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
[ 62, 8, 54, 58 ]
16
[ "62+54=116", "8*116=928", "928/58=16" ]
Current State: 16:[62, 8, 54, 58], Operations: [] Exploring Operation: 62+54=116, Resulting Numbers: [8, 58, 116] Generated Node #2: [8, 58, 116] from Operation: 62+54=116 Current State: 16:[8, 58, 116], Operations: ['62+54=116'] Exploring Operation: 8*116=928, Resulting Numbers: [58, 928] Generated Node #3: [58, 928] from Operation: 8*116=928 Current State: 16:[58, 928], Operations: ['62+54=116', '8*116=928'] Exploring Operation: 928/58=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[62, 8, 54, 58], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [62, 8, 4] Generated Node #0,0: 16:[62, 8, 4] Operation: 58-54=4 Exploring Operation: 54-8=46, Resulting Numbers: [62, 58, 46] Generated Node #0,1: 16:[62, 58, 46] Operation: 54-8=46 Exploring Operation: 62-8=54, Resulting Numbers: [54, 58, 54] Generated Node #0,2: 16:[54, 58, 54] Operation: 62-8=54 Exploring Operation: 62-54=8, Resulting Numbers: [8, 58, 8] Generated Node #0,3: 16:[8, 58, 8] Operation: 62-54=8 Exploring Operation: 62-58=4, Resulting Numbers: [8, 54, 4] Generated Node #0,4: 16:[8, 54, 4] Operation: 62-58=4 Moving to Node #0,4 Current State: 16:[8, 54, 4], Operations: ['62-58=4'] Exploring Operation: 54-4=50, Resulting Numbers: [8, 50] Generated Node #0,4,0: 16:[8, 50] Operation: 54-4=50 Exploring Operation: 8-4=4, Resulting Numbers: [54, 4] Generated Node #0,4,1: 16:[54, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [54, 2] Generated Node #0,4,2: 16:[54, 2] Operation: 8/4=2 Exploring Operation: 8+4=12, Resulting Numbers: [54, 12] Generated Node #0,4,3: 16:[54, 12] Operation: 8+4=12 Exploring Operation: 54-8=46, Resulting Numbers: [4, 46] Generated Node #0,4,4: 16:[4, 46] Operation: 54-8=46 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 16:[4, 46], Operations: ['62-58=4', '54-8=46'] Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,16 unequal: No Solution Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,16 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,16 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 #0,4,0 Current State: 16:[8, 50], Operations: ['62-58=4', '54-4=50'] Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,16 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 #0,4,1 Current State: 16:[54, 4], Operations: ['62-58=4', '8-4=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,16 unequal: No Solution Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 54*4=216, Resulting Numbers: [216] 216,16 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 #0,4,2 Current State: 16:[54, 2], Operations: ['62-58=4', '8/4=2'] Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,16 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 54*2=108, Resulting Numbers: [108] 108,16 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,16 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 #0,4,3 Current State: 16:[54, 12], Operations: ['62-58=4', '8+4=12'] Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,16 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,16 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 16:[8, 58, 8], Operations: ['62-54=8'] Exploring Operation: 8-8=0, Resulting Numbers: [58, 0] Generated Node #0,3,0: 16:[58, 0] Operation: 8-8=0 Exploring Operation: 8+8=16, Resulting Numbers: [58, 16] Generated Node #0,3,1: 16:[58, 16] Operation: 8+8=16 Exploring Operation: 8/8=1, Resulting Numbers: [58, 1] Generated Node #0,3,2: 16:[58, 1] Operation: 8/8=1 Exploring Operation: 58-8=50, Resulting Numbers: [8, 50] Generated Node #0,3,3: 16:[8, 50] Operation: 58-8=50 Exploring Operation: 58-8=50, Resulting Numbers: [8, 50] Generated Node #0,3,4: 16:[8, 50] Operation: 58-8=50 Moving to Node #0,0 Current State: 16:[62, 8, 4], Operations: ['58-54=4'] Exploring Operation: 62+4=66, Resulting Numbers: [8, 66] Generated Node #0,0,0: 16:[8, 66] Operation: 62+4=66 Exploring Operation: 62-8=54, Resulting Numbers: [4, 54] Generated Node #0,0,1: 16:[4, 54] Operation: 62-8=54 Exploring Operation: 62-4=58, Resulting Numbers: [8, 58] Generated Node #0,0,2: 16:[8, 58] Operation: 62-4=58 Exploring Operation: 8-4=4, Resulting Numbers: [62, 4] Generated Node #0,0,3: 16:[62, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [62, 2] Generated Node #0,0,4: 16:[62, 2] Operation: 8/4=2 Moving to Node #0,1 Current State: 16:[62, 58, 46], Operations: ['54-8=46'] Exploring Operation: 62-58=4, Resulting Numbers: [46, 4] Generated Node #0,1,0: 16:[46, 4] Operation: 62-58=4 Exploring Operation: 62+58=120, Resulting Numbers: [46, 120] Generated Node #0,1,1: 16:[46, 120] Operation: 62+58=120 Exploring Operation: 62-46=16, Resulting Numbers: [58, 16] Generated Node #0,1,2: 16:[58, 16] Operation: 62-46=16 Exploring Operation: 62+46=108, Resulting Numbers: [58, 108] Generated Node #0,1,3: 16:[58, 108] Operation: 62+46=108 Exploring Operation: 58-46=12, Resulting Numbers: [62, 12] Generated Node #0,1,4: 16:[62, 12] Operation: 58-46=12 Moving to Node #0,2 Current State: 16:[54, 58, 54], Operations: ['62-8=54'] Exploring Operation: 54/54=1, Resulting Numbers: [58, 1] Generated Node #0,2,0: 16:[58, 1] Operation: 54/54=1 Exploring Operation: 54+58=112, Resulting Numbers: [54, 112] Generated Node #0,2,1: 16:[54, 112] Operation: 54+58=112 Exploring Operation: 58-54=4, Resulting Numbers: [54, 4] Generated Node #0,2,2: 16:[54, 4] Operation: 58-54=4 Exploring Operation: 58-54=4, Resulting Numbers: [54, 4] Generated Node #0,2,3: 16:[54, 4] Operation: 58-54=4 Exploring Operation: 54-54=0, Resulting Numbers: [58, 0] Generated Node #0,2,4: 16:[58, 0] Operation: 54-54=0 Moving to Node #0,1,0 Current State: 16:[46, 4], Operations: ['54-8=46', '62-58=4'] Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,16 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[8, 50], Operations: ['62-54=8', '58-8=50'] Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,16 unequal: No Solution Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,16 unequal: No Solution Moving to Node #0,3,4 Current State: 16:[8, 50], Operations: ['62-54=8', '58-8=50'] Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,16 unequal: No Solution Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[4, 54], Operations: ['58-54=4', '62-8=54'] Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,16 unequal: No Solution Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[54, 4], Operations: ['62-8=54', '58-54=4'] Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 54*4=216, Resulting Numbers: [216] 216,16 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[54, 4], Operations: ['62-8=54', '58-54=4'] Exploring Operation: 54*4=216, Resulting Numbers: [216] 216,16 unequal: No Solution Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,16 unequal: No Solution Moving to Node #0,0,2 Current State: 16:[8, 58], Operations: ['58-54=4', '62-4=58'] Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,16 unequal: No Solution Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,16 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[58, 16], Operations: ['62-54=8', '8+8=16'] Exploring Operation: 58*16=928, Resulting Numbers: [928] 928,16 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 58+16=74, Resulting Numbers: [74] 74,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[58, 16], Operations: ['54-8=46', '62-46=16'] Exploring Operation: 58*16=928, Resulting Numbers: [928] 928,16 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 58+16=74, Resulting Numbers: [74] 74,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[58, 1], Operations: ['62-8=54', '54/54=1'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,16 unequal: No Solution Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[58, 1], Operations: ['62-54=8', '8/8=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,16 unequal: No Solution Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[58, 0], Operations: ['62-54=8', '8-8=0'] Exploring Operation: 58+0=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 58-0=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 58*0=0, Resulting Numbers: [0] 0,16 unequal: No Solution Moving to Node #0,2,4 Current State: 16:[58, 0], Operations: ['62-8=54', '54-54=0'] Exploring Operation: 58-0=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 58*0=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 58+0=58, Resulting Numbers: [58] 58,16 unequal: No Solution Moving to Node #0,0,4 Current State: 16:[62, 2], Operations: ['58-54=4', '8/4=2'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,16 unequal: No Solution Exploring Operation: 62*2=124, Resulting Numbers: [124] 124,16 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,16 unequal: No Solution Moving to Node #0,0,3 Current State: 16:[62, 4], Operations: ['58-54=4', '8-4=4'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 62*4=248, Resulting Numbers: [248] 248,16 unequal: No Solution Exploring Operation: 62+4=66, Resulting Numbers: [66] 66,16 unequal: No Solution Moving to Node #0,1,4 Current State: 16:[62, 12], Operations: ['54-8=46', '58-46=12'] Exploring Operation: 62*12=744, Resulting Numbers: [744] 744,16 unequal: No Solution Exploring Operation: 62+12=74, Resulting Numbers: [74] 74,16 unequal: No Solution Exploring Operation: 62-12=50, Resulting Numbers: [50] 50,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[8, 66], Operations: ['58-54=4', '62+4=66'] Exploring Operation: 8+66=74, Resulting Numbers: [74] 74,16 unequal: No Solution Exploring Operation: 8*66=528, Resulting Numbers: [528] 528,16 unequal: No Solution Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[58, 108], Operations: ['54-8=46', '62+46=108'] Exploring Operation: 58+108=166, Resulting Numbers: [166] 166,16 unequal: No Solution Exploring Operation: 108-58=50, Resulting Numbers: [50] 50,16 unequal: No Solution Exploring Operation: 58*108=6264, Resulting Numbers: [6264] 6264,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[54, 112], Operations: ['62-8=54', '54+58=112'] Exploring Operation: 54+112=166, Resulting Numbers: [166] 166,16 unequal: No Solution Exploring Operation: 54*112=6048, Resulting Numbers: [6048] 6048,16 unequal: No Solution Exploring Operation: 112-54=58, Resulting Numbers: [58] 58,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[46, 120], Operations: ['54-8=46', '62+58=120'] Exploring Operation: 120-46=74, Resulting Numbers: [74] 74,16 unequal: No Solution Exploring Operation: 46+120=166, Resulting Numbers: [166] 166,16 unequal: No Solution Exploring Operation: 46*120=5520, Resulting Numbers: [5520] 5520,16 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 34, 52, 74, 4 ]
48
[ "34+52=86", "86-74=12", "4*12=48" ]
Current State: 48:[34, 52, 74, 4], Operations: [] Exploring Operation: 34+52=86, Resulting Numbers: [74, 4, 86] Generated Node #2: [74, 4, 86] from Operation: 34+52=86 Current State: 48:[74, 4, 86], Operations: ['34+52=86'] Exploring Operation: 86-74=12, Resulting Numbers: [4, 12] Generated Node #3: [4, 12] from Operation: 86-74=12 Current State: 48:[4, 12], Operations: ['34+52=86', '86-74=12'] Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[34, 52, 74, 4], Operations: [] Exploring Operation: 74-34=40, Resulting Numbers: [52, 4, 40] Generated Node #0,0: 48:[52, 4, 40] Operation: 74-34=40 Exploring Operation: 34-4=30, Resulting Numbers: [52, 74, 30] Generated Node #0,1: 48:[52, 74, 30] Operation: 34-4=30 Exploring Operation: 52-34=18, Resulting Numbers: [74, 4, 18] Generated Node #0,2: 48:[74, 4, 18] Operation: 52-34=18 Exploring Operation: 74-52=22, Resulting Numbers: [34, 4, 22] Generated Node #0,3: 48:[34, 4, 22] Operation: 74-52=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[52, 4, 40], Operations: ['74-34=40'] Exploring Operation: 40/4=10, Resulting Numbers: [52, 10] Generated Node #0,0,0: 48:[52, 10] Operation: 40/4=10 Exploring Operation: 52-40=12, Resulting Numbers: [4, 12] Generated Node #0,0,1: 48:[4, 12] Operation: 52-40=12 Exploring Operation: 4+40=44, Resulting Numbers: [52, 44] Generated Node #0,0,2: 48:[52, 44] Operation: 4+40=44 Exploring Operation: 52-4=48, Resulting Numbers: [40, 48] Generated Node #0,0,3: 48:[40, 48] Operation: 52-4=48 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[4, 12], Operations: ['74-34=40', '52-40=12'] Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[34, 52, 74, 4], Operations: [] Exploring Operation: 74-34=40, Resulting Numbers: [52, 4, 40] Generated Node #0,0: 48:[52, 4, 40] Operation: 74-34=40 Moving to Node #0,0 Current State: 48:[52, 4, 40], Operations: ['74-34=40'] Exploring Operation: 52-40=12, Resulting Numbers: [4, 12] Generated Node #0,0,1: 48:[4, 12] Operation: 52-40=12 Moving to Node #0,0,1 Current State: 48:[4, 12], Operations: ['74-34=40', '52-40=12'] Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 10, 6, 8, 41 ]
