Numbers: [89] 89,97 unequal: No Solution Exploring Operation: 36*125=4500, Resulting Numbers: [4500] 4500,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 97:[81, 8], Operations: ['72+9=81', '44-36=8'] Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,97 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 81*8=648, Resulting Numbers: [648] 648,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[44, 72, 45], Operations: ['9+36=45'] Exploring Operation: 44+45=89, Resulting Numbers: [72, 89] Generated Node #0,2,0: 97:[72, 89] Operation: 44+45=89 Exploring Operation: 72+45=117, Resulting Numbers: [44, 117] Generated Node #0,2,1: 97:[44, 117] Operation: 72+45=117 Exploring Operation: 44+72=116, Resulting Numbers: [45, 116] Generated Node #0,2,2: 97:[45, 116] Operation: 44+72=116 Exploring Operation: 72-44=28, Resulting Numbers: [45, 28] Generated Node #0,2,3: 97:[45, 28] Operation: 72-44=28 Moving to Node #0,2,0 Current State: 97:[72, 89], Operations: ['9+36=45', '44+45=89'] Exploring Operation: 72*89=6408, Resulting Numbers: [6408] 6408,97 unequal: No Solution Exploring Operation: 72+89=161, Resulting Numbers: [161] 161,97 unequal: No Solution Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[45, 116], Operations: ['9+36=45', '44+72=116'] Exploring Operation: 45+116=161, Resulting Numbers: [161] 161,97 unequal: No Solution Exploring Operation: 116-45=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 45*116=5220, Resulting Numbers: [5220] 5220,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[44, 117], Operations: ['9+36=45', '72+45=117'] Exploring Operation: 117-44=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 44+117=161, Resulting Numbers: [161] 161,97 unequal: No Solution Exploring Operation: 44*117=5148, Resulting Numbers: [5148] 5148,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[45, 28], Operations: ['9+36=45', '72-44=28'] Exploring Operation: 45*28=1260, Resulting Numbers: [1260] 1260,97 unequal: No Solution Exploring Operation: 45+28=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 97:[72, 9, 80], Operations: ['44+36=80'] Exploring Operation: 9+80=89, Resulting Numbers: [72, 89] Generated Node #0,3,0: 97:[72, 89] Operation: 9+80=89 Exploring Operation: 72+9=81, Resulting Numbers: [80, 81] Generated Node #0,3,1: 97:[80, 81] Operation: 72+9=81 Exploring Operation: 80-9=71, Resulting Numbers: [72, 71] Generated Node #0,3,2: 97:[72, 71] Operation: 80-9=71 Exploring Operation: 72-9=63, Resulting Numbers: [80, 63] Generated Node #0,3,3: 97:[80, 63] Operation: 72-9=63 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 97:[72, 89], Operations: ['44+36=80', '9+80=89'] Exploring Operation: 72*89=6408, Resulting Numbers: [6408] 6408,97 unequal: No Solution Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,97 unequal: No Solution Exploring Operation: 72+89=161, Resulting Numbers: [161] 161,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 97:[80, 81], Operations: ['44+36=80', '72+9=81'] Exploring Operation: 81-80=1, Resulting Numbers: [1] 1,97 unequal: No Solution Exploring Operation: 80*81=6480, Resulting Numbers: [6480] 6480,97 unequal: No Solution Exploring Operation: 80+81=161, Resulting Numbers: [161] 161,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 97:[72, 71], Operations: ['44+36=80', '80-9=71'] Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,97 unequal: No Solution Exploring Operation: 72+71=143, Resulting Numbers: [143] 143,97 unequal: No Solution Exploring Operation: 72*71=5112, Resulting Numbers: [5112] 5112,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 97:[80, 63], Operations: ['44+36=80', '72-9=63'] Exploring Operation: 80-63=17, Resulting Numbers: [17] 17,97 unequal: No Solution Exploring Operation: 80*63=5040, Resulting Numbers: [5040] 5040,97 unequal: No Solution Exploring Operation: 80+63=143, Resulting Numbers: [143] 143,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 44, 38, 70, 14 ]
77
[ "44+38=82", "70/14=5", "82-5=77" ]
Current State: 77:[44, 38, 70, 14], Operations: [] Exploring Operation: 44+38=82, Resulting Numbers: [70, 14, 82] Generated Node #2: [70, 14, 82] from Operation: 44+38=82 Current State: 77:[70, 14, 82], Operations: ['44+38=82'] Exploring Operation: 70/14=5, Resulting Numbers: [82, 5] Generated Node #3: [82, 5] from Operation: 70/14=5 Current State: 77:[82, 5], Operations: ['44+38=82', '70/14=5'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[44, 38, 70, 14], Operations: [] Exploring Operation: 44+38=82, Resulting Numbers: [70, 14, 82] Generated Node #0,0: 77:[70, 14, 82] Operation: 44+38=82 Exploring Operation: 44-38=6, Resulting Numbers: [70, 14, 6] Generated Node #0,1: 77:[70, 14, 6] Operation: 44-38=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[70, 14, 6], Operations: ['44-38=6'] Exploring Operation: 70+6=76, Resulting Numbers: [14, 76] Generated Node #0,1,0: 77:[14, 76] Operation: 70+6=76 Exploring Operation: 70/14=5, Resulting Numbers: [6, 5] Generated Node #0,1,1: 77:[6, 5] Operation: 70/14=5 Moving to Node #0,1,1 Current State: 77:[6, 5], Operations: ['44-38=6', '70/14=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[14, 76], Operations: ['44-38=6', '70+6=76'] Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,77 unequal: No Solution Exploring Operation: 14+76=90, Resulting Numbers: [90] 90,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[70, 14, 82], Operations: ['44+38=82'] Exploring Operation: 70/14=5, Resulting Numbers: [82, 5] Generated Node #0,0,0: 77:[82, 5] Operation: 70/14=5 Exploring Operation: 82-70=12, Resulting Numbers: [14, 12] Generated Node #0,0,1: 77:[14, 12] Operation: 82-70=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[14, 12], Operations: ['44+38=82', '82-70=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,77 unequal: No Solution No 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: 77:[82, 5], Operations: ['44+38=82', '70/14=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,77 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[44, 38, 70, 14], Operations: [] Exploring Operation: 44+38=82, Resulting Numbers: [70, 14, 82] Generated Node #0,0: 77:[70, 14, 82] Operation: 44+38=82 Moving to Node #0,0 Current State: 77:[70, 14, 82], Operations: ['44+38=82'] Exploring Operation: 70/14=5, Resulting Numbers: [82, 5] Generated Node #0,0,0: 77:[82, 5] Operation: 70/14=5 Moving to Node #0,0,0 Current State: 77:[82, 5], Operations: ['44+38=82', '70/14=5'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 2, 54, 37, 88 ]
47
[ "88/2=44", "54+37=91", "91-44=47" ]
Current State: 47:[2, 54, 37, 88], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [54, 37, 44] Generated Node #2: [54, 37, 44] from Operation: 88/2=44 Current State: 47:[54, 37, 44], Operations: ['88/2=44'] Exploring Operation: 54+37=91, Resulting Numbers: [44, 91] Generated Node #3: [44, 91] from Operation: 54+37=91 Current State: 47:[44, 91], Operations: ['88/2=44', '54+37=91'] Exploring Operation: 91-44=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[2, 54, 37, 88], Operations: [] Exploring Operation: 2+37=39, Resulting Numbers: [54, 88, 39] Generated Node #0,0: 47:[54, 88, 39] Operation: 2+37=39 Exploring Operation: 54-2=52, Resulting Numbers: [37, 88, 52] Generated Node #0,1: 47:[37, 88, 52] Operation: 54-2=52 Exploring Operation: 88/2=44, Resulting Numbers: [54, 37, 44] Generated Node #0,2: 47:[54, 37, 44] Operation: 88/2=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[54, 37, 44], Operations: ['88/2=44'] Exploring Operation: 54-37=17, Resulting Numbers: [44, 17] Generated Node #0,2,0: 47:[44, 17] Operation: 54-37=17 Exploring Operation: 37+44=81, Resulting Numbers: [54, 81] Generated Node #0,2,1: 47:[54, 81] Operation: 37+44=81 Exploring Operation: 54+37=91, Resulting Numbers: [44, 91] Generated Node #0,2,2: 47:[44, 91] Operation: 54+37=91 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 47:[44, 17], Operations: ['88/2=44', '54-37=17'] Exploring Operation: 44+17=61, Resulting Numbers: [61] 61,47 unequal: No Solution Exploring Operation: 44*17=748, Resulting Numbers: [748] 748,47 unequal: No Solution Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 47:[54, 81], Operations: ['88/2=44', '37+44=81'] Exploring Operation: 81-54=27, Resulting Numbers: [27] 27,47 unequal: No Solution Exploring Operation: 54*81=4374, Resulting Numbers: [4374] 4374,47 unequal: No Solution Exploring Operation: 54+81=135, Resulting Numbers: [135] 135,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 47:[44, 91], Operations: ['88/2=44', '54+37=91'] Exploring Operation: 44+91=135, Resulting Numbers: [135] 135,47 unequal: No Solution Exploring Operation: 91-44=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[2, 54, 37, 88], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [54, 37, 44] Generated Node #0,2: 47:[54, 37, 44] Operation: 88/2=44 Moving to Node #0,2 Current State: 47:[54, 37, 44], Operations: ['88/2=44'] Exploring Operation: 54+37=91, Resulting Numbers: [44, 91] Generated Node #0,2,2: 47:[44, 91] Operation: 54+37=91 Moving to Node #0,2,2 Current State: 47:[44, 91], Operations: ['88/2=44', '54+37=91'] Exploring Operation: 91-44=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 90, 45, 3, 18 ]
30
[ "90-45=45", "18-3=15", "45-15=30" ]
Current State: 30:[90, 45, 3, 18], Operations: [] Exploring Operation: 90-45=45, Resulting Numbers: [3, 18, 45] Generated Node #2: [3, 18, 45] from Operation: 90-45=45 Current State: 30:[3, 18, 45], Operations: ['90-45=45'] Exploring Operation: 18-3=15, Resulting Numbers: [45, 15] Generated Node #3: [45, 15] from Operation: 18-3=15 Current State: 30:[45, 15], Operations: ['90-45=45', '18-3=15'] Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[90, 45, 3, 18], Operations: [] Exploring Operation: 90/45=2, Resulting Numbers: [3, 18, 2] Generated Node #0,0: 30:[3, 18, 2] Operation: 90/45=2 Exploring Operation: 90/18=5, Resulting Numbers: [45, 3, 5] Generated Node #0,1: 30:[45, 3, 5] Operation: 90/18=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[3, 18, 2], Operations: ['90/45=2'] Exploring Operation: 18-3=15, Resulting Numbers: [2, 15] Generated Node #0,0,0: 30:[2, 15] Operation: 18-3=15 Exploring Operation: 18/3=6, Resulting Numbers: [2, 6] Generated Node #0,0,1: 30:[2, 6] Operation: 18/3=6 Moving to Node #0,0,0 Current State: 30:[2, 15], Operations: ['90/45=2', '18-3=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[90, 45, 3, 18], Operations: [] Exploring Operation: 90/45=2, Resulting Numbers: [3, 18, 2] Generated Node #0,0: 30:[3, 18, 2] Operation: 90/45=2 Moving to Node #0,0 Current State: 30:[3, 18, 2], Operations: ['90/45=2'] Exploring Operation: 18-3=15, Resulting Numbers: [2, 15] Generated Node #0,0,0: 30:[2, 15] Operation: 18-3=15 Moving to Node #0,0,0 Current State: 30:[2, 15], Operations: ['90/45=2', '18-3=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 98, 38, 12, 4 ]
63
[ "98-38=60", "12/4=3", "60+3=63" ]
Current State: 63:[98, 38, 12, 4], Operations: [] Exploring Operation: 98-38=60, Resulting Numbers: [12, 4, 60] Generated Node #2: [12, 4, 60] from Operation: 98-38=60 Current State: 63:[12, 4, 60], Operations: ['98-38=60'] Exploring Operation: 12/4=3, Resulting Numbers: [60, 3] Generated Node #3: [60, 3] from Operation: 12/4=3 Current State: 63:[60, 3], Operations: ['98-38=60', '12/4=3'] Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[98, 38, 12, 4], Operations: [] Exploring Operation: 38+12=50, Resulting Numbers: [98, 4, 50] Generated Node #0,0: 63:[98, 4, 50] Operation: 38+12=50 Exploring Operation: 38-12=26, Resulting Numbers: [98, 4, 26] Generated Node #0,1: 63:[98, 4, 26] Operation: 38-12=26 Exploring Operation: 98-12=86, Resulting Numbers: [38, 4, 86] Generated Node #0,2: 63:[38, 4, 86] Operation: 98-12=86 Exploring Operation: 98-38=60, Resulting Numbers: [12, 4, 60] Generated Node #0,3: 63:[12, 4, 60] Operation: 98-38=60 Exploring Operation: 98-4=94, Resulting Numbers: [38, 12, 94] Generated Node #0,4: 63:[38, 12, 94] Operation: 98-4=94 Start Sub Search at level 1: Moving to Node #0,3 Current State: 63:[12, 4, 60], Operations: ['98-38=60'] Exploring Operation: 12-4=8, Resulting Numbers: [60, 8] Generated Node #0,3,0: 63:[60, 8] Operation: 12-4=8 Exploring Operation: 60/12=5, Resulting Numbers: [4, 5] Generated Node #0,3,1: 63:[4, 5] Operation: 60/12=5 Exploring Operation: 12/4=3, Resulting Numbers: [60, 3] Generated Node #0,3,2: 63:[60, 3] Operation: 12/4=3 Exploring Operation: 12+4=16, Resulting Numbers: [60, 16] Generated Node #0,3,3: 63:[60, 16] Operation: 12+4=16 Exploring Operation: 4+60=64, Resulting Numbers: [12, 64] Generated Node #0,3,4: 63:[12, 64] Operation: 4+60=64 Moving to Node #0,3,1 Current State: 63:[4, 5], Operations: ['98-38=60', '60/12=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,63 unequal: No Solution Moving to Node #0,3,2 Current State: 63:[60, 3], Operations: ['98-38=60', '12/4=3'] Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,63 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[98, 38, 12, 4], Operations: [] Exploring Operation: 98-38=60, Resulting Numbers: [12, 4, 60] Generated Node #0,3: 63:[12, 4, 60] Operation: 98-38=60 Moving to Node #0,3 Current State: 63:[12, 4, 60], Operations: ['98-38=60'] Exploring Operation: 12/4=3, Resulting Numbers: [60, 3] Generated Node #0,3,2: 63:[60, 3] Operation: 12/4=3 Moving to Node #0,3,2 Current State: 63:[60, 3], Operations: ['98-38=60', '12/4=3'] Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 1, 19, 29, 21 ]
68
[ "19-1=18", "29+21=50", "18+50=68" ]
Current State: 68:[1, 19, 29, 21], Operations: [] Exploring Operation: 19-1=18, Resulting Numbers: [29, 21, 18] Generated Node #2: [29, 21, 18] from Operation: 19-1=18 Current State: 68:[29, 21, 18], Operations: ['19-1=18'] Exploring Operation: 29+21=50, Resulting Numbers: [18, 50] Generated Node #3: [18, 50] from Operation: 29+21=50 Current State: 68:[18, 50], Operations: ['19-1=18', '29+21=50'] Exploring Operation: 18+50=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[1, 19, 29, 21], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [1, 19, 8] Generated Node #0,0: 68:[1, 19, 8] Operation: 29-21=8 Exploring Operation: 21-19=2, Resulting Numbers: [1, 29, 2] Generated Node #0,1: 68:[1, 29, 2] Operation: 21-19=2 Moving to Node #0,1 Current State: 68:[1, 29, 2], Operations: ['21-19=2'] Exploring Operation: 1+29=30, Resulting Numbers: [2, 30] Generated Node #0,1,0: 68:[2, 30] Operation: 1+29=30 Exploring Operation: 29+2=31, Resulting Numbers: [1, 31] Generated Node #0,1,1: 68:[1, 31] Operation: 29+2=31 Moving to Node #0,0 Current State: 68:[1, 19, 8], Operations: ['29-21=8'] Exploring Operation: 19-1=18, Resulting Numbers: [8, 18] Generated Node #0,0,0: 68:[8, 18] Operation: 19-1=18 Exploring Operation: 8-1=7, Resulting Numbers: [19, 7] Generated Node #0,0,1: 68:[19, 7] Operation: 8-1=7 Moving to Node #0,1,0 Current State: 68:[2, 30], Operations: ['21-19=2', '1+29=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,68 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[1, 31], Operations: ['21-19=2', '29+2=31'] Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,68 unequal: No Solution Exploring Operation: 1+31=32, Resulting Numbers: [32] 32,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[19, 7], Operations: ['29-21=8', '8-1=7'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[8, 18], Operations: ['29-21=8', '19-1=18'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,68 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 4, 67, 20, 38 ]
65
[ "4*38=152", "67+20=87", "152-87=65" ]
Current State: 65:[4, 67, 20, 38], Operations: [] Exploring Operation: 4*38=152, Resulting Numbers: [67, 20, 152] Generated Node #2: [67, 20, 152] from Operation: 4*38=152 Current State: 65:[67, 20, 152], Operations: ['4*38=152'] Exploring Operation: 67+20=87, Resulting Numbers: [152, 87] Generated Node #3: [152, 87] from Operation: 67+20=87 Current State: 65:[152, 87], Operations: ['4*38=152', '67+20=87'] Exploring Operation: 152-87=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[4, 67, 20, 38], Operations: [] Exploring Operation: 38-20=18, Resulting Numbers: [4, 67, 18] Generated Node #0,0: 65:[4, 67, 18] Operation: 38-20=18 Exploring Operation: 67-38=29, Resulting Numbers: [4, 20, 29] Generated Node #0,1: 65:[4, 20, 29] Operation: 67-38=29 Exploring Operation: 20/4=5, Resulting Numbers: [67, 38, 5] Generated Node #0,2: 65:[67, 38, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [67, 38, 16] Generated Node #0,3: 65:[67, 38, 16] Operation: 20-4=16 Exploring Operation: 20+38=58, Resulting Numbers: [4, 67, 58] Generated Node #0,4: 65:[4, 67, 58] Operation: 20+38=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[4, 67, 18], Operations: ['38-20=18'] Exploring Operation: 4+67=71, Resulting Numbers: [18, 71] Generated Node #0,0,0: 65:[18, 71] Operation: 4+67=71 Exploring Operation: 67-4=63, Resulting Numbers: [18, 63] Generated Node #0,0,1: 65:[18, 63] Operation: 67-4=63 Exploring Operation: 18-4=14, Resulting Numbers: [67, 14] Generated Node #0,0,2: 65:[67, 14] Operation: 18-4=14 Exploring Operation: 4*18=72, Resulting Numbers: [67, 72] Generated Node #0,0,3: 65:[67, 72] Operation: 4*18=72 Exploring Operation: 4+18=22, Resulting Numbers: [67, 22] Generated Node #0,0,4: 65:[67, 22] Operation: 4+18=22 Moving to Node #0,0,2 Current State: 65:[67, 14], Operations: ['38-20=18', '18-4=14'] Exploring Operation: 67*14=938, Resulting Numbers: [938] 938,65 unequal: No Solution Exploring Operation: 67+14=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[18, 63], Operations: ['38-20=18', '67-4=63'] Exploring Operation: 18*63=1134, Resulting Numbers: [1134] 1134,65 unequal: No Solution Exploring Operation: 18+63=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[67, 72], Operations: ['38-20=18', '4*18=72'] Exploring Operation: 72-67=5, Resulting Numbers: [5] 5,65 unequal: No Solution Exploring Operation: 67*72=4824, Resulting Numbers: [4824] 4824,65 unequal: No Solution Exploring Operation: 67+72=139, Resulting Numbers: [139] 139,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[18, 71], Operations: ['38-20=18', '4+67=71'] Exploring Operation: 18+71=89, Resulting Numbers: [89] 89,65 unequal: No Solution Exploring Operation: 18*71=1278, Resulting Numbers: [1278] 1278,65 unequal: No Solution Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,65 unequal: No Solution Moving to Node #0,0,4 Current State: 65:[67, 22], Operations: ['38-20=18', '4+18=22'] Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,65 unequal: No Solution Exploring Operation: 67*22=1474, Resulting Numbers: [1474] 1474,65 unequal: No Solution Exploring Operation: 67+22=89, Resulting Numbers: [89] 89,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 65:[4, 67, 58], Operations: ['20+38=58'] Exploring Operation: 4+58=62, Resulting Numbers: [67, 62] Generated Node #0,4,0: 65:[67, 62] Operation: 4+58=62 Exploring Operation: 4+67=71, Resulting Numbers: [58, 71] Generated Node #0,4,1: 65:[58, 71] Operation: 4+67=71 Exploring Operation: 67-58=9, Resulting Numbers: [4, 9] Generated Node #0,4,2: 65:[4, 9] Operation: 67-58=9 Exploring Operation: 67-4=63, Resulting Numbers: [58, 63] Generated Node #0,4,3: 65:[58, 63] Operation: 67-4=63 Exploring Operation: 58-4=54, Resulting Numbers: [67, 54] Generated Node #0,4,4: 65:[67, 54] Operation: 58-4=54 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 65:[67, 62], Operations: ['20+38=58', '4+58=62'] Exploring Operation: 67*62=4154, Resulting Numbers: [4154] 4154,65 unequal: No Solution Exploring Operation: 67+62=129, Resulting Numbers: [129] 129,65 unequal: No Solution Exploring Operation: 67-62=5, Resulting Numbers: [5] 5,65 unequal: No Solution No 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: 65:[4, 9], Operations: ['20+38=58', '67-58=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,65 unequal: No Solution No 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: 65:[58, 63], Operations: ['20+38=58', '67-4=63'] Exploring Operation: 58+63=121, Resulting Numbers: [121] 121,65 unequal: No Solution Exploring Operation: 58*63=3654, Resulting Numbers: [3654] 3654,65 unequal: No Solution Exploring Operation: 63-58=5, Resulting Numbers: [5] 5,65 unequal: No Solution No 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: 65:[58, 71], Operations: ['20+38=58', '4+67=71'] Exploring Operation: 71-58=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 58+71=129, Resulting Numbers: [129] 129,65 unequal: No Solution Exploring Operation: 58*71=4118, Resulting Numbers: [4118] 4118,65 unequal: No Solution No 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: 65:[67, 54], Operations: ['20+38=58', '58-4=54'] Exploring Operation: 67*54=3618, Resulting Numbers: [3618] 3618,65 unequal: No Solution Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 67+54=121, Resulting Numbers: [121] 121,65 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: 65:[4, 20, 29], Operations: ['67-38=29'] Exploring Operation: 29-4=25, Resulting Numbers: [20, 25] Generated Node #0,1,0: 65:[20, 25] Operation: 29-4=25 Exploring Operation: 20-4=16, Resulting Numbers: [29, 16] Generated Node #0,1,1: 65:[29, 16] Operation: 20-4=16 Exploring Operation: 20+29=49, Resulting Numbers: [4, 49] Generated Node #0,1,2: 65:[4, 49] Operation: 20+29=49 Exploring Operation: 20/4=5, Resulting Numbers: [29, 5] Generated Node #0,1,3: 65:[29, 5] Operation: 20/4=5 Exploring Operation: 29-20=9, Resulting Numbers: [4, 9] Generated Node #0,1,4: 65:[4, 9] Operation: 29-20=9 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 65:[4, 9], Operations: ['67-38=29', '29-20=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,65 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,65 unequal: No Solution No 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: 65:[29, 5], Operations: ['67-38=29', '20/4=5'] Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,65 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,65 unequal: No Solution No 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: 65:[4, 49], Operations: ['67-38=29', '20+29=49'] Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,65 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,65 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,65 unequal: No Solution No 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: 65:[20, 25], Operations: ['67-38=29', '29-4=25'] Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,65 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,65 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,65 unequal: No Solution No 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: 65:[29, 16], Operations: ['67-38=29', '20-4=16'] Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,65 unequal: No Solution Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,65 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,65 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: 65:[67, 38, 5], Operations: ['20/4=5'] Exploring Operation: 38-5=33, Resulting Numbers: [67, 33] Generated Node #0,2,0: 65:[67, 33] Operation: 38-5=33 Exploring Operation: 67-38=29, Resulting Numbers: [5, 29] Generated Node #0,2,1: 65:[5, 29] Operation: 67-38=29 Exploring Operation: 67+5=72, Resulting Numbers: [38, 72] Generated Node #0,2,2: 65:[38, 72] Operation: 67+5=72 Exploring Operation: 38+5=43, Resulting Numbers: [67, 43] Generated Node #0,2,3: 65:[67, 43] Operation: 38+5=43 Exploring Operation: 67-5=62, Resulting Numbers: [38, 62] Generated Node #0,2,4: 65:[38, 62] Operation: 67-5=62 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 65:[5, 29], Operations: ['20/4=5', '67-38=29'] Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,65 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,65 unequal: No Solution No 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: 65:[67, 33], Operations: ['20/4=5', '38-5=33'] Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 67*33=2211, Resulting Numbers: [2211] 2211,65 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,65 unequal: No Solution No 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: 65:[67, 43], Operations: ['20/4=5', '38+5=43'] Exploring Operation: 67*43=2881, Resulting Numbers: [2881] 2881,65 unequal: No Solution Exploring Operation: 67+43=110, Resulting Numbers: [110] 110,65 unequal: No Solution Exploring Operation: 67-43=24, Resulting Numbers: [24] 24,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 65:[38, 62], Operations: ['20/4=5', '67-5=62'] Exploring Operation: 62-38=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 38+62=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 38*62=2356, Resulting Numbers: [2356] 2356,65 unequal: No Solution No 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: 65:[38, 72], Operations: ['20/4=5', '67+5=72'] Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 38*72=2736, Resulting Numbers: [2736] 2736,65 unequal: No Solution Exploring Operation: 38+72=110, Resulting Numbers: [110] 110,65 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: 65:[67, 38, 16], Operations: ['20-4=16'] Exploring Operation: 67+38=105, Resulting Numbers: [16, 105] Generated Node #0,3,0: 65:[16, 105] Operation: 67+38=105 Exploring Operation: 67-16=51, Resulting Numbers: [38, 51] Generated Node #0,3,1: 65:[38, 51] Operation: 67-16=51 Exploring Operation: 38+16=54, Resulting Numbers: [67, 54] Generated Node #0,3,2: 65:[67, 54] Operation: 38+16=54 Exploring Operation: 67-38=29, Resulting Numbers: [16, 29] Generated Node #0,3,3: 65:[16, 29] Operation: 67-38=29 Exploring Operation: 38-16=22, Resulting Numbers: [67, 22] Generated Node #0,3,4: 65:[67, 22] Operation: 38-16=22 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 65:[67, 22], Operations: ['20-4=16', '38-16=22'] Exploring Operation: 67+22=89, Resulting Numbers: [89] 89,65 unequal: No Solution Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,65 unequal: No Solution Exploring Operation: 67*22=1474, Resulting Numbers: [1474] 1474,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 65:[67, 54], Operations: ['20-4=16', '38+16=54'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 67+54=121, Resulting Numbers: [121] 121,65 unequal: No Solution Exploring Operation: 67*54=3618, Resulting Numbers: [3618] 3618,65 unequal: No Solution No 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: 65:[16, 29], Operations: ['20-4=16', '67-38=29'] Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,65 unequal: No Solution Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,65 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,65 unequal: No Solution No 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: 65:[38, 51], Operations: ['20-4=16', '67-16=51'] Exploring Operation: 38*51=1938, Resulting Numbers: [1938] 1938,65 unequal: No Solution Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 38+51=89, Resulting Numbers: [89] 89,65 unequal: No Solution No 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: 65:[16, 105], Operations: ['20-4=16', '67+38=105'] Exploring Operation: 16+105=121, Resulting Numbers: [121] 121,65 unequal: No Solution Exploring Operation: 105-16=89, Resulting Numbers: [89] 89,65 unequal: No Solution Exploring Operation: 16*105=1680, Resulting Numbers: [1680] 1680,65 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
[ 50, 72, 79, 1 ]
45
[ "50*72=3600", "79+1=80", "3600/80=45" ]
Current State: 45:[50, 72, 79, 1], Operations: [] Exploring Operation: 50*72=3600, Resulting Numbers: [79, 1, 3600] Generated Node #2: [79, 1, 3600] from Operation: 50*72=3600 Current State: 45:[79, 1, 3600], Operations: ['50*72=3600'] Exploring Operation: 79+1=80, Resulting Numbers: [3600, 80] Generated Node #3: [3600, 80] from Operation: 79+1=80 Current State: 45:[3600, 80], Operations: ['50*72=3600', '79+1=80'] Exploring Operation: 3600/80=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[50, 72, 79, 1], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [79, 1, 22] Generated Node #0,0: 45:[79, 1, 22] Operation: 72-50=22 Exploring Operation: 72-1=71, Resulting Numbers: [50, 79, 71] Generated Node #0,1: 45:[50, 79, 71] Operation: 72-1=71 Exploring Operation: 79-72=7, Resulting Numbers: [50, 1, 7] Generated Node #0,2: 45:[50, 1, 7] Operation: 79-72=7 Exploring Operation: 79-50=29, Resulting Numbers: [72, 1, 29] Generated Node #0,3: 45:[72, 1, 29] Operation: 79-50=29 Exploring Operation: 50-1=49, Resulting Numbers: [72, 79, 49] Generated Node #0,4: 45:[72, 79, 49] Operation: 50-1=49 Moving to Node #0,2 Current State: 45:[50, 1, 7], Operations: ['79-72=7'] Exploring Operation: 7-1=6, Resulting Numbers: [50, 6] Generated Node #0,2,0: 45:[50, 6] Operation: 7-1=6 Exploring Operation: 50-1=49, Resulting Numbers: [7, 49] Generated Node #0,2,1: 45:[7, 49] Operation: 50-1=49 Exploring Operation: 50*1=50, Resulting Numbers: [7, 50] Generated Node #0,2,2: 45:[7, 50] Operation: 50*1=50 Exploring Operation: 50-7=43, Resulting Numbers: [1, 43] Generated Node #0,2,3: 45:[1, 43] Operation: 50-7=43 Exploring Operation: 1+7=8, Resulting Numbers: [50, 8] Generated Node #0,2,4: 45:[50, 8] Operation: 1+7=8 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 45:[1, 43], Operations: ['79-72=7', '50-7=43'] Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,45 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 1+43=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,45 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:[50, 6], Operations: ['79-72=7', '7-1=6'] Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,45 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:[7, 49], Operations: ['79-72=7', '50-1=49'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,45 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 #0,2,4 Current State: 45:[50, 8], Operations: ['79-72=7', '1+7=8'] Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 50*8=400, Resulting Numbers: [400] 400,45 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,45 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:[7, 50], Operations: ['79-72=7', '50*1=50'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,45 unequal: No Solution Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,45 unequal: No Solution Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,45 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:[72, 1, 29], Operations: ['79-50=29'] Exploring Operation: 72/1=72, Resulting Numbers: [29, 72] Generated Node #0,3,0: 45:[29, 72] Operation: 72/1=72 Exploring Operation: 72-1=71, Resulting Numbers: [29, 71] Generated Node #0,3,1: 45:[29, 71] Operation: 72-1=71 Exploring Operation: 72*1=72, Resulting Numbers: [29, 72] Generated Node #0,3,2: 45:[29, 72] Operation: 72*1=72 Exploring Operation: 29-1=28, Resulting Numbers: [72, 28] Generated Node #0,3,3: 45:[72, 28] Operation: 29-1=28 Exploring Operation: 72-29=43, Resulting Numbers: [1, 43] Generated Node #0,3,4: 45:[1, 43] Operation: 72-29=43 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 45:[1, 43], Operations: ['79-50=29', '72-29=43'] Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,45 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 1+43=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,45 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 #0,3,1 Current State: 45:[29, 71], Operations: ['79-50=29', '72-1=71'] Exploring Operation: 29+71=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 29*71=2059, Resulting Numbers: [2059] 2059,45 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 #0,3,3 Current State: 45:[72, 28], Operations: ['79-50=29', '29-1=28'] Exploring Operation: 72+28=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 72*28=2016, Resulting Numbers: [2016] 2016,45 unequal: No Solution Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,45 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 #0,3,0 Current State: 45:[29, 72], Operations: ['79-50=29', '72/1=72'] Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,45 unequal: No Solution Exploring Operation: 29+72=101, Resulting Numbers: [101] 101,45 unequal: No Solution Exploring Operation: 29*72=2088, Resulting Numbers: [2088] 2088,45 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 #0,3,2 Current State: 45:[29, 72], Operations: ['79-50=29', '72*1=72'] Exploring Operation: 29*72=2088, Resulting Numbers: [2088] 2088,45 unequal: No Solution Exploring Operation: 29+72=101, Resulting Numbers: [101] 101,45 unequal: No Solution Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,45 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: 45:[79, 1, 22], Operations: ['72-50=22'] Exploring Operation: 79/1=79, Resulting Numbers: [22, 79] Generated Node #0,0,0: 45:[22, 79] Operation: 79/1=79 Exploring Operation: 22-1=21, Resulting Numbers: [79, 21] Generated Node #0,0,1: 45:[79, 21] Operation: 22-1=21 Exploring Operation: 79*1=79, Resulting Numbers: [22, 79] Generated Node #0,0,2: 45:[22, 79] Operation: 79*1=79 Exploring Operation: 79-1=78, Resulting Numbers: [22, 78] Generated Node #0,0,3: 45:[22, 78] Operation: 79-1=78 Exploring Operation: 79-22=57, Resulting Numbers: [1, 57] Generated Node #0,0,4: 45:[1, 57] Operation: 79-22=57 Moving to Node #0,1 Current State: 45:[50, 79, 71], Operations: ['72-1=71'] Exploring Operation: 50+71=121, Resulting Numbers: [79, 121] Generated Node #0,1,0: 45:[79, 121] Operation: 50+71=121 Exploring Operation: 50+79=129, Resulting Numbers: [71, 129] Generated Node #0,1,1: 45:[71, 129] Operation: 50+79=129 Exploring Operation: 71-50=21, Resulting Numbers: [79, 21] Generated Node #0,1,2: 45:[79, 21] Operation: 71-50=21 Exploring Operation: 79-71=8, Resulting Numbers: [50, 8] Generated Node #0,1,3: 45:[50, 8] Operation: 79-71=8 Exploring Operation: 79-50=29, Resulting Numbers: [71, 29] Generated Node #0,1,4: 45:[71, 29] Operation: 79-50=29 Moving to Node #0,4 Current State: 45:[72, 79, 49], Operations: ['50-1=49'] Exploring Operation: 72-49=23, Resulting Numbers: [79, 23] Generated Node #0,4,0: 45:[79, 23] Operation: 72-49=23 Exploring Operation: 79-72=7, Resulting Numbers: [49, 7] Generated Node #0,4,1: 45:[49, 7] Operation: 79-72=7 Exploring Operation: 72+79=151, Resulting Numbers: [49, 151] Generated Node #0,4,2: 45:[49, 151] Operation: 72+79=151 Exploring Operation: 79-49=30, Resulting Numbers: [72, 30] Generated Node #0,4,3: 45:[72, 30] Operation: 79-49=30 Exploring Operation: 72+49=121, Resulting Numbers: [79, 121] Generated Node #0,4,4: 45:[79, 121] Operation: 72+49=121 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 45:[49, 7], Operations: ['50-1=49', '79-72=7'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,45 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,45 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 #0,4,0 Current State: 45:[79, 23], Operations: ['50-1=49', '72-49=23'] Exploring Operation: 79+23=102, Resulting Numbers: [102] 102,45 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 79*23=1817, Resulting Numbers: [1817] 1817,45 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 #0,4,3 Current State: 45:[72, 30], Operations: ['50-1=49', '79-49=30'] Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,45 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,45 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 #0,4,2 Current State: 45:[49, 151], Operations: ['50-1=49', '72+79=151'] Exploring Operation: 151-49=102, Resulting Numbers: [102] 102,45 unequal: No Solution Exploring Operation: 49*151=7399, Resulting Numbers: [7399] 7399,45 unequal: No Solution Exploring Operation: 49+151=200, Resulting Numbers: [200] 200,45 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 #0,4,4 Current State: 45:[79, 121], Operations: ['50-1=49', '72+49=121'] Exploring Operation: 79+121=200, Resulting Numbers: [200] 200,45 unequal: No Solution Exploring Operation: 79*121=9559, Resulting Numbers: [9559] 9559,45 unequal: No Solution Exploring Operation: 121-79=42, Resulting Numbers: [42] 42,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 45:[50, 8], Operations: ['72-1=71', '79-71=8'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 50*8=400, Resulting Numbers: [400] 400,45 unequal: No Solution Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,45 unequal: No Solution Moving to Node #0,0,4 Current State: 45:[1, 57], Operations: ['72-50=22', '79-22=57'] Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[79, 21], Operations: ['72-1=71', '71-50=21'] Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 79*21=1659, Resulting Numbers: [1659] 1659,45 unequal: No Solution Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[22, 78], Operations: ['72-50=22', '79-1=78'] Exploring Operation: 22*78=1716, Resulting Numbers: [1716] 1716,45 unequal: No Solution Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 22+78=100, Resulting Numbers: [100] 100,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[79, 21], Operations: ['72-50=22', '22-1=21'] Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 79*21=1659, Resulting Numbers: [1659] 1659,45 unequal: No Solution Moving to Node #0,1,4 Current State: 45:[71, 29], Operations: ['72-1=71', '79-50=29'] Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,45 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[22, 79], Operations: ['72-50=22', '79/1=79'] Exploring Operation: 22+79=101, Resulting Numbers: [101] 101,45 unequal: No Solution Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 22*79=1738, Resulting Numbers: [1738] 1738,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[22, 79], Operations: ['72-50=22', '79*1=79'] Exploring Operation: 22*79=1738, Resulting Numbers: [1738] 1738,45 unequal: No Solution Exploring Operation: 22+79=101, Resulting Numbers: [101] 101,45 unequal: No Solution Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[71, 129], Operations: ['72-1=71', '50+79=129'] Exploring Operation: 71+129=200, Resulting Numbers: [200] 200,45 unequal: No Solution Exploring Operation: 71*129=9159, Resulting Numbers: [9159] 9159,45 unequal: No Solution Exploring Operation: 129-71=58, Resulting Numbers: [58] 58,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[79, 121], Operations: ['72-1=71', '50+71=121'] Exploring Operation: 121-79=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 79+121=200, Resulting Numbers: [200] 200,45 unequal: No Solution Exploring Operation: 79*121=9559, Resulting Numbers: [9559] 9559,45 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 25, 46, 28, 31 ]