82
[ "10+6=16", "16/8=2", "41*2=82" ]
Current State: 82:[10, 6, 8, 41], Operations: [] Exploring Operation: 10+6=16, Resulting Numbers: [8, 41, 16] Generated Node #2: [8, 41, 16] from Operation: 10+6=16 Current State: 82:[8, 41, 16], Operations: ['10+6=16'] Exploring Operation: 16/8=2, Resulting Numbers: [41, 2] Generated Node #3: [41, 2] from Operation: 16/8=2 Current State: 82:[41, 2], Operations: ['10+6=16', '16/8=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[10, 6, 8, 41], Operations: [] Exploring Operation: 8-6=2, Resulting Numbers: [10, 41, 2] Generated Node #0,0: 82:[10, 41, 2] Operation: 8-6=2 Exploring Operation: 10*8=80, Resulting Numbers: [6, 41, 80] Generated Node #0,1: 82:[6, 41, 80] Operation: 10*8=80 Exploring Operation: 10-6=4, Resulting Numbers: [8, 41, 4] Generated Node #0,2: 82:[8, 41, 4] Operation: 10-6=4 Exploring Operation: 10-8=2, Resulting Numbers: [6, 41, 2] Generated Node #0,3: 82:[6, 41, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[6, 41, 2], Operations: ['10-8=2'] Exploring Operation: 41*2=82, Resulting Numbers: [6, 82] Generated Node #0,3,0: 82:[6, 82] Operation: 41*2=82 Exploring Operation: 6+41=47, Resulting Numbers: [2, 47] Generated Node #0,3,1: 82:[2, 47] Operation: 6+41=47 Exploring Operation: 6-2=4, Resulting Numbers: [41, 4] Generated Node #0,3,2: 82:[41, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [41, 3] Generated Node #0,3,3: 82:[41, 3] Operation: 6/2=3 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 82:[41, 3], Operations: ['10-8=2', '6/2=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,82 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 82:[41, 4], Operations: ['10-8=2', '6-2=4'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 41*4=164, Resulting Numbers: [164] 164,82 unequal: No Solution Exploring Operation: 41+4=45, Resulting Numbers: [45] 45,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 82:[6, 82], Operations: ['10-8=2', '41*2=82'] Exploring Operation: 6+82=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,82 unequal: No Solution Exploring Operation: 6*82=492, Resulting Numbers: [492] 492,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 82:[2, 47], Operations: ['10-8=2', '6+41=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,82 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[6, 41, 80], Operations: ['10*8=80'] Exploring Operation: 6+80=86, Resulting Numbers: [41, 86] Generated Node #0,1,0: 82:[41, 86] Operation: 6+80=86 Exploring Operation: 80-41=39, Resulting Numbers: [6, 39] Generated Node #0,1,1: 82:[6, 39] Operation: 80-41=39 Exploring Operation: 6+41=47, Resulting Numbers: [80, 47] Generated Node #0,1,2: 82:[80, 47] Operation: 6+41=47 Exploring Operation: 41-6=35, Resulting Numbers: [80, 35] Generated Node #0,1,3: 82:[80, 35] Operation: 41-6=35 Moving to Node #0,1,0 Current State: 82:[41, 86], Operations: ['10*8=80', '6+80=86'] Exploring Operation: 41+86=127, Resulting Numbers: [127] 127,82 unequal: No Solution Exploring Operation: 41*86=3526, Resulting Numbers: [3526] 3526,82 unequal: No Solution Exploring Operation: 86-41=45, Resulting Numbers: [45] 45,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[6, 39], Operations: ['10*8=80', '80-41=39'] Exploring Operation: 6+39=45, Resulting Numbers: [45] 45,82 unequal: No Solution Exploring Operation: 6*39=234, Resulting Numbers: [234] 234,82 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[80, 35], Operations: ['10*8=80', '41-6=35'] Exploring Operation: 80*35=2800, Resulting Numbers: [2800] 2800,82 unequal: No Solution Exploring Operation: 80+35=115, Resulting Numbers: [115] 115,82 unequal: No Solution Exploring Operation: 80-35=45, Resulting Numbers: [45] 45,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[80, 47], Operations: ['10*8=80', '6+41=47'] Exploring Operation: 80*47=3760, Resulting Numbers: [3760] 3760,82 unequal: No Solution Exploring Operation: 80-47=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 80+47=127, Resulting Numbers: [127] 127,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[10, 41, 2], Operations: ['8-6=2'] Exploring Operation: 41*2=82, Resulting Numbers: [10, 82] Generated Node #0,0,0: 82:[10, 82] Operation: 41*2=82 Exploring Operation: 10+41=51, Resulting Numbers: [2, 51] Generated Node #0,0,1: 82:[2, 51] Operation: 10+41=51 Exploring Operation: 10/2=5, Resulting Numbers: [41, 5] Generated Node #0,0,2: 82:[41, 5] Operation: 10/2=5 Exploring Operation: 10-2=8, Resulting Numbers: [41, 8] Generated Node #0,0,3: 82:[41, 8] Operation: 10-2=8 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[41, 5], Operations: ['8-6=2', '10/2=5'] Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,82 unequal: No Solution Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,82 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 82:[41, 8], Operations: ['8-6=2', '10-2=8'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[10, 82], Operations: ['8-6=2', '41*2=82'] Exploring Operation: 10+82=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 82-10=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 10*82=820, Resulting Numbers: [820] 820,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[2, 51], Operations: ['8-6=2', '10+41=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,82 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,82 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[8, 41, 4], Operations: ['10-6=4'] Exploring Operation: 8-4=4, Resulting Numbers: [41, 4] Generated Node #0,2,0: 82:[41, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [41, 2] Generated Node #0,2,1: 82:[41, 2] Operation: 8/4=2 Exploring Operation: 8+41=49, Resulting Numbers: [4, 49] Generated Node #0,2,2: 82:[4, 49] Operation: 8+41=49 Exploring Operation: 8*4=32, Resulting Numbers: [41, 32] Generated Node #0,2,3: 82:[41, 32] Operation: 8*4=32 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[41, 2], Operations: ['10-6=4', '8/4=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[10, 6, 8, 41], Operations: [] Exploring Operation: 10-6=4, Resulting Numbers: [8, 41, 4] Generated Node #0,2: 82:[8, 41, 4] Operation: 10-6=4 Moving to Node #0,2 Current State: 82:[8, 41, 4], Operations: ['10-6=4'] Exploring Operation: 8/4=2, Resulting Numbers: [41, 2] Generated Node #0,2,1: 82:[41, 2] Operation: 8/4=2 Moving to Node #0,2,1 Current State: 82:[41, 2], Operations: ['10-6=4', '8/4=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.947049