74
[ "25+46=71", "31-28=3", "71+3=74" ]
Current State: 74:[25, 46, 28, 31], Operations: [] Exploring Operation: 25+46=71, Resulting Numbers: [28, 31, 71] Generated Node #2: [28, 31, 71] from Operation: 25+46=71 Current State: 74:[28, 31, 71], Operations: ['25+46=71'] Exploring Operation: 31-28=3, Resulting Numbers: [71, 3] Generated Node #3: [71, 3] from Operation: 31-28=3 Current State: 74:[71, 3], Operations: ['25+46=71', '31-28=3'] Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[25, 46, 28, 31], Operations: [] Exploring Operation: 46+28=74, Resulting Numbers: [25, 31, 74] Generated Node #0,0: 74:[25, 31, 74] Operation: 46+28=74 Exploring Operation: 25+46=71, Resulting Numbers: [28, 31, 71] Generated Node #0,1: 74:[28, 31, 71] Operation: 25+46=71 Exploring Operation: 28-25=3, Resulting Numbers: [46, 31, 3] Generated Node #0,2: 74:[46, 31, 3] Operation: 28-25=3 Exploring Operation: 31-25=6, Resulting Numbers: [46, 28, 6] Generated Node #0,3: 74:[46, 28, 6] Operation: 31-25=6 Exploring Operation: 31-28=3, Resulting Numbers: [25, 46, 3] Generated Node #0,4: 74:[25, 46, 3] Operation: 31-28=3 Moving to Node #0,2 Current State: 74:[46, 31, 3], Operations: ['28-25=3'] Exploring Operation: 31+3=34, Resulting Numbers: [46, 34] Generated Node #0,2,0: 74:[46, 34] Operation: 31+3=34 Exploring Operation: 46+31=77, Resulting Numbers: [3, 77] Generated Node #0,2,1: 74:[3, 77] Operation: 46+31=77 Exploring Operation: 46+3=49, Resulting Numbers: [31, 49] Generated Node #0,2,2: 74:[31, 49] Operation: 46+3=49 Exploring Operation: 46-31=15, Resulting Numbers: [3, 15] Generated Node #0,2,3: 74:[3, 15] Operation: 46-31=15 Exploring Operation: 46-3=43, Resulting Numbers: [31, 43] Generated Node #0,2,4: 74:[31, 43] Operation: 46-3=43 Moving to Node #0,1 Current State: 74:[28, 31, 71], Operations: ['25+46=71'] Exploring Operation: 31-28=3, Resulting Numbers: [71, 3] Generated Node #0,1,0: 74:[71, 3] Operation: 31-28=3 Exploring Operation: 71-28=43, Resulting Numbers: [31, 43] Generated Node #0,1,1: 74:[31, 43] Operation: 71-28=43 Exploring Operation: 71-31=40, Resulting Numbers: [28, 40] Generated Node #0,1,2: 74:[28, 40] Operation: 71-31=40 Exploring Operation: 28+31=59, Resulting Numbers: [71, 59] Generated Node #0,1,3: 74:[71, 59] Operation: 28+31=59 Exploring Operation: 28+71=99, Resulting Numbers: [31, 99] Generated Node #0,1,4: 74:[31, 99] Operation: 28+71=99 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[71, 3], Operations: ['25+46=71', '31-28=3'] Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[25, 46, 28, 31], Operations: [] Exploring Operation: 25+46=71, Resulting Numbers: [28, 31, 71] Generated Node #0,1: 74:[28, 31, 71] Operation: 25+46=71 Moving to Node #0,1 Current State: 74:[28, 31, 71], Operations: ['25+46=71'] Exploring Operation: 31-28=3, Resulting Numbers: [71, 3] Generated Node #0,1,0: 74:[71, 3] Operation: 31-28=3 Moving to Node #0,1,0 Current State: 74:[71, 3], Operations: ['25+46=71', '31-28=3'] Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 6, 8, 20, 51 ]
60
[ "6*8=48", "51-48=3", "20*3=60" ]
Current State: 60:[6, 8, 20, 51], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [20, 51, 48] Generated Node #2: [20, 51, 48] from Operation: 6*8=48 Current State: 60:[20, 51, 48], Operations: ['6*8=48'] Exploring Operation: 51-48=3, Resulting Numbers: [20, 3] Generated Node #3: [20, 3] from Operation: 51-48=3 Current State: 60:[20, 3], Operations: ['6*8=48', '51-48=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[6, 8, 20, 51], Operations: [] Exploring Operation: 8+51=59, Resulting Numbers: [6, 20, 59] Generated Node #0,0: 60:[6, 20, 59] Operation: 8+51=59 Exploring Operation: 6+51=57, Resulting Numbers: [8, 20, 57] Generated Node #0,1: 60:[8, 20, 57] Operation: 6+51=57 Exploring Operation: 8-6=2, Resulting Numbers: [20, 51, 2] Generated Node #0,2: 60:[20, 51, 2] Operation: 8-6=2 Exploring Operation: 51-20=31, Resulting Numbers: [6, 8, 31] Generated Node #0,3: 60:[6, 8, 31] Operation: 51-20=31 Moving to Node #0,0 Current State: 60:[6, 20, 59], Operations: ['8+51=59'] Exploring Operation: 6+20=26, Resulting Numbers: [59, 26] Generated Node #0,0,0: 60:[59, 26] Operation: 6+20=26 Exploring Operation: 20-6=14, Resulting Numbers: [59, 14] Generated Node #0,0,1: 60:[59, 14] Operation: 20-6=14 Exploring Operation: 6+59=65, Resulting Numbers: [20, 65] Generated Node #0,0,2: 60:[20, 65] Operation: 6+59=65 Exploring Operation: 59-6=53, Resulting Numbers: [20, 53] Generated Node #0,0,3: 60:[20, 53] Operation: 59-6=53 Moving to Node #0,3 Current State: 60:[6, 8, 31], Operations: ['51-20=31'] Exploring Operation: 31-8=23, Resulting Numbers: [6, 23] Generated Node #0,3,0: 60:[6, 23] Operation: 31-8=23 Exploring Operation: 31-6=25, Resulting Numbers: [8, 25] Generated Node #0,3,1: 60:[8, 25] Operation: 31-6=25 Exploring Operation: 8-6=2, Resulting Numbers: [31, 2] Generated Node #0,3,2: 60:[31, 2] Operation: 8-6=2 Exploring Operation: 6+8=14, Resulting Numbers: [31, 14] Generated Node #0,3,3: 60:[31, 14] Operation: 6+8=14 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 60:[31, 2], Operations: ['51-20=31', '8-6=2'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,60 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 60:[31, 14], Operations: ['51-20=31', '6+8=14'] Exploring Operation: 31*14=434, Resulting Numbers: [434] 434,60 unequal: No Solution Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 60:[6, 23], Operations: ['51-20=31', '31-8=23'] Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,60 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 60:[8, 25], Operations: ['51-20=31', '31-6=25'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,60 unequal: No Solution Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 60:[8, 20, 57], Operations: ['6+51=57'] Exploring Operation: 8+20=28, Resulting Numbers: [57, 28] Generated Node #0,1,0: 60:[57, 28] Operation: 8+20=28 Exploring Operation: 57-20=37, Resulting Numbers: [8, 37] Generated Node #0,1,1: 60:[8, 37] Operation: 57-20=37 Exploring Operation: 20-8=12, Resulting Numbers: [57, 12] Generated Node #0,1,2: 60:[57, 12] Operation: 20-8=12 Exploring Operation: 8+57=65, Resulting Numbers: [20, 65] Generated Node #0,1,3: 60:[20, 65] Operation: 8+57=65 Moving to Node #0,2 Current State: 60:[20, 51, 2], Operations: ['8-6=2'] Exploring Operation: 51+2=53, Resulting Numbers: [20, 53] Generated Node #0,2,0: 60:[20, 53] Operation: 51+2=53 Exploring Operation: 20+51=71, Resulting Numbers: [2, 71] Generated Node #0,2,1: 60:[2, 71] Operation: 20+51=71 Exploring Operation: 51-20=31, Resulting Numbers: [2, 31] Generated Node #0,2,2: 60:[2, 31] Operation: 51-20=31 Exploring Operation: 20/2=10, Resulting Numbers: [51, 10] Generated Node #0,2,3: 60:[51, 10] Operation: 20/2=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 60:[2, 31], Operations: ['8-6=2', '51-20=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,60 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,60 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[20, 53], Operations: ['8-6=2', '51+2=53'] Exploring Operation: 20*53=1060, Resulting Numbers: [1060] 1060,60 unequal: No Solution Exploring Operation: 20+53=73, Resulting Numbers: [73] 73,60 unequal: No Solution Exploring Operation: 53-20=33, Resulting Numbers: [33] 33,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 60:[51, 10], Operations: ['8-6=2', '20/2=10'] Exploring Operation: 51+10=61, Resulting Numbers: [61] 61,60 unequal: No Solution Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,60 unequal: No Solution Exploring Operation: 51*10=510, Resulting Numbers: [510] 510,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[2, 71], Operations: ['8-6=2', '20+51=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,60 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,60 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,60 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: 60:[59, 14], Operations: ['8+51=59', '20-6=14'] Exploring Operation: 59+14=73, Resulting Numbers: [73] 73,60 unequal: No Solution Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 59*14=826, Resulting Numbers: [826] 826,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[57, 12], Operations: ['6+51=57', '20-8=12'] Exploring Operation: 57-12=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 57+12=69, Resulting Numbers: [69] 69,60 unequal: No Solution Exploring Operation: 57*12=684, Resulting Numbers: [684] 684,60 unequal: No Solution Moving to Node #0,0,2 Current State: 60:[20, 65], Operations: ['8+51=59', '6+59=65'] Exploring Operation: 65-20=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 20*65=1300, Resulting Numbers: [1300] 1300,60 unequal: No Solution Exploring Operation: 20+65=85, Resulting Numbers: [85] 85,60 unequal: No Solution Moving to Node #0,1,0 Current State: 60:[57, 28], Operations: ['6+51=57', '8+20=28'] Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 57+28=85, Resulting Numbers: [85] 85,60 unequal: No Solution Exploring Operation: 57*28=1596, Resulting Numbers: [1596] 1596,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[20, 65], Operations: ['6+51=57', '8+57=65'] Exploring Operation: 20+65=85, Resulting Numbers: [85] 85,60 unequal: No Solution Exploring Operation: 20*65=1300, Resulting Numbers: [1300] 1300,60 unequal: No Solution Exploring Operation: 65-20=45, Resulting Numbers: [45] 45,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[59, 26], Operations: ['8+51=59', '6+20=26'] Exploring Operation: 59*26=1534, Resulting Numbers: [1534] 1534,60 unequal: No Solution Exploring Operation: 59+26=85, Resulting Numbers: [85] 85,60 unequal: No Solution Exploring Operation: 59-26=33, Resulting Numbers: [33] 33,60 unequal: No Solution Moving to Node #0,0,3 Current State: 60:[20, 53], Operations: ['8+51=59', '59-6=53'] Exploring Operation: 20*53=1060, Resulting Numbers: [1060] 1060,60 unequal: No Solution Exploring Operation: 20+53=73, Resulting Numbers: [73] 73,60 unequal: No Solution Exploring Operation: 53-20=33, Resulting Numbers: [33] 33,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[8, 37], Operations: ['6+51=57', '57-20=37'] Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,60 unequal: No Solution Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,60 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 39, 51, 13, 70 ]
22
[ "39/13=3", "70-51=19", "3+19=22" ]
Current State: 22:[39, 51, 13, 70], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [51, 70, 3] Generated Node #2: [51, 70, 3] from Operation: 39/13=3 Current State: 22:[51, 70, 3], Operations: ['39/13=3'] Exploring Operation: 70-51=19, Resulting Numbers: [3, 19] Generated Node #3: [3, 19] from Operation: 70-51=19 Current State: 22:[3, 19], Operations: ['39/13=3', '70-51=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[39, 51, 13, 70], Operations: [] Exploring Operation: 70-39=31, Resulting Numbers: [51, 13, 31] Generated Node #0,0: 22:[51, 13, 31] Operation: 70-39=31 Exploring Operation: 51-39=12, Resulting Numbers: [13, 70, 12] Generated Node #0,1: 22:[13, 70, 12] Operation: 51-39=12 Exploring Operation: 70-51=19, Resulting Numbers: [39, 13, 19] Generated Node #0,2: 22:[39, 13, 19] Operation: 70-51=19 Moving to Node #0,2 Current State: 22:[39, 13, 19], Operations: ['70-51=19'] Exploring Operation: 39/13=3, Resulting Numbers: [19, 3] Generated Node #0,2,0: 22:[19, 3] Operation: 39/13=3 Exploring Operation: 39-19=20, Resulting Numbers: [13, 20] Generated Node #0,2,1: 22:[13, 20] Operation: 39-19=20 Exploring Operation: 39-13=26, Resulting Numbers: [19, 26] Generated Node #0,2,2: 22:[19, 26] Operation: 39-13=26 Moving to Node #0,0 Current State: 22:[51, 13, 31], Operations: ['70-39=31'] Exploring Operation: 31-13=18, Resulting Numbers: [51, 18] Generated Node #0,0,0: 22:[51, 18] Operation: 31-13=18 Exploring Operation: 51-31=20, Resulting Numbers: [13, 20] Generated Node #0,0,1: 22:[13, 20] Operation: 51-31=20 Exploring Operation: 51-13=38, Resulting Numbers: [31, 38] Generated Node #0,0,2: 22:[31, 38] Operation: 51-13=38 Moving to Node #0,1 Current State: 22:[13, 70, 12], Operations: ['51-39=12'] Exploring Operation: 13-12=1, Resulting Numbers: [70, 1] Generated Node #0,1,0: 22:[70, 1] Operation: 13-12=1 Exploring Operation: 70-12=58, Resulting Numbers: [13, 58] Generated Node #0,1,1: 22:[13, 58] Operation: 70-12=58 Exploring Operation: 70-13=57, Resulting Numbers: [12, 57] Generated Node #0,1,2: 22:[12, 57] Operation: 70-13=57 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 22:[12, 57], Operations: ['51-39=12', '70-13=57'] Exploring Operation: 12+57=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 12*57=684, Resulting Numbers: [684] 684,22 unequal: No Solution Exploring Operation: 57-12=45, Resulting Numbers: [45] 45,22 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:[13, 58], Operations: ['51-39=12', '70-12=58'] Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,22 unequal: No Solution Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,22 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,22 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:[70, 1], Operations: ['51-39=12', '13-12=1'] Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,22 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: 22:[19, 3], Operations: ['70-51=19', '39/13=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,22 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[39, 51, 13, 70], Operations: [] Exploring Operation: 70-51=19, Resulting Numbers: [39, 13, 19] Generated Node #0,2: 22:[39, 13, 19] Operation: 70-51=19 Moving to Node #0,2 Current State: 22:[39, 13, 19], Operations: ['70-51=19'] Exploring Operation: 39/13=3, Resulting Numbers: [19, 3] Generated Node #0,2,0: 22:[19, 3] Operation: 39/13=3 Moving to Node #0,2,0 Current State: 22:[19, 3], Operations: ['70-51=19', '39/13=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.975694
hs_3
sum_heuristic
[ 57, 63, 2, 65 ]
58
[ "63+2=65", "65/65=1", "57+1=58" ]
Current State: 58:[57, 63, 2, 65], Operations: [] Exploring Operation: 63+2=65, Resulting Numbers: [57, 65, 65] Generated Node #2: [57, 65, 65] from Operation: 63+2=65 Current State: 58:[57, 65, 65], Operations: ['63+2=65'] Exploring Operation: 65/65=1, Resulting Numbers: [57, 1] Generated Node #3: [57, 1] from Operation: 65/65=1 Current State: 58:[57, 1], Operations: ['63+2=65', '65/65=1'] Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[57, 63, 2, 65], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [2, 65, 6] Generated Node #0,0: 58:[2, 65, 6] Operation: 63-57=6 Exploring Operation: 65-63=2, Resulting Numbers: [57, 2, 2] Generated Node #0,1: 58:[57, 2, 2] Operation: 65-63=2 Exploring Operation: 65-2=63, Resulting Numbers: [57, 63, 63] Generated Node #0,2: 58:[57, 63, 63] Operation: 65-2=63 Exploring Operation: 65-57=8, Resulting Numbers: [63, 2, 8] Generated Node #0,3: 58:[63, 2, 8] Operation: 65-57=8 Exploring Operation: 63-2=61, Resulting Numbers: [57, 65, 61] Generated Node #0,4: 58:[57, 65, 61] Operation: 63-2=61 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[57, 2, 2], Operations: ['65-63=2'] Exploring Operation: 2/2=1, Resulting Numbers: [57, 1] Generated Node #0,1,0: 58:[57, 1] Operation: 2/2=1 Exploring Operation: 57-2=55, Resulting Numbers: [2, 55] Generated Node #0,1,1: 58:[2, 55] Operation: 57-2=55 Exploring Operation: 57+2=59, Resulting Numbers: [2, 59] Generated Node #0,1,2: 58:[2, 59] Operation: 57+2=59 Exploring Operation: 57-2=55, Resulting Numbers: [2, 55] Generated Node #0,1,3: 58:[2, 55] Operation: 57-2=55 Exploring Operation: 57+2=59, Resulting Numbers: [2, 59] Generated Node #0,1,4: 58:[2, 59] Operation: 57+2=59 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 58:[2, 59], Operations: ['65-63=2', '57+2=59'] Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,58 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,58 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,58 unequal: No Solution No 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: 58:[2, 59], Operations: ['65-63=2', '57+2=59'] Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,58 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,58 unequal: No Solution No 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: 58:[57, 1], Operations: ['65-63=2', '2/2=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[57, 63, 2, 65], Operations: [] Exploring Operation: 65-63=2, Resulting Numbers: [57, 2, 2] Generated Node #0,1: 58:[57, 2, 2] Operation: 65-63=2 Moving to Node #0,1 Current State: 58:[57, 2, 2], Operations: ['65-63=2'] Exploring Operation: 2/2=1, Resulting Numbers: [57, 1] Generated Node #0,1,0: 58:[57, 1] Operation: 2/2=1 Moving to Node #0,1,0 Current State: 58:[57, 1], Operations: ['65-63=2', '2/2=1'] Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 86, 25, 72, 90 ]
43
[ "86-25=61", "90-72=18", "61-18=43" ]
Current State: 43:[86, 25, 72, 90], Operations: [] Exploring Operation: 86-25=61, Resulting Numbers: [72, 90, 61] Generated Node #2: [72, 90, 61] from Operation: 86-25=61 Current State: 43:[72, 90, 61], Operations: ['86-25=61'] Exploring Operation: 90-72=18, Resulting Numbers: [61, 18] Generated Node #3: [61, 18] from Operation: 90-72=18 Current State: 43:[61, 18], Operations: ['86-25=61', '90-72=18'] Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[86, 25, 72, 90], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [25, 72, 4] Generated Node #0,0: 43:[25, 72, 4] Operation: 90-86=4 Exploring Operation: 90-72=18, Resulting Numbers: [86, 25, 18] Generated Node #0,1: 43:[86, 25, 18] Operation: 90-72=18 Exploring Operation: 86-25=61, Resulting Numbers: [72, 90, 61] Generated Node #0,2: 43:[72, 90, 61] Operation: 86-25=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[25, 72, 4], Operations: ['90-86=4'] Exploring Operation: 72-25=47, Resulting Numbers: [4, 47] Generated Node #0,0,0: 43:[4, 47] Operation: 72-25=47 Exploring Operation: 72-4=68, Resulting Numbers: [25, 68] Generated Node #0,0,1: 43:[25, 68] Operation: 72-4=68 Exploring Operation: 25+4=29, Resulting Numbers: [72, 29] Generated Node #0,0,2: 43:[72, 29] Operation: 25+4=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[4, 47], Operations: ['90-86=4', '72-25=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,43 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,43 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[86, 25, 72, 90], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [25, 72, 4] Generated Node #0,0: 43:[25, 72, 4] Operation: 90-86=4 Moving to Node #0,0 Current State: 43:[25, 72, 4], Operations: ['90-86=4'] Exploring Operation: 72-25=47, Resulting Numbers: [4, 47] Generated Node #0,0,0: 43:[4, 47] Operation: 72-25=47 Moving to Node #0,0,0 Current State: 43:[4, 47], Operations: ['90-86=4', '72-25=47'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 28, 64, 34, 73 ]
75
[ "64-28=36", "73-34=39", "36+39=75" ]
Current State: 75:[28, 64, 34, 73], Operations: [] Exploring Operation: 64-28=36, Resulting Numbers: [34, 73, 36] Generated Node #2: [34, 73, 36] from Operation: 64-28=36 Current State: 75:[34, 73, 36], Operations: ['64-28=36'] Exploring Operation: 73-34=39, Resulting Numbers: [36, 39] Generated Node #3: [36, 39] from Operation: 73-34=39 Current State: 75:[36, 39], Operations: ['64-28=36', '73-34=39'] Exploring Operation: 36+39=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[28, 64, 34, 73], Operations: [] Exploring Operation: 34-28=6, Resulting Numbers: [64, 73, 6] Generated Node #0,0: 75:[64, 73, 6] Operation: 34-28=6 Exploring Operation: 64-34=30, Resulting Numbers: [28, 73, 30] Generated Node #0,1: 75:[28, 73, 30] Operation: 64-34=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[28, 73, 30], Operations: ['64-34=30'] Exploring Operation: 28+30=58, Resulting Numbers: [73, 58] Generated Node #0,1,0: 75:[73, 58] Operation: 28+30=58 Exploring Operation: 30-28=2, Resulting Numbers: [73, 2] Generated Node #0,1,1: 75:[73, 2] Operation: 30-28=2 Moving to Node #0,1,1 Current State: 75:[73, 2], Operations: ['64-34=30', '30-28=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,75 unequal: No Solution Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[28, 64, 34, 73], Operations: [] Exploring Operation: 64-34=30, Resulting Numbers: [28, 73, 30] Generated Node #0,1: 75:[28, 73, 30] Operation: 64-34=30 Moving to Node #0,1 Current State: 75:[28, 73, 30], Operations: ['64-34=30'] Exploring Operation: 30-28=2, Resulting Numbers: [73, 2] Generated Node #0,1,1: 75:[73, 2] Operation: 30-28=2 Moving to Node #0,1,1 Current State: 75:[73, 2], Operations: ['64-34=30', '30-28=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 16, 86, 4, 61 ]
13
[ "86-16=70", "61-4=57", "70-57=13" ]
Current State: 13:[16, 86, 4, 61], Operations: [] Exploring Operation: 86-16=70, Resulting Numbers: [4, 61, 70] Generated Node #2: [4, 61, 70] from Operation: 86-16=70 Current State: 13:[4, 61, 70], Operations: ['86-16=70'] Exploring Operation: 61-4=57, Resulting Numbers: [70, 57] Generated Node #3: [70, 57] from Operation: 61-4=57 Current State: 13:[70, 57], Operations: ['86-16=70', '61-4=57'] Exploring Operation: 70-57=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[16, 86, 4, 61], Operations: [] Exploring Operation: 86-61=25, Resulting Numbers: [16, 4, 25] Generated Node #0,0: 13:[16, 4, 25] Operation: 86-61=25 Exploring Operation: 86-16=70, Resulting Numbers: [4, 61, 70] Generated Node #0,1: 13:[4, 61, 70] Operation: 86-16=70 Moving to Node #0,0 Current State: 13:[16, 4, 25], Operations: ['86-61=25'] Exploring Operation: 25-4=21, Resulting Numbers: [16, 21] Generated Node #0,0,0: 13:[16, 21] Operation: 25-4=21 Exploring Operation: 16-4=12, Resulting Numbers: [25, 12] Generated Node #0,0,1: 13:[25, 12] Operation: 16-4=12 Moving to Node #0,1 Current State: 13:[4, 61, 70], Operations: ['86-16=70'] Exploring Operation: 70-61=9, Resulting Numbers: [4, 9] Generated Node #0,1,0: 13:[4, 9] Operation: 70-61=9 Exploring Operation: 61-4=57, Resulting Numbers: [70, 57] Generated Node #0,1,1: 13:[70, 57] Operation: 61-4=57 Moving to Node #0,0,0 Current State: 13:[16, 21], Operations: ['86-61=25', '25-4=21'] Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,13 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[4, 9], Operations: ['86-16=70', '70-61=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,13 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[16, 86, 4, 61], Operations: [] Exploring Operation: 86-16=70, Resulting Numbers: [4, 61, 70] Generated Node #0,1: 13:[4, 61, 70] Operation: 86-16=70 Moving to Node #0,1 Current State: 13:[4, 61, 70], Operations: ['86-16=70'] Exploring Operation: 70-61=9, Resulting Numbers: [4, 9] Generated Node #0,1,0: 13:[4, 9] Operation: 70-61=9 Moving to Node #0,1,0 Current State: 13:[4, 9], Operations: ['86-16=70', '70-61=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.987847
hs_2
mult_heuristic
[ 39, 72, 24, 24 ]
42
[ "39*24=936", "72+936=1008", "1008/24=42" ]
Current State: 42:[39, 72, 24, 24], Operations: [] Exploring Operation: 39*24=936, Resulting Numbers: [72, 936] Generated Node #2: [72, 936] from Operation: 39*24=936 Current State: 42:[72, 936], Operations: ['39*24=936'] Exploring Operation: 72+936=1008, Resulting Numbers: [1008] 1008,42 equal: Goal Reached Exploring Operation: 1008/24=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[39, 72, 24, 24], Operations: [] Exploring Operation: 72-39=33, Resulting Numbers: [24, 24, 33] Generated Node #0,0: 42:[24, 24, 33] Operation: 72-39=33 Exploring Operation: 72/24=3, Resulting Numbers: [39, 24, 3] Generated Node #0,1: 42:[39, 24, 3] Operation: 72/24=3 Exploring Operation: 72-24=48, Resulting Numbers: [39, 24, 48] Generated Node #0,2: 42:[39, 24, 48] Operation: 72-24=48 Exploring Operation: 72-24=48, Resulting Numbers: [39, 24, 48] Generated Node #0,3: 42:[39, 24, 48] Operation: 72-24=48 Exploring Operation: 72/24=3, Resulting Numbers: [39, 24, 3] Generated Node #0,4: 42:[39, 24, 3] Operation: 72/24=3 Moving to Node #0,1 Current State: 42:[39, 24, 3], Operations: ['72/24=3'] Exploring Operation: 24-3=21, Resulting Numbers: [39, 21] Generated Node #0,1,0: 42:[39, 21] Operation: 24-3=21 Exploring Operation: 24/3=8, Resulting Numbers: [39, 8] Generated Node #0,1,1: 42:[39, 8] Operation: 24/3=8 Exploring Operation: 39/3=13, Resulting Numbers: [24, 13] Generated Node #0,1,2: 42:[24, 13] Operation: 39/3=13 Exploring Operation: 39-24=15, Resulting Numbers: [3, 15] Generated Node #0,1,3: 42:[3, 15] Operation: 39-24=15 Exploring Operation: 39+3=42, Resulting Numbers: [24, 42] Generated Node #0,1,4: 42:[24, 42] Operation: 39+3=42 Moving to Node #0,4 Current State: 42:[39, 24, 3], Operations: ['72/24=3'] Exploring Operation: 39/3=13, Resulting Numbers: [24, 13] Generated Node #0,4,0: 42:[24, 13] Operation: 39/3=13 Exploring Operation: 39-24=15, Resulting Numbers: [3, 15] Generated Node #0,4,1: 42:[3, 15] Operation: 39-24=15 Exploring Operation: 24-3=21, Resulting Numbers: [39, 21] Generated Node #0,4,2: 42:[39, 21] Operation: 24-3=21 Exploring Operation: 24/3=8, Resulting Numbers: [39, 8] Generated Node #0,4,3: 42:[39, 8] Operation: 24/3=8 Exploring Operation: 39+3=42, Resulting Numbers: [24, 42] Generated Node #0,4,4: 42:[24, 42] Operation: 39+3=42 Moving to Node #0,2 Current State: 42:[39, 24, 48], Operations: ['72-24=48'] Exploring Operation: 39+24=63, Resulting Numbers: [48, 63] Generated Node #0,2,0: 42:[48, 63] Operation: 39+24=63 Exploring Operation: 48-39=9, Resulting Numbers: [24, 9] Generated Node #0,2,1: 42:[24, 9] Operation: 48-39=9 Exploring Operation: 39-24=15, Resulting Numbers: [48, 15] Generated Node #0,2,2: 42:[48, 15] Operation: 39-24=15 Exploring Operation: 48-24=24, Resulting Numbers: [39, 24] Generated Node #0,2,3: 42:[39, 24] Operation: 48-24=24 Exploring Operation: 48/24=2, Resulting Numbers: [39, 2] Generated Node #0,2,4: 42:[39, 2] Operation: 48/24=2 Moving to Node #0,3 Current State: 42:[39, 24, 48], Operations: ['72-24=48'] Exploring Operation: 39+24=63, Resulting Numbers: [48, 63] Generated Node #0,3,0: 42:[48, 63] Operation: 39+24=63 Exploring Operation: 48-39=9, Resulting Numbers: [24, 9] Generated Node #0,3,1: 42:[24, 9] Operation: 48-39=9 Exploring Operation: 39-24=15, Resulting Numbers: [48, 15] Generated Node #0,3,2: 42:[48, 15] Operation: 39-24=15 Exploring Operation: 48/24=2, Resulting Numbers: [39, 2] Generated Node #0,3,3: 42:[39, 2] Operation: 48/24=2 Exploring Operation: 48-24=24, Resulting Numbers: [39, 24] Generated Node #0,3,4: 42:[39, 24] Operation: 48-24=24 Moving to Node #0,0 Current State: 42:[24, 24, 33], Operations: ['72-39=33'] Exploring Operation: 24+24=48, Resulting Numbers: [33, 48] Generated Node #0,0,0: 42:[33, 48] Operation: 24+24=48 Exploring Operation: 24/24=1, Resulting Numbers: [33, 1] Generated Node #0,0,1: 42:[33, 1] Operation: 24/24=1 Exploring Operation: 24-24=0, Resulting Numbers: [33, 0] Generated Node #0,0,2: 42:[33, 0] Operation: 24-24=0 Exploring Operation: 33-24=9, Resulting Numbers: [24, 9] Generated Node #0,0,3: 42:[24, 9] Operation: 33-24=9 Exploring Operation: 33-24=9, Resulting Numbers: [24, 9] Generated Node #0,0,4: 42:[24, 9] Operation: 33-24=9 Moving to Node #0,1,3 Current State: 42:[3, 15], Operations: ['72/24=3', '39-24=15'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,42 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,42 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,42 unequal: No Solution Moving to Node #0,4,1 Current State: 42:[3, 15], Operations: ['72/24=3', '39-24=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,42 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,42 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,42 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,42 unequal: No Solution Moving to Node #0,4,2 Current State: 42:[39, 21], Operations: ['72/24=3', '24-3=21'] Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,42 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,42 unequal: No Solution Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,42 unequal: No Solution Moving to Node #0,1,4 Current State: 42:[24, 42], Operations: ['72/24=3', '39+3=42'] Exploring Operation: 24*42=1008, Resulting Numbers: [1008] 1008,42 unequal: No Solution Exploring Operation: 24+42=66, Resulting Numbers: [66] 66,42 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[39, 21], Operations: ['72/24=3', '24-3=21'] Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,42 unequal: No Solution Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,42 unequal: No Solution Moving to Node #0,2,4 Current State: 42:[39, 2], Operations: ['72-24=48', '48/24=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,42 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,42 unequal: No Solution Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,42 unequal: No Solution Moving to Node #0,4,4 Current State: 42:[24, 42], Operations: ['72/24=3', '39+3=42'] Exploring Operation: 24+42=66, Resulting Numbers: [66] 66,42 unequal: No Solution Exploring Operation: 24*42=1008, Resulting Numbers: [1008] 1008,42 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,42 unequal: No Solution Moving to Node #0,3,3 Current State: 42:[39, 2], Operations: ['72-24=48', '48/24=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,42 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[24, 13], Operations: ['72/24=3', '39/3=13'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,42 unequal: No Solution Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,42 unequal: No Solution Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,42 unequal: No Solution Moving to Node #0,4,3 Current State: 42:[39, 8], Operations: ['72/24=3', '24/3=8'] Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,42 unequal: No Solution Exploring Operation: 39*8=312, Resulting Numbers: [312] 312,42 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,42 unequal: No Solution Moving to Node #0,4,0 Current State: 42:[24, 13], Operations: ['72/24=3', '39/3=13'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,42 unequal: No Solution Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,42 unequal: No Solution Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[39, 8], Operations: ['72/24=3', '24/3=8'] Exploring Operation: 39*8=312, Resulting Numbers: [312] 312,42 unequal: No Solution Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,42 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[24, 9], Operations: ['72-24=48', '48-39=9'] Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,42 unequal: No Solution Moving to Node #0,0,4 Current State: 42:[24, 9], Operations: ['72-39=33', '33-24=9'] Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,42 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,0,3 Current State: 42:[24, 9], Operations: ['72-39=33', '33-24=9'] Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[24, 9], Operations: ['72-24=48', '48-39=9'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,42 unequal: No Solution Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,42 unequal: No Solution Moving to Node #0,2,3 Current State: 42:[39, 24], Operations: ['72-24=48', '48-24=24'] Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,42 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,3,4 Current State: 42:[39, 24], Operations: ['72-24=48', '48-24=24'] Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,42 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[48, 15], Operations: ['72-24=48', '39-24=15'] Exploring Operation: 48*15=720, Resulting Numbers: [720] 720,42 unequal: No Solution Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 48+15=63, Resulting Numbers: [63] 63,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[48, 15], Operations: ['72-24=48', '39-24=15'] Exploring Operation: 48*15=720, Resulting Numbers: [720] 720,42 unequal: No Solution Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 48+15=63, Resulting Numbers: [63] 63,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[33, 1], Operations: ['72-39=33', '24/24=1'] Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,42 unequal: No Solution Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[33, 0], Operations: ['72-39=33', '24-24=0'] Exploring Operation: 33+0=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 33-0=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 33*0=0, Resulting Numbers: [0] 0,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[33, 48], Operations: ['72-39=33', '24+24=48'] Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,42 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,42 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[48, 63], Operations: ['72-24=48', '39+24=63'] Exploring Operation: 48*63=3024, Resulting Numbers: [3024] 3024,42 unequal: No Solution Exploring Operation: 48+63=111, Resulting Numbers: [111] 111,42 unequal: No Solution Exploring Operation: 63-48=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[48, 63], Operations: ['72-24=48', '39+24=63'] Exploring Operation: 63-48=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 48+63=111, Resulting Numbers: [111] 111,42 unequal: No Solution Exploring Operation: 48*63=3024, Resulting Numbers: [3024] 3024,42 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 36, 42, 59, 9 ]
28
[ "36+42=78", "59-9=50", "78-50=28" ]
Current State: 28:[36, 42, 59, 9], Operations: [] Exploring Operation: 36+42=78, Resulting Numbers: [59, 9, 78] Generated Node #2: [59, 9, 78] from Operation: 36+42=78 Current State: 28:[59, 9, 78], Operations: ['36+42=78'] Exploring Operation: 59-9=50, Resulting Numbers: [78, 50] Generated Node #3: [78, 50] from Operation: 59-9=50 Current State: 28:[78, 50], Operations: ['36+42=78', '59-9=50'] Exploring Operation: 78-50=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[36, 42, 59, 9], Operations: [] Exploring Operation: 42-36=6, Resulting Numbers: [59, 9, 6] Generated Node #0,0: 28:[59, 9, 6] Operation: 42-36=6 Exploring Operation: 59-42=17, Resulting Numbers: [36, 9, 17] Generated Node #0,1: 28:[36, 9, 17] Operation: 59-42=17 Exploring Operation: 59-36=23, Resulting Numbers: [42, 9, 23] Generated Node #0,2: 28:[42, 9, 23] Operation: 59-36=23 Exploring Operation: 42-9=33, Resulting Numbers: [36, 59, 33] Generated Node #0,3: 28:[36, 59, 33] Operation: 42-9=33 Moving to Node #0,1 Current State: 28:[36, 9, 17], Operations: ['59-42=17'] Exploring Operation: 36-9=27, Resulting Numbers: [17, 27] Generated Node #0,1,0: 28:[17, 27] Operation: 36-9=27 Exploring Operation: 17-9=8, Resulting Numbers: [36, 8] Generated Node #0,1,1: 28:[36, 8] Operation: 17-9=8 Exploring Operation: 36-17=19, Resulting Numbers: [9, 19] Generated Node #0,1,2: 28:[9, 19] Operation: 36-17=19 Exploring Operation: 36/9=4, Resulting Numbers: [17, 4] Generated Node #0,1,3: 28:[17, 4] Operation: 36/9=4 Moving to Node #0,2 Current State: 28:[42, 9, 23], Operations: ['59-36=23'] Exploring Operation: 9+23=32, Resulting Numbers: [42, 32] Generated Node #0,2,0: 28:[42, 32] Operation: 9+23=32 Exploring Operation: 23-9=14, Resulting Numbers: [42, 14] Generated Node #0,2,1: 28:[42, 14] Operation: 23-9=14 Exploring Operation: 42-23=19, Resulting Numbers: [9, 19] Generated Node #0,2,2: 28:[9, 19] Operation: 42-23=19 Exploring Operation: 42-9=33, Resulting Numbers: [23, 33] Generated Node #0,2,3: 28:[23, 33] Operation: 42-9=33 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 28:[9, 19], Operations: ['59-36=23', '42-23=19'] Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[36, 42, 59, 9], Operations: [] Exploring Operation: 59-36=23, Resulting Numbers: [42, 9, 23] Generated Node #0,2: 28:[42, 9, 23] Operation: 59-36=23 Moving to Node #0,2 Current State: 28:[42, 9, 23], Operations: ['59-36=23'] Exploring Operation: 42-23=19, Resulting Numbers: [9, 19] Generated Node #0,2,2: 28:[9, 19] Operation: 42-23=19 Moving to Node #0,2,2 Current State: 28:[9, 19], Operations: ['59-36=23', '42-23=19'] Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 62, 95, 49, 14 ]
30
[ "95-62=33", "49+14=63", "63-33=30" ]
Current State: 30:[62, 95, 49, 14], Operations: [] Exploring Operation: 95-62=33, Resulting Numbers: [49, 14, 33] Generated Node #2: [49, 14, 33] from Operation: 95-62=33 Current State: 30:[49, 14, 33], Operations: ['95-62=33'] Exploring Operation: 49+14=63, Resulting Numbers: [33, 63] Generated Node #3: [33, 63] from Operation: 49+14=63 Current State: 30:[33, 63], Operations: ['95-62=33', '49+14=63'] Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[62, 95, 49, 14], Operations: [] Exploring Operation: 62-49=13, Resulting Numbers: [95, 14, 13] Generated Node #0,0: 30:[95, 14, 13] Operation: 62-49=13 Exploring Operation: 95-49=46, Resulting Numbers: [62, 14, 46] Generated Node #0,1: 30:[62, 14, 46] Operation: 95-49=46 Exploring Operation: 95-62=33, Resulting Numbers: [49, 14, 33] Generated Node #0,2: 30:[49, 14, 33] Operation: 95-62=33 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[49, 14, 33], Operations: ['95-62=33'] Exploring Operation: 33-14=19, Resulting Numbers: [49, 19] Generated Node #0,2,0: 30:[49, 19] Operation: 33-14=19 Exploring Operation: 49-33=16, Resulting Numbers: [14, 16] Generated Node #0,2,1: 30:[14, 16] Operation: 49-33=16 Exploring Operation: 49-14=35, Resulting Numbers: [33, 35] Generated Node #0,2,2: 30:[33, 35] Operation: 49-14=35 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[14, 16], Operations: ['95-62=33', '49-33=16'] Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[62, 95, 49, 14], Operations: [] Exploring Operation: 95-62=33, Resulting Numbers: [49, 14, 33] Generated Node #0,2: 30:[49, 14, 33] Operation: 95-62=33 Moving to Node #0,2 Current State: 30:[49, 14, 33], Operations: ['95-62=33'] Exploring Operation: 49-33=16, Resulting Numbers: [14, 16] Generated Node #0,2,1: 30:[14, 16] Operation: 49-33=16 Moving to Node #0,2,1 Current State: 30:[14, 16], Operations: ['95-62=33', '49-33=16'] Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 44, 88, 87, 48 ]
41
[ "88/44=2", "87-48=39", "2+39=41" ]
Current State: 41:[44, 88, 87, 48], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [87, 48, 2] Generated Node #2: [87, 48, 2] from Operation: 88/44=2 Current State: 41:[87, 48, 2], Operations: ['88/44=2'] Exploring Operation: 87-48=39, Resulting Numbers: [2, 39] Generated Node #3: [2, 39] from Operation: 87-48=39 Current State: 41:[2, 39], Operations: ['88/44=2', '87-48=39'] Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[44, 88, 87, 48], Operations: [] Exploring Operation: 88-87=1, Resulting Numbers: [44, 48, 1] Generated Node #0,0: 41:[44, 48, 1] Operation: 88-87=1 Moving to Node #0,0 Current State: 41:[44, 48, 1], Operations: ['88-87=1'] Exploring Operation: 44-1=43, Resulting Numbers: [48, 43] Generated Node #0,0,0: 41:[48, 43] Operation: 44-1=43 Moving to Node #0,0,0 Current State: 41:[48, 43], Operations: ['88-87=1', '44-1=43'] Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,41 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 65, 79, 55, 75 ]
81
[ "55+75=130", "130/65=2", "79+2=81" ]
Current State: 81:[65, 79, 55, 75], Operations: [] Exploring Operation: 55+75=130, Resulting Numbers: [65, 79, 130] Generated Node #2: [65, 79, 130] from Operation: 55+75=130 Current State: 81:[65, 79, 130], Operations: ['55+75=130'] Exploring Operation: 130/65=2, Resulting Numbers: [79, 2] Generated Node #3: [79, 2] from Operation: 130/65=2 Current State: 81:[79, 2], Operations: ['55+75=130', '130/65=2'] Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[65, 79, 55, 75], Operations: [] Exploring Operation: 65-55=10, Resulting Numbers: [79, 75, 10] Generated Node #0,0: 81:[79, 75, 10] Operation: 65-55=10 Exploring Operation: 79-65=14, Resulting Numbers: [55, 75, 14] Generated Node #0,1: 81:[55, 75, 14] Operation: 79-65=14 Exploring Operation: 75-65=10, Resulting Numbers: [79, 55, 10] Generated Node #0,2: 81:[79, 55, 10] Operation: 75-65=10 Exploring Operation: 79-55=24, Resulting Numbers: [65, 75, 24] Generated Node #0,3: 81:[65, 75, 24] Operation: 79-55=24 Exploring Operation: 75-55=20, Resulting Numbers: [65, 79, 20] Generated Node #0,4: 81:[65, 79, 20] Operation: 75-55=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[79, 75, 10], Operations: ['65-55=10'] Exploring Operation: 79+10=89, Resulting Numbers: [75, 89] Generated Node #0,0,0: 81:[75, 89] Operation: 79+10=89 Exploring Operation: 79-10=69, Resulting Numbers: [75, 69] Generated Node #0,0,1: 81:[75, 69] Operation: 79-10=69 Exploring Operation: 79-75=4, Resulting Numbers: [10, 4] Generated Node #0,0,2: 81:[10, 4] Operation: 79-75=4 Exploring Operation: 75-10=65, Resulting Numbers: [79, 65] Generated Node #0,0,3: 81:[79, 65] Operation: 75-10=65 Exploring Operation: 75+10=85, Resulting Numbers: [79, 85] Generated Node #0,0,4: 81:[79, 85] Operation: 75+10=85 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 81:[10, 4], Operations: ['65-55=10', '79-75=4'] Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,81 unequal: No Solution No 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: 81:[79, 85], Operations: ['65-55=10', '75+10=85'] Exploring Operation: 85-79=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 79+85=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 79*85=6715, Resulting Numbers: [6715] 6715,81 unequal: No Solution No 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: 81:[75, 89], Operations: ['65-55=10', '79+10=89'] Exploring Operation: 75*89=6675, Resulting Numbers: [6675] 6675,81 unequal: No Solution Exploring Operation: 75+89=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 89-75=14, Resulting Numbers: [14] 14,81 unequal: No Solution No 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: 81:[75, 69], Operations: ['65-55=10', '79-10=69'] Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 75*69=5175, Resulting Numbers: [5175] 5175,81 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,81 unequal: No Solution No 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: 81:[79, 65], Operations: ['65-55=10', '75-10=65'] Exploring Operation: 79*65=5135, Resulting Numbers: [5135] 5135,81 unequal: No Solution Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 79+65=144, Resulting Numbers: [144] 144,81 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[65, 75, 24], Operations: ['79-55=24'] Exploring Operation: 75+24=99, Resulting Numbers: [65, 99] Generated Node #0,3,0: 81:[65, 99] Operation: 75+24=99 Exploring Operation: 75-24=51, Resulting Numbers: [65, 51] Generated Node #0,3,1: 81:[65, 51] Operation: 75-24=51 Exploring Operation: 65+24=89, Resulting Numbers: [75, 89] Generated Node #0,3,2: 81:[75, 89] Operation: 65+24=89 Exploring Operation: 65-24=41, Resulting Numbers: [75, 41] Generated Node #0,3,3: 81:[75, 41] Operation: 65-24=41 Exploring Operation: 75-65=10, Resulting Numbers: [24, 10] Generated Node #0,3,4: 81:[24, 10] Operation: 75-65=10 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 81:[24, 10], Operations: ['79-55=24', '75-65=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,81 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 81:[75, 89], Operations: ['79-55=24', '65+24=89'] Exploring Operation: 75+89=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 89-75=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 75*89=6675, Resulting Numbers: [6675] 6675,81 unequal: No Solution No 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: 81:[75, 41], Operations: ['79-55=24', '65-24=41'] Exploring Operation: 75+41=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 75*41=3075, Resulting Numbers: [3075] 3075,81 unequal: No Solution No 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: 81:[65, 99], Operations: ['79-55=24', '75+24=99'] Exploring Operation: 65*99=6435, Resulting Numbers: [6435] 6435,81 unequal: No Solution Exploring Operation: 65+99=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,81 unequal: No Solution No 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: 81:[65, 51], Operations: ['79-55=24', '75-24=51'] Exploring Operation: 65-51=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 65*51=3315, Resulting Numbers: [3315] 3315,81 unequal: No Solution Exploring Operation: 65+51=116, Resulting Numbers: [116] 116,81 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 Start Sub Search at level 1: Moving to Node #0,4 Current State: 81:[65, 79, 20], Operations: ['75-55=20'] Exploring Operation: 79-20=59, Resulting Numbers: [65, 59] Generated Node #0,4,0: 81:[65, 59] Operation: 79-20=59 Exploring Operation: 65-20=45, Resulting Numbers: [79, 45] Generated Node #0,4,1: 81:[79, 45] Operation: 65-20=45 Exploring Operation: 79-65=14, Resulting Numbers: [20, 14] Generated Node #0,4,2: 81:[20, 14] Operation: 79-65=14 Exploring Operation: 65+20=85, Resulting Numbers: [79, 85] Generated Node #0,4,3: 81:[79, 85] Operation: 65+20=85 Exploring Operation: 79+20=99, Resulting Numbers: [65, 99] Generated Node #0,4,4: 81:[65, 99] Operation: 79+20=99 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 81:[79, 85], Operations: ['75-55=20', '65+20=85'] Exploring Operation: 79*85=6715, Resulting Numbers: [6715] 6715,81 unequal: No Solution Exploring Operation: 79+85=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 85-79=6, Resulting Numbers: [6] 6,81 unequal: No Solution No 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: 81:[20, 14], Operations: ['75-55=20', '79-65=14'] Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,81 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,81 unequal: No Solution No 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: 81:[79, 45], Operations: ['75-55=20', '65-20=45'] Exploring Operation: 79+45=124, Resulting Numbers: [124] 124,81 unequal: No Solution Exploring Operation: 79*45=3555, Resulting Numbers: [3555] 3555,81 unequal: No Solution Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,81 unequal: No Solution No 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: 81:[65, 99], Operations: ['75-55=20', '79+20=99'] Exploring Operation: 65*99=6435, Resulting Numbers: [6435] 6435,81 unequal: No Solution Exploring Operation: 65+99=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,81 unequal: No Solution No 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: 81:[65, 59], Operations: ['75-55=20', '79-20=59'] Exploring Operation: 65-59=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 65+59=124, Resulting Numbers: [124] 124,81 unequal: No Solution Exploring Operation: 65*59=3835, Resulting Numbers: [3835] 3835,81 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[79, 55, 10], Operations: ['75-65=10'] Exploring Operation: 79-55=24, Resulting Numbers: [10, 24] Generated Node #0,2,0: 81:[10, 24] Operation: 79-55=24 Exploring Operation: 55-10=45, Resulting Numbers: [79, 45] Generated Node #0,2,1: 81:[79, 45] Operation: 55-10=45 Exploring Operation: 79-10=69, Resulting Numbers: [55, 69] Generated Node #0,2,2: 81:[55, 69] Operation: 79-10=69 Exploring Operation: 79+10=89, Resulting Numbers: [55, 89] Generated Node #0,2,3: 81:[55, 89] Operation: 79+10=89 Exploring Operation: 55+10=65, Resulting Numbers: [79, 65] Generated Node #0,2,4: 81:[79, 65] Operation: 55+10=65 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[10, 24], Operations: ['75-65=10', '79-55=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,81 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 81:[79, 65], Operations: ['75-65=10', '55+10=65'] Exploring Operation: 79+65=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 79*65=5135, Resulting Numbers: [5135] 5135,81 unequal: No Solution Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,81 unequal: No Solution No 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: 81:[79, 45], Operations: ['75-65=10', '55-10=45'] Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 79+45=124, Resulting Numbers: [124] 124,81 unequal: No Solution Exploring Operation: 79*45=3555, Resulting Numbers: [3555] 3555,81 unequal: No Solution No 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: 81:[55, 89], Operations: ['75-65=10', '79+10=89'] Exploring Operation: 89-55=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 55*89=4895, Resulting Numbers: [4895] 4895,81 unequal: No Solution Exploring Operation: 55+89=144, Resulting Numbers: [144] 144,81 unequal: No Solution No 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: 81:[55, 69], Operations: ['75-65=10', '79-10=69'] Exploring Operation: 69-55=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 55+69=124, Resulting Numbers: [124] 124,81 unequal: No Solution Exploring Operation: 55*69=3795, Resulting Numbers: [3795] 3795,81 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[55, 75, 14], Operations: ['79-65=14'] Exploring Operation: 55+14=69, Resulting Numbers: [75, 69] Generated Node #0,1,0: 81:[75, 69] Operation: 55+14=69 Exploring Operation: 75-14=61, Resulting Numbers: [55, 61] Generated Node #0,1,1: 81:[55, 61] Operation: 75-14=61 Exploring Operation: 75+14=89, Resulting Numbers: [55, 89] Generated Node #0,1,2: 81:[55, 89] Operation: 75+14=89 Exploring Operation: 55-14=41, Resulting Numbers: [75, 41] Generated Node #0,1,3: 81:[75, 41] Operation: 55-14=41 Exploring Operation: 75-55=20, Resulting Numbers: [14, 20] Generated Node #0,1,4: 81:[14, 20] Operation: 75-55=20 Moving to Node #0,1,4 Current State: 81:[14, 20], Operations: ['79-65=14', '75-55=20'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 14*20=280, Resulting Numbers: [280] 280,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[75, 69], Operations: ['79-65=14', '55+14=69'] Exploring Operation: 75*69=5175, Resulting Numbers: [5175] 5175,81 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[75, 41], Operations: ['79-65=14', '55-14=41'] Exploring Operation: 75+41=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 75*41=3075, Resulting Numbers: [3075] 3075,81 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[55, 89], Operations: ['79-65=14', '75+14=89'] Exploring Operation: 55+89=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 55*89=4895, Resulting Numbers: [4895] 4895,81 unequal: No Solution Exploring Operation: 89-55=34, Resulting Numbers: [34] 34,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[55, 61], Operations: ['79-65=14', '75-14=61'] Exploring Operation: 55+61=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 61-55=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 55*61=3355, Resulting Numbers: [3355] 3355,81 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
[ 2, 83, 7, 77 ]
11
[ "83-2=81", "77-7=70", "81-70=11" ]
Current State: 11:[2, 83, 7, 77], Operations: [] Exploring Operation: 83-2=81, Resulting Numbers: [7, 77, 81] Generated Node #2: [7, 77, 81] from Operation: 83-2=81 Current State: 11:[7, 77, 81], Operations: ['83-2=81'] Exploring Operation: 77-7=70, Resulting Numbers: [81, 70] Generated Node #3: [81, 70] from Operation: 77-7=70 Current State: 11:[81, 70], Operations: ['83-2=81', '77-7=70'] Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[2, 83, 7, 77], Operations: [] Exploring Operation: 2+7=9, Resulting Numbers: [83, 77, 9] Generated Node #0,0: 11:[83, 77, 9] Operation: 2+7=9 Exploring Operation: 83-77=6, Resulting Numbers: [2, 7, 6] Generated Node #0,1: 11:[2, 7, 6] Operation: 83-77=6 Exploring Operation: 83-2=81, Resulting Numbers: [7, 77, 81] Generated Node #0,2: 11:[7, 77, 81] Operation: 83-2=81 Exploring Operation: 77/7=11, Resulting Numbers: [2, 83, 11] Generated Node #0,3: 11:[2, 83, 11] Operation: 77/7=11 Moving to Node #0,1 Current State: 11:[2, 7, 6], Operations: ['83-77=6'] Exploring Operation: 2*7=14, Resulting Numbers: [6, 14] Generated Node #0,1,0: 11:[6, 14] Operation: 2*7=14 Exploring Operation: 2+6=8, Resulting Numbers: [7, 8] Generated Node #0,1,1: 11:[7, 8] Operation: 2+6=8 Exploring Operation: 2+7=9, Resulting Numbers: [6, 9] Generated Node #0,1,2: 11:[6, 9] Operation: 2+7=9 Exploring Operation: 2*6=12, Resulting Numbers: [7, 12] Generated Node #0,1,3: 11:[7, 12] Operation: 2*6=12 Moving to Node #0,3 Current State: 11:[2, 83, 11], Operations: ['77/7=11'] Exploring Operation: 83-2=81, Resulting Numbers: [11, 81] Generated Node #0,3,0: 11:[11, 81] Operation: 83-2=81 Exploring Operation: 83-11=72, Resulting Numbers: [2, 72] Generated Node #0,3,1: 11:[2, 72] Operation: 83-11=72 Exploring Operation: 2+83=85, Resulting Numbers: [11, 85] Generated Node #0,3,2: 11:[11, 85] Operation: 2+83=85 Exploring Operation: 2+11=13, Resulting Numbers: [83, 13] Generated Node #0,3,3: 11:[83, 13] Operation: 2+11=13 Moving to Node #0,2 Current State: 11:[7, 77, 81], Operations: ['83-2=81'] Exploring Operation: 77/7=11, Resulting Numbers: [81, 11] Generated Node #0,2,0: 11:[81, 11] Operation: 77/7=11 Exploring Operation: 81-77=4, Resulting Numbers: [7, 4] Generated Node #0,2,1: 11:[7, 4] Operation: 81-77=4 Exploring Operation: 77-7=70, Resulting Numbers: [81, 70] Generated Node #0,2,2: 11:[81, 70] Operation: 77-7=70 Exploring Operation: 81-7=74, Resulting Numbers: [77, 74] Generated Node #0,2,3: 11:[77, 74] Operation: 81-7=74 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[7, 4], Operations: ['83-2=81', '81-77=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[2, 83, 7, 77], Operations: [] Exploring Operation: 83-2=81, Resulting Numbers: [7, 77, 81] Generated Node #0,2: 11:[7, 77, 81] Operation: 83-2=81 Moving to Node #0,2 Current State: 11:[7, 77, 81], Operations: ['83-2=81'] Exploring Operation: 81-77=4, Resulting Numbers: [7, 4] Generated Node #0,2,1: 11:[7, 4] Operation: 81-77=4 Moving to Node #0,2,1 Current State: 11:[7, 4], Operations: ['83-2=81', '81-77=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 83, 10, 89, 4 ]
53
[ "83+89=172", "172/4=43", "10+43=53" ]
Current State: 53:[83, 10, 89, 4], Operations: [] Exploring Operation: 83+89=172, Resulting Numbers: [10, 4, 172] Generated Node #2: [10, 4, 172] from Operation: 83+89=172 Current State: 53:[10, 4, 172], Operations: ['83+89=172'] Exploring Operation: 172/4=43, Resulting Numbers: [10, 43] Generated Node #3: [10, 43] from Operation: 172/4=43 Current State: 53:[10, 43], Operations: ['83+89=172', '172/4=43'] Exploring Operation: 10+43=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[83, 10, 89, 4], Operations: [] Exploring Operation: 83-4=79, Resulting Numbers: [10, 89, 79] Generated Node #0,0: 53:[10, 89, 79] Operation: 83-4=79 Exploring Operation: 10*4=40, Resulting Numbers: [83, 89, 40] Generated Node #0,1: 53:[83, 89, 40] Operation: 10*4=40 Exploring Operation: 83-10=73, Resulting Numbers: [89, 4, 73] Generated Node #0,2: 53:[89, 4, 73] Operation: 83-10=73 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[83, 89, 40], Operations: ['10*4=40'] Exploring Operation: 89-40=49, Resulting Numbers: [83, 49] Generated Node #0,1,0: 53:[83, 49] Operation: 89-40=49 Exploring Operation: 83-40=43, Resulting Numbers: [89, 43] Generated Node #0,1,1: 53:[89, 43] Operation: 83-40=43 Exploring Operation: 89-83=6, Resulting Numbers: [40, 6] Generated Node #0,1,2: 53:[40, 6] Operation: 89-83=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[83, 49], Operations: ['10*4=40', '89-40=49'] Exploring Operation: 83*49=4067, Resulting Numbers: [4067] 4067,53 unequal: No Solution Exploring Operation: 83+49=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 83-49=34, Resulting Numbers: [34] 34,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[89, 43], Operations: ['10*4=40', '83-40=43'] Exploring Operation: 89*43=3827, Resulting Numbers: [3827] 3827,53 unequal: No Solution Exploring Operation: 89-43=46, Resulting Numbers: [46] 46,53 unequal: No Solution Exploring Operation: 89+43=132, Resulting Numbers: [132] 132,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[40, 6], Operations: ['10*4=40', '89-83=6'] Exploring Operation: 40*6=240, Resulting Numbers: [240] 240,53 unequal: No Solution Exploring Operation: 40+6=46, Resulting Numbers: [46] 46,53 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[10, 89, 79], Operations: ['83-4=79'] Exploring Operation: 10+89=99, Resulting Numbers: [79, 99] Generated Node #0,0,0: 53:[79, 99] Operation: 10+89=99 Exploring Operation: 89-10=79, Resulting Numbers: [79, 79] Generated Node #0,0,1: 53:[79, 79] Operation: 89-10=79 Exploring Operation: 79-10=69, Resulting Numbers: [89, 69] Generated Node #0,0,2: 53:[89, 69] Operation: 79-10=69 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[79, 79], Operations: ['83-4=79', '89-10=79'] Exploring Operation: 79+79=158, Resulting Numbers: [158] 158,53 unequal: No Solution Exploring Operation: 79-79=0, Resulting Numbers: [0] 0,53 unequal: No Solution Exploring Operation: 79/79=1, Resulting Numbers: [1] 1,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 53:[89, 69], Operations: ['83-4=79', '79-10=69'] Exploring Operation: 89*69=6141, Resulting Numbers: [6141] 6141,53 unequal: No Solution Exploring Operation: 89-69=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 89+69=158, Resulting Numbers: [158] 158,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[79, 99], Operations: ['83-4=79', '10+89=99'] Exploring Operation: 99-79=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 79*99=7821, Resulting Numbers: [7821] 7821,53 unequal: No Solution Exploring Operation: 79+99=178, Resulting Numbers: [178] 178,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[89, 4, 73], Operations: ['83-10=73'] Exploring Operation: 89+4=93, Resulting Numbers: [73, 93] Generated Node #0,2,0: 53:[73, 93] Operation: 89+4=93 Exploring Operation: 73-4=69, Resulting Numbers: [89, 69] Generated Node #0,2,1: 53:[89, 69] Operation: 73-4=69 Exploring Operation: 89-4=85, Resulting Numbers: [73, 85] Generated Node #0,2,2: 53:[73, 85] Operation: 89-4=85 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 53:[89, 69], Operations: ['83-10=73', '73-4=69'] Exploring Operation: 89+69=158, Resulting Numbers: [158] 158,53 unequal: No Solution Exploring Operation: 89*69=6141, Resulting Numbers: [6141] 6141,53 unequal: No Solution Exploring Operation: 89-69=20, Resulting Numbers: [20] 20,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[73, 85], Operations: ['83-10=73', '89-4=85'] Exploring Operation: 73*85=6205, Resulting Numbers: [6205] 6205,53 unequal: No Solution Exploring Operation: 73+85=158, Resulting Numbers: [158] 158,53 unequal: No Solution Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 53:[73, 93], Operations: ['83-10=73', '89+4=93'] Exploring Operation: 73*93=6789, Resulting Numbers: [6789] 6789,53 unequal: No Solution Exploring Operation: 73+93=166, Resulting Numbers: [166] 166,53 unequal: No Solution Exploring Operation: 93-73=20, Resulting Numbers: [20] 20,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 74, 20, 10, 15 ]
29
[ "74-20=54", "10+15=25", "54-25=29" ]
Current State: 29:[74, 20, 10, 15], Operations: [] Exploring Operation: 74-20=54, Resulting Numbers: [10, 15, 54] Generated Node #2: [10, 15, 54] from Operation: 74-20=54 Current State: 29:[10, 15, 54], Operations: ['74-20=54'] Exploring Operation: 10+15=25, Resulting Numbers: [54, 25] Generated Node #3: [54, 25] from Operation: 10+15=25 Current State: 29:[54, 25], Operations: ['74-20=54', '10+15=25'] Exploring Operation: 54-25=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[74, 20, 10, 15], Operations: [] Exploring Operation: 74-15=59, Resulting Numbers: [20, 10, 59] Generated Node #0,0: 29:[20, 10, 59] Operation: 74-15=59 Exploring Operation: 10+15=25, Resulting Numbers: [74, 20, 25] Generated Node #0,1: 29:[74, 20, 25] Operation: 10+15=25 Exploring Operation: 74-20=54, Resulting Numbers: [10, 15, 54] Generated Node #0,2: 29:[10, 15, 54] Operation: 74-20=54 Exploring Operation: 20+10=30, Resulting Numbers: [74, 15, 30] Generated Node #0,3: 29:[74, 15, 30] Operation: 20+10=30 Exploring Operation: 74-10=64, Resulting Numbers: [20, 15, 64] Generated Node #0,4: 29:[20, 15, 64] Operation: 74-10=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[20, 10, 59], Operations: ['74-15=59'] Exploring Operation: 20-10=10, Resulting Numbers: [59, 10] Generated Node #0,0,0: 29:[59, 10] Operation: 20-10=10 Exploring Operation: 59-20=39, Resulting Numbers: [10, 39] Generated Node #0,0,1: 29:[10, 39] Operation: 59-20=39 Exploring Operation: 10+59=69, Resulting Numbers: [20, 69] Generated Node #0,0,2: 29:[20, 69] Operation: 10+59=69 Exploring Operation: 20+10=30, Resulting Numbers: [59, 30] Generated Node #0,0,3: 29:[59, 30] Operation: 20+10=30 Exploring Operation: 59-10=49, Resulting Numbers: [20, 49] Generated Node #0,0,4: 29:[20, 49] Operation: 59-10=49 Moving to Node #0,0,1 Current State: 29:[10, 39], Operations: ['74-15=59', '59-20=39'] Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,29 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[74, 20, 10, 15], Operations: [] Exploring Operation: 74-15=59, Resulting Numbers: [20, 10, 59] Generated Node #0,0: 29:[20, 10, 59] Operation: 74-15=59 Moving to Node #0,0 Current State: 29:[20, 10, 59], Operations: ['74-15=59'] Exploring Operation: 59-20=39, Resulting Numbers: [10, 39] Generated Node #0,0,1: 29:[10, 39] Operation: 59-20=39 Moving to Node #0,0,1 Current State: 29:[10, 39], Operations: ['74-15=59', '59-20=39'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 16, 39, 88, 9 ]
47
[ "88-16=72", "72/9=8", "39+8=47" ]
Current State: 47:[16, 39, 88, 9], Operations: [] Exploring Operation: 88-16=72, Resulting Numbers: [39, 9, 72] Generated Node #2: [39, 9, 72] from Operation: 88-16=72 Current State: 47:[39, 9, 72], Operations: ['88-16=72'] Exploring Operation: 72/9=8, Resulting Numbers: [39, 8] Generated Node #3: [39, 8] from Operation: 72/9=8 Current State: 47:[39, 8], Operations: ['88-16=72', '72/9=8'] Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[16, 39, 88, 9], Operations: [] Exploring Operation: 88-16=72, Resulting Numbers: [39, 9, 72] Generated Node #0,0: 47:[39, 9, 72] Operation: 88-16=72 Exploring Operation: 16+9=25, Resulting Numbers: [39, 88, 25] Generated Node #0,1: 47:[39, 88, 25] Operation: 16+9=25 Exploring Operation: 39+9=48, Resulting Numbers: [16, 88, 48] Generated Node #0,2: 47:[16, 88, 48] Operation: 39+9=48 Exploring Operation: 88-39=49, Resulting Numbers: [16, 9, 49] Generated Node #0,3: 47:[16, 9, 49] Operation: 88-39=49 Exploring Operation: 88-9=79, Resulting Numbers: [16, 39, 79] Generated Node #0,4: 47:[16, 39, 79] Operation: 88-9=79 Moving to Node #0,0 Current State: 47:[39, 9, 72], Operations: ['88-16=72'] Exploring Operation: 72/9=8, Resulting Numbers: [39, 8] Generated Node #0,0,0: 47:[39, 8] Operation: 72/9=8 Exploring Operation: 39+9=48, Resulting Numbers: [72, 48] Generated Node #0,0,1: 47:[72, 48] Operation: 39+9=48 Exploring Operation: 39-9=30, Resulting Numbers: [72, 30] Generated Node #0,0,2: 47:[72, 30] Operation: 39-9=30 Exploring Operation: 72-9=63, Resulting Numbers: [39, 63] Generated Node #0,0,3: 47:[39, 63] Operation: 72-9=63 Exploring Operation: 9+72=81, Resulting Numbers: [39, 81] Generated Node #0,0,4: 47:[39, 81] Operation: 9+72=81 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[39, 63], Operations: ['88-16=72', '72-9=63'] Exploring Operation: 39+63=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 39*63=2457, Resulting Numbers: [2457] 2457,47 unequal: No Solution Exploring Operation: 63-39=24, Resulting Numbers: [24] 24,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[72, 48], Operations: ['88-16=72', '39+9=48'] Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,47 unequal: No Solution Exploring Operation: 72+48=120, Resulting Numbers: [120] 120,47 unequal: No Solution Exploring Operation: 72*48=3456, Resulting Numbers: [3456] 3456,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[72, 30], Operations: ['88-16=72', '39-9=30'] Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,47 unequal: No Solution Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 47:[39, 81], Operations: ['88-16=72', '9+72=81'] Exploring Operation: 39*81=3159, Resulting Numbers: [3159] 3159,47 unequal: No Solution Exploring Operation: 39+81=120, Resulting Numbers: [120] 120,47 unequal: No Solution Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[39, 8], Operations: ['88-16=72', '72/9=8'] Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[16, 39, 88, 9], Operations: [] Exploring Operation: 88-16=72, Resulting Numbers: [39, 9, 72] Generated Node #0,0: 47:[39, 9, 72] Operation: 88-16=72 Moving to Node #0,0 Current State: 47:[39, 9, 72], Operations: ['88-16=72'] Exploring Operation: 72/9=8, Resulting Numbers: [39, 8] Generated Node #0,0,0: 47:[39, 8] Operation: 72/9=8 Moving to Node #0,0,0 Current State: 47:[39, 8], Operations: ['88-16=72', '72/9=8'] Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 82, 50, 2, 29 ]
93
[ "82-50=32", "2*32=64", "29+64=93" ]
Current State: 93:[82, 50, 2, 29], Operations: [] Exploring Operation: 82-50=32, Resulting Numbers: [2, 29, 32] Generated Node #2: [2, 29, 32] from Operation: 82-50=32 Current State: 93:[2, 29, 32], Operations: ['82-50=32'] Exploring Operation: 2*32=64, Resulting Numbers: [29, 64] Generated Node #3: [29, 64] from Operation: 2*32=64 Current State: 93:[29, 64], Operations: ['82-50=32', '2*32=64'] Exploring Operation: 29+64=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[82, 50, 2, 29], Operations: [] Exploring Operation: 82-50=32, Resulting Numbers: [2, 29, 32] Generated Node #0,0: 93:[2, 29, 32] Operation: 82-50=32 Moving to Node #0,0 Current State: 93:[2, 29, 32], Operations: ['82-50=32'] Exploring Operation: 2+29=31, Resulting Numbers: [32, 31] Generated Node #0,0,0: 93:[32, 31] Operation: 2+29=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[32, 31], Operations: ['82-50=32', '2+29=31'] Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,93 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
[ 31, 5, 48, 18 ]
66
[ "31+5=36", "48-18=30", "36+30=66" ]
Current State: 66:[31, 5, 48, 18], Operations: [] Exploring Operation: 31+5=36, Resulting Numbers: [48, 18, 36] Generated Node #2: [48, 18, 36] from Operation: 31+5=36 Current State: 66:[48, 18, 36], Operations: ['31+5=36'] Exploring Operation: 48-18=30, Resulting Numbers: [36, 30] Generated Node #3: [36, 30] from Operation: 48-18=30 Current State: 66:[36, 30], Operations: ['31+5=36', '48-18=30'] Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[31, 5, 48, 18], Operations: [] Exploring Operation: 48-5=43, Resulting Numbers: [31, 18, 43] Generated Node #0,0: 66:[31, 18, 43] Operation: 48-5=43 Exploring Operation: 48-18=30, Resulting Numbers: [31, 5, 30] Generated Node #0,1: 66:[31, 5, 30] Operation: 48-18=30 Exploring Operation: 48-31=17, Resulting Numbers: [5, 18, 17] Generated Node #0,2: 66:[5, 18, 17] Operation: 48-31=17 Exploring Operation: 48+18=66, Resulting Numbers: [31, 5, 66] Generated Node #0,3: 66:[31, 5, 66] Operation: 48+18=66 Exploring Operation: 31+48=79, Resulting Numbers: [5, 18, 79] Generated Node #0,4: 66:[5, 18, 79] Operation: 31+48=79 Moving to Node #0,3 Current State: 66:[31, 5, 66], Operations: ['48+18=66'] Exploring Operation: 31+5=36, Resulting Numbers: [66, 36] Generated Node #0,3,0: 66:[66, 36] Operation: 31+5=36 Exploring Operation: 31-5=26, Resulting Numbers: [66, 26] Generated Node #0,3,1: 66:[66, 26] Operation: 31-5=26 Exploring Operation: 66-31=35, Resulting Numbers: [5, 35] Generated Node #0,3,2: 66:[5, 35] Operation: 66-31=35 Exploring Operation: 66-5=61, Resulting Numbers: [31, 61] Generated Node #0,3,3: 66:[31, 61] Operation: 66-5=61 Exploring Operation: 5+66=71, Resulting Numbers: [31, 71] Generated Node #0,3,4: 66:[31, 71] Operation: 5+66=71 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 66:[66, 36], Operations: ['48+18=66', '31+5=36'] Exploring Operation: 66*36=2376, Resulting Numbers: [2376] 2376,66 unequal: No Solution Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 66+36=102, Resulting Numbers: [102] 102,66 unequal: No Solution No 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: 66:[5, 35], Operations: ['48+18=66', '66-31=35'] Exploring Operation: 5+35=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,66 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 5*35=175, Resulting Numbers: [175] 175,66 unequal: No Solution No 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: 66:[66, 26], Operations: ['48+18=66', '31-5=26'] Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,66 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,66 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,66 unequal: No Solution No 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: 66:[31, 61], Operations: ['48+18=66', '66-5=61'] Exploring Operation: 31*61=1891, Resulting Numbers: [1891] 1891,66 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 31+61=92, Resulting Numbers: [92] 92,66 unequal: No Solution No 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: 66:[31, 71], Operations: ['48+18=66', '5+66=71'] Exploring Operation: 31*71=2201, Resulting Numbers: [2201] 2201,66 unequal: No Solution Exploring Operation: 31+71=102, Resulting Numbers: [102] 102,66 unequal: No Solution Exploring Operation: 71-31=40, Resulting Numbers: [40] 40,66 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: 66:[31, 5, 30], Operations: ['48-18=30'] Exploring Operation: 30/5=6, Resulting Numbers: [31, 6] Generated Node #0,1,0: 66:[31, 6] Operation: 30/5=6 Exploring Operation: 31-30=1, Resulting Numbers: [5, 1] Generated Node #0,1,1: 66:[5, 1] Operation: 31-30=1 Exploring Operation: 31+5=36, Resulting Numbers: [30, 36] Generated Node #0,1,2: 66:[30, 36] Operation: 31+5=36 Exploring Operation: 5+30=35, Resulting Numbers: [31, 35] Generated Node #0,1,3: 66:[31, 35] Operation: 5+30=35 Exploring Operation: 30-5=25, Resulting Numbers: [31, 25] Generated Node #0,1,4: 66:[31, 25] Operation: 30-5=25 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[31, 6], Operations: ['48-18=30', '30/5=6'] Exploring Operation: 31*6=186, Resulting Numbers: [186] 186,66 unequal: No Solution Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,66 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,66 unequal: No Solution No 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: 66:[5, 1], Operations: ['48-18=30', '31-30=1'] Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,66 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,66 unequal: No Solution No 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: 66:[31, 35], Operations: ['48-18=30', '5+30=35'] Exploring Operation: 35-31=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 31*35=1085, Resulting Numbers: [1085] 1085,66 unequal: No Solution Exploring Operation: 31+35=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[31, 5, 48, 18], Operations: [] Exploring Operation: 48-18=30, Resulting Numbers: [31, 5, 30] Generated Node #0,1: 66:[31, 5, 30] Operation: 48-18=30 Moving to Node #0,1 Current State: 66:[31, 5, 30], Operations: ['48-18=30'] Exploring Operation: 5+30=35, Resulting Numbers: [31, 35] Generated Node #0,1,3: 66:[31, 35] Operation: 5+30=35 Moving to Node #0,1,3 Current State: 66:[31, 35], Operations: ['48-18=30', '5+30=35'] Exploring Operation: 31+35=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_5
mult_heuristic
[ 10, 52, 60, 10 ]
49
[ "10+10=20", "60/20=3", "52-3=49" ]
Current State: 49:[10, 52, 60, 10], Operations: [] Exploring Operation: 10+10=20, Resulting Numbers: [52, 60, 20] Generated Node #2: [52, 60, 20] from Operation: 10+10=20 Current State: 49:[52, 60, 20], Operations: ['10+10=20'] Exploring Operation: 60/20=3, Resulting Numbers: [52, 3] Generated Node #3: [52, 3] from Operation: 60/20=3 Current State: 49:[52, 3], Operations: ['10+10=20', '60/20=3'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[10, 52, 60, 10], Operations: [] Exploring Operation: 60-10=50, Resulting Numbers: [10, 52, 50] Generated Node #0,0: 49:[10, 52, 50] Operation: 60-10=50 Exploring Operation: 60-52=8, Resulting Numbers: [10, 10, 8] Generated Node #0,1: 49:[10, 10, 8] Operation: 60-52=8 Exploring Operation: 60-10=50, Resulting Numbers: [52, 10, 50] Generated Node #0,2: 49:[52, 10, 50] Operation: 60-10=50 Exploring Operation: 60/10=6, Resulting Numbers: [52, 10, 6] Generated Node #0,3: 49:[52, 10, 6] Operation: 60/10=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[10, 52, 50], Operations: ['60-10=50'] Exploring Operation: 50-10=40, Resulting Numbers: [52, 40] Generated Node #0,0,0: 49:[52, 40] Operation: 50-10=40 Exploring Operation: 50/10=5, Resulting Numbers: [52, 5] Generated Node #0,0,1: 49:[52, 5] Operation: 50/10=5 Exploring Operation: 52-50=2, Resulting Numbers: [10, 2] Generated Node #0,0,2: 49:[10, 2] Operation: 52-50=2 Exploring Operation: 52-10=42, Resulting Numbers: [50, 42] Generated Node #0,0,3: 49:[50, 42] Operation: 52-10=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[52, 5], Operations: ['60-10=50', '50/10=5'] Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,49 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[10, 2], Operations: ['60-10=50', '52-50=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 49:[50, 42], Operations: ['60-10=50', '52-10=42'] Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,49 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[52, 40], Operations: ['60-10=50', '50-10=40'] Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,49 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,49 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[10, 10, 8], Operations: ['60-52=8'] Exploring Operation: 10/10=1, Resulting Numbers: [8, 1] Generated Node #0,1,0: 49:[8, 1] Operation: 10/10=1 Exploring Operation: 10-8=2, Resulting Numbers: [10, 2] Generated Node #0,1,1: 49:[10, 2] Operation: 10-8=2 Exploring Operation: 10-10=0, Resulting Numbers: [8, 0] Generated Node #0,1,2: 49:[8, 0] Operation: 10-10=0 Exploring Operation: 10-8=2, Resulting Numbers: [10, 2] Generated Node #0,1,3: 49:[10, 2] Operation: 10-8=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[8, 1], Operations: ['60-52=8', '10/10=1'] Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,49 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:[10, 2], Operations: ['60-52=8', '10-8=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,49 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:[8, 0], Operations: ['60-52=8', '10-10=0'] Exploring Operation: 8-0=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 8+0=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 8*0=0, Resulting Numbers: [0] 0,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 49:[10, 2], Operations: ['60-52=8', '10-8=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,49 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:[52, 10, 50], Operations: ['60-10=50'] Exploring Operation: 52-50=2, Resulting Numbers: [10, 2] Generated Node #0,2,0: 49:[10, 2] Operation: 52-50=2 Exploring Operation: 50-10=40, Resulting Numbers: [52, 40] Generated Node #0,2,1: 49:[52, 40] Operation: 50-10=40 Exploring Operation: 50/10=5, Resulting Numbers: [52, 5] Generated Node #0,2,2: 49:[52, 5] Operation: 50/10=5 Exploring Operation: 52-10=42, Resulting Numbers: [50, 42] Generated Node #0,2,3: 49:[50, 42] Operation: 52-10=42 Moving to Node #0,2,2 Current State: 49:[52, 5], Operations: ['60-10=50', '50/10=5'] Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,49 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,49 unequal: No Solution Moving to Node #0,2,3 Current State: 49:[50, 42], Operations: ['60-10=50', '52-10=42'] Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,49 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[10, 2], Operations: ['60-10=50', '52-50=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[52, 40], Operations: ['60-10=50', '50-10=40'] Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,49 unequal: No Solution Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[52, 10, 6], Operations: ['60/10=6'] Exploring Operation: 52-10=42, Resulting Numbers: [6, 42] Generated Node #0,3,0: 49:[6, 42] Operation: 52-10=42 Exploring Operation: 52+6=58, Resulting Numbers: [10, 58] Generated Node #0,3,1: 49:[10, 58] Operation: 52+6=58 Exploring Operation: 52-6=46, Resulting Numbers: [10, 46] Generated Node #0,3,2: 49:[10, 46] Operation: 52-6=46 Exploring Operation: 10-6=4, Resulting Numbers: [52, 4] Generated Node #0,3,3: 49:[52, 4] Operation: 10-6=4 Moving to Node #0,3,2 Current State: 49:[10, 46], Operations: ['60/10=6', '52-6=46'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,49 unequal: No Solution Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,49 unequal: No Solution Moving to Node #0,3,3 Current State: 49:[52, 4], Operations: ['60/10=6', '10-6=4'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,49 unequal: No Solution Exploring Operation: 52*4=208, Resulting Numbers: [208] 208,49 unequal: No Solution Moving to Node #0,3,0 Current State: 49:[6, 42], Operations: ['60/10=6', '52-10=42'] Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[10, 58], Operations: ['60/10=6', '52+6=58'] Exploring Operation: 10*58=580, Resulting Numbers: [580] 580,49 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 10+58=68, Resulting Numbers: [68] 68,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 86, 52, 26, 55 ]