hs_4
sum_heuristic
[ 77, 21, 87, 82 ]
61
[ "77-21=56", "87-82=5", "56+5=61" ]
Current State: 61:[77, 21, 87, 82], Operations: [] Exploring Operation: 77-21=56, Resulting Numbers: [87, 82, 56] Generated Node #2: [87, 82, 56] from Operation: 77-21=56 Current State: 61:[87, 82, 56], Operations: ['77-21=56'] Exploring Operation: 87-82=5, Resulting Numbers: [56, 5] Generated Node #3: [56, 5] from Operation: 87-82=5 Current State: 61:[56, 5], Operations: ['77-21=56', '87-82=5'] Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[77, 21, 87, 82], Operations: [] Exploring Operation: 87-21=66, Resulting Numbers: [77, 82, 66] Generated Node #0,0: 61:[77, 82, 66] Operation: 87-21=66 Exploring Operation: 82-21=61, Resulting Numbers: [77, 87, 61] Generated Node #0,1: 61:[77, 87, 61] Operation: 82-21=61 Exploring Operation: 77-21=56, Resulting Numbers: [87, 82, 56] Generated Node #0,2: 61:[87, 82, 56] Operation: 77-21=56 Moving to Node #0,0 Current State: 61:[77, 82, 66], Operations: ['87-21=66'] Exploring Operation: 77-66=11, Resulting Numbers: [82, 11] Generated Node #0,0,0: 61:[82, 11] Operation: 77-66=11 Exploring Operation: 82-77=5, Resulting Numbers: [66, 5] Generated Node #0,0,1: 61:[66, 5] Operation: 82-77=5 Exploring Operation: 82-66=16, Resulting Numbers: [77, 16] Generated Node #0,0,2: 61:[77, 16] Operation: 82-66=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[66, 5], Operations: ['87-21=66', '82-77=5'] Exploring Operation: 66*5=330, Resulting Numbers: [330] 330,61 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[77, 21, 87, 82], Operations: [] Exploring Operation: 87-21=66, Resulting Numbers: [77, 82, 66] Generated Node #0,0: 61:[77, 82, 66] Operation: 87-21=66 Moving to Node #0,0 Current State: 61:[77, 82, 66], Operations: ['87-21=66'] Exploring Operation: 82-77=5, Resulting Numbers: [66, 5] Generated Node #0,0,1: 61:[66, 5] Operation: 82-77=5 Moving to Node #0,0,1 Current State: 61:[66, 5], Operations: ['87-21=66', '82-77=5'] Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 48, 33, 18, 45 ]
47
[ "48+18=66", "66/33=2", "45+2=47" ]
Current State: 47:[48, 33, 18, 45], Operations: [] Exploring Operation: 48+18=66, Resulting Numbers: [33, 45, 66] Generated Node #2: [33, 45, 66] from Operation: 48+18=66 Current State: 47:[33, 45, 66], Operations: ['48+18=66'] Exploring Operation: 66/33=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 66/33=2 Current State: 47:[45, 2], Operations: ['48+18=66', '66/33=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[48, 33, 18, 45], Operations: [] Exploring Operation: 48+18=66, Resulting Numbers: [33, 45, 66] Generated Node #0,0: 47:[33, 45, 66] Operation: 48+18=66 Exploring Operation: 33+18=51, Resulting Numbers: [48, 45, 51] Generated Node #0,1: 47:[48, 45, 51] Operation: 33+18=51 Exploring Operation: 48-18=30, Resulting Numbers: [33, 45, 30] Generated Node #0,2: 47:[33, 45, 30] Operation: 48-18=30 Exploring Operation: 18+45=63, Resulting Numbers: [48, 33, 63] Generated Node #0,3: 47:[48, 33, 63] Operation: 18+45=63 Exploring Operation: 33-18=15, Resulting Numbers: [48, 45, 15] Generated Node #0,4: 47:[48, 45, 15] Operation: 33-18=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[48, 45, 51], Operations: ['33+18=51'] Exploring Operation: 48+45=93, Resulting Numbers: [51, 93] Generated Node #0,1,0: 47:[51, 93] Operation: 48+45=93 Exploring Operation: 51-48=3, Resulting Numbers: [45, 3] Generated Node #0,1,1: 47:[45, 3] Operation: 51-48=3 Exploring Operation: 45+51=96, Resulting Numbers: [48, 96] Generated Node #0,1,2: 47:[48, 96] Operation: 45+51=96 Exploring Operation: 48-45=3, Resulting Numbers: [51, 3] Generated Node #0,1,3: 47:[51, 3] Operation: 48-45=3 Exploring Operation: 51-45=6, Resulting Numbers: [48, 6] Generated Node #0,1,4: 47:[48, 6] Operation: 51-45=6 Moving to Node #0,1,4 Current State: 47:[48, 6], Operations: ['33+18=51', '51-45=6'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,47 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,47 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[45, 3], Operations: ['33+18=51', '51-48=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,47 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 45*3=135, Resulting Numbers: [135] 135,47 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[51, 3], Operations: ['33+18=51', '48-45=3'] Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 51*3=153, Resulting Numbers: [153] 153,47 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[51, 93], Operations: ['33+18=51', '48+45=93'] Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,47 unequal: No Solution Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[48, 96], Operations: ['33+18=51', '45+51=96'] Exploring Operation: 48+96=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 48*96=4608, Resulting Numbers: [4608] 4608,47 unequal: No Solution Exploring Operation: 96/48=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 96-48=48, Resulting Numbers: [48] 48,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 47:[48, 33, 63], Operations: ['18+45=63'] Exploring Operation: 63-48=15, Resulting Numbers: [33, 15] Generated Node #0,3,0: 47:[33, 15] Operation: 63-48=15 Exploring Operation: 63-33=30, Resulting Numbers: [48, 30] Generated Node #0,3,1: 47:[48, 30] Operation: 63-33=30 Exploring Operation: 48+33=81, Resulting Numbers: [63, 81] Generated Node #0,3,2: 47:[63, 81] Operation: 48+33=81 Exploring Operation: 48-33=15, Resulting Numbers: [63, 15] Generated Node #0,3,3: 47:[63, 15] Operation: 48-33=15 Exploring Operation: 33+63=96, Resulting Numbers: [48, 96] Generated Node #0,3,4: 47:[48, 96] Operation: 33+63=96 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 47:[48, 30], Operations: ['18+45=63', '63-33=30'] Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,47 unequal: No Solution Exploring Operation: 48*30=1440, Resulting Numbers: [1440] 1440,47 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 #0,3,0 Current State: 