24
[ "52/26=2", "55*2=110", "110-86=24" ]
Current State: 24:[86, 52, 26, 55], Operations: [] Exploring Operation: 52/26=2, Resulting Numbers: [86, 55, 2] Generated Node #2: [86, 55, 2] from Operation: 52/26=2 Current State: 24:[86, 55, 2], Operations: ['52/26=2'] Exploring Operation: 55*2=110, Resulting Numbers: [86, 110] Generated Node #3: [86, 110] from Operation: 55*2=110 Current State: 24:[86, 110], Operations: ['52/26=2', '55*2=110'] Exploring Operation: 110-86=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[86, 52, 26, 55], Operations: [] Exploring Operation: 86-55=31, Resulting Numbers: [52, 26, 31] Generated Node #0,0: 24:[52, 26, 31] Operation: 86-55=31 Exploring Operation: 52/26=2, Resulting Numbers: [86, 55, 2] Generated Node #0,1: 24:[86, 55, 2] Operation: 52/26=2 Exploring Operation: 86-26=60, Resulting Numbers: [52, 55, 60] Generated Node #0,2: 24:[52, 55, 60] Operation: 86-26=60 Exploring Operation: 86-52=34, Resulting Numbers: [26, 55, 34] Generated Node #0,3: 24:[26, 55, 34] Operation: 86-52=34 Exploring Operation: 55-52=3, Resulting Numbers: [86, 26, 3] Generated Node #0,4: 24:[86, 26, 3] Operation: 55-52=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[52, 26, 31], Operations: ['86-55=31'] Exploring Operation: 31-26=5, Resulting Numbers: [52, 5] Generated Node #0,0,0: 24:[52, 5] Operation: 31-26=5 Exploring Operation: 52+26=78, Resulting Numbers: [31, 78] Generated Node #0,0,1: 24:[31, 78] Operation: 52+26=78 Exploring Operation: 52-26=26, Resulting Numbers: [31, 26] Generated Node #0,0,2: 24:[31, 26] Operation: 52-26=26 Exploring Operation: 52/26=2, Resulting Numbers: [31, 2] Generated Node #0,0,3: 24:[31, 2] Operation: 52/26=2 Exploring Operation: 52-31=21, Resulting Numbers: [26, 21] Generated Node #0,0,4: 24:[26, 21] Operation: 52-31=21 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 24:[26, 21], Operations: ['86-55=31', '52-31=21'] Exploring Operation: 26*21=546, Resulting Numbers: [546] 546,24 unequal: No Solution Exploring Operation: 26+21=47, Resulting Numbers: [47] 47,24 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,24 unequal: No Solution No 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: 24:[31, 2], Operations: ['86-55=31', '52/26=2'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,24 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,24 unequal: No Solution No 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: 24:[31, 26], Operations: ['86-55=31', '52-26=26'] Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,24 unequal: No Solution Exploring Operation: 31*26=806, Resulting Numbers: [806] 806,24 unequal: No Solution No 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: 24:[52, 5], Operations: ['86-55=31', '31-26=5'] Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,24 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,24 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,24 unequal: No Solution No 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: 24:[31, 78], Operations: ['86-55=31', '52+26=78'] Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,24 unequal: No Solution Exploring Operation: 31*78=2418, Resulting Numbers: [2418] 2418,24 unequal: No Solution Exploring Operation: 31+78=109, Resulting Numbers: [109] 109,24 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: 24:[26, 55, 34], Operations: ['86-52=34'] Exploring Operation: 55-34=21, Resulting Numbers: [26, 21] Generated Node #0,3,0: 24:[26, 21] Operation: 55-34=21 Exploring Operation: 34-26=8, Resulting Numbers: [55, 8] Generated Node #0,3,1: 24:[55, 8] Operation: 34-26=8 Exploring Operation: 55-26=29, Resulting Numbers: [34, 29] Generated Node #0,3,2: 24:[34, 29] Operation: 55-26=29 Exploring Operation: 26+55=81, Resulting Numbers: [34, 81] Generated Node #0,3,3: 24:[34, 81] Operation: 26+55=81 Exploring Operation: 26+34=60, Resulting Numbers: [55, 60] Generated Node #0,3,4: 24:[55, 60] Operation: 26+34=60 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 24:[26, 21], Operations: ['86-52=34', '55-34=21'] Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 26+21=47, Resulting Numbers: [47] 47,24 unequal: No Solution Exploring Operation: 26*21=546, Resulting Numbers: [546] 546,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 24:[34, 29], Operations: ['86-52=34', '55-26=29'] Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,24 unequal: No Solution Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,24 unequal: No Solution No 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: 24:[55, 8], Operations: ['86-52=34', '34-26=8'] Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,24 unequal: No Solution Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,24 unequal: No Solution No 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: 24:[34, 81], Operations: ['86-52=34', '26+55=81'] Exploring Operation: 81-34=47, Resulting Numbers: [47] 47,24 unequal: No Solution Exploring Operation: 34+81=115, Resulting Numbers: [115] 115,24 unequal: No Solution Exploring Operation: 34*81=2754, Resulting Numbers: [2754] 2754,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 24:[55, 60], Operations: ['86-52=34', '26+34=60'] Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,24 unequal: No Solution Exploring Operation: 55*60=3300, Resulting Numbers: [3300] 3300,24 unequal: No Solution Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 24:[86, 26, 3], Operations: ['55-52=3'] Exploring Operation: 86-3=83, Resulting Numbers: [26, 83] Generated Node #0,4,0: 24:[26, 83] Operation: 86-3=83 Exploring Operation: 26+3=29, Resulting Numbers: [86, 29] Generated Node #0,4,1: 24:[86, 29] Operation: 26+3=29 Exploring Operation: 26-3=23, Resulting Numbers: [86, 23] Generated Node #0,4,2: 24:[86, 23] Operation: 26-3=23 Exploring Operation: 86+3=89, Resulting Numbers: [26, 89] Generated Node #0,4,3: 24:[26, 89] Operation: 86+3=89 Exploring Operation: 86-26=60, Resulting Numbers: [3, 60] Generated Node #0,4,4: 24:[3, 60] Operation: 86-26=60 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 24:[3, 60], Operations: ['55-52=3', '86-26=60'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,24 unequal: No Solution Exploring Operation: 3*60=180, Resulting Numbers: [180] 180,24 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,24 unequal: No Solution No 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: 24:[26, 83], Operations: ['55-52=3', '86-3=83'] Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,24 unequal: No Solution Exploring Operation: 26+83=109, Resulting Numbers: [109] 109,24 unequal: No Solution Exploring Operation: 26*83=2158, Resulting Numbers: [2158] 2158,24 unequal: No Solution No 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: 24:[86, 23], Operations: ['55-52=3', '26-3=23'] Exploring Operation: 86*23=1978, Resulting Numbers: [1978] 1978,24 unequal: No Solution Exploring Operation: 86-23=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 86+23=109, Resulting Numbers: [109] 109,24 unequal: No Solution No 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: 24:[86, 29], Operations: ['55-52=3', '26+3=29'] Exploring Operation: 86+29=115, Resulting Numbers: [115] 115,24 unequal: No Solution Exploring Operation: 86*29=2494, Resulting Numbers: [2494] 2494,24 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,24 unequal: No Solution No 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: 24:[26, 89], Operations: ['55-52=3', '86+3=89'] Exploring Operation: 26+89=115, Resulting Numbers: [115] 115,24 unequal: No Solution Exploring Operation: 26*89=2314, Resulting Numbers: [2314] 2314,24 unequal: No Solution Exploring Operation: 89-26=63, Resulting Numbers: [63] 63,24 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: 24:[86, 55, 2], Operations: ['52/26=2'] Exploring Operation: 55-2=53, Resulting Numbers: [86, 53] Generated Node #0,1,0: 24:[86, 53] Operation: 55-2=53 Exploring Operation: 86-55=31, Resulting Numbers: [2, 31] Generated Node #0,1,1: 24:[2, 31] Operation: 86-55=31 Exploring Operation: 86-2=84, Resulting Numbers: [55, 84] Generated Node #0,1,2: 24:[55, 84] Operation: 86-2=84 Exploring Operation: 86+2=88, Resulting Numbers: [55, 88] Generated Node #0,1,3: 24:[55, 88] Operation: 86+2=88 Exploring Operation: 86/2=43, Resulting Numbers: [55, 43] Generated Node #0,1,4: 24:[55, 43] Operation: 86/2=43 Moving to Node #0,1,1 Current State: 24:[2, 31], Operations: ['52/26=2', '86-55=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,24 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,24 unequal: No Solution Moving to Node #0,1,4 Current State: 24:[55, 43], Operations: ['52/26=2', '86/2=43'] Exploring Operation: 55+43=98, Resulting Numbers: [98] 98,24 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 55*43=2365, Resulting Numbers: [2365] 2365,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[86, 53], Operations: ['52/26=2', '55-2=53'] Exploring Operation: 86+53=139, Resulting Numbers: [139] 139,24 unequal: No Solution Exploring Operation: 86-53=33, Resulting Numbers: [33] 33,24 unequal: No Solution Exploring Operation: 86*53=4558, Resulting Numbers: [4558] 4558,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[55, 84], Operations: ['52/26=2', '86-2=84'] Exploring Operation: 84-55=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 55+84=139, Resulting Numbers: [139] 139,24 unequal: No Solution Exploring Operation: 55*84=4620, Resulting Numbers: [4620] 4620,24 unequal: No Solution Moving to Node #0,1,3 Current State: 24:[55, 88], Operations: ['52/26=2', '86+2=88'] Exploring Operation: 55+88=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,24 unequal: No Solution Exploring Operation: 55*88=4840, Resulting Numbers: [4840] 4840,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[52, 55, 60], Operations: ['86-26=60'] Exploring Operation: 60-55=5, Resulting Numbers: [52, 5] Generated Node #0,2,0: 24:[52, 5] Operation: 60-55=5 Exploring Operation: 60-52=8, Resulting Numbers: [55, 8] Generated Node #0,2,1: 24:[55, 8] Operation: 60-52=8 Exploring Operation: 52+55=107, Resulting Numbers: [60, 107] Generated Node #0,2,2: 24:[60, 107] Operation: 52+55=107 Exploring Operation: 55-52=3, Resulting Numbers: [60, 3] Generated Node #0,2,3: 24:[60, 3] Operation: 55-52=3 Exploring Operation: 52+60=112, Resulting Numbers: [55, 112] Generated Node #0,2,4: 24:[55, 112] Operation: 52+60=112 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 24:[52, 5], Operations: ['86-26=60', '60-55=5'] Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,24 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,24 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,24 unequal: No Solution No 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: 24:[55, 8], Operations: ['86-26=60', '60-52=8'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,24 unequal: No Solution Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,24 unequal: No Solution No 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: 24:[60, 3], Operations: ['86-26=60', '55-52=3'] Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,24 unequal: No Solution Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,24 unequal: No Solution No 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: 24:[60, 107], Operations: ['86-26=60', '52+55=107'] Exploring Operation: 60+107=167, Resulting Numbers: [167] 167,24 unequal: No Solution Exploring Operation: 107-60=47, Resulting Numbers: [47] 47,24 unequal: No Solution Exploring Operation: 60*107=6420, Resulting Numbers: [6420] 6420,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 24:[55, 112], Operations: ['86-26=60', '52+60=112'] Exploring Operation: 55+112=167, Resulting Numbers: [167] 167,24 unequal: No Solution Exploring Operation: 55*112=6160, Resulting Numbers: [6160] 6160,24 unequal: No Solution Exploring Operation: 112-55=57, Resulting Numbers: [57] 57,24 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
[ 97, 46, 2, 85 ]
63
[ "97*2=194", "46+85=131", "194-131=63" ]
Current State: 63:[97, 46, 2, 85], Operations: [] Exploring Operation: 97*2=194, Resulting Numbers: [46, 85, 194] Generated Node #2: [46, 85, 194] from Operation: 97*2=194 Current State: 63:[46, 85, 194], Operations: ['97*2=194'] Exploring Operation: 46+85=131, Resulting Numbers: [194, 131] Generated Node #3: [194, 131] from Operation: 46+85=131 Current State: 63:[194, 131], Operations: ['97*2=194', '46+85=131'] Exploring Operation: 194-131=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[97, 46, 2, 85], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [46, 2, 12] Generated Node #0,0: 63:[46, 2, 12] Operation: 97-85=12 Exploring Operation: 97-46=51, Resulting Numbers: [2, 85, 51] Generated Node #0,1: 63:[2, 85, 51] Operation: 97-46=51 Exploring Operation: 46/2=23, Resulting Numbers: [97, 85, 23] Generated Node #0,2: 63:[97, 85, 23] Operation: 46/2=23 Exploring Operation: 97-2=95, Resulting Numbers: [46, 85, 95] Generated Node #0,3: 63:[46, 85, 95] Operation: 97-2=95 Exploring Operation: 85-46=39, Resulting Numbers: [97, 2, 39] Generated Node #0,4: 63:[97, 2, 39] Operation: 85-46=39 Moving to Node #0,0 Current State: 63:[46, 2, 12], Operations: ['97-85=12'] Exploring Operation: 46+2=48, Resulting Numbers: [12, 48] Generated Node #0,0,0: 63:[12, 48] Operation: 46+2=48 Exploring Operation: 46/2=23, Resulting Numbers: [12, 23] Generated Node #0,0,1: 63:[12, 23] Operation: 46/2=23 Exploring Operation: 46+12=58, Resulting Numbers: [2, 58] Generated Node #0,0,2: 63:[2, 58] Operation: 46+12=58 Exploring Operation: 46-12=34, Resulting Numbers: [2, 34] Generated Node #0,0,3: 63:[2, 34] Operation: 46-12=34 Exploring Operation: 12-2=10, Resulting Numbers: [46, 10] Generated Node #0,0,4: 63:[46, 10] Operation: 12-2=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[12, 23], Operations: ['97-85=12', '46/2=23'] Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[2, 58], Operations: ['97-85=12', '46+12=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,63 unequal: No Solution Exploring Operation: 2*58=116, Resulting Numbers: [116] 116,63 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 63:[2, 34], Operations: ['97-85=12', '46-12=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,63 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,63 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[12, 48], Operations: ['97-85=12', '46+2=48'] Exploring Operation: 12+48=60, Resulting Numbers: [60] 60,63 unequal: No Solution Exploring Operation: 12*48=576, Resulting Numbers: [576] 576,63 unequal: No Solution Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,63 unequal: No Solution Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 63:[46, 10], Operations: ['97-85=12', '12-2=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,63 unequal: No Solution Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,63 unequal: No Solution Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,63 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: 63:[2, 85, 51], Operations: ['97-46=51'] Exploring Operation: 51-2=49, Resulting Numbers: [85, 49] Generated Node #0,1,0: 63:[85, 49] Operation: 51-2=49 Exploring Operation: 85-2=83, Resulting Numbers: [51, 83] Generated Node #0,1,1: 63:[51, 83] Operation: 85-2=83 Exploring Operation: 2+51=53, Resulting Numbers: [85, 53] Generated Node #0,1,2: 63:[85, 53] Operation: 2+51=53 Exploring Operation: 2+85=87, Resulting Numbers: [51, 87] Generated Node #0,1,3: 63:[51, 87] Operation: 2+85=87 Exploring Operation: 85-51=34, Resulting Numbers: [2, 34] Generated Node #0,1,4: 63:[2, 34] Operation: 85-51=34 Moving to Node #0,4 Current State: 63:[97, 2, 39], Operations: ['85-46=39'] Exploring Operation: 97+2=99, Resulting Numbers: [39, 99] Generated Node #0,4,0: 63:[39, 99] Operation: 97+2=99 Exploring Operation: 2*39=78, Resulting Numbers: [97, 78] Generated Node #0,4,1: 63:[97, 78] Operation: 2*39=78 Exploring Operation: 97-39=58, Resulting Numbers: [2, 58] Generated Node #0,4,2: 63:[2, 58] Operation: 97-39=58 Exploring Operation: 97-2=95, Resulting Numbers: [39, 95] Generated Node #0,4,3: 63:[39, 95] Operation: 97-2=95 Exploring Operation: 39-2=37, Resulting Numbers: [97, 37] Generated Node #0,4,4: 63:[97, 37] Operation: 39-2=37 Moving to Node #0,2 Current State: 63:[97, 85, 23], Operations: ['46/2=23'] Exploring Operation: 85-23=62, Resulting Numbers: [97, 62] Generated Node #0,2,0: 63:[97, 62] Operation: 85-23=62 Exploring Operation: 85+23=108, Resulting Numbers: [97, 108] Generated Node #0,2,1: 63:[97, 108] Operation: 85+23=108 Exploring Operation: 97+23=120, Resulting Numbers: [85, 120] Generated Node #0,2,2: 63:[85, 120] Operation: 97+23=120 Exploring Operation: 97-23=74, Resulting Numbers: [85, 74] Generated Node #0,2,3: 63:[85, 74] Operation: 97-23=74 Exploring Operation: 97-85=12, Resulting Numbers: [23, 12] Generated Node #0,2,4: 63:[23, 12] Operation: 97-85=12 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 63:[23, 12], Operations: ['46/2=23', '97-85=12'] Exploring Operation: 23*12=276, Resulting Numbers: [276] 276,63 unequal: No Solution Exploring Operation: 23+12=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 63:[85, 74], Operations: ['46/2=23', '97-23=74'] Exploring Operation: 85+74=159, Resulting Numbers: [159] 159,63 unequal: No Solution Exploring Operation: 85-74=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 85*74=6290, Resulting Numbers: [6290] 6290,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[97, 62], Operations: ['46/2=23', '85-23=62'] Exploring Operation: 97+62=159, Resulting Numbers: [159] 159,63 unequal: No Solution Exploring Operation: 97-62=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 97*62=6014, Resulting Numbers: [6014] 6014,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[97, 108], Operations: ['46/2=23', '85+23=108'] Exploring Operation: 108-97=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 97+108=205, Resulting Numbers: [205] 205,63 unequal: No Solution Exploring Operation: 97*108=10476, Resulting Numbers: [10476] 10476,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 63:[85, 120], Operations: ['46/2=23', '97+23=120'] Exploring Operation: 120-85=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 85+120=205, Resulting Numbers: [205] 205,63 unequal: No Solution Exploring Operation: 85*120=10200, Resulting Numbers: [10200] 10200,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 63:[46, 85, 95], Operations: ['97-2=95'] Exploring Operation: 85-46=39, Resulting Numbers: [95, 39] Generated Node #0,3,0: 63:[95, 39] Operation: 85-46=39 Exploring Operation: 95-46=49, Resulting Numbers: [85, 49] Generated Node #0,3,1: 63:[85, 49] Operation: 95-46=49 Exploring Operation: 46+95=141, Resulting Numbers: [85, 141] Generated Node #0,3,2: 63:[85, 141] Operation: 46+95=141 Exploring Operation: 95-85=10, Resulting Numbers: [46, 10] Generated Node #0,3,3: 63:[46, 10] Operation: 95-85=10 Exploring Operation: 46+85=131, Resulting Numbers: [95, 131] Generated Node #0,3,4: 63:[95, 131] Operation: 46+85=131 Moving to Node #0,4,2 Current State: 63:[2, 58], Operations: ['85-46=39', '97-39=58'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,63 unequal: No Solution Exploring Operation: 2*58=116, Resulting Numbers: [116] 116,63 unequal: No Solution Moving to Node #0,1,4 Current State: 63:[2, 34], Operations: ['97-46=51', '85-51=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,63 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,63 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,63 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,63 unequal: No Solution Moving to Node #0,3,3 Current State: 63:[46, 10], Operations: ['97-2=95', '95-85=10'] Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,63 unequal: No Solution Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[85, 53], Operations: ['97-46=51', '2+51=53'] Exploring Operation: 85+53=138, Resulting Numbers: [138] 138,63 unequal: No Solution Exploring Operation: 85-53=32, Resulting Numbers: [32] 32,63 unequal: No Solution Exploring Operation: 85*53=4505, Resulting Numbers: [4505] 4505,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[51, 83], Operations: ['97-46=51', '85-2=83'] Exploring Operation: 51*83=4233, Resulting Numbers: [4233] 4233,63 unequal: No Solution Exploring Operation: 83-51=32, Resulting Numbers: [32] 32,63 unequal: No Solution Exploring Operation: 51+83=134, Resulting Numbers: [134] 134,63 unequal: No Solution Moving to Node #0,3,1 Current State: 63:[85, 49], Operations: ['97-2=95', '95-46=49'] Exploring Operation: 85+49=134, Resulting Numbers: [134] 134,63 unequal: No Solution Exploring Operation: 85-49=36, Resulting Numbers: [36] 36,63 unequal: No Solution Exploring Operation: 85*49=4165, Resulting Numbers: [4165] 4165,63 unequal: No Solution Moving to Node #0,1,3 Current State: 63:[51, 87], Operations: ['97-46=51', '2+85=87'] Exploring Operation: 51+87=138, Resulting Numbers: [138] 138,63 unequal: No Solution Exploring Operation: 51*87=4437, Resulting Numbers: [4437] 4437,63 unequal: No Solution Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[85, 49], Operations: ['97-46=51', '51-2=49'] Exploring Operation: 85*49=4165, Resulting Numbers: [4165] 4165,63 unequal: No Solution Exploring Operation: 85-49=36, Resulting Numbers: [36] 36,63 unequal: No Solution Exploring Operation: 85+49=134, Resulting Numbers: [134] 134,63 unequal: No Solution Moving to Node #0,4,1 Current State: 63:[97, 78], Operations: ['85-46=39', '2*39=78'] Exploring Operation: 97*78=7566, Resulting Numbers: [7566] 7566,63 unequal: No Solution Exploring Operation: 97-78=19, Resulting Numbers: [19] 19,63 unequal: No Solution Exploring Operation: 97+78=175, Resulting Numbers: [175] 175,63 unequal: No Solution Moving to Node #0,3,0 Current State: 63:[95, 39], Operations: ['97-2=95', '85-46=39'] Exploring Operation: 95+39=134, Resulting Numbers: [134] 134,63 unequal: No Solution Exploring Operation: 95*39=3705, Resulting Numbers: [3705] 3705,63 unequal: No Solution Exploring Operation: 95-39=56, Resulting Numbers: [56] 56,63 unequal: No Solution Moving to Node #0,4,4 Current State: 63:[97, 37], Operations: ['85-46=39', '39-2=37'] Exploring Operation: 97-37=60, Resulting Numbers: [60] 60,63 unequal: No Solution Exploring Operation: 97*37=3589, Resulting Numbers: [3589] 3589,63 unequal: No Solution Exploring Operation: 97+37=134, Resulting Numbers: [134] 134,63 unequal: No Solution Moving to Node #0,4,3 Current State: 63:[39, 95], Operations: ['85-46=39', '97-2=95'] Exploring Operation: 39+95=134, Resulting Numbers: [134] 134,63 unequal: No Solution Exploring Operation: 39*95=3705, Resulting Numbers: [3705] 3705,63 unequal: No Solution Exploring Operation: 95-39=56, Resulting Numbers: [56] 56,63 unequal: No Solution Moving to Node #0,4,0 Current State: 63:[39, 99], Operations: ['85-46=39', '97+2=99'] Exploring Operation: 39*99=3861, Resulting Numbers: [3861] 3861,63 unequal: No Solution Exploring Operation: 39+99=138, Resulting Numbers: [138] 138,63 unequal: No Solution Exploring Operation: 99-39=60, Resulting Numbers: [60] 60,63 unequal: No Solution Moving to Node #0,3,2 Current State: 63:[85, 141], Operations: ['97-2=95', '46+95=141'] Exploring Operation: 85*141=11985, Resulting Numbers: [11985] 11985,63 unequal: No Solution Exploring Operation: 85+141=226, Resulting Numbers: [226] 226,63 unequal: No Solution Exploring Operation: 141-85=56, Resulting Numbers: [56] 56,63 unequal: No Solution Moving to Node #0,3,4 Current State: 63:[95, 131], Operations: ['97-2=95', '46+85=131'] Exploring Operation: 95+131=226, Resulting Numbers: [226] 226,63 unequal: No Solution Exploring Operation: 95*131=12445, Resulting Numbers: [12445] 12445,63 unequal: No Solution Exploring Operation: 131-95=36, Resulting Numbers: [36] 36,63 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 78, 92, 6, 19 ]
100
[ "92-78=14", "6*19=114", "114-14=100" ]
Current State: 100:[78, 92, 6, 19], Operations: [] Exploring Operation: 92-78=14, Resulting Numbers: [6, 19, 14] Generated Node #2: [6, 19, 14] from Operation: 92-78=14 Current State: 100:[6, 19, 14], Operations: ['92-78=14'] Exploring Operation: 6*19=114, Resulting Numbers: [14, 114] Generated Node #3: [14, 114] from Operation: 6*19=114 Current State: 100:[14, 114], Operations: ['92-78=14', '6*19=114'] Exploring Operation: 114-14=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[78, 92, 6, 19], Operations: [] Exploring Operation: 78+19=97, Resulting Numbers: [92, 6, 97] Generated Node #0,0: 100:[92, 6, 97] Operation: 78+19=97 Exploring Operation: 78/6=13, Resulting Numbers: [92, 19, 13] Generated Node #0,1: 100:[92, 19, 13] Operation: 78/6=13 Exploring Operation: 92-78=14, Resulting Numbers: [6, 19, 14] Generated Node #0,2: 100:[6, 19, 14] Operation: 92-78=14 Exploring Operation: 78-19=59, Resulting Numbers: [92, 6, 59] Generated Node #0,3: 100:[92, 6, 59] Operation: 78-19=59 Exploring Operation: 78+6=84, Resulting Numbers: [92, 19, 84] Generated Node #0,4: 100:[92, 19, 84] Operation: 78+6=84 Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[6, 19, 14], Operations: ['92-78=14'] Exploring Operation: 6+19=25, Resulting Numbers: [14, 25] Generated Node #0,2,0: 100:[14, 25] Operation: 6+19=25 Exploring Operation: 14-6=8, Resulting Numbers: [19, 8] Generated Node #0,2,1: 100:[19, 8] Operation: 14-6=8 Exploring Operation: 6+14=20, Resulting Numbers: [19, 20] Generated Node #0,2,2: 100:[19, 20] Operation: 6+14=20 Exploring Operation: 19-6=13, Resulting Numbers: [14, 13] Generated Node #0,2,3: 100:[14, 13] Operation: 19-6=13 Exploring Operation: 19-14=5, Resulting Numbers: [6, 5] Generated Node #0,2,4: 100:[6, 5] Operation: 19-14=5 Moving to Node #0,2,2 Current State: 100:[19, 20], Operations: ['92-78=14', '6+14=20'] Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,100 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,100 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,100 unequal: No Solution Moving to Node #0,2,4 Current State: 100:[6, 5], Operations: ['92-78=14', '19-14=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[19, 8], Operations: ['92-78=14', '14-6=8'] Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,100 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,100 unequal: No Solution Moving to Node #0,2,0 Current State: 100:[14, 25], Operations: ['92-78=14', '6+19=25'] Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,100 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,100 unequal: No Solution Moving to Node #0,2,3 Current State: 100:[14, 13], Operations: ['92-78=14', '19-6=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[92, 6, 97], Operations: ['78+19=97'] Exploring Operation: 92-6=86, Resulting Numbers: [97, 86] Generated Node #0,0,0: 100:[97, 86] Operation: 92-6=86 Exploring Operation: 92+6=98, Resulting Numbers: [97, 98] Generated Node #0,0,1: 100:[97, 98] Operation: 92+6=98 Exploring Operation: 97-6=91, Resulting Numbers: [92, 91] Generated Node #0,0,2: 100:[92, 91] Operation: 97-6=91 Exploring Operation: 97-92=5, Resulting Numbers: [6, 5] Generated Node #0,0,3: 100:[6, 5] Operation: 97-92=5 Exploring Operation: 6+97=103, Resulting Numbers: [92, 103] Generated Node #0,0,4: 100:[92, 103] Operation: 6+97=103 Moving to Node #0,0,3 Current State: 100:[6, 5], Operations: ['78+19=97', '97-92=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[97, 98], Operations: ['78+19=97', '92+6=98'] Exploring Operation: 98-97=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 97+98=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 97*98=9506, Resulting Numbers: [9506] 9506,100 unequal: No Solution Moving to Node #0,0,4 Current State: 100:[92, 103], Operations: ['78+19=97', '6+97=103'] Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[97, 86], Operations: ['78+19=97', '92-6=86'] Exploring Operation: 97+86=183, Resulting Numbers: [183] 183,100 unequal: No Solution Exploring Operation: 97*86=8342, Resulting Numbers: [8342] 8342,100 unequal: No Solution Exploring Operation: 97-86=11, Resulting Numbers: [11] 11,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[92, 91], Operations: ['78+19=97', '97-6=91'] Exploring Operation: 92+91=183, Resulting Numbers: [183] 183,100 unequal: No Solution Exploring Operation: 92-91=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 92*91=8372, Resulting Numbers: [8372] 8372,100 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:[92, 19, 13], Operations: ['78/6=13'] Exploring Operation: 92-13=79, Resulting Numbers: [19, 79] Generated Node #0,1,0: 100:[19, 79] Operation: 92-13=79 Exploring Operation: 19-13=6, Resulting Numbers: [92, 6] Generated Node #0,1,1: 100:[92, 6] Operation: 19-13=6 Exploring Operation: 19+13=32, Resulting Numbers: [92, 32] Generated Node #0,1,2: 100:[92, 32] Operation: 19+13=32 Exploring Operation: 92+13=105, Resulting Numbers: [19, 105] Generated Node #0,1,3: 100:[19, 105] Operation: 92+13=105 Exploring Operation: 92+19=111, Resulting Numbers: [13, 111] Generated Node #0,1,4: 100:[13, 111] Operation: 92+19=111 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 100:[19, 105], Operations: ['78/6=13', '92+13=105'] Exploring Operation: 19*105=1995, Resulting Numbers: [1995] 1995,100 unequal: No Solution Exploring Operation: 105-19=86, Resulting Numbers: [86] 86,100 unequal: No Solution Exploring Operation: 19+105=124, Resulting Numbers: [124] 124,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[92, 6], Operations: ['78/6=13', '19-13=6'] Exploring Operation: 92*6=552, Resulting Numbers: [552] 552,100 unequal: No Solution Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,100 unequal: No Solution Exploring Operation: 92+6=98, Resulting Numbers: [98] 98,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 100:[13, 111], Operations: ['78/6=13', '92+19=111'] Exploring Operation: 13*111=1443, Resulting Numbers: [1443] 1443,100 unequal: No Solution Exploring Operation: 111-13=98, Resulting Numbers: [98] 98,100 unequal: No Solution Exploring Operation: 13+111=124, Resulting Numbers: [124] 124,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 100:[92, 32], Operations: ['78/6=13', '19+13=32'] Exploring Operation: 92-32=60, Resulting Numbers: [60] 60,100 unequal: No Solution Exploring Operation: 92*32=2944, Resulting Numbers: [2944] 2944,100 unequal: No Solution Exploring Operation: 92+32=124, Resulting Numbers: [124] 124,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[19, 79], Operations: ['78/6=13', '92-13=79'] Exploring Operation: 19*79=1501, Resulting Numbers: [1501] 1501,100 unequal: No Solution Exploring Operation: 19+79=98, Resulting Numbers: [98] 98,100 unequal: No Solution Exploring Operation: 79-19=60, Resulting Numbers: [60] 60,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[92, 6, 59], Operations: ['78-19=59'] Exploring Operation: 6+59=65, Resulting Numbers: [92, 65] Generated Node #0,3,0: 100:[92, 65] Operation: 6+59=65 Exploring Operation: 92+6=98, Resulting Numbers: [59, 98] Generated Node #0,3,1: 100:[59, 98] Operation: 92+6=98 Exploring Operation: 92-6=86, Resulting Numbers: [59, 86] Generated Node #0,3,2: 100:[59, 86] Operation: 92-6=86 Exploring Operation: 59-6=53, Resulting Numbers: [92, 53] Generated Node #0,3,3: 100:[92, 53] Operation: 59-6=53 Exploring Operation: 92-59=33, Resulting Numbers: [6, 33] Generated Node #0,3,4: 100:[6, 33] Operation: 92-59=33 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 100:[6, 33], Operations: ['78-19=59', '92-59=33'] Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,100 unequal: No Solution Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 100:[59, 98], Operations: ['78-19=59', '92+6=98'] Exploring Operation: 98-59=39, Resulting Numbers: [39] 39,100 unequal: No Solution Exploring Operation: 59*98=5782, Resulting Numbers: [5782] 5782,100 unequal: No Solution Exploring Operation: 59+98=157, Resulting Numbers: [157] 157,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 100:[92, 53], Operations: ['78-19=59', '59-6=53'] Exploring Operation: 92+53=145, Resulting Numbers: [145] 145,100 unequal: No Solution Exploring Operation: 92-53=39, Resulting Numbers: [39] 39,100 unequal: No Solution Exploring Operation: 92*53=4876, Resulting Numbers: [4876] 4876,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 100:[92, 65], Operations: ['78-19=59', '6+59=65'] Exploring Operation: 92+65=157, Resulting Numbers: [157] 157,100 unequal: No Solution Exploring Operation: 92*65=5980, Resulting Numbers: [5980] 5980,100 unequal: No Solution Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 100:[59, 86], Operations: ['78-19=59', '92-6=86'] Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 59*86=5074, Resulting Numbers: [5074] 5074,100 unequal: No Solution Exploring Operation: 59+86=145, Resulting Numbers: [145] 145,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 100:[92, 19, 84], Operations: ['78+6=84'] Exploring Operation: 92-19=73, Resulting Numbers: [84, 73] Generated Node #0,4,0: 100:[84, 73] Operation: 92-19=73 Exploring Operation: 84-19=65, Resulting Numbers: [92, 65] Generated Node #0,4,1: 100:[92, 65] Operation: 84-19=65 Exploring Operation: 19+84=103, Resulting Numbers: [92, 103] Generated Node #0,4,2: 100:[92, 103] Operation: 19+84=103 Exploring Operation: 92+19=111, Resulting Numbers: [84, 111] Generated Node #0,4,3: 100:[84, 111] Operation: 92+19=111 Exploring Operation: 92-84=8, Resulting Numbers: [19, 8] Generated Node #0,4,4: 100:[19, 8] Operation: 92-84=8 Moving to Node #0,4,4 Current State: 100:[19, 8], Operations: ['78+6=84', '92-84=8'] Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,100 unequal: No Solution Moving to Node #0,4,2 Current State: 100:[92, 103], Operations: ['78+6=84', '19+84=103'] Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,100 unequal: No Solution Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,100 unequal: No Solution Moving to Node #0,4,1 Current State: 100:[92, 65], Operations: ['78+6=84', '84-19=65'] Exploring Operation: 92+65=157, Resulting Numbers: [157] 157,100 unequal: No Solution Exploring Operation: 92*65=5980, Resulting Numbers: [5980] 5980,100 unequal: No Solution Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,100 unequal: No Solution Moving to Node #0,4,3 Current State: 100:[84, 111], Operations: ['78+6=84', '92+19=111'] Exploring Operation: 111-84=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 84+111=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 84*111=9324, Resulting Numbers: [9324] 9324,100 unequal: No Solution Moving to Node #0,4,0 Current State: 100:[84, 73], Operations: ['78+6=84', '92-19=73'] Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 84*73=6132, Resulting Numbers: [6132] 6132,100 unequal: No Solution Exploring Operation: 84+73=157, Resulting Numbers: [157] 157,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 2, 29, 50, 80 ]
57
[ "29-2=27", "80-50=30", "27+30=57" ]
Current State: 57:[2, 29, 50, 80], Operations: [] Exploring Operation: 29-2=27, Resulting Numbers: [50, 80, 27] Generated Node #2: [50, 80, 27] from Operation: 29-2=27 Current State: 57:[50, 80, 27], Operations: ['29-2=27'] Exploring Operation: 80-50=30, Resulting Numbers: [27, 30] Generated Node #3: [27, 30] from Operation: 80-50=30 Current State: 57:[27, 30], Operations: ['29-2=27', '80-50=30'] Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[2, 29, 50, 80], Operations: [] Exploring Operation: 80-29=51, Resulting Numbers: [2, 50, 51] Generated Node #0,0: 57:[2, 50, 51] Operation: 80-29=51 Exploring Operation: 80-50=30, Resulting Numbers: [2, 29, 30] Generated Node #0,1: 57:[2, 29, 30] Operation: 80-50=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[2, 50, 51], Operations: ['80-29=51'] Exploring Operation: 2+50=52, Resulting Numbers: [51, 52] Generated Node #0,0,0: 57:[51, 52] Operation: 2+50=52 Exploring Operation: 51-50=1, Resulting Numbers: [2, 1] Generated Node #0,0,1: 57:[2, 1] Operation: 51-50=1 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[2, 1], Operations: ['80-29=51', '51-50=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[51, 52], Operations: ['80-29=51', '2+50=52'] Exploring Operation: 51+52=103, Resulting Numbers: [103] 103,57 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,57 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: 57:[2, 29, 30], Operations: ['80-50=30'] Exploring Operation: 29+30=59, Resulting Numbers: [2, 59] Generated Node #0,1,0: 57:[2, 59] Operation: 29+30=59 Exploring Operation: 30-29=1, Resulting Numbers: [2, 1] Generated Node #0,1,1: 57:[2, 1] Operation: 30-29=1 Moving to Node #0,1,0 Current State: 57:[2, 59], Operations: ['80-50=30', '29+30=59'] Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,57 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[2, 29, 50, 80], Operations: [] Exploring Operation: 80-50=30, Resulting Numbers: [2, 29, 30] Generated Node #0,1: 57:[2, 29, 30] Operation: 80-50=30 Moving to Node #0,1 Current State: 57:[2, 29, 30], Operations: ['80-50=30'] Exploring Operation: 29+30=59, Resulting Numbers: [2, 59] Generated Node #0,1,0: 57:[2, 59] Operation: 29+30=59 Moving to Node #0,1,0 Current State: 57:[2, 59], Operations: ['80-50=30', '29+30=59'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 84, 67, 71, 54 ]
34
[ "84-67=17", "71-54=17", "17+17=34" ]
Current State: 34:[84, 67, 71, 54], Operations: [] Exploring Operation: 84-67=17, Resulting Numbers: [71, 54, 17] Generated Node #2: [71, 54, 17] from Operation: 84-67=17 Current State: 34:[71, 54, 17], Operations: ['84-67=17'] Exploring Operation: 71-54=17, Resulting Numbers: [17, 17] Generated Node #3: [17, 17] from Operation: 71-54=17 Current State: 34:[17, 17], Operations: ['84-67=17', '71-54=17'] Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[84, 67, 71, 54], Operations: [] Exploring Operation: 84-67=17, Resulting Numbers: [71, 54, 17] Generated Node #0,0: 34:[71, 54, 17] Operation: 84-67=17 Exploring Operation: 84-71=13, Resulting Numbers: [67, 54, 13] Generated Node #0,1: 34:[67, 54, 13] Operation: 84-71=13 Moving to Node #0,0 Current State: 34:[71, 54, 17], Operations: ['84-67=17'] Exploring Operation: 71-17=54, Resulting Numbers: [54, 54] Generated Node #0,0,0: 34:[54, 54] Operation: 71-17=54 Exploring Operation: 71-54=17, Resulting Numbers: [17, 17] Generated Node #0,0,1: 34:[17, 17] Operation: 71-54=17 Moving to Node #0,1 Current State: 34:[67, 54, 13], Operations: ['84-71=13'] Exploring Operation: 67-13=54, Resulting Numbers: [54, 54] Generated Node #0,1,0: 34:[54, 54] Operation: 67-13=54 Exploring Operation: 67-54=13, Resulting Numbers: [13, 13] Generated Node #0,1,1: 34:[13, 13] Operation: 67-54=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[13, 13], Operations: ['84-71=13', '67-54=13'] Exploring Operation: 13/13=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[54, 54], Operations: ['84-71=13', '67-13=54'] Exploring Operation: 54/54=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 54-54=0, Resulting Numbers: [0] 0,34 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: 34:[17, 17], Operations: ['84-67=17', '71-54=17'] Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[84, 67, 71, 54], Operations: [] Exploring Operation: 84-67=17, Resulting Numbers: [71, 54, 17] Generated Node #0,0: 34:[71, 54, 17] Operation: 84-67=17 Moving to Node #0,0 Current State: 34:[71, 54, 17], Operations: ['84-67=17'] Exploring Operation: 71-54=17, Resulting Numbers: [17, 17] Generated Node #0,0,1: 34:[17, 17] Operation: 71-54=17 Moving to Node #0,0,1 Current State: 34:[17, 17], Operations: ['84-67=17', '71-54=17'] Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 24, 98, 21, 13 ]
94
[ "21-13=8", "24*8=192", "192-98=94" ]
Current State: 94:[24, 98, 21, 13], Operations: [] Exploring Operation: 21-13=8, Resulting Numbers: [24, 98, 8] Generated Node #2: [24, 98, 8] from Operation: 21-13=8 Current State: 94:[24, 98, 8], Operations: ['21-13=8'] Exploring Operation: 24*8=192, Resulting Numbers: [98, 192] Generated Node #3: [98, 192] from Operation: 24*8=192 Current State: 94:[98, 192], Operations: ['21-13=8', '24*8=192'] Exploring Operation: 192-98=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[24, 98, 21, 13], Operations: [] Exploring Operation: 24+21=45, Resulting Numbers: [98, 13, 45] Generated Node #0,0: 94:[98, 13, 45] Operation: 24+21=45 Exploring Operation: 24-21=3, Resulting Numbers: [98, 13, 3] Generated Node #0,1: 94:[98, 13, 3] Operation: 24-21=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[98, 13, 3], Operations: ['24-21=3'] Exploring Operation: 98-13=85, Resulting Numbers: [3, 85] Generated Node #0,1,0: 94:[3, 85] Operation: 98-13=85 Exploring Operation: 98-3=95, Resulting Numbers: [13, 95] Generated Node #0,1,1: 94:[13, 95] Operation: 98-3=95 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[3, 85], Operations: ['24-21=3', '98-13=85'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,94 unequal: No Solution Exploring Operation: 3+85=88, Resulting Numbers: [88] 88,94 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 #0,1,1 Current State: 94:[13, 95], Operations: ['24-21=3', '98-3=95'] Exploring Operation: 13+95=108, Resulting Numbers: [108] 108,94 unequal: No Solution Exploring Operation: 95-13=82, Resulting Numbers: [82] 82,94 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 #0,0 Current State: 94:[98, 13, 45], Operations: ['24+21=45'] Exploring Operation: 13+45=58, Resulting Numbers: [98, 58] Generated Node #0,0,0: 94:[98, 58] Operation: 13+45=58 Exploring Operation: 98-13=85, Resulting Numbers: [45, 85] Generated Node #0,0,1: 94:[45, 85] Operation: 98-13=85 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[45, 85], Operations: ['24+21=45', '98-13=85'] Exploring Operation: 45+85=130, Resulting Numbers: [130] 130,94 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,94 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:[98, 58], Operations: ['24+21=45', '13+45=58'] Exploring Operation: 98+58=156, Resulting Numbers: [156] 156,94 unequal: No Solution Exploring Operation: 98-58=40, Resulting Numbers: [40] 40,94 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_2
mult_heuristic
[ 30, 77, 1, 7 ]
19
[ "30*1=30", "77/7=11", "30-11=19" ]
Current State: 19:[30, 77, 1, 7], Operations: [] Exploring Operation: 30*1=30, Resulting Numbers: [77, 7, 30] Generated Node #2: [77, 7, 30] from Operation: 30*1=30 Current State: 19:[77, 7, 30], Operations: ['30*1=30'] Exploring Operation: 77/7=11, Resulting Numbers: [30, 11] Generated Node #3: [30, 11] from Operation: 77/7=11 Current State: 19:[30, 11], Operations: ['30*1=30', '77/7=11'] Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[30, 77, 1, 7], Operations: [] Exploring Operation: 77/7=11, Resulting Numbers: [30, 1, 11] Generated Node #0,0: 19:[30, 1, 11] Operation: 77/7=11 Moving to Node #0,0 Current State: 19:[30, 1, 11], Operations: ['77/7=11'] Exploring Operation: 30-1=29, Resulting Numbers: [11, 29] Generated Node #0,0,0: 19:[11, 29] Operation: 30-1=29 Moving to Node #0,0,0 Current State: 19:[11, 29], Operations: ['77/7=11', '30-1=29'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,19 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 37, 45, 65, 34 ]
51
[ "37+45=82", "65-34=31", "82-31=51" ]
Current State: 51:[37, 45, 65, 34], Operations: [] Exploring Operation: 37+45=82, Resulting Numbers: [65, 34, 82] Generated Node #2: [65, 34, 82] from Operation: 37+45=82 Current State: 51:[65, 34, 82], Operations: ['37+45=82'] Exploring Operation: 65-34=31, Resulting Numbers: [82, 31] Generated Node #3: [82, 31] from Operation: 65-34=31 Current State: 51:[82, 31], Operations: ['37+45=82', '65-34=31'] Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[37, 45, 65, 34], Operations: [] Exploring Operation: 45-34=11, Resulting Numbers: [37, 65, 11] Generated Node #0,0: 51:[37, 65, 11] Operation: 45-34=11 Exploring Operation: 65-37=28, Resulting Numbers: [45, 34, 28] Generated Node #0,1: 51:[45, 34, 28] Operation: 65-37=28 Exploring Operation: 65-45=20, Resulting Numbers: [37, 34, 20] Generated Node #0,2: 51:[37, 34, 20] Operation: 65-45=20 Exploring Operation: 37-34=3, Resulting Numbers: [45, 65, 3] Generated Node #0,3: 51:[45, 65, 3] Operation: 37-34=3 Moving to Node #0,3 Current State: 51:[45, 65, 3], Operations: ['37-34=3'] Exploring Operation: 65-45=20, Resulting Numbers: [3, 20] Generated Node #0,3,0: 51:[3, 20] Operation: 65-45=20 Exploring Operation: 45/3=15, Resulting Numbers: [65, 15] Generated Node #0,3,1: 51:[65, 15] Operation: 45/3=15 Exploring Operation: 65-3=62, Resulting Numbers: [45, 62] Generated Node #0,3,2: 51:[45, 62] Operation: 65-3=62 Exploring Operation: 45+3=48, Resulting Numbers: [65, 48] Generated Node #0,3,3: 51:[65, 48] Operation: 45+3=48 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 51:[3, 20], Operations: ['37-34=3', '65-45=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,51 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,51 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 51:[65, 15], Operations: ['37-34=3', '45/3=15'] Exploring Operation: 65+15=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 65*15=975, Resulting Numbers: [975] 975,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 51:[45, 62], Operations: ['37-34=3', '65-3=62'] Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,51 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,51 unequal: No Solution Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 51:[65, 48], Operations: ['37-34=3', '45+3=48'] Exploring Operation: 65+48=113, Resulting Numbers: [113] 113,51 unequal: No Solution Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,51 unequal: No Solution Exploring Operation: 65*48=3120, Resulting Numbers: [3120] 3120,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 51:[45, 34, 28], Operations: ['65-37=28'] Exploring Operation: 45-28=17, Resulting Numbers: [34, 17] Generated Node #0,1,0: 51:[34, 17] Operation: 45-28=17 Exploring Operation: 45-34=11, Resulting Numbers: [28, 11] Generated Node #0,1,1: 51:[28, 11] Operation: 45-34=11 Exploring Operation: 34-28=6, Resulting Numbers: [45, 6] Generated Node #0,1,2: 51:[45, 6] Operation: 34-28=6 Exploring Operation: 34+28=62, Resulting Numbers: [45, 62] Generated Node #0,1,3: 51:[45, 62] Operation: 34+28=62 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 51:[45, 6], Operations: ['65-37=28', '34-28=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[37, 45, 65, 34], Operations: [] Exploring Operation: 65-37=28, Resulting Numbers: [45, 34, 28] Generated Node #0,1: 51:[45, 34, 28] Operation: 65-37=28 Moving to Node #0,1 Current State: 51:[45, 34, 28], Operations: ['65-37=28'] Exploring Operation: 34-28=6, Resulting Numbers: [45, 6] Generated Node #0,1,2: 51:[45, 6] Operation: 34-28=6 Moving to Node #0,1,2 Current State: 51:[45, 6], Operations: ['65-37=28', '34-28=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 34, 27, 32, 2 ]
31
[ "34+27=61", "32-2=30", "61-30=31" ]
Current State: 31:[34, 27, 32, 2], Operations: [] Exploring Operation: 34+27=61, Resulting Numbers: [32, 2, 61] Generated Node #2: [32, 2, 61] from Operation: 34+27=61 Current State: 31:[32, 2, 61], Operations: ['34+27=61'] Exploring Operation: 32-2=30, Resulting Numbers: [61, 30] Generated Node #3: [61, 30] from Operation: 32-2=30 Current State: 31:[61, 30], Operations: ['34+27=61', '32-2=30'] Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[34, 27, 32, 2], Operations: [] Exploring Operation: 34-2=32, Resulting Numbers: [27, 32, 32] Generated Node #0,0: 31:[27, 32, 32] Operation: 34-2=32 Exploring Operation: 27+2=29, Resulting Numbers: [34, 32, 29] Generated Node #0,1: 31:[34, 32, 29] Operation: 27+2=29 Exploring Operation: 34+2=36, Resulting Numbers: [27, 32, 36] Generated Node #0,2: 31:[27, 32, 36] Operation: 34+2=36 Exploring Operation: 32-2=30, Resulting Numbers: [34, 27, 30] Generated Node #0,3: 31:[34, 27, 30] Operation: 32-2=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[27, 32, 32], Operations: ['34-2=32'] Exploring Operation: 32-27=5, Resulting Numbers: [32, 5] Generated Node #0,0,0: 31:[32, 5] Operation: 32-27=5 Exploring Operation: 32-27=5, Resulting Numbers: [32, 5] Generated Node #0,0,1: 31:[32, 5] Operation: 32-27=5 Exploring Operation: 27+32=59, Resulting Numbers: [32, 59] Generated Node #0,0,2: 31:[32, 59] Operation: 27+32=59 Exploring Operation: 27+32=59, Resulting Numbers: [32, 59] Generated Node #0,0,3: 31:[32, 59] Operation: 27+32=59 Moving to Node #0,0,0 Current State: 31:[32, 5], Operations: ['34-2=32', '32-27=5'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[32, 5], Operations: ['34-2=32', '32-27=5'] Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,31 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[32, 59], Operations: ['34-2=32', '27+32=59'] Exploring Operation: 32+59=91, Resulting Numbers: [91] 91,31 unequal: No Solution Exploring Operation: 32*59=1888, Resulting Numbers: [1888] 1888,31 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[32, 59], Operations: ['34-2=32', '27+32=59'] Exploring Operation: 32*59=1888, Resulting Numbers: [1888] 1888,31 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 32+59=91, Resulting Numbers: [91] 91,31 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 Current State: 31:[34, 32, 29], Operations: ['27+2=29'] Exploring Operation: 32-29=3, Resulting Numbers: [34, 3] Generated Node #0,1,0: 31:[34, 3] Operation: 32-29=3 Exploring Operation: 34+29=63, Resulting Numbers: [32, 63] Generated Node #0,1,1: 31:[32, 63] Operation: 34+29=63 Exploring Operation: 34-32=2, Resulting Numbers: [29, 2] Generated Node #0,1,2: 31:[29, 2] Operation: 34-32=2 Exploring Operation: 34-29=5, Resulting Numbers: [32, 5] Generated Node #0,1,3: 31:[32, 5] Operation: 34-29=5 Moving to Node #0,1,3 Current State: 31:[32, 5], Operations: ['27+2=29', '34-29=5'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[29, 2], Operations: ['27+2=29', '34-32=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[34, 27, 32, 2], Operations: [] Exploring Operation: 27+2=29, Resulting Numbers: [34, 32, 29] Generated Node #0,1: 31:[34, 32, 29] Operation: 27+2=29 Moving to Node #0,1 Current State: 31:[34, 32, 29], Operations: ['27+2=29'] Exploring Operation: 34-32=2, Resulting Numbers: [29, 2] Generated Node #0,1,2: 31:[29, 2] Operation: 34-32=2 Moving to Node #0,1,2 Current State: 31:[29, 2], Operations: ['27+2=29', '34-32=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 62, 42, 75, 86 ]
93
[ "62+42=104", "86-75=11", "104-11=93" ]
Current State: 93:[62, 42, 75, 86], Operations: [] Exploring Operation: 62+42=104, Resulting Numbers: [75, 86, 104] Generated Node #2: [75, 86, 104] from Operation: 62+42=104 Current State: 93:[75, 86, 104], Operations: ['62+42=104'] Exploring Operation: 86-75=11, Resulting Numbers: [104, 11] Generated Node #3: [104, 11] from Operation: 86-75=11 Current State: 93:[104, 11], Operations: ['62+42=104', '86-75=11'] Exploring Operation: 104-11=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[62, 42, 75, 86], Operations: [] Exploring Operation: 62+42=104, Resulting Numbers: [75, 86, 104] Generated Node #0,0: 93:[75, 86, 104] Operation: 62+42=104 Exploring Operation: 75-62=13, Resulting Numbers: [42, 86, 13] Generated Node #0,1: 93:[42, 86, 13] Operation: 75-62=13 Exploring Operation: 75-42=33, Resulting Numbers: [62, 86, 33] Generated Node #0,2: 93:[62, 86, 33] Operation: 75-42=33 Exploring Operation: 86-62=24, Resulting Numbers: [42, 75, 24] Generated Node #0,3: 93:[42, 75, 24] Operation: 86-62=24 Exploring Operation: 62-42=20, Resulting Numbers: [75, 86, 20] Generated Node #0,4: 93:[75, 86, 20] Operation: 62-42=20 Moving to Node #0,1 Current State: 93:[42, 86, 13], Operations: ['75-62=13'] Exploring Operation: 42-13=29, Resulting Numbers: [86, 29] Generated Node #0,1,0: 93:[86, 29] Operation: 42-13=29 Exploring Operation: 86-42=44, Resulting Numbers: [13, 44] Generated Node #0,1,1: 93:[13, 44] Operation: 86-42=44 Exploring Operation: 86+13=99, Resulting Numbers: [42, 99] Generated Node #0,1,2: 93:[42, 99] Operation: 86+13=99 Exploring Operation: 42+13=55, Resulting Numbers: [86, 55] Generated Node #0,1,3: 93:[86, 55] Operation: 42+13=55 Exploring Operation: 86-13=73, Resulting Numbers: [42, 73] Generated Node #0,1,4: 93:[42, 73] Operation: 86-13=73 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 93:[86, 29], Operations: ['75-62=13', '42-13=29'] Exploring Operation: 86+29=115, Resulting Numbers: [115] 115,93 unequal: No Solution Exploring Operation: 86*29=2494, Resulting Numbers: [2494] 2494,93 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,93 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 #0,1,2 Current State: 93:[42, 99], Operations: ['75-62=13', '86+13=99'] Exploring Operation: 42+99=141, Resulting Numbers: [141] 141,93 unequal: No Solution Exploring Operation: 99-42=57, Resulting Numbers: [57] 57,93 unequal: No Solution Exploring Operation: 42*99=4158, Resulting Numbers: [4158] 4158,93 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 #0,1,1 Current State: 93:[13, 44], Operations: ['75-62=13', '86-42=44'] Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,93 unequal: No Solution Exploring Operation: 13+44=57, Resulting Numbers: [57] 57,93 unequal: No Solution Exploring Operation: 13*44=572, Resulting Numbers: [572] 572,93 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 #0,1,3 Current State: 93:[86, 55], Operations: ['75-62=13', '42+13=55'] Exploring Operation: 86+55=141, Resulting Numbers: [141] 141,93 unequal: No Solution Exploring Operation: 86*55=4730, Resulting Numbers: [4730] 4730,93 unequal: No Solution Exploring Operation: 86-55=31, Resulting Numbers: [31] 31,93 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 #0,1,4 Current State: 93:[42, 73], Operations: ['75-62=13', '86-13=73'] Exploring Operation: 42*73=3066, Resulting Numbers: [3066] 3066,93 unequal: No Solution Exploring Operation: 42+73=115, Resulting Numbers: [115] 115,93 unequal: No Solution Exploring Operation: 73-42=31, Resulting Numbers: [31] 31,93 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: 93:[42, 75, 24], Operations: ['86-62=24'] Exploring Operation: 75-42=33, Resulting Numbers: [24, 33] Generated Node #0,3,0: 93:[24, 33] Operation: 75-42=33 Exploring Operation: 42-24=18, Resulting Numbers: [75, 18] Generated Node #0,3,1: 93:[75, 18] Operation: 42-24=18 Exploring Operation: 42+75=117, Resulting Numbers: [24, 117] Generated Node #0,3,2: 93:[24, 117] Operation: 42+75=117 Exploring Operation: 75+24=99, Resulting Numbers: [42, 99] Generated Node #0,3,3: 93:[42, 99] Operation: 75+24=99 Exploring Operation: 75-24=51, Resulting Numbers: [42, 51] Generated Node #0,3,4: 93:[42, 51] Operation: 75-24=51 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 93:[24, 33], Operations: ['86-62=24', '75-42=33'] Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,93 unequal: No Solution Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,93 unequal: No Solution Exploring Operation: 24*33=792, Resulting Numbers: [792] 792,93 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 #0,3,3 Current State: 93:[42, 99], Operations: ['86-62=24', '75+24=99'] Exploring Operation: 42+99=141, Resulting Numbers: [141] 141,93 unequal: No Solution Exploring Operation: 42*99=4158, Resulting Numbers: [4158] 4158,93 unequal: No Solution Exploring Operation: 99-42=57, Resulting Numbers: [57] 57,93 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 #0,3,1 Current State: 93:[75, 18], Operations: ['86-62=24', '42-24=18'] Exploring Operation: 75*18=1350, Resulting Numbers: [1350] 1350,93 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,93 unequal: No Solution Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[62, 42, 75, 86], Operations: [] Exploring Operation: 86-62=24, Resulting Numbers: [42, 75, 24] Generated Node #0,3: 93:[42, 75, 24] Operation: 86-62=24 Moving to Node #0,3 Current State: 93:[42, 75, 24], Operations: ['86-62=24'] Exploring Operation: 42-24=18, Resulting Numbers: [75, 18] Generated Node #0,3,1: 93:[75, 18] Operation: 42-24=18 Moving to Node #0,3,1 Current State: 93:[75, 18], Operations: ['86-62=24', '42-24=18'] Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
mult_heuristic
[ 27, 68, 60, 8 ]
37
[ "68-60=8", "8*8=64", "64-27=37" ]
Current State: 37:[27, 68, 60, 8], Operations: [] Exploring Operation: 68-60=8, Resulting Numbers: [27, 8, 8] Generated Node #2: [27, 8, 8] from Operation: 68-60=8 Current State: 37:[27, 8, 8], Operations: ['68-60=8'] Exploring Operation: 8*8=64, Resulting Numbers: [27, 64] Generated Node #3: [27, 64] from Operation: 8*8=64 Current State: 37:[27, 64], Operations: ['68-60=8', '8*8=64'] Exploring Operation: 64-27=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[27, 68, 60, 8], Operations: [] Exploring Operation: 68-8=60, Resulting Numbers: [27, 60, 60] Generated Node #0,0: 37:[27, 60, 60] Operation: 68-8=60 Exploring Operation: 60-8=52, Resulting Numbers: [27, 68, 52] Generated Node #0,1: 37:[27, 68, 52] Operation: 60-8=52 Exploring Operation: 27+8=35, Resulting Numbers: [68, 60, 35] Generated Node #0,2: 37:[68, 60, 35] Operation: 27+8=35 Exploring Operation: 68-27=41, Resulting Numbers: [60, 8, 41] Generated Node #0,3: 37:[60, 8, 41] Operation: 68-27=41 Exploring Operation: 60-27=33, Resulting Numbers: [68, 8, 33] Generated Node #0,4: 37:[68, 8, 33] Operation: 60-27=33 Moving to Node #0,0 Current State: 37:[27, 60, 60], Operations: ['68-8=60'] Exploring Operation: 60-27=33, Resulting Numbers: [60, 33] Generated Node #0,0,0: 37:[60, 33] Operation: 60-27=33 Exploring Operation: 60/60=1, Resulting Numbers: [27, 1] Generated Node #0,0,1: 37:[27, 1] Operation: 60/60=1 Exploring Operation: 60-27=33, Resulting Numbers: [60, 33] Generated Node #0,0,2: 37:[60, 33] Operation: 60-27=33 Exploring Operation: 27+60=87, Resulting Numbers: [60, 87] Generated Node #0,0,3: 37:[60, 87] Operation: 27+60=87 Exploring Operation: 60-60=0, Resulting Numbers: [27, 0] Generated Node #0,0,4: 37:[27, 0] Operation: 60-60=0 Moving to Node #0,2 Current State: 37:[68, 60, 35], Operations: ['27+8=35'] Exploring Operation: 68+35=103, Resulting Numbers: [60, 103] Generated Node #0,2,0: 37:[60, 103] Operation: 68+35=103 Exploring Operation: 68-35=33, Resulting Numbers: [60, 33] Generated Node #0,2,1: 37:[60, 33] Operation: 68-35=33 Exploring Operation: 60+35=95, Resulting Numbers: [68, 95] Generated Node #0,2,2: 37:[68, 95] Operation: 60+35=95 Exploring Operation: 68-60=8, Resulting Numbers: [35, 8] Generated Node #0,2,3: 37:[35, 8] Operation: 68-60=8 Exploring Operation: 60-35=25, Resulting Numbers: [68, 25] Generated Node #0,2,4: 37:[68, 25] Operation: 60-35=25 Moving to Node #0,1 Current State: 37:[27, 68, 52], Operations: ['60-8=52'] Exploring Operation: 27+52=79, Resulting Numbers: [68, 79] Generated Node #0,1,0: 37:[68, 79] Operation: 27+52=79 Exploring Operation: 27+68=95, Resulting Numbers: [52, 95] Generated Node #0,1,1: 37:[52, 95] Operation: 27+68=95 Exploring Operation: 68-52=16, Resulting Numbers: [27, 16] Generated Node #0,1,2: 37:[27, 16] Operation: 68-52=16 Exploring Operation: 68-27=41, Resulting Numbers: [52, 41] Generated Node #0,1,3: 37:[52, 41] Operation: 68-27=41 Exploring Operation: 52-27=25, Resulting Numbers: [68, 25] Generated Node #0,1,4: 37:[68, 25] Operation: 52-27=25 Moving to Node #0,3 Current State: 37:[60, 8, 41], Operations: ['68-27=41'] Exploring Operation: 60-41=19, Resulting Numbers: [8, 19] Generated Node #0,3,0: 37:[8, 19] Operation: 60-41=19 Exploring Operation: 60+8=68, Resulting Numbers: [41, 68] Generated Node #0,3,1: 37:[41, 68] Operation: 60+8=68 Exploring Operation: 60-8=52, Resulting Numbers: [41, 52] Generated Node #0,3,2: 37:[41, 52] Operation: 60-8=52 Exploring Operation: 8+41=49, Resulting Numbers: [60, 49] Generated Node #0,3,3: 37:[60, 49] Operation: 8+41=49 Exploring Operation: 41-8=33, Resulting Numbers: [60, 33] Generated Node #0,3,4: 37:[60, 33] Operation: 41-8=33 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 37:[41, 52], Operations: ['68-27=41', '60-8=52'] Exploring Operation: 41+52=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 41*52=2132, Resulting Numbers: [2132] 2132,37 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,37 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 #0,3,4 Current State: 37:[60, 33], Operations: ['68-27=41', '41-8=33'] Exploring Operation: 60+33=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 60*33=1980, Resulting Numbers: [1980] 1980,37 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,37 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:[41, 68], Operations: ['68-27=41', '60+8=68'] Exploring Operation: 68-41=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 41+68=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 41*68=2788, Resulting Numbers: [2788] 2788,37 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:[60, 49], Operations: ['68-27=41', '8+41=49'] Exploring Operation: 60*49=2940, Resulting Numbers: [2940] 2940,37 unequal: No Solution Exploring Operation: 60+49=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,37 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:[8, 19], Operations: ['68-27=41', '60-41=19'] Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,37 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,37 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: 37:[68, 8, 33], Operations: ['60-27=33'] Exploring Operation: 8+33=41, Resulting Numbers: [68, 41] Generated Node #0,4,0: 37:[68, 41] Operation: 8+33=41 Exploring Operation: 68-33=35, Resulting Numbers: [8, 35] Generated Node #0,4,1: 37:[8, 35] Operation: 68-33=35 Exploring Operation: 68-8=60, Resulting Numbers: [33, 60] Generated Node #0,4,2: 37:[33, 60] Operation: 68-8=60 Exploring Operation: 68+8=76, Resulting Numbers: [33, 76] Generated Node #0,4,3: 37:[33, 76] Operation: 68+8=76 Exploring Operation: 33-8=25, Resulting Numbers: [68, 25] Generated Node #0,4,4: 37:[68, 25] Operation: 33-8=25 Moving to Node #0,1,3 Current State: 37:[52, 41], Operations: ['60-8=52', '68-27=41'] Exploring Operation: 52+41=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 52*41=2132, Resulting Numbers: [2132] 2132,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[60, 33], Operations: ['27+8=35', '68-35=33'] Exploring Operation: 60+33=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 60*33=1980, Resulting Numbers: [1980] 1980,37 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[60, 33], Operations: ['68-8=60', '60-27=33'] Exploring Operation: 60+33=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 60*33=1980, Resulting Numbers: [1980] 1980,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[60, 33], Operations: ['68-8=60', '60-27=33'] Exploring Operation: 60+33=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 60*33=1980, Resulting Numbers: [1980] 1980,37 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,37 unequal: No Solution Moving to Node #0,4,2 Current State: 37:[33, 60], Operations: ['60-27=33', '68-8=60'] Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 33+60=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 33*60=1980, Resulting Numbers: [1980] 1980,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[35, 8], Operations: ['27+8=35', '68-60=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[27, 16], Operations: ['60-8=52', '68-52=16'] Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 27*16=432, Resulting Numbers: [432] 432,37 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,37 unequal: No Solution Moving to Node #0,4,1 Current State: 37:[8, 35], Operations: ['60-27=33', '68-33=35'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 8*35=280, Resulting Numbers: [280] 280,37 unequal: No Solution Moving to Node #0,4,0 Current State: 37:[68, 41], Operations: ['60-27=33', '8+33=41'] Exploring Operation: 68+41=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 68*41=2788, Resulting Numbers: [2788] 2788,37 unequal: No Solution Exploring Operation: 68-41=27, Resulting Numbers: [27] 27,37 unequal: No Solution Moving to Node #0,1,4 Current State: 37:[68, 25], Operations: ['60-8=52', '52-27=25'] Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 68+25=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 68*25=1700, Resulting Numbers: [1700] 1700,37 unequal: No Solution Moving to Node #0,4,4 Current State: 37:[68, 25], Operations: ['60-27=33', '33-8=25'] Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 68*25=1700, Resulting Numbers: [1700] 1700,37 unequal: No Solution Exploring Operation: 68+25=93, Resulting Numbers: [93] 93,37 unequal: No Solution Moving to Node #0,4,3 Current State: 37:[33, 76], Operations: ['60-27=33', '68+8=76'] Exploring Operation: 33*76=2508, Resulting Numbers: [2508] 2508,37 unequal: No Solution Exploring Operation: 33+76=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 76-33=43, Resulting Numbers: [43] 43,37 unequal: No Solution Moving to Node #0,2,4 Current State: 37:[68, 25], Operations: ['27+8=35', '60-35=25'] Exploring Operation: 68+25=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 68*25=1700, Resulting Numbers: [1700] 1700,37 unequal: No Solution Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[27, 1], Operations: ['68-8=60', '60/60=1'] Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,37 unequal: No Solution Moving to Node #0,0,4 Current State: 37:[27, 0], Operations: ['68-8=60', '60-60=0'] Exploring Operation: 27*0=0, Resulting Numbers: [0] 0,37 unequal: No Solution Exploring Operation: 27+0=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 27-0=27, Resulting Numbers: [27] 27,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[52, 95], Operations: ['60-8=52', '27+68=95'] Exploring Operation: 52+95=147, Resulting Numbers: [147] 147,37 unequal: No Solution Exploring Operation: 95-52=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 52*95=4940, Resulting Numbers: [4940] 4940,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[68, 79], Operations: ['60-8=52', '27+52=79'] Exploring Operation: 68*79=5372, Resulting Numbers: [5372] 5372,37 unequal: No Solution Exploring Operation: 79-68=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 68+79=147, Resulting Numbers: [147] 147,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[60, 87], Operations: ['68-8=60', '27+60=87'] Exploring Operation: 87-60=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 60*87=5220, Resulting Numbers: [5220] 5220,37 unequal: No Solution Exploring Operation: 60+87=147, Resulting Numbers: [147] 147,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[60, 103], Operations: ['27+8=35', '68+35=103'] Exploring Operation: 60*103=6180, Resulting Numbers: [6180] 6180,37 unequal: No Solution Exploring Operation: 103-60=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 60+103=163, Resulting Numbers: [163] 163,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[68, 95], Operations: ['27+8=35', '60+35=95'] Exploring Operation: 68+95=163, Resulting Numbers: [163] 163,37 unequal: No Solution Exploring Operation: 95-68=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 68*95=6460, Resulting Numbers: [6460] 6460,37 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 38, 73, 57, 8 ]
54
[ "73+8=81", "38*81=3078", "3078/57=54" ]
Current State: 54:[38, 73, 57, 8], Operations: [] Exploring Operation: 73+8=81, Resulting Numbers: [38, 57, 81] Generated Node #2: [38, 57, 81] from Operation: 73+8=81 Current State: 54:[38, 57, 81], Operations: ['73+8=81'] Exploring Operation: 38*81=3078, Resulting Numbers: [57, 3078] Generated Node #3: [57, 3078] from Operation: 38*81=3078 Current State: 54:[57, 3078], Operations: ['73+8=81', '38*81=3078'] Exploring Operation: 3078/57=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[38, 73, 57, 8], Operations: [] Exploring Operation: 57-38=19, Resulting Numbers: [73, 8, 19] Generated Node #0,0: 54:[73, 8, 19] Operation: 57-38=19 Exploring Operation: 73-57=16, Resulting Numbers: [38, 8, 16] Generated Node #0,1: 54:[38, 8, 16] Operation: 73-57=16 Exploring Operation: 38-8=30, Resulting Numbers: [73, 57, 30] Generated Node #0,2: 54:[73, 57, 30] Operation: 38-8=30 Exploring Operation: 73-38=35, Resulting Numbers: [57, 8, 35] Generated Node #0,3: 54:[57, 8, 35] Operation: 73-38=35 Moving to Node #0,3 Current State: 54:[57, 8, 35], Operations: ['73-38=35'] Exploring Operation: 8+35=43, Resulting Numbers: [57, 43] Generated Node #0,3,0: 54:[57, 43] Operation: 8+35=43 Exploring Operation: 57-35=22, Resulting Numbers: [8, 22] Generated Node #0,3,1: 54:[8, 22] Operation: 57-35=22 Exploring Operation: 35-8=27, Resulting Numbers: [57, 27] Generated Node #0,3,2: 54:[57, 27] Operation: 35-8=27 Exploring Operation: 57-8=49, Resulting Numbers: [35, 49] Generated Node #0,3,3: 54:[35, 49] Operation: 57-8=49 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 54:[57, 27], Operations: ['73-38=35', '35-8=27'] Exploring Operation: 57-27=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 57*27=1539, Resulting Numbers: [1539] 1539,54 unequal: No Solution Exploring Operation: 57+27=84, Resulting Numbers: [84] 84,54 unequal: No Solution No 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: 54:[8, 22], Operations: ['73-38=35', '57-35=22'] Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,54 unequal: No Solution No 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: 54:[35, 49], Operations: ['73-38=35', '57-8=49'] Exploring Operation: 35+49=84, Resulting Numbers: [84] 84,54 unequal: No Solution Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 35*49=1715, Resulting Numbers: [1715] 1715,54 unequal: No Solution No 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: 54:[57, 43], Operations: ['73-38=35', '8+35=43'] Exploring Operation: 57-43=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 57+43=100, Resulting Numbers: [100] 100,54 unequal: No Solution Exploring Operation: 57*43=2451, Resulting Numbers: [2451] 2451,54 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: 54:[38, 8, 16], Operations: ['73-57=16'] Exploring Operation: 38-8=30, Resulting Numbers: [16, 30] Generated Node #0,1,0: 54:[16, 30] Operation: 38-8=30 Exploring Operation: 38+8=46, Resulting Numbers: [16, 46] Generated Node #0,1,1: 54:[16, 46] Operation: 38+8=46 Exploring Operation: 38-16=22, Resulting Numbers: [8, 22] Generated Node #0,1,2: 54:[8, 22] Operation: 38-16=22 Exploring Operation: 38+16=54, Resulting Numbers: [8, 54] Generated Node #0,1,3: 54:[8, 54] Operation: 38+16=54 Moving to Node #0,0 Current State: 54:[73, 8, 19], Operations: ['57-38=19'] Exploring Operation: 73-8=65, Resulting Numbers: [19, 65] Generated Node #0,0,0: 54:[19, 65] Operation: 73-8=65 Exploring Operation: 73-19=54, Resulting Numbers: [8, 54] Generated Node #0,0,1: 54:[8, 54] Operation: 73-19=54 Exploring Operation: 19-8=11, Resulting Numbers: [73, 11] Generated Node #0,0,2: 54:[73, 11] Operation: 19-8=11 Exploring Operation: 8+19=27, Resulting Numbers: [73, 27] Generated Node #0,0,3: 54:[73, 27] Operation: 8+19=27 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[8, 54], Operations: ['57-38=19', '73-19=54'] Exploring Operation: 8+54=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 8*54=432, Resulting Numbers: [432] 432,54 unequal: No Solution No 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: 54:[19, 65], Operations: ['57-38=19', '73-8=65'] Exploring Operation: 19+65=84, Resulting Numbers: [84] 84,54 unequal: No Solution Exploring Operation: 19*65=1235, Resulting Numbers: [1235] 1235,54 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,54 unequal: No Solution No 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: 54:[73, 27], Operations: ['57-38=19', '8+19=27'] Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 73*27=1971, Resulting Numbers: [1971] 1971,54 unequal: No Solution Exploring Operation: 73+27=100, Resulting Numbers: [100] 100,54 unequal: No Solution No 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: 54:[73, 11], Operations: ['57-38=19', '19-8=11'] Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 73+11=84, Resulting Numbers: [84] 84,54 unequal: No Solution Exploring Operation: 73*11=803, Resulting Numbers: [803] 803,54 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: 54:[73, 57, 30], Operations: ['38-8=30'] Exploring Operation: 73-57=16, Resulting Numbers: [30, 16] Generated Node #0,2,0: 54:[30, 16] Operation: 73-57=16 Exploring Operation: 73-30=43, Resulting Numbers: [57, 43] Generated Node #0,2,1: 54:[57, 43] Operation: 73-30=43 Exploring Operation: 57-30=27, Resulting Numbers: [73, 27] Generated Node #0,2,2: 54:[73, 27] Operation: 57-30=27 Exploring Operation: 73+30=103, Resulting Numbers: [57, 103] Generated Node #0,2,3: 54:[57, 103] Operation: 73+30=103 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[30, 16], Operations: ['38-8=30', '73-57=16'] Exploring Operation: 30*16=480, Resulting Numbers: [480] 480,54 unequal: No Solution Exploring Operation: 30+16=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,54 unequal: No Solution No 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: 54:[57, 43], Operations: ['38-8=30', '73-30=43'] Exploring Operation: 57-43=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 57*43=2451, Resulting Numbers: [2451] 2451,54 unequal: No Solution Exploring Operation: 57+43=100, Resulting Numbers: [100] 100,54 unequal: No Solution No 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: 54:[73, 27], Operations: ['38-8=30', '57-30=27'] Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 73+27=100, Resulting Numbers: [100] 100,54 unequal: No Solution Exploring Operation: 73*27=1971, Resulting Numbers: [1971] 1971,54 unequal: No Solution No 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: 54:[57, 103], Operations: ['38-8=30', '73+30=103'] Exploring Operation: 103-57=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 57+103=160, Resulting Numbers: [160] 160,54 unequal: No Solution Exploring Operation: 57*103=5871, Resulting Numbers: [5871] 5871,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 54:[8, 54], Operations: ['73-57=16', '38+16=54'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 8+54=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 8*54=432, Resulting Numbers: [432] 432,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[8, 22], Operations: ['73-57=16', '38-16=22'] Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,54 unequal: No Solution Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[16, 30], Operations: ['73-57=16', '38-8=30'] Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[16, 46], Operations: ['73-57=16', '38+8=46'] Exploring Operation: 16+46=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 16*46=736, Resulting Numbers: [736] 736,54 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,54 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 52, 55, 42, 72 ]
58
[ "55-52=3", "42/3=14", "72-14=58" ]