47:[33, 15], Operations: ['18+45=63', '63-48=15'] Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,47 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,47 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,47 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 #0,3,3 Current State: 47:[63, 15], Operations: ['18+45=63', '48-33=15'] Exploring Operation: 63+15=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 63*15=945, Resulting Numbers: [945] 945,47 unequal: No Solution Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,47 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 #0,3,2 Current State: 47:[63, 81], Operations: ['18+45=63', '48+33=81'] Exploring Operation: 63+81=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 81-63=18, Resulting Numbers: [18] 18,47 unequal: No Solution Exploring Operation: 63*81=5103, Resulting Numbers: [5103] 5103,47 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 #0,3,4 Current State: 47:[48, 96], Operations: ['18+45=63', '33+63=96'] Exploring Operation: 96/48=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 96-48=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 48+96=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 48*96=4608, Resulting Numbers: [4608] 4608,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[33, 45, 30], Operations: ['48-18=30'] Exploring Operation: 33+45=78, Resulting Numbers: [30, 78] Generated Node #0,2,0: 47:[30, 78] Operation: 33+45=78 Exploring Operation: 45-30=15, Resulting Numbers: [33, 15] Generated Node #0,2,1: 47:[33, 15] Operation: 45-30=15 Exploring Operation: 45+30=75, Resulting Numbers: [33, 75] Generated Node #0,2,2: 47:[33, 75] Operation: 45+30=75 Exploring Operation: 33+30=63, Resulting Numbers: [45, 63] Generated Node #0,2,3: 47:[45, 63] Operation: 33+30=63 Exploring Operation: 33-30=3, Resulting Numbers: [45, 3] Generated Node #0,2,4: 47:[45, 3] Operation: 33-30=3 Moving to Node #0,2,3 Current State: 47:[45, 63], Operations: ['48-18=30', '33+30=63'] Exploring Operation: 45+63=108, Resulting Numbers: [108] 108,47 unequal: No Solution Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,47 unequal: No Solution Exploring Operation: 45*63=2835, Resulting Numbers: [2835] 2835,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[33, 75], Operations: ['48-18=30', '45+30=75'] Exploring Operation: 33+75=108, Resulting Numbers: [108] 108,47 unequal: No Solution Exploring Operation: 33*75=2475, Resulting Numbers: [2475] 2475,47 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[33, 15], Operations: ['48-18=30', '45-30=15'] Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,47 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,47 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,47 unequal: No Solution Moving to Node #0,2,4 Current State: 47:[45, 3], Operations: ['48-18=30', '33-30=3'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,47 unequal: No Solution Exploring Operation: 45*3=135, Resulting Numbers: [135] 135,47 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[30, 78], Operations: ['48-18=30', '33+45=78'] Exploring Operation: 30*78=2340, Resulting Numbers: [2340] 2340,47 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 30+78=108, Resulting Numbers: [108] 108,47 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 Current State: 47:[33, 45, 66], Operations: ['48+18=66'] Exploring Operation: 33+45=78, Resulting Numbers: [66, 78] Generated Node #0,0,0: 47:[66, 78] Operation: 33+45=78 Exploring Operation: 66/33=2, Resulting Numbers: [45, 2] Generated Node #0,0,1: 47:[45, 2] Operation: 66/33=2 Exploring Operation: 66-45=21, Resulting Numbers: [33, 21] Generated Node #0,0,2: 47:[33, 21] Operation: 66-45=21 Exploring Operation: 66-33=33, Resulting Numbers: [45, 33] Generated Node #0,0,3: 47:[45, 33] Operation: 66-33=33 Exploring Operation: 45-33=12, Resulting Numbers: [66, 12] Generated Node #0,0,4: 47:[66, 12] Operation: 45-33=12 Moving to Node #0,0,3 Current State: 47:[45, 33], Operations: ['48+18=66', '66-33=33'] Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,47 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[33, 21], Operations: ['48+18=66', '66-45=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[45, 2], Operations: ['48+18=66', '66/33=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[48, 33, 18, 45], Operations: [] Exploring Operation: 48+18=66, Resulting Numbers: [33, 45, 66] Generated Node #0,0: 47:[33, 45, 66] Operation: 48+18=66 Moving to Node #0,0 Current State: 47:[33, 45, 66], Operations: ['48+18=66'] Exploring Operation: 66/33=2, Resulting Numbers: [45, 2] Generated Node #0,0,1: 47:[45, 2] Operation: 66/33=2 Moving to Node #0,0,1 Current State: 47:[45, 2], Operations: ['48+18=66', '66/33=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.924479
hs_5
sum_heuristic
[ 39, 45, 10, 41 ]
53
[ "39+45=84", "41-10=31", "84-31=53" ]
Current State: 53:[39, 45, 10, 41], Operations: [] Exploring Operation: 39+45=84, Resulting Numbers: [10, 41, 84] Generated Node #2: [10, 41, 84] from Operation: 39+45=84 Current State: 53:[10, 41, 84], Operations: ['39+45=84'] Exploring Operation: 41-10=31, Resulting Numbers: [84, 31] Generated Node #3: [84, 31] from Operation: 41-10=31 Current State: 53:[84, 31], Operations: ['39+45=84', '41-10=31'] Exploring Operation: 84-31=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[39, 45, 10, 41], Operations: [] Exploring Operation: 45+10=55, Resulting Numbers: [39, 41, 55] Generated Node #0,0: 53:[39, 41, 55] Operation: 45+10=55 Exploring Operation: 10+41=51, Resulting Numbers: [39, 45, 51] Generated Node #0,1: 53:[39, 45, 51] Operation: 10+41=51 Exploring Operation: 39+10=49, Resulting Numbers: [45, 41, 49] Generated Node #0,2: 53:[45, 41, 49] Operation: 39+10=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[39, 45, 51], Operations: ['10+41=51'] Exploring Operation: 39+45=84, Resulting Numbers: [51, 84] Generated Node #0,1,0: 53:[51, 84] Operation: 39+45=84 Exploring Operation: 45-39=6, Resulting Numbers: [51, 6] Generated Node #0,1,1: 53:[51, 6] Operation: 45-39=6 Exploring Operation: 39+51=90, Resulting Numbers: [45, 90] Generated Node #0,1,2: 53:[45, 90] Operation: 39+51=90 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[51, 84], Operations: ['10+41=51', '39+45=84'] Exploring Operation: 51*84=4284, Resulting Numbers: [4284] 4284,53 unequal: No Solution Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,53 unequal: No Solution Exploring Operation: 51+84=135, Resulting Numbers: [135] 135,53 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:[45, 90], Operations: ['10+41=51', '39+51=90'] Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,53 unequal: No Solution Exploring Operation: 45+90=135, Resulting Numbers: [135] 135,53 unequal: No Solution Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[51, 6], Operations: ['10+41=51', '45-39=6'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,53 unequal: No Solution Exploring Operation: 51*6=306, Resulting Numbers: [306] 306,53 unequal: No Solution Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,53 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:[45, 41, 49], Operations: ['39+10=49'] Exploring Operation: 45-41=4, Resulting Numbers: [49, 4] Generated Node #0,2,0: 53:[49, 4] Operation: 45-41=4 Exploring Operation: 45+41=86, Resulting Numbers: [49, 86] Generated Node #0,2,1: 53:[49, 86] Operation: 45+41=86 Exploring Operation: 41+49=90, Resulting Numbers: [45, 90] Generated Node #0,2,2: 53:[45, 90] Operation: 41+49=90 Moving to Node #0,2,1 Current State: 53:[49, 86], Operations: ['39+10=49', '45+41=86'] Exploring Operation: 49+86=135, Resulting Numbers: [135] 135,53 unequal: No Solution Exploring Operation: 49*86=4214, Resulting Numbers: [4214] 4214,53 unequal: No Solution Exploring Operation: 86-49=37, Resulting Numbers: [37] 37,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[45, 90], Operations: ['39+10=49', '41+49=90'] Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,53 unequal: No Solution Exploring Operation: 45+90=135, Resulting Numbers: [135] 135,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[49, 4], Operations: ['39+10=49', '45-41=4'] Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[39, 45, 10, 41], Operations: [] Exploring Operation: 39+10=49, Resulting Numbers: [45, 41, 49] Generated Node #0,2: 53:[45, 41, 49] Operation: 39+10=49 Moving to Node #0,2 Current State: 53:[45, 41, 49], Operations: ['39+10=49'] Exploring Operation: 45-41=4, Resulting Numbers: [49, 4] Generated Node #0,2,0: 53:[49, 4] Operation: 45-41=4 Moving to Node #0,2,0 Current State: 53:[49, 4], Operations: ['39+10=49', '45-41=4'] Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 47, 5, 18, 82 ]
39
[ "47+82=129", "5*18=90", "129-90=39" ]
Current State: 39:[47, 5, 18, 82], Operations: [] Exploring Operation: 47+82=129, Resulting Numbers: [5, 18, 129] Generated Node #2: [5, 18, 129] from Operation: 47+82=129 Current State: 39:[5, 18, 129], Operations: ['47+82=129'] Exploring Operation: 5*18=90, Resulting Numbers: [129, 90] Generated Node #3: [129, 90] from Operation: 5*18=90 Current State: 39:[129, 90], Operations: ['47+82=129', '5*18=90'] Exploring Operation: 129-90=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[47, 5, 18, 82], Operations: [] Exploring Operation: 82-47=35, Resulting Numbers: [5, 18, 35] Generated Node #0,0: 39:[5, 18, 35] Operation: 82-47=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[5, 18, 35], Operations: ['82-47=35'] Exploring Operation: 18-5=13, Resulting Numbers: [35, 13] Generated Node #0,0,0: 39:[35, 13] Operation: 18-5=13 Moving to Node #0,0,0 Current State: 39:[35, 13], Operations: ['82-47=35', '18-5=13'] Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 77, 75, 6, 48 ]
18
[ "77-75=2", "48/2=24", "24-6=18" ]
Current State: 18:[77, 75, 6, 48], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [6, 48, 2] Generated Node #2: [6, 48, 2] from Operation: 77-75=2 Current State: 18:[6, 48, 2], Operations: ['77-75=2'] Exploring Operation: 48/2=24, Resulting Numbers: [6, 24] Generated Node #3: [6, 24] from Operation: 48/2=24 Current State: 18:[6, 24], Operations: ['77-75=2', '48/2=24'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[77, 75, 6, 48], Operations: [] Exploring Operation: 77-48=29, Resulting Numbers: [75, 6, 29] Generated Node #0,0: 18:[75, 6, 29] Operation: 77-48=29 Exploring Operation: 77-75=2, Resulting Numbers: [6, 48, 2] Generated Node #0,1: 18:[6, 48, 2] Operation: 77-75=2 Exploring Operation: 75-48=27, Resulting Numbers: [77, 6, 27] Generated Node #0,2: 18:[77, 6, 27] Operation: 75-48=27 Moving to Node #0,1 Current State: 18:[6, 48, 2], Operations: ['77-75=2'] Exploring Operation: 48/2=24, Resulting Numbers: [6, 24] Generated Node #0,1,0: 18:[6, 24] Operation: 48/2=24 Exploring Operation: 48-6=42, Resulting Numbers: [2, 42] Generated Node #0,1,1: 18:[2, 42] Operation: 48-6=42 Exploring Operation: 48/6=8, Resulting Numbers: [2, 8] Generated Node #0,1,2: 18:[2, 8] Operation: 48/6=8 Moving to Node #0,0 Current State: 18:[75, 6, 29], Operations: ['77-48=29'] Exploring Operation: 75-29=46, Resulting Numbers: [6, 46] Generated Node #0,0,0: 18:[6, 46] Operation: 75-29=46 Exploring Operation: 29-6=23, Resulting Numbers: [75, 23] Generated Node #0,0,1: 18:[75, 23] Operation: 29-6=23 Exploring Operation: 75-6=69, Resulting Numbers: [29, 69] Generated Node #0,0,2: 18:[29, 69] Operation: 75-6=69 Moving to Node #0,2 Current State: 18:[77, 6, 27], Operations: ['75-48=27'] Exploring Operation: 27-6=21, Resulting Numbers: [77, 21] Generated Node #0,2,0: 18:[77, 21] Operation: 27-6=21 Exploring Operation: 77-6=71, Resulting Numbers: [27, 71] Generated Node #0,2,1: 18:[27, 71] Operation: 77-6=71 Exploring Operation: 77-27=50, Resulting Numbers: [6, 50] Generated Node #0,2,2: 18:[6, 50] Operation: 77-27=50 Moving to Node #0,1,2 Current State: 18:[2, 8], Operations: ['77-75=2', '48/6=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[6, 24], Operations: ['77-75=2', '48/2=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[77, 75, 6, 48], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [6, 48, 2] Generated Node #0,1: 18:[6, 48, 2] Operation: 77-75=2 Moving to Node #0,1 Current State: 18:[6, 48, 2], Operations: ['77-75=2'] Exploring Operation: 48/2=24, Resulting Numbers: [6, 24] Generated Node #0,1,0: 18:[6, 24] Operation: 48/2=24 Moving to Node #0,1,0 Current State: 18:[6, 24], Operations: ['77-75=2', '48/2=24'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.980903
hs_3
sum_heuristic
[ 20, 53, 55, 81 ]
15
[ "20*81=1620", "53+55=108", "1620/108=15" ]