Current State: 58:[52, 55, 42, 72], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [42, 72, 3] Generated Node #2: [42, 72, 3] from Operation: 55-52=3 Current State: 58:[42, 72, 3], Operations: ['55-52=3'] Exploring Operation: 42/3=14, Resulting Numbers: [72, 14] Generated Node #3: [72, 14] from Operation: 42/3=14 Current State: 58:[72, 14], Operations: ['55-52=3', '42/3=14'] Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[52, 55, 42, 72], Operations: [] Exploring Operation: 52-42=10, Resulting Numbers: [55, 72, 10] Generated Node #0,0: 58:[55, 72, 10] Operation: 52-42=10 Exploring Operation: 72-42=30, Resulting Numbers: [52, 55, 30] Generated Node #0,1: 58:[52, 55, 30] Operation: 72-42=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[52, 55, 30], Operations: ['72-42=30'] Exploring Operation: 55-52=3, Resulting Numbers: [30, 3] Generated Node #0,1,0: 58:[30, 3] Operation: 55-52=3 Exploring Operation: 52-30=22, Resulting Numbers: [55, 22] Generated Node #0,1,1: 58:[55, 22] Operation: 52-30=22 Moving to Node #0,1,0 Current State: 58:[30, 3], Operations: ['72-42=30', '55-52=3'] Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[55, 22], Operations: ['72-42=30', '52-30=22'] Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,58 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[55, 72, 10], Operations: ['52-42=10'] Exploring Operation: 72-55=17, Resulting Numbers: [10, 17] Generated Node #0,0,0: 58:[10, 17] Operation: 72-55=17 Exploring Operation: 72-10=62, Resulting Numbers: [55, 62] Generated Node #0,0,1: 58:[55, 62] Operation: 72-10=62 Moving to Node #0,0,1 Current State: 58:[55, 62], Operations: ['52-42=10', '72-10=62'] Exploring Operation: 55+62=117, Resulting Numbers: [117] 117,58 unequal: No Solution Exploring Operation: 62-55=7, Resulting Numbers: [7] 7,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[10, 17], Operations: ['52-42=10', '72-55=17'] Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,58 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
[ 15, 70, 12, 90 ]
18
[ "15+90=105", "12*105=1260", "1260/70=18" ]
Current State: 18:[15, 70, 12, 90], Operations: [] Exploring Operation: 15+90=105, Resulting Numbers: [70, 12, 105] Generated Node #2: [70, 12, 105] from Operation: 15+90=105 Current State: 18:[70, 12, 105], Operations: ['15+90=105'] Exploring Operation: 12*105=1260, Resulting Numbers: [70, 1260] Generated Node #3: [70, 1260] from Operation: 12*105=1260 Current State: 18:[70, 1260], Operations: ['15+90=105', '12*105=1260'] Exploring Operation: 1260/70=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[15, 70, 12, 90], Operations: [] Exploring Operation: 90-15=75, Resulting Numbers: [70, 12, 75] Generated Node #0,0: 18:[70, 12, 75] Operation: 90-15=75 Exploring Operation: 90-70=20, Resulting Numbers: [15, 12, 20] Generated Node #0,1: 18:[15, 12, 20] Operation: 90-70=20 Exploring Operation: 70-12=58, Resulting Numbers: [15, 90, 58] Generated Node #0,2: 18:[15, 90, 58] Operation: 70-12=58 Exploring Operation: 70-15=55, Resulting Numbers: [12, 90, 55] Generated Node #0,3: 18:[12, 90, 55] Operation: 70-15=55 Exploring Operation: 90/15=6, Resulting Numbers: [70, 12, 6] Generated Node #0,4: 18:[70, 12, 6] Operation: 90/15=6 Moving to Node #0,1 Current State: 18:[15, 12, 20], Operations: ['90-70=20'] Exploring Operation: 12+20=32, Resulting Numbers: [15, 32] Generated Node #0,1,0: 18:[15, 32] Operation: 12+20=32 Exploring Operation: 15-12=3, Resulting Numbers: [20, 3] Generated Node #0,1,1: 18:[20, 3] Operation: 15-12=3 Exploring Operation: 20-15=5, Resulting Numbers: [12, 5] Generated Node #0,1,2: 18:[12, 5] Operation: 20-15=5 Exploring Operation: 15+12=27, Resulting Numbers: [20, 27] Generated Node #0,1,3: 18:[20, 27] Operation: 15+12=27 Exploring Operation: 20-12=8, Resulting Numbers: [15, 8] Generated Node #0,1,4: 18:[15, 8] Operation: 20-12=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[20, 3], Operations: ['90-70=20', '15-12=3'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[12, 5], Operations: ['90-70=20', '20-15=5'] Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[15, 8], Operations: ['90-70=20', '20-12=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,18 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[20, 27], Operations: ['90-70=20', '15+12=27'] Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 20*27=540, Resulting Numbers: [540] 540,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[15, 32], Operations: ['90-70=20', '12+20=32'] Exploring Operation: 15*32=480, Resulting Numbers: [480] 480,18 unequal: No Solution Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 18:[70, 12, 6], Operations: ['90/15=6'] Exploring Operation: 12+6=18, Resulting Numbers: [70, 18] Generated Node #0,4,0: 18:[70, 18] Operation: 12+6=18 Exploring Operation: 12/6=2, Resulting Numbers: [70, 2] Generated Node #0,4,1: 18:[70, 2] Operation: 12/6=2 Exploring Operation: 70-12=58, Resulting Numbers: [6, 58] Generated Node #0,4,2: 18:[6, 58] Operation: 70-12=58 Exploring Operation: 12-6=6, Resulting Numbers: [70, 6] Generated Node #0,4,3: 18:[70, 6] Operation: 12-6=6 Exploring Operation: 70-6=64, Resulting Numbers: [12, 64] Generated Node #0,4,4: 18:[12, 64] Operation: 70-6=64 Moving to Node #0,0 Current State: 18:[70, 12, 75], Operations: ['90-15=75'] Exploring Operation: 75-70=5, Resulting Numbers: [12, 5] Generated Node #0,0,0: 18:[12, 5] Operation: 75-70=5 Exploring Operation: 75-12=63, Resulting Numbers: [70, 63] Generated Node #0,0,1: 18:[70, 63] Operation: 75-12=63 Exploring Operation: 70-12=58, Resulting Numbers: [75, 58] Generated Node #0,0,2: 18:[75, 58] Operation: 70-12=58 Exploring Operation: 70+12=82, Resulting Numbers: [75, 82] Generated Node #0,0,3: 18:[75, 82] Operation: 70+12=82 Exploring Operation: 12+75=87, Resulting Numbers: [70, 87] Generated Node #0,0,4: 18:[70, 87] Operation: 12+75=87 Moving to Node #0,3 Current State: 18:[12, 90, 55], Operations: ['70-15=55'] Exploring Operation: 55-12=43, Resulting Numbers: [90, 43] Generated Node #0,3,0: 18:[90, 43] Operation: 55-12=43 Exploring Operation: 90-12=78, Resulting Numbers: [55, 78] Generated Node #0,3,1: 18:[55, 78] Operation: 90-12=78 Exploring Operation: 90-55=35, Resulting Numbers: [12, 35] Generated Node #0,3,2: 18:[12, 35] Operation: 90-55=35 Exploring Operation: 12+55=67, Resulting Numbers: [90, 67] Generated Node #0,3,3: 18:[90, 67] Operation: 12+55=67 Exploring Operation: 12+90=102, Resulting Numbers: [55, 102] Generated Node #0,3,4: 18:[55, 102] Operation: 12+90=102 Moving to Node #0,2 Current State: 18:[15, 90, 58], Operations: ['70-12=58'] Exploring Operation: 90-15=75, Resulting Numbers: [58, 75] Generated Node #0,2,0: 18:[58, 75] Operation: 90-15=75 Exploring Operation: 90/15=6, Resulting Numbers: [58, 6] Generated Node #0,2,1: 18:[58, 6] Operation: 90/15=6 Exploring Operation: 90-58=32, Resulting Numbers: [15, 32] Generated Node #0,2,2: 18:[15, 32] Operation: 90-58=32 Exploring Operation: 58-15=43, Resulting Numbers: [90, 43] Generated Node #0,2,3: 18:[90, 43] Operation: 58-15=43 Exploring Operation: 15+90=105, Resulting Numbers: [58, 105] Generated Node #0,2,4: 18:[58, 105] Operation: 15+90=105 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[15, 32], Operations: ['70-12=58', '90-58=32'] Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 15*32=480, Resulting Numbers: [480] 480,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[58, 6], Operations: ['70-12=58', '90/15=6'] Exploring Operation: 58+6=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 58*6=348, Resulting Numbers: [348] 348,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[58, 75], Operations: ['70-12=58', '90-15=75'] Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 58*75=4350, Resulting Numbers: [4350] 4350,18 unequal: No Solution Exploring Operation: 58+75=133, Resulting Numbers: [133] 133,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[90, 43], Operations: ['70-12=58', '58-15=43'] Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,18 unequal: No Solution Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[58, 105], Operations: ['70-12=58', '15+90=105'] Exploring Operation: 58+105=163, Resulting Numbers: [163] 163,18 unequal: No Solution Exploring Operation: 105-58=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 58*105=6090, Resulting Numbers: [6090] 6090,18 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: 18:[12, 5], Operations: ['90-15=75', '75-70=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[12, 35], Operations: ['70-15=55', '90-55=35'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,18 unequal: No Solution Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,18 unequal: No Solution Moving to Node #0,4,2 Current State: 18:[6, 58], Operations: ['90/15=6', '70-12=58'] Exploring Operation: 6*58=348, Resulting Numbers: [348] 348,18 unequal: No Solution Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 6+58=64, Resulting Numbers: [64] 64,18 unequal: No Solution Moving to Node #0,4,4 Current State: 18:[12, 64], Operations: ['90/15=6', '70-6=64'] Exploring Operation: 12*64=768, Resulting Numbers: [768] 768,18 unequal: No Solution Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 12+64=76, Resulting Numbers: [76] 76,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[70, 18], Operations: ['90/15=6', '12+6=18'] Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,18 unequal: No Solution Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,18 unequal: No Solution Moving to Node #0,4,3 Current State: 18:[70, 6], Operations: ['90/15=6', '12-6=6'] Exploring Operation: 70*6=420, Resulting Numbers: [420] 420,18 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,18 unequal: No Solution Moving to Node #0,4,1 Current State: 18:[70, 2], Operations: ['90/15=6', '12/6=2'] Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,18 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,18 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[70, 63], Operations: ['90-15=75', '75-12=63'] Exploring Operation: 70+63=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 70*63=4410, Resulting Numbers: [4410] 4410,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[90, 43], Operations: ['70-15=55', '55-12=43'] Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,18 unequal: No Solution Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[55, 78], Operations: ['70-15=55', '90-12=78'] Exploring Operation: 55+78=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 55*78=4290, Resulting Numbers: [4290] 4290,18 unequal: No Solution Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[75, 58], Operations: ['90-15=75', '70-12=58'] Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 75+58=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 75*58=4350, Resulting Numbers: [4350] 4350,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[90, 67], Operations: ['70-15=55', '12+55=67'] Exploring Operation: 90-67=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 90*67=6030, Resulting Numbers: [6030] 6030,18 unequal: No Solution Exploring Operation: 90+67=157, Resulting Numbers: [157] 157,18 unequal: No Solution Moving to Node #0,0,4 Current State: 18:[70, 87], Operations: ['90-15=75', '12+75=87'] Exploring Operation: 87-70=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 70+87=157, Resulting Numbers: [157] 157,18 unequal: No Solution Exploring Operation: 70*87=6090, Resulting Numbers: [6090] 6090,18 unequal: No Solution Moving to Node #0,3,4 Current State: 18:[55, 102], Operations: ['70-15=55', '12+90=102'] Exploring Operation: 55+102=157, Resulting Numbers: [157] 157,18 unequal: No Solution Exploring Operation: 55*102=5610, Resulting Numbers: [5610] 5610,18 unequal: No Solution Exploring Operation: 102-55=47, Resulting Numbers: [47] 47,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[75, 82], Operations: ['90-15=75', '70+12=82'] Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 75+82=157, Resulting Numbers: [157] 157,18 unequal: No Solution Exploring Operation: 75*82=6150, Resulting Numbers: [6150] 6150,18 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 35, 17, 24, 97 ]
91
[ "35-17=18", "97-24=73", "18+73=91" ]
Current State: 91:[35, 17, 24, 97], Operations: [] Exploring Operation: 35-17=18, Resulting Numbers: [24, 97, 18] Generated Node #2: [24, 97, 18] from Operation: 35-17=18 Current State: 91:[24, 97, 18], Operations: ['35-17=18'] Exploring Operation: 97-24=73, Resulting Numbers: [18, 73] Generated Node #3: [18, 73] from Operation: 97-24=73 Current State: 91:[18, 73], Operations: ['35-17=18', '97-24=73'] Exploring Operation: 18+73=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[35, 17, 24, 97], Operations: [] Exploring Operation: 24-17=7, Resulting Numbers: [35, 97, 7] Generated Node #0,0: 91:[35, 97, 7] Operation: 24-17=7 Exploring Operation: 35+24=59, Resulting Numbers: [17, 97, 59] Generated Node #0,1: 91:[17, 97, 59] Operation: 35+24=59 Exploring Operation: 97-35=62, Resulting Numbers: [17, 24, 62] Generated Node #0,2: 91:[17, 24, 62] Operation: 97-35=62 Exploring Operation: 35-24=11, Resulting Numbers: [17, 97, 11] Generated Node #0,3: 91:[17, 97, 11] Operation: 35-24=11 Exploring Operation: 35-17=18, Resulting Numbers: [24, 97, 18] Generated Node #0,4: 91:[24, 97, 18] Operation: 35-17=18 Moving to Node #0,3 Current State: 91:[17, 97, 11], Operations: ['35-24=11'] Exploring Operation: 97-11=86, Resulting Numbers: [17, 86] Generated Node #0,3,0: 91:[17, 86] Operation: 97-11=86 Exploring Operation: 17-11=6, Resulting Numbers: [97, 6] Generated Node #0,3,1: 91:[97, 6] Operation: 17-11=6 Exploring Operation: 97-17=80, Resulting Numbers: [11, 80] Generated Node #0,3,2: 91:[11, 80] Operation: 97-17=80 Exploring Operation: 97+11=108, Resulting Numbers: [17, 108] Generated Node #0,3,3: 91:[17, 108] Operation: 97+11=108 Exploring Operation: 17+11=28, Resulting Numbers: [97, 28] Generated Node #0,3,4: 91:[97, 28] Operation: 17+11=28 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 91:[97, 6], Operations: ['35-24=11', '17-11=6'] Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[35, 17, 24, 97], Operations: [] Exploring Operation: 35-24=11, Resulting Numbers: [17, 97, 11] Generated Node #0,3: 91:[17, 97, 11] Operation: 35-24=11 Moving to Node #0,3 Current State: 91:[17, 97, 11], Operations: ['35-24=11'] Exploring Operation: 17-11=6, Resulting Numbers: [97, 6] Generated Node #0,3,1: 91:[97, 6] Operation: 17-11=6 Moving to Node #0,3,1 Current State: 91:[97, 6], Operations: ['35-24=11', '17-11=6'] Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 2, 22, 47, 39 ]
13
[ "2*22=44", "47-44=3", "39/3=13" ]
Current State: 13:[2, 22, 47, 39], Operations: [] Exploring Operation: 2*22=44, Resulting Numbers: [47, 39, 44] Generated Node #2: [47, 39, 44] from Operation: 2*22=44 Current State: 13:[47, 39, 44], Operations: ['2*22=44'] Exploring Operation: 47-44=3, Resulting Numbers: [39, 3] Generated Node #3: [39, 3] from Operation: 47-44=3 Current State: 13:[39, 3], Operations: ['2*22=44', '47-44=3'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[2, 22, 47, 39], Operations: [] Exploring Operation: 22/2=11, Resulting Numbers: [47, 39, 11] Generated Node #0,0: 13:[47, 39, 11] Operation: 22/2=11 Exploring Operation: 39-22=17, Resulting Numbers: [2, 47, 17] Generated Node #0,1: 13:[2, 47, 17] Operation: 39-22=17 Exploring Operation: 47-39=8, Resulting Numbers: [2, 22, 8] Generated Node #0,2: 13:[2, 22, 8] Operation: 47-39=8 Exploring Operation: 47-22=25, Resulting Numbers: [2, 39, 25] Generated Node #0,3: 13:[2, 39, 25] Operation: 47-22=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[2, 22, 8], Operations: ['47-39=8'] Exploring Operation: 22-2=20, Resulting Numbers: [8, 20] Generated Node #0,2,0: 13:[8, 20] Operation: 22-2=20 Exploring Operation: 22/2=11, Resulting Numbers: [8, 11] Generated Node #0,2,1: 13:[8, 11] Operation: 22/2=11 Exploring Operation: 2+8=10, Resulting Numbers: [22, 10] Generated Node #0,2,2: 13:[22, 10] Operation: 2+8=10 Exploring Operation: 2*8=16, Resulting Numbers: [22, 16] Generated Node #0,2,3: 13:[22, 16] Operation: 2*8=16 Moving to Node #0,2,1 Current State: 13:[8, 11], Operations: ['47-39=8', '22/2=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,13 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[22, 10], Operations: ['47-39=8', '2+8=10'] Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 22*10=220, Resulting Numbers: [220] 220,13 unequal: No Solution Exploring Operation: 22+10=32, Resulting Numbers: [32] 32,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[8, 20], Operations: ['47-39=8', '22-2=20'] Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 8*20=160, Resulting Numbers: [160] 160,13 unequal: No Solution Moving to Node #0,2,3 Current State: 13:[22, 16], Operations: ['47-39=8', '2*8=16'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,13 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[2, 47, 17], Operations: ['39-22=17'] Exploring Operation: 47-17=30, Resulting Numbers: [2, 30] Generated Node #0,1,0: 13:[2, 30] Operation: 47-17=30 Exploring Operation: 2+47=49, Resulting Numbers: [17, 49] Generated Node #0,1,1: 13:[17, 49] Operation: 2+47=49 Exploring Operation: 17-2=15, Resulting Numbers: [47, 15] Generated Node #0,1,2: 13:[47, 15] Operation: 17-2=15 Exploring Operation: 47-2=45, Resulting Numbers: [17, 45] Generated Node #0,1,3: 13:[17, 45] Operation: 47-2=45 Moving to Node #0,1,0 Current State: 13:[2, 30], Operations: ['39-22=17', '47-17=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,13 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,13 unequal: No Solution Moving to Node #0,1,3 Current State: 13:[17, 45], Operations: ['39-22=17', '47-2=45'] Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,13 unequal: No Solution Exploring Operation: 17*45=765, Resulting Numbers: [765] 765,13 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[47, 15], Operations: ['39-22=17', '17-2=15'] Exploring Operation: 47+15=62, Resulting Numbers: [62] 62,13 unequal: No Solution Exploring Operation: 47*15=705, Resulting Numbers: [705] 705,13 unequal: No Solution Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[17, 49], Operations: ['39-22=17', '2+47=49'] Exploring Operation: 17+49=66, Resulting Numbers: [66] 66,13 unequal: No Solution Exploring Operation: 17*49=833, Resulting Numbers: [833] 833,13 unequal: No Solution Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[2, 39, 25], Operations: ['47-22=25'] Exploring Operation: 25-2=23, Resulting Numbers: [39, 23] Generated Node #0,3,0: 13:[39, 23] Operation: 25-2=23 Exploring Operation: 39-2=37, Resulting Numbers: [25, 37] Generated Node #0,3,1: 13:[25, 37] Operation: 39-2=37 Exploring Operation: 39-25=14, Resulting Numbers: [2, 14] Generated Node #0,3,2: 13:[2, 14] Operation: 39-25=14 Exploring Operation: 2+39=41, Resulting Numbers: [25, 41] Generated Node #0,3,3: 13:[25, 41] Operation: 2+39=41 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 13:[2, 14], Operations: ['47-22=25', '39-25=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 13:[39, 23], Operations: ['47-22=25', '25-2=23'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,13 unequal: No Solution Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 13:[25, 37], Operations: ['47-22=25', '39-2=37'] Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,13 unequal: No Solution Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 13:[25, 41], Operations: ['47-22=25', '2+39=41'] Exploring Operation: 25*41=1025, Resulting Numbers: [1025] 1025,13 unequal: No Solution Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[47, 39, 11], Operations: ['22/2=11'] Exploring Operation: 47+11=58, Resulting Numbers: [39, 58] Generated Node #0,0,0: 13:[39, 58] Operation: 47+11=58 Exploring Operation: 47-39=8, Resulting Numbers: [11, 8] Generated Node #0,0,1: 13:[11, 8] Operation: 47-39=8 Exploring Operation: 39-11=28, Resulting Numbers: [47, 28] Generated Node #0,0,2: 13:[47, 28] Operation: 39-11=28 Exploring Operation: 47-11=36, Resulting Numbers: [39, 36] Generated Node #0,0,3: 13:[39, 36] Operation: 47-11=36 Moving to Node #0,0,1 Current State: 13:[11, 8], Operations: ['22/2=11', '47-39=8'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 11+8=19, Resulting Numbers: [19] 19,13 unequal: No Solution Exploring Operation: 11*8=88, Resulting Numbers: [88] 88,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[39, 36], Operations: ['22/2=11', '47-11=36'] Exploring Operation: 39*36=1404, Resulting Numbers: [1404] 1404,13 unequal: No Solution Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,13 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[47, 28], Operations: ['22/2=11', '39-11=28'] Exploring Operation: 47*28=1316, Resulting Numbers: [1316] 1316,13 unequal: No Solution Exploring Operation: 47+28=75, Resulting Numbers: [75] 75,13 unequal: No Solution Exploring Operation: 47-28=19, Resulting Numbers: [19] 19,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[39, 58], Operations: ['22/2=11', '47+11=58'] Exploring Operation: 39+58=97, Resulting Numbers: [97] 97,13 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,13 unequal: No Solution Exploring Operation: 39*58=2262, Resulting Numbers: [2262] 2262,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 7, 66, 57, 35 ]
21
[ "7*66=462", "57-35=22", "462/22=21" ]
Current State: 21:[7, 66, 57, 35], Operations: [] Exploring Operation: 7*66=462, Resulting Numbers: [57, 35, 462] Generated Node #2: [57, 35, 462] from Operation: 7*66=462 Current State: 21:[57, 35, 462], Operations: ['7*66=462'] Exploring Operation: 57-35=22, Resulting Numbers: [462, 22] Generated Node #3: [462, 22] from Operation: 57-35=22 Current State: 21:[462, 22], Operations: ['7*66=462', '57-35=22'] Exploring Operation: 462/22=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[7, 66, 57, 35], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [7, 35, 9] Generated Node #0,0: 21:[7, 35, 9] Operation: 66-57=9 Exploring Operation: 66-35=31, Resulting Numbers: [7, 57, 31] Generated Node #0,1: 21:[7, 57, 31] Operation: 66-35=31 Moving to Node #0,0 Current State: 21:[7, 35, 9], Operations: ['66-57=9'] Exploring Operation: 35-9=26, Resulting Numbers: [7, 26] Generated Node #0,0,0: 21:[7, 26] Operation: 35-9=26 Exploring Operation: 35/7=5, Resulting Numbers: [9, 5] Generated Node #0,0,1: 21:[9, 5] Operation: 35/7=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[9, 5], Operations: ['66-57=9', '35/7=5'] Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,21 unequal: No Solution No 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: 21:[7, 26], Operations: ['66-57=9', '35-9=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,21 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: 21:[7, 57, 31], Operations: ['66-35=31'] Exploring Operation: 57-31=26, Resulting Numbers: [7, 26] Generated Node #0,1,0: 21:[7, 26] Operation: 57-31=26 Exploring Operation: 57-7=50, Resulting Numbers: [31, 50] Generated Node #0,1,1: 21:[31, 50] Operation: 57-7=50 Moving to Node #0,1,0 Current State: 21:[7, 26], Operations: ['66-35=31', '57-31=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[31, 50], Operations: ['66-35=31', '57-7=50'] Exploring Operation: 31+50=81, Resulting Numbers: [81] 81,21 unequal: No Solution Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,21 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 77, 12, 93, 33 ]
29
[ "77+12=89", "93-33=60", "89-60=29" ]
Current State: 29:[77, 12, 93, 33], Operations: [] Exploring Operation: 77+12=89, Resulting Numbers: [93, 33, 89] Generated Node #2: [93, 33, 89] from Operation: 77+12=89 Current State: 29:[93, 33, 89], Operations: ['77+12=89'] Exploring Operation: 93-33=60, Resulting Numbers: [89, 60] Generated Node #3: [89, 60] from Operation: 93-33=60 Current State: 29:[89, 60], Operations: ['77+12=89', '93-33=60'] Exploring Operation: 89-60=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[77, 12, 93, 33], Operations: [] Exploring Operation: 93-77=16, Resulting Numbers: [12, 33, 16] Generated Node #0,0: 29:[12, 33, 16] Operation: 93-77=16 Exploring Operation: 77-33=44, Resulting Numbers: [12, 93, 44] Generated Node #0,1: 29:[12, 93, 44] Operation: 77-33=44 Moving to Node #0,0 Current State: 29:[12, 33, 16], Operations: ['93-77=16'] Exploring Operation: 12+16=28, Resulting Numbers: [33, 28] Generated Node #0,0,0: 29:[33, 28] Operation: 12+16=28 Exploring Operation: 33-12=21, Resulting Numbers: [16, 21] Generated Node #0,0,1: 29:[16, 21] Operation: 33-12=21 Moving to Node #0,1 Current State: 29:[12, 93, 44], Operations: ['77-33=44'] Exploring Operation: 93-44=49, Resulting Numbers: [12, 49] Generated Node #0,1,0: 29:[12, 49] Operation: 93-44=49 Exploring Operation: 93-12=81, Resulting Numbers: [44, 81] Generated Node #0,1,1: 29:[44, 81] Operation: 93-12=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[12, 49], Operations: ['77-33=44', '93-44=49'] Exploring Operation: 49-12=37, Resulting Numbers: [37] 37,29 unequal: No Solution Exploring Operation: 12+49=61, Resulting Numbers: [61] 61,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[44, 81], Operations: ['77-33=44', '93-12=81'] Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,29 unequal: No Solution Exploring Operation: 44+81=125, Resulting Numbers: [125] 125,29 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: 29:[33, 28], Operations: ['93-77=16', '12+16=28'] Exploring Operation: 33+28=61, Resulting Numbers: [61] 61,29 unequal: No Solution Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[16, 21], Operations: ['93-77=16', '33-12=21'] Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,29 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,29 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 57, 53, 16, 76 ]
80
[ "57-53=4", "16/4=4", "76+4=80" ]
Current State: 80:[57, 53, 16, 76], Operations: [] Exploring Operation: 57-53=4, Resulting Numbers: [16, 76, 4] Generated Node #2: [16, 76, 4] from Operation: 57-53=4 Current State: 80:[16, 76, 4], Operations: ['57-53=4'] Exploring Operation: 16/4=4, Resulting Numbers: [76, 4] Generated Node #3: [76, 4] from Operation: 16/4=4 Current State: 80:[76, 4], Operations: ['57-53=4', '16/4=4'] Exploring Operation: 76+4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[57, 53, 16, 76], Operations: [] Exploring Operation: 57-16=41, Resulting Numbers: [53, 76, 41] Generated Node #0,0: 80:[53, 76, 41] Operation: 57-16=41 Exploring Operation: 76-57=19, Resulting Numbers: [53, 16, 19] Generated Node #0,1: 80:[53, 16, 19] Operation: 76-57=19 Exploring Operation: 57-53=4, Resulting Numbers: [16, 76, 4] Generated Node #0,2: 80:[16, 76, 4] Operation: 57-53=4 Moving to Node #0,2 Current State: 80:[16, 76, 4], Operations: ['57-53=4'] Exploring Operation: 16+4=20, Resulting Numbers: [76, 20] Generated Node #0,2,0: 80:[76, 20] Operation: 16+4=20 Exploring Operation: 76/4=19, Resulting Numbers: [16, 19] Generated Node #0,2,1: 80:[16, 19] Operation: 76/4=19 Exploring Operation: 76+4=80, Resulting Numbers: [16, 80] Generated Node #0,2,2: 80:[16, 80] Operation: 76+4=80 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[16, 80], Operations: ['57-53=4', '76+4=80'] Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 16+80=96, Resulting Numbers: [96] 96,80 unequal: No Solution Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,80 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 #0,2,1 Current State: 80:[16, 19], Operations: ['57-53=4', '76/4=19'] Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,80 unequal: No Solution Exploring Operation: 16*19=304, Resulting Numbers: [304] 304,80 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,80 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 #0,2,0 Current State: 80:[76, 20], Operations: ['57-53=4', '16+4=20'] Exploring Operation: 76+20=96, Resulting Numbers: [96] 96,80 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 76*20=1520, Resulting Numbers: [1520] 1520,80 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: 80:[53, 16, 19], Operations: ['76-57=19'] Exploring Operation: 53-19=34, Resulting Numbers: [16, 34] Generated Node #0,1,0: 80:[16, 34] Operation: 53-19=34 Exploring Operation: 53+19=72, Resulting Numbers: [16, 72] Generated Node #0,1,1: 80:[16, 72] Operation: 53+19=72 Exploring Operation: 53-16=37, Resulting Numbers: [19, 37] Generated Node #0,1,2: 80:[19, 37] Operation: 53-16=37 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[19, 37], Operations: ['76-57=19', '53-16=37'] Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,80 unequal: No Solution Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,80 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 #0,1,0 Current State: 80:[16, 34], Operations: ['76-57=19', '53-19=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,80 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,80 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 #0,1,1 Current State: 80:[16, 72], Operations: ['76-57=19', '53+19=72'] Exploring Operation: 16+72=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 16*72=1152, Resulting Numbers: [1152] 1152,80 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,80 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: 80:[53, 76, 41], Operations: ['57-16=41'] Exploring Operation: 53+41=94, Resulting Numbers: [76, 94] Generated Node #0,0,0: 80:[76, 94] Operation: 53+41=94 Exploring Operation: 76-53=23, Resulting Numbers: [41, 23] Generated Node #0,0,1: 80:[41, 23] Operation: 76-53=23 Exploring Operation: 53-41=12, Resulting Numbers: [76, 12] Generated Node #0,0,2: 80:[76, 12] Operation: 53-41=12 Moving to Node #0,0,1 Current State: 80:[41, 23], Operations: ['57-16=41', '76-53=23'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,80 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[76, 12], Operations: ['57-16=41', '53-41=12'] Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 76*12=912, Resulting Numbers: [912] 912,80 unequal: No Solution Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[76, 94], Operations: ['57-16=41', '53+41=94'] Exploring Operation: 76*94=7144, Resulting Numbers: [7144] 7144,80 unequal: No Solution Exploring Operation: 94-76=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 76+94=170, Resulting Numbers: [170] 170,80 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 79, 82, 31, 61 ]
90
[ "82-79=3", "61-31=30", "3*30=90" ]
Current State: 90:[79, 82, 31, 61], Operations: [] Exploring Operation: 82-79=3, Resulting Numbers: [31, 61, 3] Generated Node #2: [31, 61, 3] from Operation: 82-79=3 Current State: 90:[31, 61, 3], Operations: ['82-79=3'] Exploring Operation: 61-31=30, Resulting Numbers: [3, 30] Generated Node #3: [3, 30] from Operation: 61-31=30 Current State: 90:[3, 30], Operations: ['82-79=3', '61-31=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[79, 82, 31, 61], Operations: [] Exploring Operation: 82-79=3, Resulting Numbers: [31, 61, 3] Generated Node #0,0: 90:[31, 61, 3] Operation: 82-79=3 Exploring Operation: 82-61=21, Resulting Numbers: [79, 31, 21] Generated Node #0,1: 90:[79, 31, 21] Operation: 82-61=21 Exploring Operation: 79-61=18, Resulting Numbers: [82, 31, 18] Generated Node #0,2: 90:[82, 31, 18] Operation: 79-61=18 Moving to Node #0,2 Current State: 90:[82, 31, 18], Operations: ['79-61=18'] Exploring Operation: 31-18=13, Resulting Numbers: [82, 13] Generated Node #0,2,0: 90:[82, 13] Operation: 31-18=13 Exploring Operation: 82+18=100, Resulting Numbers: [31, 100] Generated Node #0,2,1: 90:[31, 100] Operation: 82+18=100 Exploring Operation: 82-31=51, Resulting Numbers: [18, 51] Generated Node #0,2,2: 90:[18, 51] Operation: 82-31=51 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[18, 51], Operations: ['79-61=18', '82-31=51'] Exploring Operation: 18+51=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 18*51=918, Resulting Numbers: [918] 918,90 unequal: No Solution Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[82, 13], Operations: ['79-61=18', '31-18=13'] Exploring Operation: 82+13=95, Resulting Numbers: [95] 95,90 unequal: No Solution Exploring Operation: 82*13=1066, Resulting Numbers: [1066] 1066,90 unequal: No Solution Exploring Operation: 82-13=69, Resulting Numbers: [69] 69,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 90:[31, 100], Operations: ['79-61=18', '82+18=100'] Exploring Operation: 31*100=3100, Resulting Numbers: [3100] 3100,90 unequal: No Solution Exploring Operation: 31+100=131, Resulting Numbers: [131] 131,90 unequal: No Solution Exploring Operation: 100-31=69, Resulting Numbers: [69] 69,90 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: 90:[79, 31, 21], Operations: ['82-61=21'] Exploring Operation: 79+21=100, Resulting Numbers: [31, 100] Generated Node #0,1,0: 90:[31, 100] Operation: 79+21=100 Exploring Operation: 79-31=48, Resulting Numbers: [21, 48] Generated Node #0,1,1: 90:[21, 48] Operation: 79-31=48 Exploring Operation: 31-21=10, Resulting Numbers: [79, 10] Generated Node #0,1,2: 90:[79, 10] Operation: 31-21=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[21, 48], Operations: ['82-61=21', '79-31=48'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 21*48=1008, Resulting Numbers: [1008] 1008,90 unequal: No Solution Exploring Operation: 21+48=69, Resulting Numbers: [69] 69,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[31, 100], Operations: ['82-61=21', '79+21=100'] Exploring Operation: 31*100=3100, Resulting Numbers: [3100] 3100,90 unequal: No Solution Exploring Operation: 31+100=131, Resulting Numbers: [131] 131,90 unequal: No Solution Exploring Operation: 100-31=69, Resulting Numbers: [69] 69,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[79, 10], Operations: ['82-61=21', '31-21=10'] Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 79*10=790, Resulting Numbers: [790] 790,90 unequal: No Solution Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,90 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: 90:[31, 61, 3], Operations: ['82-79=3'] Exploring Operation: 61-31=30, Resulting Numbers: [3, 30] Generated Node #0,0,0: 90:[3, 30] Operation: 61-31=30 Exploring Operation: 31+61=92, Resulting Numbers: [3, 92] Generated Node #0,0,1: 90:[3, 92] Operation: 31+61=92 Exploring Operation: 61-3=58, Resulting Numbers: [31, 58] Generated Node #0,0,2: 90:[31, 58] Operation: 61-3=58 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[3, 30], Operations: ['82-79=3', '61-31=30'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[79, 82, 31, 61], Operations: [] Exploring Operation: 82-79=3, Resulting Numbers: [31, 61, 3] Generated Node #0,0: 90:[31, 61, 3] Operation: 82-79=3 Moving to Node #0,0 Current State: 90:[31, 61, 3], Operations: ['82-79=3'] Exploring Operation: 61-31=30, Resulting Numbers: [3, 30] Generated Node #0,0,0: 90:[3, 30] Operation: 61-31=30 Moving to Node #0,0,0 Current State: 90:[3, 30], Operations: ['82-79=3', '61-31=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 19, 87, 32, 17 ]
26
[ "87+32=119", "119/17=7", "19+7=26" ]
Current State: 26:[19, 87, 32, 17], Operations: [] Exploring Operation: 87+32=119, Resulting Numbers: [19, 17, 119] Generated Node #2: [19, 17, 119] from Operation: 87+32=119 Current State: 26:[19, 17, 119], Operations: ['87+32=119'] Exploring Operation: 119/17=7, Resulting Numbers: [19, 7] Generated Node #3: [19, 7] from Operation: 119/17=7 Current State: 26:[19, 7], Operations: ['87+32=119', '119/17=7'] Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[19, 87, 32, 17], Operations: [] Exploring Operation: 87-32=55, Resulting Numbers: [19, 17, 55] Generated Node #0,0: 26:[19, 17, 55] Operation: 87-32=55 Exploring Operation: 87-17=70, Resulting Numbers: [19, 32, 70] Generated Node #0,1: 26:[19, 32, 70] Operation: 87-17=70 Exploring Operation: 87-19=68, Resulting Numbers: [32, 17, 68] Generated Node #0,2: 26:[32, 17, 68] Operation: 87-19=68 Exploring Operation: 32-19=13, Resulting Numbers: [87, 17, 13] Generated Node #0,3: 26:[87, 17, 13] Operation: 32-19=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[19, 17, 55], Operations: ['87-32=55'] Exploring Operation: 19-17=2, Resulting Numbers: [55, 2] Generated Node #0,0,0: 26:[55, 2] Operation: 19-17=2 Exploring Operation: 55-17=38, Resulting Numbers: [19, 38] Generated Node #0,0,1: 26:[19, 38] Operation: 55-17=38 Exploring Operation: 19+17=36, Resulting Numbers: [55, 36] Generated Node #0,0,2: 26:[55, 36] Operation: 19+17=36 Exploring Operation: 55-19=36, Resulting Numbers: [17, 36] Generated Node #0,0,3: 26:[17, 36] Operation: 55-19=36 Moving to Node #0,0,3 Current State: 26:[17, 36], Operations: ['87-32=55', '55-19=36'] Exploring Operation: 17+36=53, Resulting Numbers: [53] 53,26 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,26 unequal: No Solution Exploring Operation: 17*36=612, Resulting Numbers: [612] 612,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[19, 38], Operations: ['87-32=55', '55-17=38'] Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,26 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,26 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[55, 2], Operations: ['87-32=55', '19-17=2'] Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,26 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,26 unequal: No Solution Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[55, 36], Operations: ['87-32=55', '19+17=36'] Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,26 unequal: No Solution Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,26 unequal: No Solution Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,26 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 #0,2 Current State: 26:[32, 17, 68], Operations: ['87-19=68'] Exploring Operation: 32-17=15, Resulting Numbers: [68, 15] Generated Node #0,2,0: 26:[68, 15] Operation: 32-17=15 Exploring Operation: 68/17=4, Resulting Numbers: [32, 4] Generated Node #0,2,1: 26:[32, 4] Operation: 68/17=4 Exploring Operation: 68-17=51, Resulting Numbers: [32, 51] Generated Node #0,2,2: 26:[32, 51] Operation: 68-17=51 Exploring Operation: 68-32=36, Resulting Numbers: [17, 36] Generated Node #0,2,3: 26:[17, 36] Operation: 68-32=36 Moving to Node #0,2,1 Current State: 26:[32, 4], Operations: ['87-19=68', '68/17=4'] Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,26 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,26 unequal: No Solution Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[17, 36], Operations: ['87-19=68', '68-32=36'] Exploring Operation: 17*36=612, Resulting Numbers: [612] 612,26 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,26 unequal: No Solution Exploring Operation: 17+36=53, Resulting Numbers: [53] 53,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[32, 51], Operations: ['87-19=68', '68-17=51'] Exploring Operation: 32*51=1632, Resulting Numbers: [1632] 1632,26 unequal: No Solution Exploring Operation: 51-32=19, Resulting Numbers: [19] 19,26 unequal: No Solution Exploring Operation: 32+51=83, Resulting Numbers: [83] 83,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[68, 15], Operations: ['87-19=68', '32-17=15'] Exploring Operation: 68+15=83, Resulting Numbers: [83] 83,26 unequal: No Solution Exploring Operation: 68*15=1020, Resulting Numbers: [1020] 1020,26 unequal: No Solution Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[19, 32, 70], Operations: ['87-17=70'] Exploring Operation: 32-19=13, Resulting Numbers: [70, 13] Generated Node #0,1,0: 26:[70, 13] Operation: 32-19=13 Exploring Operation: 70-19=51, Resulting Numbers: [32, 51] Generated Node #0,1,1: 26:[32, 51] Operation: 70-19=51 Exploring Operation: 19+32=51, Resulting Numbers: [70, 51] Generated Node #0,1,2: 26:[70, 51] Operation: 19+32=51 Exploring Operation: 70-32=38, Resulting Numbers: [19, 38] Generated Node #0,1,3: 26:[19, 38] Operation: 70-32=38 Moving to Node #0,1,3 Current State: 26:[19, 38], Operations: ['87-17=70', '70-32=38'] Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,26 unequal: No Solution Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,26 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[32, 51], Operations: ['87-17=70', '70-19=51'] Exploring Operation: 32*51=1632, Resulting Numbers: [1632] 1632,26 unequal: No Solution Exploring Operation: 32+51=83, Resulting Numbers: [83] 83,26 unequal: No Solution Exploring Operation: 51-32=19, Resulting Numbers: [19] 19,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[70, 13], Operations: ['87-17=70', '32-19=13'] Exploring Operation: 70*13=910, Resulting Numbers: [910] 910,26 unequal: No Solution Exploring Operation: 70+13=83, Resulting Numbers: [83] 83,26 unequal: No Solution Exploring Operation: 70-13=57, Resulting Numbers: [57] 57,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[70, 51], Operations: ['87-17=70', '19+32=51'] Exploring Operation: 70*51=3570, Resulting Numbers: [3570] 3570,26 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,26 unequal: No Solution Exploring Operation: 70+51=121, Resulting Numbers: [121] 121,26 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 #0,3 Current State: 26:[87, 17, 13], Operations: ['32-19=13'] Exploring Operation: 17-13=4, Resulting Numbers: [87, 4] Generated Node #0,3,0: 26:[87, 4] Operation: 17-13=4 Exploring Operation: 87-13=74, Resulting Numbers: [17, 74] Generated Node #0,3,1: 26:[17, 74] Operation: 87-13=74 Exploring Operation: 17+13=30, Resulting Numbers: [87, 30] Generated Node #0,3,2: 26:[87, 30] Operation: 17+13=30 Exploring Operation: 87-17=70, Resulting Numbers: [13, 70] Generated Node #0,3,3: 26:[13, 70] Operation: 87-17=70 Moving to Node #0,3,3 Current State: 26:[13, 70], Operations: ['32-19=13', '87-17=70'] Exploring Operation: 13*70=910, Resulting Numbers: [910] 910,26 unequal: No Solution Exploring Operation: 70-13=57, Resulting Numbers: [57] 57,26 unequal: No Solution Exploring Operation: 13+70=83, Resulting Numbers: [83] 83,26 unequal: No Solution Moving to Node #0,3,1 Current State: 26:[17, 74], Operations: ['32-19=13', '87-13=74'] Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,26 unequal: No Solution Exploring Operation: 17*74=1258, Resulting Numbers: [1258] 1258,26 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,26 unequal: No Solution Moving to Node #0,3,0 Current State: 26:[87, 4], Operations: ['32-19=13', '17-13=4'] Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,26 unequal: No Solution Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,26 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,26 unequal: No Solution Moving to Node #0,3,2 Current State: 26:[87, 30], Operations: ['32-19=13', '17+13=30'] Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,26 unequal: No Solution Exploring Operation: 87*30=2610, Resulting Numbers: [2610] 2610,26 unequal: No Solution Exploring Operation: 87+30=117, Resulting Numbers: [117] 117,26 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
[ 37, 65, 39, 18 ]
94
[ "39-37=2", "65-18=47", "2*47=94" ]
Current State: 94:[37, 65, 39, 18], Operations: [] Exploring Operation: 39-37=2, Resulting Numbers: [65, 18, 2] Generated Node #2: [65, 18, 2] from Operation: 39-37=2 Current State: 94:[65, 18, 2], Operations: ['39-37=2'] Exploring Operation: 65-18=47, Resulting Numbers: [2, 47] Generated Node #3: [2, 47] from Operation: 65-18=47 Current State: 94:[2, 47], Operations: ['39-37=2', '65-18=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[37, 65, 39, 18], Operations: [] Exploring Operation: 65-18=47, Resulting Numbers: [37, 39, 47] Generated Node #0,0: 94:[37, 39, 47] Operation: 65-18=47 Exploring Operation: 65+18=83, Resulting Numbers: [37, 39, 83] Generated Node #0,1: 94:[37, 39, 83] Operation: 65+18=83 Exploring Operation: 37+65=102, Resulting Numbers: [39, 18, 102] Generated Node #0,2: 94:[39, 18, 102] Operation: 37+65=102 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[37, 39, 47], Operations: ['65-18=47'] Exploring Operation: 47-37=10, Resulting Numbers: [39, 10] Generated Node #0,0,0: 94:[39, 10] Operation: 47-37=10 Exploring Operation: 39-37=2, Resulting Numbers: [47, 2] Generated Node #0,0,1: 94:[47, 2] Operation: 39-37=2 Exploring Operation: 47-39=8, Resulting Numbers: [37, 8] Generated Node #0,0,2: 94:[37, 8] Operation: 47-39=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[47, 2], Operations: ['65-18=47', '39-37=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[37, 65, 39, 18], Operations: [] Exploring Operation: 65-18=47, Resulting Numbers: [37, 39, 47] Generated Node #0,0: 94:[37, 39, 47] Operation: 65-18=47 Moving to Node #0,0 Current State: 94:[37, 39, 47], Operations: ['65-18=47'] Exploring Operation: 39-37=2, Resulting Numbers: [47, 2] Generated Node #0,0,1: 94:[47, 2] Operation: 39-37=2 Moving to Node #0,0,1 Current State: 94:[47, 2], Operations: ['65-18=47', '39-37=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 67, 30, 82, 24 ]
42
[ "67*30=2010", "82*24=1968", "2010-1968=42" ]
Current State: 42:[67, 30, 82, 24], Operations: [] Exploring Operation: 67*30=2010, Resulting Numbers: [82, 24, 2010] Generated Node #2: [82, 24, 2010] from Operation: 67*30=2010 Current State: 42:[82, 24, 2010], Operations: ['67*30=2010'] Exploring Operation: 82*24=1968, Resulting Numbers: [2010, 1968] Generated Node #3: [2010, 1968] from Operation: 82*24=1968 Current State: 42:[2010, 1968], Operations: ['67*30=2010', '82*24=1968'] Exploring Operation: 2010-1968=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[67, 30, 82, 24], Operations: [] Exploring Operation: 82-67=15, Resulting Numbers: [30, 24, 15] Generated Node #0,0: 42:[30, 24, 15] Operation: 82-67=15 Moving to Node #0,0 Current State: 42:[30, 24, 15], Operations: ['82-67=15'] Exploring Operation: 30-24=6, Resulting Numbers: [15, 6] Generated Node #0,0,0: 42:[15, 6] Operation: 30-24=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[15, 6], Operations: ['82-67=15', '30-24=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,42 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
[ 41, 38, 80, 40 ]
82
[ "80-38=42", "42-40=2", "41*2=82" ]
Current State: 82:[41, 38, 80, 40], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [41, 40, 42] Generated Node #2: [41, 40, 42] from Operation: 80-38=42 Current State: 82:[41, 40, 42], Operations: ['80-38=42'] Exploring Operation: 42-40=2, Resulting Numbers: [41, 2] Generated Node #3: [41, 2] from Operation: 42-40=2 Current State: 82:[41, 2], Operations: ['80-38=42', '42-40=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[41, 38, 80, 40], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [41, 40, 42] Generated Node #0,0: 82:[41, 40, 42] Operation: 80-38=42 Exploring Operation: 40-38=2, Resulting Numbers: [41, 80, 2] Generated Node #0,1: 82:[41, 80, 2] Operation: 40-38=2 Moving to Node #0,0 Current State: 82:[41, 40, 42], Operations: ['80-38=42'] Exploring Operation: 40+42=82, Resulting Numbers: [41, 82] Generated Node #0,0,0: 82:[41, 82] Operation: 40+42=82 Exploring Operation: 42-40=2, Resulting Numbers: [41, 2] Generated Node #0,0,1: 82:[41, 2] Operation: 42-40=2 Moving to Node #0,1 Current State: 82:[41, 80, 2], Operations: ['40-38=2'] Exploring Operation: 80+2=82, Resulting Numbers: [41, 82] Generated Node #0,1,0: 82:[41, 82] Operation: 80+2=82 Exploring Operation: 80/2=40, Resulting Numbers: [41, 40] Generated Node #0,1,1: 82:[41, 40] Operation: 80/2=40 Moving to Node #0,0,0 Current State: 82:[41, 82], Operations: ['80-38=42', '40+42=82'] Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,82 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[41, 82], Operations: ['40-38=2', '80+2=82'] Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,82 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[41, 2], Operations: ['80-38=42', '42-40=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[41, 38, 80, 40], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [41, 40, 42] Generated Node #0,0: 82:[41, 40, 42] Operation: 80-38=42 Moving to Node #0,0 Current State: 82:[41, 40, 42], Operations: ['80-38=42'] Exploring Operation: 42-40=2, Resulting Numbers: [41, 2] Generated Node #0,0,1: 82:[41, 2] Operation: 42-40=2 Moving to Node #0,0,1 Current State: 82:[41, 2], Operations: ['80-38=42', '42-40=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 55, 42, 3, 9 ]
39
[ "55-42=13", "9/3=3", "13*3=39" ]
Current State: 39:[55, 42, 3, 9], Operations: [] Exploring Operation: 55-42=13, Resulting Numbers: [3, 9, 13] Generated Node #2: [3, 9, 13] from Operation: 55-42=13 Current State: 39:[3, 9, 13], Operations: ['55-42=13'] Exploring Operation: 9/3=3, Resulting Numbers: [13, 3] Generated Node #3: [13, 3] from Operation: 9/3=3 Current State: 39:[13, 3], Operations: ['55-42=13', '9/3=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[55, 42, 3, 9], Operations: [] Exploring Operation: 55-9=46, Resulting Numbers: [42, 3, 46] Generated Node #0,0: 39:[42, 3, 46] Operation: 55-9=46 Exploring Operation: 9/3=3, Resulting Numbers: [55, 42, 3] Generated Node #0,1: 39:[55, 42, 3] Operation: 9/3=3 Exploring Operation: 55-3=52, Resulting Numbers: [42, 9, 52] Generated Node #0,2: 39:[42, 9, 52] Operation: 55-3=52 Exploring Operation: 55-42=13, Resulting Numbers: [3, 9, 13] Generated Node #0,3: 39:[3, 9, 13] Operation: 55-42=13 Exploring Operation: 42-3=39, Resulting Numbers: [55, 9, 39] Generated Node #0,4: 39:[55, 9, 39] Operation: 42-3=39 Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[3, 9, 13], Operations: ['55-42=13'] Exploring Operation: 3+9=12, Resulting Numbers: [13, 12] Generated Node #0,3,0: 39:[13, 12] Operation: 3+9=12 Exploring Operation: 3*13=39, Resulting Numbers: [9, 39] Generated Node #0,3,1: 39:[9, 39] Operation: 3*13=39 Exploring Operation: 13-9=4, Resulting Numbers: [3, 4] Generated Node #0,3,2: 39:[3, 4] Operation: 13-9=4 Exploring Operation: 9/3=3, Resulting Numbers: [13, 3] Generated Node #0,3,3: 39:[13, 3] Operation: 9/3=3 Exploring Operation: 9-3=6, Resulting Numbers: [13, 6] Generated Node #0,3,4: 39:[13, 6] Operation: 9-3=6 Moving to Node #0,3,3 Current State: 39:[13, 3], Operations: ['55-42=13', '9/3=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[55, 42, 3, 9], Operations: [] Exploring Operation: 55-42=13, Resulting Numbers: [3, 9, 13] Generated Node #0,3: 39:[3, 9, 13] Operation: 55-42=13 Moving to Node #0,3 Current State: 39:[3, 9, 13], Operations: ['55-42=13'] Exploring Operation: 9/3=3, Resulting Numbers: [13, 3] Generated Node #0,3,3: 39:[13, 3] Operation: 9/3=3 Moving to Node #0,3,3 Current State: 39:[13, 3], Operations: ['55-42=13', '9/3=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 78, 4, 34, 42 ]
46
[ "42-34=8", "4*8=32", "78-32=46" ]
Current State: 46:[78, 4, 34, 42], Operations: [] Exploring Operation: 42-34=8, Resulting Numbers: [78, 4, 8] Generated Node #2: [78, 4, 8] from Operation: 42-34=8 Current State: 46:[78, 4, 8], Operations: ['42-34=8'] Exploring Operation: 4*8=32, Resulting Numbers: [78, 32] Generated Node #3: [78, 32] from Operation: 4*8=32 Current State: 46:[78, 32], Operations: ['42-34=8', '4*8=32'] Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[78, 4, 34, 42], Operations: [] Exploring Operation: 78-34=44, Resulting Numbers: [4, 42, 44] Generated Node #0,0: 46:[4, 42, 44] Operation: 78-34=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[4, 42, 44], Operations: ['78-34=44'] Exploring Operation: 4+42=46, Resulting Numbers: [44, 46] Generated Node #0,0,0: 46:[44, 46] Operation: 4+42=46 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[44, 46], Operations: ['78-34=44', '4+42=46'] Exploring Operation: 46-44=2, Resulting Numbers: [2] 2,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 23, 75, 57, 56 ]
98
[ "23+75=98", "57-56=1", "98*1=98" ]
Current State: 98:[23, 75, 57, 56], Operations: [] Exploring Operation: 23+75=98, Resulting Numbers: [57, 56, 98] Generated Node #2: [57, 56, 98] from Operation: 23+75=98 Current State: 98:[57, 56, 98], Operations: ['23+75=98'] Exploring Operation: 57-56=1, Resulting Numbers: [98, 1] Generated Node #3: [98, 1] from Operation: 57-56=1 Current State: 98:[98, 1], Operations: ['23+75=98', '57-56=1'] Exploring Operation: 98*1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[23, 75, 57, 56], Operations: [] Exploring Operation: 75-23=52, Resulting Numbers: [57, 56, 52] Generated Node #0,0: 98:[57, 56, 52] Operation: 75-23=52 Exploring Operation: 75-57=18, Resulting Numbers: [23, 56, 18] Generated Node #0,1: 98:[23, 56, 18] Operation: 75-57=18 Exploring Operation: 23+75=98, Resulting Numbers: [57, 56, 98] Generated Node #0,2: 98:[57, 56, 98] Operation: 23+75=98 Exploring Operation: 75-56=19, Resulting Numbers: [23, 57, 19] Generated Node #0,3: 98:[23, 57, 19] Operation: 75-56=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[57, 56, 98], Operations: ['23+75=98'] Exploring Operation: 98-56=42, Resulting Numbers: [57, 42] Generated Node #0,2,0: 98:[57, 42] Operation: 98-56=42 Exploring Operation: 57+56=113, Resulting Numbers: [98, 113] Generated Node #0,2,1: 98:[98, 113] Operation: 57+56=113 Exploring Operation: 98-57=41, Resulting Numbers: [56, 41] Generated Node #0,2,2: 98:[56, 41] Operation: 98-57=41 Exploring Operation: 57-56=1, Resulting Numbers: [98, 1] Generated Node #0,2,3: 98:[98, 1] Operation: 57-56=1 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 98:[98, 1], Operations: ['23+75=98', '57-56=1'] Exploring Operation: 98*1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[23, 75, 57, 56], Operations: [] Exploring Operation: 23+75=98, Resulting Numbers: [57, 56, 98] Generated Node #0,2: 98:[57, 56, 98] Operation: 23+75=98 Moving to Node #0,2 Current State: 98:[57, 56, 98], Operations: ['23+75=98'] Exploring Operation: 57-56=1, Resulting Numbers: [98, 1] Generated Node #0,2,3: 98:[98, 1] Operation: 57-56=1 Moving to Node #0,2,3 Current State: 98:[98, 1], Operations: ['23+75=98', '57-56=1'] Exploring Operation: 98*1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 14, 56, 10, 2 ]
45
[ "14+56=70", "70/2=35", "10+35=45" ]
Current State: 45:[14, 56, 10, 2], Operations: [] Exploring Operation: 14+56=70, Resulting Numbers: [10, 2, 70] Generated Node #2: [10, 2, 70] from Operation: 14+56=70 Current State: 45:[10, 2, 70], Operations: ['14+56=70'] Exploring Operation: 70/2=35, Resulting Numbers: [10, 35] Generated Node #3: [10, 35] from Operation: 70/2=35 Current State: 45:[10, 35], Operations: ['14+56=70', '70/2=35'] Exploring Operation: 10+35=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[14, 56, 10, 2], Operations: [] Exploring Operation: 56/14=4, Resulting Numbers: [10, 2, 4] Generated Node #0,0: 45:[10, 2, 4] Operation: 56/14=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[10, 2, 4], Operations: ['56/14=4'] Exploring Operation: 10/2=5, Resulting Numbers: [4, 5] Generated Node #0,0,0: 45:[4, 5] Operation: 10/2=5 Moving to Node #0,0,0 Current State: 45:[4, 5], Operations: ['56/14=4', '10/2=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,45 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
[ 38, 77, 62, 18 ]
14
[ "62*18=1116", "1116-38=1078", "1078/77=14" ]
Current State: 14:[38, 77, 62, 18], Operations: [] Exploring Operation: 62*18=1116, Resulting Numbers: [38, 77, 1116] Generated Node #2: [38, 77, 1116] from Operation: 62*18=1116 Current State: 14:[38, 77, 1116], Operations: ['62*18=1116'] Exploring Operation: 1116-38=1078, Resulting Numbers: [77, 1078] Generated Node #3: [77, 1078] from Operation: 1116-38=1078 Current State: 14:[77, 1078], Operations: ['62*18=1116', '1116-38=1078'] Exploring Operation: 1078/77=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[38, 77, 62, 18], Operations: [] Exploring Operation: 77-38=39, Resulting Numbers: [62, 18, 39] Generated Node #0,0: 14:[62, 18, 39] Operation: 77-38=39 Exploring Operation: 77-62=15, Resulting Numbers: [38, 18, 15] Generated Node #0,1: 14:[38, 18, 15] Operation: 77-62=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[38, 18, 15], Operations: ['77-62=15'] Exploring Operation: 38-15=23, Resulting Numbers: [18, 23] Generated Node #0,1,0: 14:[18, 23] Operation: 38-15=23 Exploring Operation: 38-18=20, Resulting Numbers: [15, 20] Generated Node #0,1,1: 14:[15, 20] Operation: 38-18=20 Moving to Node #0,1,1 Current State: 14:[15, 20], Operations: ['77-62=15', '38-18=20'] Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[18, 23], Operations: ['77-62=15', '38-15=23'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 18+23=41, Resulting Numbers: [41] 41,14 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 #0,0 Current State: 14:[62, 18, 39], Operations: ['77-38=39'] Exploring Operation: 62-18=44, Resulting Numbers: [39, 44] Generated Node #0,0,0: 14:[39, 44] Operation: 62-18=44 Exploring Operation: 62-39=23, Resulting Numbers: [18, 23] Generated Node #0,0,1: 14:[18, 23] Operation: 62-39=23 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 14:[18, 23], Operations: ['77-38=39', '62-39=23'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 18+23=41, Resulting Numbers: [41] 41,14 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 #0,0,0 Current State: 14:[39, 44], Operations: ['77-38=39', '62-18=44'] Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 39+44=83, Resulting Numbers: [83] 83,14 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 No solution found.
0
hs_2
sum_heuristic
[ 46, 71, 67, 79 ]
76
[ "71+67=138", "138/46=3", "79-3=76" ]
Current State: 76:[46, 71, 67, 79], Operations: [] Exploring Operation: 71+67=138, Resulting Numbers: [46, 79, 138] Generated Node #2: [46, 79, 138] from Operation: 71+67=138 Current State: 76:[46, 79, 138], Operations: ['71+67=138'] Exploring Operation: 138/46=3, Resulting Numbers: [79, 3] Generated Node #3: [79, 3] from Operation: 138/46=3 Current State: 76:[79, 3], Operations: ['71+67=138', '138/46=3'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[46, 71, 67, 79], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [46, 79, 4] Generated Node #0,0: 76:[46, 79, 4] Operation: 71-67=4 Exploring Operation: 67-46=21, Resulting Numbers: [71, 79, 21] Generated Node #0,1: 76:[71, 79, 21] Operation: 67-46=21 Moving to Node #0,1 Current State: 76:[71, 79, 21], Operations: ['67-46=21'] Exploring Operation: 71-21=50, Resulting Numbers: [79, 50] Generated Node #0,1,0: 76:[79, 50] Operation: 71-21=50 Exploring Operation: 79-71=8, Resulting Numbers: [21, 8] Generated Node #0,1,1: 76:[21, 8] Operation: 79-71=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[21, 8], Operations: ['67-46=21', '79-71=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,76 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,76 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:[79, 50], Operations: ['67-46=21', '71-21=50'] Exploring Operation: 79+50=129, Resulting Numbers: [129] 129,76 unequal: No Solution Exploring Operation: 79-50=29, Resulting Numbers: [29] 29,76 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:[46, 79, 4], Operations: ['71-67=4'] Exploring Operation: 79-46=33, Resulting Numbers: [4, 33] Generated Node #0,0,0: 76:[4, 33] Operation: 79-46=33 Exploring Operation: 46-4=42, Resulting Numbers: [79, 42] Generated Node #0,0,1: 76:[79, 42] Operation: 46-4=42 Moving to Node #0,0,0 Current State: 76:[4, 33], Operations: ['71-67=4', '79-46=33'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,76 unequal: No Solution Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[79, 42], Operations: ['71-67=4', '46-4=42'] Exploring Operation: 79+42=121, Resulting Numbers: [121] 121,76 unequal: No Solution Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,76 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 60, 82, 59, 57 ]
44
[ "82-60=22", "59-57=2", "22*2=44" ]
Current State: 44:[60, 82, 59, 57], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [59, 57, 22] Generated Node #2: [59, 57, 22] from Operation: 82-60=22 Current State: 44:[59, 57, 22], Operations: ['82-60=22'] Exploring Operation: 59-57=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 59-57=2 Current State: 44:[22, 2], Operations: ['82-60=22', '59-57=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[60, 82, 59, 57], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [59, 57, 22] Generated Node #0,0: 44:[59, 57, 22] Operation: 82-60=22 Exploring Operation: 82-59=23, Resulting Numbers: [60, 57, 23] Generated Node #0,1: 44:[60, 57, 23] Operation: 82-59=23 Exploring Operation: 82-57=25, Resulting Numbers: [60, 59, 25] Generated Node #0,2: 44:[60, 59, 25] Operation: 82-57=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[59, 57, 22], Operations: ['82-60=22'] Exploring Operation: 59-22=37, Resulting Numbers: [57, 37] Generated Node #0,0,0: 44:[57, 37] Operation: 59-22=37 Exploring Operation: 59-57=2, Resulting Numbers: [22, 2] Generated Node #0,0,1: 44:[22, 2] Operation: 59-57=2 Exploring Operation: 57-22=35, Resulting Numbers: [59, 35] Generated Node #0,0,2: 44:[59, 35] Operation: 57-22=35 Moving to Node #0,0,1 Current State: 44:[22, 2], Operations: ['82-60=22', '59-57=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[60, 82, 59, 57], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [59, 57, 22] Generated Node #0,0: 44:[59, 57, 22] Operation: 82-60=22 Moving to Node #0,0 Current State: 44:[59, 57, 22], Operations: ['82-60=22'] Exploring Operation: 59-57=2, Resulting Numbers: [22, 2] Generated Node #0,0,1: 44:[22, 2] Operation: 59-57=2 Moving to Node #0,0,1 Current State: 44:[22, 2], Operations: ['82-60=22', '59-57=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 96, 14, 42, 8 ]
89
[ "14+42=56", "56/8=7", "96-7=89" ]
Current State: 89:[96, 14, 42, 8], Operations: [] Exploring Operation: 14+42=56, Resulting Numbers: [96, 8, 56] Generated Node #2: [96, 8, 56] from Operation: 14+42=56 Current State: 89:[96, 8, 56], Operations: ['14+42=56'] Exploring Operation: 56/8=7, Resulting Numbers: [96, 7] Generated Node #3: [96, 7] from Operation: 56/8=7 Current State: 89:[96, 7], Operations: ['14+42=56', '56/8=7'] Exploring Operation: 96-7=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[96, 14, 42, 8], Operations: [] Exploring Operation: 14*8=112, Resulting Numbers: [96, 42, 112] Generated Node #0,0: 89:[96, 42, 112] Operation: 14*8=112 Exploring Operation: 14+42=56, Resulting Numbers: [96, 8, 56] Generated Node #0,1: 89:[96, 8, 56] Operation: 14+42=56 Moving to Node #0,0 Current State: 89:[96, 42, 112], Operations: ['14*8=112'] Exploring Operation: 96-42=54, Resulting Numbers: [112, 54] Generated Node #0,0,0: 89:[112, 54] Operation: 96-42=54 Exploring Operation: 112-42=70, Resulting Numbers: [96, 70] Generated Node #0,0,1: 89:[96, 70] Operation: 112-42=70 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[96, 70], Operations: ['14*8=112', '112-42=70'] Exploring Operation: 96+70=166, Resulting Numbers: [166] 166,89 unequal: No Solution Exploring Operation: 96-70=26, Resulting Numbers: [26] 26,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[112, 54], Operations: ['14*8=112', '96-42=54'] Exploring Operation: 112+54=166, Resulting Numbers: [166] 166,89 unequal: No Solution Exploring Operation: 112-54=58, Resulting Numbers: [58] 58,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[96, 8, 56], Operations: ['14+42=56'] Exploring Operation: 8+56=64, Resulting Numbers: [96, 64] Generated Node #0,1,0: 89:[96, 64] Operation: 8+56=64 Exploring Operation: 96-8=88, Resulting Numbers: [56, 88] Generated Node #0,1,1: 89:[56, 88] Operation: 96-8=88 Moving to Node #0,1,0 Current State: 89:[96, 64], Operations: ['14+42=56', '8+56=64'] Exploring Operation: 96-64=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 96+64=160, Resulting Numbers: [160] 160,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[56, 88], Operations: ['14+42=56', '96-8=88'] Exploring Operation: 56+88=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 88-56=32, Resulting Numbers: [32] 32,89 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 50, 60, 23, 38 ]
50
[ "60-23=37", "38-37=1", "50*1=50" ]
Current State: 50:[50, 60, 23, 38], Operations: [] Exploring Operation: 60-23=37, Resulting Numbers: [50, 38, 37] Generated Node #2: [50, 38, 37] from Operation: 60-23=37 Current State: 50:[50, 38, 37], Operations: ['60-23=37'] Exploring Operation: 38-37=1, Resulting Numbers: [50, 1] Generated Node #3: [50, 1] from Operation: 38-37=1 Current State: 50:[50, 1], Operations: ['60-23=37', '38-37=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[50, 60, 23, 38], Operations: [] Exploring Operation: 60-38=22, Resulting Numbers: [50, 23, 22] Generated Node #0,0: 50:[50, 23, 22] Operation: 60-38=22 Moving to Node #0,0 Current State: 50:[50, 23, 22], Operations: ['60-38=22'] Exploring Operation: 23-22=1, Resulting Numbers: [50, 1] Generated Node #0,0,0: 50:[50, 1] Operation: 23-22=1 Moving to Node #0,0,0 Current State: 50:[50, 1], Operations: ['60-38=22', '23-22=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[50, 60, 23, 38], Operations: [] Exploring Operation: 60-38=22, Resulting Numbers: [50, 23, 22] Generated Node #0,0: 50:[50, 23, 22] Operation: 60-38=22 Moving to Node #0,0 Current State: 50:[50, 23, 22], Operations: ['60-38=22'] Exploring Operation: 23-22=1, Resulting Numbers: [50, 1] Generated Node #0,0,0: 50:[50, 1] Operation: 23-22=1 Moving to Node #0,0,0 Current State: 50:[50, 1], Operations: ['60-38=22', '23-22=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 7, 47, 25, 29 ]
50
[ "7+47=54", "29-25=4", "54-4=50" ]
Current State: 50:[7, 47, 25, 29], Operations: [] Exploring Operation: 7+47=54, Resulting Numbers: [25, 29, 54] Generated Node #2: [25, 29, 54] from Operation: 7+47=54 Current State: 50:[25, 29, 54], Operations: ['7+47=54'] Exploring Operation: 29-25=4, Resulting Numbers: [54, 4] Generated Node #3: [54, 4] from Operation: 29-25=4 Current State: 50:[54, 4], Operations: ['7+47=54', '29-25=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[7, 47, 25, 29], Operations: [] Exploring Operation: 29-25=4, Resulting Numbers: [7, 47, 4] Generated Node #0,0: 50:[7, 47, 4] Operation: 29-25=4 Exploring Operation: 29-7=22, Resulting Numbers: [47, 25, 22] Generated Node #0,1: 50:[47, 25, 22] Operation: 29-7=22 Moving to Node #0,0 Current State: 50:[7, 47, 4], Operations: ['29-25=4'] Exploring Operation: 7+4=11, Resulting Numbers: [47, 11] Generated Node #0,0,0: 50:[47, 11] Operation: 7+4=11 Exploring Operation: 47+4=51, Resulting Numbers: [7, 51] Generated Node #0,0,1: 50:[7, 51] Operation: 47+4=51 Moving to Node #0,1 Current State: 50:[47, 25, 22], Operations: ['29-7=22'] Exploring Operation: 47-22=25, Resulting Numbers: [25, 25] Generated Node #0,1,0: 50:[25, 25] Operation: 47-22=25 Exploring Operation: 25-22=3, Resulting Numbers: [47, 3] Generated Node #0,1,1: 50:[47, 3] Operation: 25-22=3 Moving to Node #0,1,0 Current State: 50:[25, 25], Operations: ['29-7=22', '47-22=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[7, 47, 25, 29], Operations: [] Exploring Operation: 29-7=22, Resulting Numbers: [47, 25, 22] Generated Node #0,1: 50:[47, 25, 22] Operation: 29-7=22 Moving to Node #0,1 Current State: 50:[47, 25, 22], Operations: ['29-7=22'] Exploring Operation: 47-22=25, Resulting Numbers: [25, 25] Generated Node #0,1,0: 50:[25, 25] Operation: 47-22=25 Moving to Node #0,1,0 Current State: 50:[25, 25], Operations: ['29-7=22', '47-22=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 85, 40, 27, 2 ]
100
[ "85+40=125", "27-2=25", "125-25=100" ]
Current State: 100:[85, 40, 27, 2], Operations: [] Exploring Operation: 85+40=125, Resulting Numbers: [27, 2, 125] Generated Node #2: [27, 2, 125] from Operation: 85+40=125 Current State: 100:[27, 2, 125], Operations: ['85+40=125'] Exploring Operation: 27-2=25, Resulting Numbers: [125, 25] Generated Node #3: [125, 25] from Operation: 27-2=25 Current State: 100:[125, 25], Operations: ['85+40=125', '27-2=25'] Exploring Operation: 125-25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[85, 40, 27, 2], Operations: [] Exploring Operation: 40/2=20, Resulting Numbers: [85, 27, 20] Generated Node #0,0: 100:[85, 27, 20] Operation: 40/2=20 Exploring Operation: 85-40=45, Resulting Numbers: [27, 2, 45] Generated Node #0,1: 100:[27, 2, 45] Operation: 85-40=45 Moving to Node #0,1 Current State: 100:[27, 2, 45], Operations: ['85-40=45'] Exploring Operation: 45-27=18, Resulting Numbers: [2, 18] Generated Node #0,1,0: 100:[2, 18] Operation: 45-27=18 Exploring Operation: 27-2=25, Resulting Numbers: [45, 25] Generated Node #0,1,1: 100:[45, 25] Operation: 27-2=25 Moving to Node #0,0 Current State: 100:[85, 27, 20], Operations: ['40/2=20'] Exploring Operation: 85+20=105, Resulting Numbers: [27, 105] Generated Node #0,0,0: 100:[27, 105] Operation: 85+20=105 Exploring Operation: 85-27=58, Resulting Numbers: [20, 58] Generated Node #0,0,1: 100:[20, 58] Operation: 85-27=58 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[27, 105], Operations: ['40/2=20', '85+20=105'] Exploring Operation: 27+105=132, Resulting Numbers: [132] 132,100 unequal: No Solution Exploring Operation: 105-27=78, Resulting Numbers: [78] 78,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[20, 58], Operations: ['40/2=20', '85-27=58'] Exploring Operation: 58-20=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 20+58=78, Resulting Numbers: [78] 78,100 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: 100:[2, 18], Operations: ['85-40=45', '45-27=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[45, 25], Operations: ['85-40=45', '27-2=25'] Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 39, 97, 2, 19 ]
10
[ "97-39=58", "58/2=29", "29-19=10" ]
Current State: 10:[39, 97, 2, 19], Operations: [] Exploring Operation: 97-39=58, Resulting Numbers: [2, 19, 58] Generated Node #2: [2, 19, 58] from Operation: 97-39=58 Current State: 10:[2, 19, 58], Operations: ['97-39=58'] Exploring Operation: 58/2=29, Resulting Numbers: [19, 29] Generated Node #3: [19, 29] from Operation: 58/2=29 Current State: 10:[19, 29], Operations: ['97-39=58', '58/2=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[39, 97, 2, 19], Operations: [] Exploring Operation: 97-19=78, Resulting Numbers: [39, 2, 78] Generated Node #0,0: 10:[39, 2, 78] Operation: 97-19=78 Exploring Operation: 39-19=20, Resulting Numbers: [97, 2, 20] Generated Node #0,1: 10:[97, 2, 20] Operation: 39-19=20 Exploring Operation: 97-39=58, Resulting Numbers: [2, 19, 58] Generated Node #0,2: 10:[2, 19, 58] Operation: 97-39=58 Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[2, 19, 58], Operations: ['97-39=58'] Exploring Operation: 58-19=39, Resulting Numbers: [2, 39] Generated Node #0,2,0: 10:[2, 39] Operation: 58-19=39 Exploring Operation: 58/2=29, Resulting Numbers: [19, 29] Generated Node #0,2,1: 10:[19, 29] Operation: 58/2=29 Exploring Operation: 19-2=17, Resulting Numbers: [58, 17] Generated Node #0,2,2: 10:[58, 17] Operation: 19-2=17 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 10:[19, 29], Operations: ['97-39=58', '58/2=29'] Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,10 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[39, 97, 2, 19], Operations: [] Exploring Operation: 97-39=58, Resulting Numbers: [2, 19, 58] Generated Node #0,2: 10:[2, 19, 58] Operation: 97-39=58 Moving to Node #0,2 Current State: 10:[2, 19, 58], Operations: ['97-39=58'] Exploring Operation: 58/2=29, Resulting Numbers: [19, 29] Generated Node #0,2,1: 10:[19, 29] Operation: 58/2=29 Moving to Node #0,2,1 Current State: 10:[19, 29], Operations: ['97-39=58', '58/2=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 62, 12, 19, 13 ]
56
[ "62-12=50", "19-13=6", "50+6=56" ]
Current State: 56:[62, 12, 19, 13], Operations: [] Exploring Operation: 62-12=50, Resulting Numbers: [19, 13, 50] Generated Node #2: [19, 13, 50] from Operation: 62-12=50 Current State: 56:[19, 13, 50], Operations: ['62-12=50'] Exploring Operation: 19-13=6, Resulting Numbers: [50, 6] Generated Node #3: [50, 6] from Operation: 19-13=6 Current State: 56:[50, 6], Operations: ['62-12=50', '19-13=6'] Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[62, 12, 19, 13], Operations: [] Exploring Operation: 19-12=7, Resulting Numbers: [62, 13, 7] Generated Node #0,0: 56:[62, 13, 7] Operation: 19-12=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[62, 13, 7], Operations: ['19-12=7'] Exploring Operation: 62-7=55, Resulting Numbers: [13, 55] Generated Node #0,0,0: 56:[13, 55] Operation: 62-7=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[13, 55], Operations: ['19-12=7', '62-7=55'] Exploring Operation: 13+55=68, Resulting Numbers: [68] 68,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 5, 95, 34, 38 ]
23
[ "95/5=19", "38-34=4", "19+4=23" ]
Current State: 23:[5, 95, 34, 38], Operations: [] Exploring Operation: 95/5=19, Resulting Numbers: [34, 38, 19] Generated Node #2: [34, 38, 19] from Operation: 95/5=19 Current State: 23:[34, 38, 19], Operations: ['95/5=19'] Exploring Operation: 38-34=4, Resulting Numbers: [19, 4] Generated Node #3: [19, 4] from Operation: 38-34=4 Current State: 23:[19, 4], Operations: ['95/5=19', '38-34=4'] Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[5, 95, 34, 38], Operations: [] Exploring Operation: 95-34=61, Resulting Numbers: [5, 38, 61] Generated Node #0,0: 23:[5, 38, 61] Operation: 95-34=61 Exploring Operation: 95-38=57, Resulting Numbers: [5, 34, 57] Generated Node #0,1: 23:[5, 34, 57] Operation: 95-38=57 Exploring Operation: 95/5=19, Resulting Numbers: [34, 38, 19] Generated Node #0,2: 23:[34, 38, 19] Operation: 95/5=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[34, 38, 19], Operations: ['95/5=19'] Exploring Operation: 38-34=4, Resulting Numbers: [19, 4] Generated Node #0,2,0: 23:[19, 4] Operation: 38-34=4 Exploring Operation: 38-19=19, Resulting Numbers: [34, 19] Generated Node #0,2,1: 23:[34, 19] Operation: 38-19=19 Exploring Operation: 34-19=15, Resulting Numbers: [38, 15] Generated Node #0,2,2: 23:[38, 15] Operation: 34-19=15 Moving to Node #0,2,1 Current State: 23:[34, 19], Operations: ['95/5=19', '38-19=19'] Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 34*19=646, Resulting Numbers: [646] 646,23 unequal: No Solution Exploring Operation: 34+19=53, Resulting Numbers: [53] 53,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[19, 4], Operations: ['95/5=19', '38-34=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[5, 95, 34, 38], Operations: [] Exploring Operation: 95/5=19, Resulting Numbers: [34, 38, 19] Generated Node #0,2: 23:[34, 38, 19] Operation: 95/5=19 Moving to Node #0,2 Current State: 23:[34, 38, 19], Operations: ['95/5=19'] Exploring Operation: 38-34=4, Resulting Numbers: [19, 4] Generated Node #0,2,0: 23:[19, 4] Operation: 38-34=4 Moving to Node #0,2,0 Current State: 23:[19, 4], Operations: ['95/5=19', '38-34=4'] Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 36, 2, 12, 9 ]
31
[ "36-2=34", "12-9=3", "34-3=31" ]
Current State: 31:[36, 2, 12, 9], Operations: [] Exploring Operation: 36-2=34, Resulting Numbers: [12, 9, 34] Generated Node #2: [12, 9, 34] from Operation: 36-2=34 Current State: 31:[12, 9, 34], Operations: ['36-2=34'] Exploring Operation: 12-9=3, Resulting Numbers: [34, 3] Generated Node #3: [34, 3] from Operation: 12-9=3 Current State: 31:[34, 3], Operations: ['36-2=34', '12-9=3'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[36, 2, 12, 9], Operations: [] Exploring Operation: 2*12=24, Resulting Numbers: [36, 9, 24] Generated Node #0,0: 31:[36, 9, 24] Operation: 2*12=24 Exploring Operation: 2*9=18, Resulting Numbers: [36, 12, 18] Generated Node #0,1: 31:[36, 12, 18] Operation: 2*9=18 Moving to Node #0,0 Current State: 31:[36, 9, 24], Operations: ['2*12=24'] Exploring Operation: 36-9=27, Resulting Numbers: [24, 27] Generated Node #0,0,0: 31:[24, 27] Operation: 36-9=27 Exploring Operation: 9+24=33, Resulting Numbers: [36, 33] Generated Node #0,0,1: 31:[36, 33] Operation: 9+24=33 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[36, 33], Operations: ['2*12=24', '9+24=33'] Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,31 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[24, 27], Operations: ['2*12=24', '36-9=27'] Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 24+27=51, Resulting Numbers: [51] 51,31 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: 31:[36, 12, 18], Operations: ['2*9=18'] Exploring Operation: 36-12=24, Resulting Numbers: [18, 24] Generated Node #0,1,0: 31:[18, 24] Operation: 36-12=24 Exploring Operation: 12+18=30, Resulting Numbers: [36, 30] Generated Node #0,1,1: 31:[36, 30] Operation: 12+18=30 Moving to Node #0,1,1 Current State: 31:[36, 30], Operations: ['2*9=18', '12+18=30'] Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[18, 24], Operations: ['2*9=18', '36-12=24'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,31 unequal: No Solution Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,31 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 6, 72, 89, 34 ]
45
[ "6+72=78", "89+34=123", "123-78=45" ]