Current State: 15:[20, 53, 55, 81], Operations: [] Exploring Operation: 20*81=1620, Resulting Numbers: [53, 55, 1620] Generated Node #2: [53, 55, 1620] from Operation: 20*81=1620 Current State: 15:[53, 55, 1620], Operations: ['20*81=1620'] Exploring Operation: 53+55=108, Resulting Numbers: [1620, 108] Generated Node #3: [1620, 108] from Operation: 53+55=108 Current State: 15:[1620, 108], Operations: ['20*81=1620', '53+55=108'] Exploring Operation: 1620/108=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[20, 53, 55, 81], Operations: [] Exploring Operation: 53-20=33, Resulting Numbers: [55, 81, 33] Generated Node #0,0: 15:[55, 81, 33] Operation: 53-20=33 Exploring Operation: 81-53=28, Resulting Numbers: [20, 55, 28] Generated Node #0,1: 15:[20, 55, 28] Operation: 81-53=28 Exploring Operation: 81-55=26, Resulting Numbers: [20, 53, 26] Generated Node #0,2: 15:[20, 53, 26] Operation: 81-55=26 Exploring Operation: 55-53=2, Resulting Numbers: [20, 81, 2] Generated Node #0,3: 15:[20, 81, 2] Operation: 55-53=2 Moving to Node #0,2 Current State: 15:[20, 53, 26], Operations: ['81-55=26'] Exploring Operation: 53-26=27, Resulting Numbers: [20, 27] Generated Node #0,2,0: 15:[20, 27] Operation: 53-26=27 Exploring Operation: 53-20=33, Resulting Numbers: [26, 33] Generated Node #0,2,1: 15:[26, 33] Operation: 53-20=33 Exploring Operation: 26-20=6, Resulting Numbers: [53, 6] Generated Node #0,2,2: 15:[53, 6] Operation: 26-20=6 Exploring Operation: 20+53=73, Resulting Numbers: [26, 73] Generated Node #0,2,3: 15:[26, 73] Operation: 20+53=73 Moving to Node #0,1 Current State: 15:[20, 55, 28], Operations: ['81-53=28'] Exploring Operation: 28-20=8, Resulting Numbers: [55, 8] Generated Node #0,1,0: 15:[55, 8] Operation: 28-20=8 Exploring Operation: 55-28=27, Resulting Numbers: [20, 27] Generated Node #0,1,1: 15:[20, 27] Operation: 55-28=27 Exploring Operation: 20+55=75, Resulting Numbers: [28, 75] Generated Node #0,1,2: 15:[28, 75] Operation: 20+55=75 Exploring Operation: 55-20=35, Resulting Numbers: [28, 35] Generated Node #0,1,3: 15:[28, 35] Operation: 55-20=35 Moving to Node #0,3 Current State: 15:[20, 81, 2], Operations: ['55-53=2'] Exploring Operation: 81-2=79, Resulting Numbers: [20, 79] Generated Node #0,3,0: 15:[20, 79] Operation: 81-2=79 Exploring Operation: 81-20=61, Resulting Numbers: [2, 61] Generated Node #0,3,1: 15:[2, 61] Operation: 81-20=61 Exploring Operation: 20-2=18, Resulting Numbers: [81, 18] Generated Node #0,3,2: 15:[81, 18] Operation: 20-2=18 Exploring Operation: 20/2=10, Resulting Numbers: [81, 10] Generated Node #0,3,3: 15:[81, 10] Operation: 20/2=10 Moving to Node #0,0 Current State: 15:[55, 81, 33], Operations: ['53-20=33'] Exploring Operation: 81-33=48, Resulting Numbers: [55, 48] Generated Node #0,0,0: 15:[55, 48] Operation: 81-33=48 Exploring Operation: 81-55=26, Resulting Numbers: [33, 26] Generated Node #0,0,1: 15:[33, 26] Operation: 81-55=26 Exploring Operation: 55-33=22, Resulting Numbers: [81, 22] Generated Node #0,0,2: 15:[81, 22] Operation: 55-33=22 Exploring Operation: 55+81=136, Resulting Numbers: [33, 136] Generated Node #0,0,3: 15:[33, 136] Operation: 55+81=136 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[33, 26], Operations: ['53-20=33', '81-55=26'] Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 33+26=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 33*26=858, Resulting Numbers: [858] 858,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[55, 48], Operations: ['53-20=33', '81-33=48'] Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,15 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 15:[81, 22], Operations: ['53-20=33', '55-33=22'] Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 81+22=103, Resulting Numbers: [103] 103,15 unequal: No Solution Exploring Operation: 81*22=1782, Resulting Numbers: [1782] 1782,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 15:[33, 136], Operations: ['53-20=33', '55+81=136'] Exploring Operation: 33+136=169, Resulting Numbers: [169] 169,15 unequal: No Solution Exploring Operation: 136-33=103, Resulting Numbers: [103] 103,15 unequal: No Solution Exploring Operation: 33*136=4488, Resulting Numbers: [4488] 4488,15 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: 15:[20, 27], Operations: ['81-55=26', '53-26=27'] Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 20*27=540, Resulting Numbers: [540] 540,15 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[20, 27], Operations: ['81-53=28', '55-28=27'] Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 20*27=540, Resulting Numbers: [540] 540,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[26, 33], Operations: ['81-55=26', '53-20=33'] Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 26*33=858, Resulting Numbers: [858] 858,15 unequal: No Solution Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[28, 35], Operations: ['81-53=28', '55-20=35'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,15 unequal: No Solution Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[53, 6], Operations: ['81-55=26', '26-20=6'] Exploring Operation: 53+6=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 53*6=318, Resulting Numbers: [318] 318,15 unequal: No Solution Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[55, 8], Operations: ['81-53=28', '28-20=8'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,15 unequal: No Solution Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[2, 61], Operations: ['55-53=2', '81-20=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,15 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[20, 79], Operations: ['55-53=2', '81-2=79'] Exploring Operation: 20+79=99, Resulting Numbers: [99] 99,15 unequal: No Solution Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 20*79=1580, Resulting Numbers: [1580] 1580,15 unequal: No Solution Moving to Node #0,3,2 Current State: 15:[81, 18], Operations: ['55-53=2', '20-2=18'] Exploring Operation: 81*18=1458, Resulting Numbers: [1458] 1458,15 unequal: No Solution Exploring Operation: 81-18=63, Resulting Numbers: [63] 63,15 unequal: No Solution Exploring Operation: 81+18=99, Resulting Numbers: [99] 99,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[26, 73], Operations: ['81-55=26', '20+53=73'] Exploring Operation: 73-26=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 26+73=99, Resulting Numbers: [99] 99,15 unequal: No Solution Exploring Operation: 26*73=1898, Resulting Numbers: [1898] 1898,15 unequal: No Solution Moving to Node #0,3,3 Current State: 15:[81, 10], Operations: ['55-53=2', '20/2=10'] Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,15 unequal: No Solution Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,15 unequal: No Solution Exploring Operation: 81*10=810, Resulting Numbers: [810] 810,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[28, 75], Operations: ['81-53=28', '20+55=75'] Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 28*75=2100, Resulting Numbers: [2100] 2100,15 unequal: No Solution Exploring Operation: 28+75=103, Resulting Numbers: [103] 103,15 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 18, 11, 56, 8 ]