Current State: 45:[6, 72, 89, 34], Operations: [] Exploring Operation: 6+72=78, Resulting Numbers: [89, 34, 78] Generated Node #2: [89, 34, 78] from Operation: 6+72=78 Current State: 45:[89, 34, 78], Operations: ['6+72=78'] Exploring Operation: 89+34=123, Resulting Numbers: [78, 123] Generated Node #3: [78, 123] from Operation: 89+34=123 Current State: 45:[78, 123], Operations: ['6+72=78', '89+34=123'] Exploring Operation: 123-78=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[6, 72, 89, 34], Operations: [] Exploring Operation: 89-72=17, Resulting Numbers: [6, 34, 17] Generated Node #0,0: 45:[6, 34, 17] Operation: 89-72=17 Exploring Operation: 89-34=55, Resulting Numbers: [6, 72, 55] Generated Node #0,1: 45:[6, 72, 55] Operation: 89-34=55 Exploring Operation: 72-34=38, Resulting Numbers: [6, 89, 38] Generated Node #0,2: 45:[6, 89, 38] Operation: 72-34=38 Moving to Node #0,0 Current State: 45:[6, 34, 17], Operations: ['89-72=17'] Exploring Operation: 34/17=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 45:[6, 2] Operation: 34/17=2 Exploring Operation: 6+34=40, Resulting Numbers: [17, 40] Generated Node #0,0,1: 45:[17, 40] Operation: 6+34=40 Exploring Operation: 34-17=17, Resulting Numbers: [6, 17] Generated Node #0,0,2: 45:[6, 17] Operation: 34-17=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[6, 2], Operations: ['89-72=17', '34/17=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,45 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:[6, 17], Operations: ['89-72=17', '34-17=17'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,45 unequal: No Solution Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,45 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 #0,0,1 Current State: 45:[17, 40], Operations: ['89-72=17', '6+34=40'] Exploring Operation: 17*40=680, Resulting Numbers: [680] 680,45 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,45 unequal: No Solution Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,45 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:[6, 72, 55], Operations: ['89-34=55'] Exploring Operation: 72/6=12, Resulting Numbers: [55, 12] Generated Node #0,1,0: 45:[55, 12] Operation: 72/6=12 Exploring Operation: 72-6=66, Resulting Numbers: [55, 66] Generated Node #0,1,1: 45:[55, 66] Operation: 72-6=66 Exploring Operation: 72-55=17, Resulting Numbers: [6, 17] Generated Node #0,1,2: 45:[6, 17] Operation: 72-55=17 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[6, 17], Operations: ['89-34=55', '72-55=17'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,45 unequal: No Solution Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[55, 12], Operations: ['89-34=55', '72/6=12'] Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,45 unequal: No Solution Exploring Operation: 55+12=67, Resulting Numbers: [67] 67,45 unequal: No Solution Exploring Operation: 55*12=660, Resulting Numbers: [660] 660,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[55, 66], Operations: ['89-34=55', '72-6=66'] Exploring Operation: 55*66=3630, Resulting Numbers: [3630] 3630,45 unequal: No Solution Exploring Operation: 55+66=121, Resulting Numbers: [121] 121,45 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,45 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: 45:[6, 89, 38], Operations: ['72-34=38'] Exploring Operation: 89-6=83, Resulting Numbers: [38, 83] Generated Node #0,2,0: 45:[38, 83] Operation: 89-6=83 Exploring Operation: 6+38=44, Resulting Numbers: [89, 44] Generated Node #0,2,1: 45:[89, 44] Operation: 6+38=44 Exploring Operation: 89-38=51, Resulting Numbers: [6, 51] Generated Node #0,2,2: 45:[6, 51] Operation: 89-38=51 Moving to Node #0,2,2 Current State: 45:[6, 51], Operations: ['72-34=38', '89-38=51'] Exploring Operation: 6*51=306, Resulting Numbers: [306] 306,45 unequal: No Solution Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[6, 72, 89, 34], Operations: [] Exploring Operation: 72-34=38, Resulting Numbers: [6, 89, 38] Generated Node #0,2: 45:[6, 89, 38] Operation: 72-34=38 Moving to Node #0,2 Current State: 45:[6, 89, 38], Operations: ['72-34=38'] Exploring Operation: 89-38=51, Resulting Numbers: [6, 51] Generated Node #0,2,2: 45:[6, 51] Operation: 89-38=51 Moving to Node #0,2,2 Current State: 45:[6, 51], Operations: ['72-34=38', '89-38=51'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.967882
hs_3
mult_heuristic
[ 3, 27, 22, 3 ]
58
[ "3*3=9", "27+22=49", "9+49=58" ]
Current State: 58:[3, 27, 22, 3], Operations: [] Exploring Operation: 3*3=9, Resulting Numbers: [27, 22, 9] Generated Node #2: [27, 22, 9] from Operation: 3*3=9 Current State: 58:[27, 22, 9], Operations: ['3*3=9'] Exploring Operation: 27+22=49, Resulting Numbers: [9, 49] Generated Node #3: [9, 49] from Operation: 27+22=49 Current State: 58:[9, 49], Operations: ['3*3=9', '27+22=49'] Exploring Operation: 9+49=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[3, 27, 22, 3], Operations: [] Exploring Operation: 3+22=25, Resulting Numbers: [27, 3, 25] Generated Node #0,0: 58:[27, 3, 25] Operation: 3+22=25 Exploring Operation: 27-22=5, Resulting Numbers: [3, 3, 5] Generated Node #0,1: 58:[3, 3, 5] Operation: 27-22=5 Moving to Node #0,1 Current State: 58:[3, 3, 5], Operations: ['27-22=5'] Exploring Operation: 5-3=2, Resulting Numbers: [3, 2] Generated Node #0,1,0: 58:[3, 2] Operation: 5-3=2 Exploring Operation: 5-3=2, Resulting Numbers: [3, 2] Generated Node #0,1,1: 58:[3, 2] Operation: 5-3=2 Moving to Node #0,0 Current State: 58:[27, 3, 25], Operations: ['3+22=25'] Exploring Operation: 3+25=28, Resulting Numbers: [27, 28] Generated Node #0,0,0: 58:[27, 28] Operation: 3+25=28 Exploring Operation: 27-25=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 58:[3, 2] Operation: 27-25=2 Moving to Node #0,1,0 Current State: 58:[3, 2], Operations: ['27-22=5', '5-3=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,58 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[3, 2], Operations: ['3+22=25', '27-25=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,58 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[3, 2], Operations: ['27-22=5', '5-3=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,58 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[27, 28], Operations: ['3+22=25', '3+25=28'] Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,58 unequal: No Solution Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,58 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 20, 45, 55, 67 ]
72
[ "45+55=100", "100/20=5", "67+5=72" ]
Current State: 72:[20, 45, 55, 67], Operations: [] Exploring Operation: 45+55=100, Resulting Numbers: [20, 67, 100] Generated Node #2: [20, 67, 100] from Operation: 45+55=100 Current State: 72:[20, 67, 100], Operations: ['45+55=100'] Exploring Operation: 100/20=5, Resulting Numbers: [67, 5] Generated Node #3: [67, 5] from Operation: 100/20=5 Current State: 72:[67, 5], Operations: ['45+55=100', '100/20=5'] Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[20, 45, 55, 67], Operations: [] Exploring Operation: 55-45=10, Resulting Numbers: [20, 67, 10] Generated Node #0,0: 72:[20, 67, 10] Operation: 55-45=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[20, 67, 10], Operations: ['55-45=10'] Exploring Operation: 20/10=2, Resulting Numbers: [67, 2] Generated Node #0,0,0: 72:[67, 2] Operation: 20/10=2 Moving to Node #0,0,0 Current State: 72:[67, 2], Operations: ['55-45=10', '20/10=2'] Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,72 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
[ 45, 73, 46, 24 ]
48
[ "45+73=118", "46+24=70", "118-70=48" ]
Current State: 48:[45, 73, 46, 24], Operations: [] Exploring Operation: 45+73=118, Resulting Numbers: [46, 24, 118] Generated Node #2: [46, 24, 118] from Operation: 45+73=118 Current State: 48:[46, 24, 118], Operations: ['45+73=118'] Exploring Operation: 46+24=70, Resulting Numbers: [118, 70] Generated Node #3: [118, 70] from Operation: 46+24=70 Current State: 48:[118, 70], Operations: ['45+73=118', '46+24=70'] Exploring Operation: 118-70=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[45, 73, 46, 24], Operations: [] Exploring Operation: 73-46=27, Resulting Numbers: [45, 24, 27] Generated Node #0,0: 48:[45, 24, 27] Operation: 73-46=27 Exploring Operation: 73-45=28, Resulting Numbers: [46, 24, 28] Generated Node #0,1: 48:[46, 24, 28] Operation: 73-45=28 Exploring Operation: 73-24=49, Resulting Numbers: [45, 46, 49] Generated Node #0,2: 48:[45, 46, 49] Operation: 73-24=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[45, 24, 27], Operations: ['73-46=27'] Exploring Operation: 45-27=18, Resulting Numbers: [24, 18] Generated Node #0,0,0: 48:[24, 18] Operation: 45-27=18 Exploring Operation: 27-24=3, Resulting Numbers: [45, 3] Generated Node #0,0,1: 48:[45, 3] Operation: 27-24=3 Exploring Operation: 45-24=21, Resulting Numbers: [27, 21] Generated Node #0,0,2: 48:[27, 21] Operation: 45-24=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[24, 18], Operations: ['73-46=27', '45-27=18'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,48 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[45, 3], Operations: ['73-46=27', '27-24=3'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,48 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[45, 73, 46, 24], Operations: [] Exploring Operation: 73-46=27, Resulting Numbers: [45, 24, 27] Generated Node #0,0: 48:[45, 24, 27] Operation: 73-46=27 Moving to Node #0,0 Current State: 48:[45, 24, 27], Operations: ['73-46=27'] Exploring Operation: 27-24=3, Resulting Numbers: [45, 3] Generated Node #0,0,1: 48:[45, 3] Operation: 27-24=3 Moving to Node #0,0,1 Current State: 48:[45, 3], Operations: ['73-46=27', '27-24=3'] Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 42, 24, 8, 45 ]
90
[ "42+45=87", "24/8=3", "87+3=90" ]
Current State: 90:[42, 24, 8, 45], Operations: [] Exploring Operation: 42+45=87, Resulting Numbers: [24, 8, 87] Generated Node #2: [24, 8, 87] from Operation: 42+45=87 Current State: 90:[24, 8, 87], Operations: ['42+45=87'] Exploring Operation: 24/8=3, Resulting Numbers: [87, 3] Generated Node #3: [87, 3] from Operation: 24/8=3 Current State: 90:[87, 3], Operations: ['42+45=87', '24/8=3'] Exploring Operation: 87+3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[42, 24, 8, 45], Operations: [] Exploring Operation: 42-24=18, Resulting Numbers: [8, 45, 18] Generated Node #0,0: 90:[8, 45, 18] Operation: 42-24=18 Exploring Operation: 24+8=32, Resulting Numbers: [42, 45, 32] Generated Node #0,1: 90:[42, 45, 32] Operation: 24+8=32 Exploring Operation: 24/8=3, Resulting Numbers: [42, 45, 3] Generated Node #0,2: 90:[42, 45, 3] Operation: 24/8=3 Exploring Operation: 24-8=16, Resulting Numbers: [42, 45, 16] Generated Node #0,3: 90:[42, 45, 16] Operation: 24-8=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[8, 45, 18], Operations: ['42-24=18'] Exploring Operation: 45-8=37, Resulting Numbers: [18, 37] Generated Node #0,0,0: 90:[18, 37] Operation: 45-8=37 Exploring Operation: 45-18=27, Resulting Numbers: [8, 27] Generated Node #0,0,1: 90:[8, 27] Operation: 45-18=27 Exploring Operation: 18-8=10, Resulting Numbers: [45, 10] Generated Node #0,0,2: 90:[45, 10] Operation: 18-8=10 Exploring Operation: 8+18=26, Resulting Numbers: [45, 26] Generated Node #0,0,3: 90:[45, 26] Operation: 8+18=26 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 90:[45, 10], Operations: ['42-24=18', '18-8=10'] Exploring Operation: 45*10=450, Resulting Numbers: [450] 450,90 unequal: No Solution Exploring Operation: 45-10=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 45+10=55, Resulting Numbers: [55] 55,90 unequal: No Solution No 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: 90:[8, 27], Operations: ['42-24=18', '45-18=27'] Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,90 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,90 unequal: No Solution No 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: 90:[45, 26], Operations: ['42-24=18', '8+18=26'] Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,90 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,90 unequal: No Solution No 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: 90:[18, 37], Operations: ['42-24=18', '45-8=37'] Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,90 unequal: No Solution Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[42, 45, 3], Operations: ['24/8=3'] Exploring Operation: 42+45=87, Resulting Numbers: [3, 87] Generated Node #0,2,0: 90:[3, 87] Operation: 42+45=87 Exploring Operation: 45-42=3, Resulting Numbers: [3, 3] Generated Node #0,2,1: 90:[3, 3] Operation: 45-42=3 Exploring Operation: 42+3=45, Resulting Numbers: [45, 45] Generated Node #0,2,2: 90:[45, 45] Operation: 42+3=45 Exploring Operation: 42/3=14, Resulting Numbers: [45, 14] Generated Node #0,2,3: 90:[45, 14] Operation: 42/3=14 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 90:[3, 3], Operations: ['24/8=3', '45-42=3'] Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,90 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,90 unequal: No Solution No 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: 90:[45, 45], Operations: ['24/8=3', '42+3=45'] Exploring Operation: 45+45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[42, 24, 8, 45], Operations: [] Exploring Operation: 24/8=3, Resulting Numbers: [42, 45, 3] Generated Node #0,2: 90:[42, 45, 3] Operation: 24/8=3 Moving to Node #0,2 Current State: 90:[42, 45, 3], Operations: ['24/8=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45, 45] Generated Node #0,2,2: 90:[45, 45] Operation: 42+3=45 Moving to Node #0,2,2 Current State: 90:[45, 45], Operations: ['24/8=3', '42+3=45'] Exploring Operation: 45+45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 80, 35, 32, 54 ]
68
[ "35*32=1120", "1120/80=14", "54+14=68" ]
Current State: 68:[80, 35, 32, 54], Operations: [] Exploring Operation: 35*32=1120, Resulting Numbers: [80, 54, 1120] Generated Node #2: [80, 54, 1120] from Operation: 35*32=1120 Current State: 68:[80, 54, 1120], Operations: ['35*32=1120'] Exploring Operation: 1120/80=14, Resulting Numbers: [54, 14] Generated Node #3: [54, 14] from Operation: 1120/80=14 Current State: 68:[54, 14], Operations: ['35*32=1120', '1120/80=14'] Exploring Operation: 54+14=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[80, 35, 32, 54], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [80, 35, 22] Generated Node #0,0: 68:[80, 35, 22] Operation: 54-32=22 Exploring Operation: 35+32=67, Resulting Numbers: [80, 54, 67] Generated Node #0,1: 68:[80, 54, 67] Operation: 35+32=67 Exploring Operation: 80-54=26, Resulting Numbers: [35, 32, 26] Generated Node #0,2: 68:[35, 32, 26] Operation: 80-54=26 Exploring Operation: 54-35=19, Resulting Numbers: [80, 32, 19] Generated Node #0,3: 68:[80, 32, 19] Operation: 54-35=19 Exploring Operation: 80-35=45, Resulting Numbers: [32, 54, 45] Generated Node #0,4: 68:[32, 54, 45] Operation: 80-35=45 Moving to Node #0,2 Current State: 68:[35, 32, 26], Operations: ['80-54=26'] Exploring Operation: 35+32=67, Resulting Numbers: [26, 67] Generated Node #0,2,0: 68:[26, 67] Operation: 35+32=67 Exploring Operation: 35-32=3, Resulting Numbers: [26, 3] Generated Node #0,2,1: 68:[26, 3] Operation: 35-32=3 Exploring Operation: 32-26=6, Resulting Numbers: [35, 6] Generated Node #0,2,2: 68:[35, 6] Operation: 32-26=6 Exploring Operation: 35+26=61, Resulting Numbers: [32, 61] Generated Node #0,2,3: 68:[32, 61] Operation: 35+26=61 Exploring Operation: 35-26=9, Resulting Numbers: [32, 9] Generated Node #0,2,4: 68:[32, 9] Operation: 35-26=9 Moving to Node #0,3 Current State: 68:[80, 32, 19], Operations: ['54-35=19'] Exploring Operation: 80-32=48, Resulting Numbers: [19, 48] Generated Node #0,3,0: 68:[19, 48] Operation: 80-32=48 Exploring Operation: 32-19=13, Resulting Numbers: [80, 13] Generated Node #0,3,1: 68:[80, 13] Operation: 32-19=13 Exploring Operation: 80+19=99, Resulting Numbers: [32, 99] Generated Node #0,3,2: 68:[32, 99] Operation: 80+19=99 Exploring Operation: 80-19=61, Resulting Numbers: [32, 61] Generated Node #0,3,3: 68:[32, 61] Operation: 80-19=61 Exploring Operation: 32+19=51, Resulting Numbers: [80, 51] Generated Node #0,3,4: 68:[80, 51] Operation: 32+19=51 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 68:[32, 61], Operations: ['54-35=19', '80-19=61'] Exploring Operation: 32+61=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 32*61=1952, Resulting Numbers: [1952] 1952,68 unequal: No Solution Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 68:[19, 48], Operations: ['54-35=19', '80-32=48'] Exploring Operation: 19+48=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 19*48=912, Resulting Numbers: [912] 912,68 unequal: No Solution Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 68:[80, 13], Operations: ['54-35=19', '32-19=13'] Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 80*13=1040, Resulting Numbers: [1040] 1040,68 unequal: No Solution Exploring Operation: 80+13=93, Resulting Numbers: [93] 93,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 68:[80, 51], Operations: ['54-35=19', '32+19=51'] Exploring Operation: 80*51=4080, Resulting Numbers: [4080] 4080,68 unequal: No Solution Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,68 unequal: No Solution Exploring Operation: 80+51=131, Resulting Numbers: [131] 131,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 68:[32, 99], Operations: ['54-35=19', '80+19=99'] Exploring Operation: 32+99=131, Resulting Numbers: [131] 131,68 unequal: No Solution Exploring Operation: 99-32=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 32*99=3168, Resulting Numbers: [3168] 3168,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 68:[80, 35, 22], Operations: ['54-32=22'] Exploring Operation: 80-35=45, Resulting Numbers: [22, 45] Generated Node #0,0,0: 68:[22, 45] Operation: 80-35=45 Exploring Operation: 80-22=58, Resulting Numbers: [35, 58] Generated Node #0,0,1: 68:[35, 58] Operation: 80-22=58 Exploring Operation: 35-22=13, Resulting Numbers: [80, 13] Generated Node #0,0,2: 68:[80, 13] Operation: 35-22=13 Exploring Operation: 35+22=57, Resulting Numbers: [80, 57] Generated Node #0,0,3: 68:[80, 57] Operation: 35+22=57 Exploring Operation: 80+22=102, Resulting Numbers: [35, 102] Generated Node #0,0,4: 68:[35, 102] Operation: 80+22=102 Moving to Node #0,1 Current State: 68:[80, 54, 67], Operations: ['35+32=67'] Exploring Operation: 80-54=26, Resulting Numbers: [67, 26] Generated Node #0,1,0: 68:[67, 26] Operation: 80-54=26 Exploring Operation: 54+67=121, Resulting Numbers: [80, 121] Generated Node #0,1,1: 68:[80, 121] Operation: 54+67=121 Exploring Operation: 67-54=13, Resulting Numbers: [80, 13] Generated Node #0,1,2: 68:[80, 13] Operation: 67-54=13 Exploring Operation: 80+54=134, Resulting Numbers: [67, 134] Generated Node #0,1,3: 68:[67, 134] Operation: 80+54=134 Exploring Operation: 80-67=13, Resulting Numbers: [54, 13] Generated Node #0,1,4: 68:[54, 13] Operation: 80-67=13 Moving to Node #0,4 Current State: 68:[32, 54, 45], Operations: ['80-35=45'] Exploring Operation: 32+54=86, Resulting Numbers: [45, 86] Generated Node #0,4,0: 68:[45, 86] Operation: 32+54=86 Exploring Operation: 54-32=22, Resulting Numbers: [45, 22] Generated Node #0,4,1: 68:[45, 22] Operation: 54-32=22 Exploring Operation: 54-45=9, Resulting Numbers: [32, 9] Generated Node #0,4,2: 68:[32, 9] Operation: 54-45=9 Exploring Operation: 45-32=13, Resulting Numbers: [54, 13] Generated Node #0,4,3: 68:[54, 13] Operation: 45-32=13 Exploring Operation: 32+45=77, Resulting Numbers: [54, 77] Generated Node #0,4,4: 68:[54, 77] Operation: 32+45=77 Moving to Node #0,2,2 Current State: 68:[35, 6], Operations: ['80-54=26', '32-26=6'] Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,68 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,68 unequal: No Solution Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,68 unequal: No Solution Moving to Node #0,2,4 Current State: 68:[32, 9], Operations: ['80-54=26', '35-26=9'] Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,68 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,68 unequal: No Solution Moving to Node #0,4,2 Current State: 68:[32, 9], Operations: ['80-35=45', '54-45=9'] Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,68 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[26, 67], Operations: ['80-54=26', '35+32=67'] Exploring Operation: 26+67=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 67-26=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 26*67=1742, Resulting Numbers: [1742] 1742,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[32, 61], Operations: ['80-54=26', '35+26=61'] Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,68 unequal: No Solution Exploring Operation: 32+61=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 32*61=1952, Resulting Numbers: [1952] 1952,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[67, 26], Operations: ['35+32=67', '80-54=26'] Exploring Operation: 67-26=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 67+26=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 67*26=1742, Resulting Numbers: [1742] 1742,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[26, 3], Operations: ['80-54=26', '35-32=3'] Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,68 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[35, 58], Operations: ['54-32=22', '80-22=58'] Exploring Operation: 35*58=2030, Resulting Numbers: [2030] 2030,68 unequal: No Solution Exploring Operation: 35+58=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 58-35=23, Resulting Numbers: [23] 23,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[22, 45], Operations: ['54-32=22', '80-35=45'] Exploring Operation: 22*45=990, Resulting Numbers: [990] 990,68 unequal: No Solution Exploring Operation: 22+45=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[80, 13], Operations: ['35+32=67', '67-54=13'] Exploring Operation: 80*13=1040, Resulting Numbers: [1040] 1040,68 unequal: No Solution Exploring Operation: 80+13=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,68 unequal: No Solution Moving to Node #0,4,1 Current State: 68:[45, 22], Operations: ['80-35=45', '54-32=22'] Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,68 unequal: No Solution Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[80, 13], Operations: ['54-32=22', '35-22=13'] Exploring Operation: 80*13=1040, Resulting Numbers: [1040] 1040,68 unequal: No Solution Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 80+13=93, Resulting Numbers: [93] 93,68 unequal: No Solution Moving to Node #0,1,4 Current State: 68:[54, 13], Operations: ['35+32=67', '80-67=13'] Exploring Operation: 54*13=702, Resulting Numbers: [702] 702,68 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,68 unequal: No Solution Moving to Node #0,4,3 Current State: 68:[54, 13], Operations: ['80-35=45', '45-32=13'] Exploring Operation: 54*13=702, Resulting Numbers: [702] 702,68 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[80, 57], Operations: ['54-32=22', '35+22=57'] Exploring Operation: 80+57=137, Resulting Numbers: [137] 137,68 unequal: No Solution Exploring Operation: 80*57=4560, Resulting Numbers: [4560] 4560,68 unequal: No Solution Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,68 unequal: No Solution Moving to Node #0,4,4 Current State: 68:[54, 77], Operations: ['80-35=45', '32+45=77'] Exploring Operation: 54+77=131, Resulting Numbers: [131] 131,68 unequal: No Solution Exploring Operation: 77-54=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 54*77=4158, Resulting Numbers: [4158] 4158,68 unequal: No Solution Moving to Node #0,4,0 Current State: 68:[45, 86], Operations: ['80-35=45', '32+54=86'] Exploring Operation: 86-45=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 45+86=131, Resulting Numbers: [131] 131,68 unequal: No Solution Exploring Operation: 45*86=3870, Resulting Numbers: [3870] 3870,68 unequal: No Solution Moving to Node #0,0,4 Current State: 68:[35, 102], Operations: ['54-32=22', '80+22=102'] Exploring Operation: 35+102=137, Resulting Numbers: [137] 137,68 unequal: No Solution Exploring Operation: 35*102=3570, Resulting Numbers: [3570] 3570,68 unequal: No Solution Exploring Operation: 102-35=67, Resulting Numbers: [67] 67,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[80, 121], Operations: ['35+32=67', '54+67=121'] Exploring Operation: 121-80=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 80+121=201, Resulting Numbers: [201] 201,68 unequal: No Solution Exploring Operation: 80*121=9680, Resulting Numbers: [9680] 9680,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[67, 134], Operations: ['35+32=67', '80+54=134'] Exploring Operation: 67*134=8978, Resulting Numbers: [8978] 8978,68 unequal: No Solution Exploring Operation: 134/67=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 67+134=201, Resulting Numbers: [201] 201,68 unequal: No Solution Exploring Operation: 134-67=67, Resulting Numbers: [67] 67,68 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 3, 19, 85, 16 ]
84
[ "19-3=16", "16/16=1", "85-1=84" ]
Current State: 84:[3, 19, 85, 16], Operations: [] Exploring Operation: 19-3=16, Resulting Numbers: [85, 16, 16] Generated Node #2: [85, 16, 16] from Operation: 19-3=16 Current State: 84:[85, 16, 16], Operations: ['19-3=16'] Exploring Operation: 16/16=1, Resulting Numbers: [85, 1] Generated Node #3: [85, 1] from Operation: 16/16=1 Current State: 84:[85, 1], Operations: ['19-3=16', '16/16=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[3, 19, 85, 16], Operations: [] Exploring Operation: 19-3=16, Resulting Numbers: [85, 16, 16] Generated Node #0,0: 84:[85, 16, 16] Operation: 19-3=16 Exploring Operation: 16-3=13, Resulting Numbers: [19, 85, 13] Generated Node #0,1: 84:[19, 85, 13] Operation: 16-3=13 Exploring Operation: 3+19=22, Resulting Numbers: [85, 16, 22] Generated Node #0,2: 84:[85, 16, 22] Operation: 3+19=22 Exploring Operation: 19-16=3, Resulting Numbers: [3, 85, 3] Generated Node #0,3: 84:[3, 85, 3] Operation: 19-16=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[3, 85, 3], Operations: ['19-16=3'] Exploring Operation: 85-3=82, Resulting Numbers: [3, 82] Generated Node #0,3,0: 84:[3, 82] Operation: 85-3=82 Exploring Operation: 85-3=82, Resulting Numbers: [3, 82] Generated Node #0,3,1: 84:[3, 82] Operation: 85-3=82 Exploring Operation: 3+3=6, Resulting Numbers: [85, 6] Generated Node #0,3,2: 84:[85, 6] Operation: 3+3=6 Exploring Operation: 3/3=1, Resulting Numbers: [85, 1] Generated Node #0,3,3: 84:[85, 1] Operation: 3/3=1 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 84:[85, 6], Operations: ['19-16=3', '3+3=6'] Exploring Operation: 85+6=91, Resulting Numbers: [91] 91,84 unequal: No Solution Exploring Operation: 85*6=510, Resulting Numbers: [510] 510,84 unequal: No Solution Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 84:[3, 82], Operations: ['19-16=3', '85-3=82'] Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,84 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 84:[3, 82], Operations: ['19-16=3', '85-3=82'] Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,84 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,84 unequal: No Solution Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 84:[85, 1], Operations: ['19-16=3', '3/3=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[3, 19, 85, 16], Operations: [] Exploring Operation: 19-16=3, Resulting Numbers: [3, 85, 3] Generated Node #0,3: 84:[3, 85, 3] Operation: 19-16=3 Moving to Node #0,3 Current State: 84:[3, 85, 3], Operations: ['19-16=3'] Exploring Operation: 3/3=1, Resulting Numbers: [85, 1] Generated Node #0,3,3: 84:[85, 1] Operation: 3/3=1 Moving to Node #0,3,3 Current State: 84:[85, 1], Operations: ['19-16=3', '3/3=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 70, 89, 42, 14 ]
16
[ "89-70=19", "42/14=3", "19-3=16" ]
Current State: 16:[70, 89, 42, 14], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [42, 14, 19] Generated Node #2: [42, 14, 19] from Operation: 89-70=19 Current State: 16:[42, 14, 19], Operations: ['89-70=19'] Exploring Operation: 42/14=3, Resulting Numbers: [19, 3] Generated Node #3: [19, 3] from Operation: 42/14=3 Current State: 16:[19, 3], Operations: ['89-70=19', '42/14=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[70, 89, 42, 14], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [42, 14, 19] Generated Node #0,0: 16:[42, 14, 19] Operation: 89-70=19 Exploring Operation: 70/14=5, Resulting Numbers: [89, 42, 5] Generated Node #0,1: 16:[89, 42, 5] Operation: 70/14=5 Exploring Operation: 89-42=47, Resulting Numbers: [70, 14, 47] Generated Node #0,2: 16:[70, 14, 47] Operation: 89-42=47 Exploring Operation: 70-42=28, Resulting Numbers: [89, 14, 28] Generated Node #0,3: 16:[89, 14, 28] Operation: 70-42=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[42, 14, 19], Operations: ['89-70=19'] Exploring Operation: 19-14=5, Resulting Numbers: [42, 5] Generated Node #0,0,0: 16:[42, 5] Operation: 19-14=5 Exploring Operation: 42-14=28, Resulting Numbers: [19, 28] Generated Node #0,0,1: 16:[19, 28] Operation: 42-14=28 Exploring Operation: 42/14=3, Resulting Numbers: [19, 3] Generated Node #0,0,2: 16:[19, 3] Operation: 42/14=3 Exploring Operation: 42-19=23, Resulting Numbers: [14, 23] Generated Node #0,0,3: 16:[14, 23] Operation: 42-19=23 Moving to Node #0,0,2 Current State: 16:[19, 3], Operations: ['89-70=19', '42/14=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[70, 89, 42, 14], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [42, 14, 19] Generated Node #0,0: 16:[42, 14, 19] Operation: 89-70=19 Moving to Node #0,0 Current State: 16:[42, 14, 19], Operations: ['89-70=19'] Exploring Operation: 42/14=3, Resulting Numbers: [19, 3] Generated Node #0,0,2: 16:[19, 3] Operation: 42/14=3 Moving to Node #0,0,2 Current State: 16:[19, 3], Operations: ['89-70=19', '42/14=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 72, 45, 27, 53 ]
37
[ "72+45=117", "27+53=80", "117-80=37" ]
Current State: 37:[72, 45, 27, 53], Operations: [] Exploring Operation: 72+45=117, Resulting Numbers: [27, 53, 117] Generated Node #2: [27, 53, 117] from Operation: 72+45=117 Current State: 37:[27, 53, 117], Operations: ['72+45=117'] Exploring Operation: 27+53=80, Resulting Numbers: [117, 80] Generated Node #3: [117, 80] from Operation: 27+53=80 Current State: 37:[117, 80], Operations: ['72+45=117', '27+53=80'] Exploring Operation: 117-80=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[72, 45, 27, 53], Operations: [] Exploring Operation: 72-27=45, Resulting Numbers: [45, 53, 45] Generated Node #0,0: 37:[45, 53, 45] Operation: 72-27=45 Exploring Operation: 72-45=27, Resulting Numbers: [27, 53, 27] Generated Node #0,1: 37:[27, 53, 27] Operation: 72-45=27 Exploring Operation: 72-53=19, Resulting Numbers: [45, 27, 19] Generated Node #0,2: 37:[45, 27, 19] Operation: 72-53=19 Exploring Operation: 53-27=26, Resulting Numbers: [72, 45, 26] Generated Node #0,3: 37:[72, 45, 26] Operation: 53-27=26 Moving to Node #0,0 Current State: 37:[45, 53, 45], Operations: ['72-27=45'] Exploring Operation: 45-45=0, Resulting Numbers: [53, 0] Generated Node #0,0,0: 37:[53, 0] Operation: 45-45=0 Exploring Operation: 53-45=8, Resulting Numbers: [45, 8] Generated Node #0,0,1: 37:[45, 8] Operation: 53-45=8 Exploring Operation: 45/45=1, Resulting Numbers: [53, 1] Generated Node #0,0,2: 37:[53, 1] Operation: 45/45=1 Exploring Operation: 53-45=8, Resulting Numbers: [45, 8] Generated Node #0,0,3: 37:[45, 8] Operation: 53-45=8 Moving to Node #0,2 Current State: 37:[45, 27, 19], Operations: ['72-53=19'] Exploring Operation: 45+19=64, Resulting Numbers: [27, 64] Generated Node #0,2,0: 37:[27, 64] Operation: 45+19=64 Exploring Operation: 45-19=26, Resulting Numbers: [27, 26] Generated Node #0,2,1: 37:[27, 26] Operation: 45-19=26 Exploring Operation: 27+19=46, Resulting Numbers: [45, 46] Generated Node #0,2,2: 37:[45, 46] Operation: 27+19=46 Exploring Operation: 45-27=18, Resulting Numbers: [19, 18] Generated Node #0,2,3: 37:[19, 18] Operation: 45-27=18 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 37:[45, 46], Operations: ['72-53=19', '27+19=46'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,37 unequal: No Solution Exploring Operation: 45+46=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 #0,2,1 Current State: 37:[27, 26], Operations: ['72-53=19', '45-19=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,37 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,37 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 #0,2,0 Current State: 37:[27, 64], Operations: ['72-53=19', '45+19=64'] Exploring Operation: 64-27=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[72, 45, 27, 53], Operations: [] Exploring Operation: 72-53=19, Resulting Numbers: [45, 27, 19] Generated Node #0,2: 37:[45, 27, 19] Operation: 72-53=19 Moving to Node #0,2 Current State: 37:[45, 27, 19], Operations: ['72-53=19'] Exploring Operation: 45+19=64, Resulting Numbers: [27, 64] Generated Node #0,2,0: 37:[27, 64] Operation: 45+19=64 Moving to Node #0,2,0 Current State: 37:[27, 64], Operations: ['72-53=19', '45+19=64'] Exploring Operation: 64-27=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
sum_heuristic
[ 22, 92, 53, 22 ]
92
[ "22-22=0", "53*0=0", "92+0=92" ]
Current State: 92:[22, 92, 53, 22], Operations: [] Exploring Operation: 22-22=0, Resulting Numbers: [92, 53, 0] Generated Node #2: [92, 53, 0] from Operation: 22-22=0 Current State: 92:[92, 53, 0], Operations: ['22-22=0'] Exploring Operation: 53*0=0, Resulting Numbers: [92, 0] Generated Node #3: [92, 0] from Operation: 53*0=0 Current State: 92:[92, 0], Operations: ['22-22=0', '53*0=0'] Exploring Operation: 92+0=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[22, 92, 53, 22], Operations: [] Exploring Operation: 53-22=31, Resulting Numbers: [92, 22, 31] Generated Node #0,0: 92:[92, 22, 31] Operation: 53-22=31 Exploring Operation: 22/22=1, Resulting Numbers: [92, 53, 1] Generated Node #0,1: 92:[92, 53, 1] Operation: 22/22=1 Exploring Operation: 22+22=44, Resulting Numbers: [92, 53, 44] Generated Node #0,2: 92:[92, 53, 44] Operation: 22+22=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[92, 53, 1], Operations: ['22/22=1'] Exploring Operation: 92*1=92, Resulting Numbers: [53, 92] Generated Node #0,1,0: 92:[53, 92] Operation: 92*1=92 Exploring Operation: 92/1=92, Resulting Numbers: [53, 92] Generated Node #0,1,1: 92:[53, 92] Operation: 92/1=92 Exploring Operation: 53-1=52, Resulting Numbers: [92, 52] Generated Node #0,1,2: 92:[92, 52] Operation: 53-1=52 Moving to Node #0,1,2 Current State: 92:[92, 52], Operations: ['22/22=1', '53-1=52'] Exploring Operation: 92*52=4784, Resulting Numbers: [4784] 4784,92 unequal: No Solution Exploring Operation: 92+52=144, Resulting Numbers: [144] 144,92 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[53, 92], Operations: ['22/22=1', '92*1=92'] Exploring Operation: 92-53=39, Resulting Numbers: [39] 39,92 unequal: No Solution Exploring Operation: 53*92=4876, Resulting Numbers: [4876] 4876,92 unequal: No Solution Exploring Operation: 53+92=145, Resulting Numbers: [145] 145,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[53, 92], Operations: ['22/22=1', '92/1=92'] Exploring Operation: 92-53=39, Resulting Numbers: [39] 39,92 unequal: No Solution Exploring Operation: 53*92=4876, Resulting Numbers: [4876] 4876,92 unequal: No Solution Exploring Operation: 53+92=145, Resulting Numbers: [145] 145,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[92, 22, 31], Operations: ['53-22=31'] Exploring Operation: 22+31=53, Resulting Numbers: [92, 53] Generated Node #0,0,0: 92:[92, 53] Operation: 22+31=53 Exploring Operation: 31-22=9, Resulting Numbers: [92, 9] Generated Node #0,0,1: 92:[92, 9] Operation: 31-22=9 Exploring Operation: 92-31=61, Resulting Numbers: [22, 61] Generated Node #0,0,2: 92:[22, 61] Operation: 92-31=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 92:[92, 9], Operations: ['53-22=31', '31-22=9'] Exploring Operation: 92+9=101, Resulting Numbers: [101] 101,92 unequal: No Solution Exploring Operation: 92*9=828, Resulting Numbers: [828] 828,92 unequal: No Solution Exploring Operation: 92-9=83, Resulting Numbers: [83] 83,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[92, 53], Operations: ['53-22=31', '22+31=53'] Exploring Operation: 92+53=145, Resulting Numbers: [145] 145,92 unequal: No Solution Exploring Operation: 92*53=4876, Resulting Numbers: [4876] 4876,92 unequal: No Solution Exploring Operation: 92-53=39, Resulting Numbers: [39] 39,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 92:[22, 61], Operations: ['53-22=31', '92-31=61'] Exploring Operation: 22*61=1342, Resulting Numbers: [1342] 1342,92 unequal: No Solution Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,92 unequal: No Solution Exploring Operation: 22+61=83, Resulting Numbers: [83] 83,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[92, 53, 44], Operations: ['22+22=44'] Exploring Operation: 53-44=9, Resulting Numbers: [92, 9] Generated Node #0,2,0: 92:[92, 9] Operation: 53-44=9 Exploring Operation: 53+44=97, Resulting Numbers: [92, 97] Generated Node #0,2,1: 92:[92, 97] Operation: 53+44=97 Exploring Operation: 92-53=39, Resulting Numbers: [44, 39] Generated Node #0,2,2: 92:[44, 39] Operation: 92-53=39 Moving to Node #0,2,0 Current State: 92:[92, 9], Operations: ['22+22=44', '53-44=9'] Exploring Operation: 92+9=101, Resulting Numbers: [101] 101,92 unequal: No Solution Exploring Operation: 92*9=828, Resulting Numbers: [828] 828,92 unequal: No Solution Exploring Operation: 92-9=83, Resulting Numbers: [83] 83,92 unequal: No Solution Moving to Node #0,2,1 Current State: 92:[92, 97], Operations: ['22+22=44', '53+44=97'] Exploring Operation: 92+97=189, Resulting Numbers: [189] 189,92 unequal: No Solution Exploring Operation: 97-92=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 92*97=8924, Resulting Numbers: [8924] 8924,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[44, 39], Operations: ['22+22=44', '92-53=39'] Exploring Operation: 44*39=1716, Resulting Numbers: [1716] 1716,92 unequal: No Solution Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,92 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