57
[ "18-11=7", "56+8=64", "64-7=57" ]
Current State: 57:[18, 11, 56, 8], Operations: [] Exploring Operation: 18-11=7, Resulting Numbers: [56, 8, 7] Generated Node #2: [56, 8, 7] from Operation: 18-11=7 Current State: 57:[56, 8, 7], Operations: ['18-11=7'] Exploring Operation: 56+8=64, Resulting Numbers: [7, 64] Generated Node #3: [7, 64] from Operation: 56+8=64 Current State: 57:[7, 64], Operations: ['18-11=7', '56+8=64'] Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[18, 11, 56, 8], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [18, 11, 7] Generated Node #0,0: 57:[18, 11, 7] Operation: 56/8=7 Exploring Operation: 11-8=3, Resulting Numbers: [18, 56, 3] Generated Node #0,1: 57:[18, 56, 3] Operation: 11-8=3 Exploring Operation: 18-11=7, Resulting Numbers: [56, 8, 7] Generated Node #0,2: 57:[56, 8, 7] Operation: 18-11=7 Exploring Operation: 11+8=19, Resulting Numbers: [18, 56, 19] Generated Node #0,3: 57:[18, 56, 19] Operation: 11+8=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[18, 56, 3], Operations: ['11-8=3'] Exploring Operation: 56+3=59, Resulting Numbers: [18, 59] Generated Node #0,1,0: 57:[18, 59] Operation: 56+3=59 Exploring Operation: 18*3=54, Resulting Numbers: [56, 54] Generated Node #0,1,1: 57:[56, 54] Operation: 18*3=54 Exploring Operation: 18+3=21, Resulting Numbers: [56, 21] Generated Node #0,1,2: 57:[56, 21] Operation: 18+3=21 Exploring Operation: 18/3=6, Resulting Numbers: [56, 6] Generated Node #0,1,3: 57:[56, 6] Operation: 18/3=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[18, 59], Operations: ['11-8=3', '56+3=59'] Exploring Operation: 18*59=1062, Resulting Numbers: [1062] 1062,57 unequal: No Solution Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,57 unequal: No Solution Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,57 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 #0,1,2 Current State: 57:[56, 21], Operations: ['11-8=3', '18+3=21'] Exploring Operation: 56+21=77, Resulting Numbers: [77] 77,57 unequal: No Solution Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 56*21=1176, Resulting Numbers: [1176] 1176,57 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 #0,1,1 Current State: 57:[56, 54], Operations: ['11-8=3', '18*3=54'] Exploring Operation: 56+54=110, Resulting Numbers: [110] 110,57 unequal: No Solution Exploring Operation: 56*54=3024, Resulting Numbers: [3024] 3024,57 unequal: No Solution Exploring Operation: 56-54=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 #0,1,3 Current State: 57:[56, 6], Operations: ['11-8=3', '18/3=6'] Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,57 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,57 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,57 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 #0,3 Current State: 57:[18, 56, 19], Operations: ['11+8=19'] Exploring Operation: 18+19=37, Resulting Numbers: [56, 37] Generated Node #0,3,0: 57:[56, 37] Operation: 18+19=37 Exploring Operation: 19-18=1, Resulting Numbers: [56, 1] Generated Node #0,3,1: 57:[56, 1] Operation: 19-18=1 Exploring Operation: 18+56=74, Resulting Numbers: [19, 74] Generated Node #0,3,2: 57:[19, 74] Operation: 18+56=74 Exploring Operation: 56-18=38, Resulting Numbers: [19, 38] Generated Node #0,3,3: 57:[19, 38] Operation: 56-18=38 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 57:[56, 1], Operations: ['11+8=19', '19-18=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,57 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[18, 11, 56, 8], Operations: [] Exploring Operation: 11+8=19, Resulting Numbers: [18, 56, 19] Generated Node #0,3: 57:[18, 56, 19] Operation: 11+8=19 Moving to Node #0,3 Current State: 57:[18, 56, 19], Operations: ['11+8=19'] Exploring Operation: 19-18=1, Resulting Numbers: [56, 1] Generated Node #0,3,1: 57:[56, 1] Operation: 19-18=1 Moving to Node #0,3,1 Current State: 57:[56, 1], Operations: ['11+8=19', '19-18=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 89, 26, 91, 66 ]
59
[ "91-89=2", "66/2=33", "26+33=59" ]
Current State: 59:[89, 26, 91, 66], Operations: [] Exploring Operation: 91-89=2, Resulting Numbers: [26, 66, 2] Generated Node #2: [26, 66, 2] from Operation: 91-89=2 Current State: 59:[26, 66, 2], Operations: ['91-89=2'] Exploring Operation: 66/2=33, Resulting Numbers: [26, 33] Generated Node #3: [26, 33] from Operation: 66/2=33 Current State: 59:[26, 33], Operations: ['91-89=2', '66/2=33'] Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[89, 26, 91, 66], Operations: [] Exploring Operation: 89-26=63, Resulting Numbers: [91, 66, 63] Generated Node #0,0: 59:[91, 66, 63] Operation: 89-26=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[91, 66, 63], Operations: ['89-26=63'] Exploring Operation: 91-66=25, Resulting Numbers: [63, 25] Generated Node #0,0,0: 59:[63, 25] Operation: 91-66=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[63, 25], Operations: ['89-26=63', '91-66=25'] Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 35, 20, 7, 13 ]
12
[ "35/7=5", "20-13=7", "5+7=12" ]
Current State: 12:[35, 20, 7, 13], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [20, 13, 5] Generated Node #2: [20, 13, 5] from Operation: 35/7=5 Current State: 12:[20, 13, 5], Operations: ['35/7=5'] Exploring Operation: 20-13=7, Resulting Numbers: [5, 7] Generated Node #3: [5, 7] from Operation: 20-13=7 Current State: 12:[5, 7], Operations: ['35/7=5', '20-13=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[35, 20, 7, 13], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [20, 13, 5] Generated Node #0,0: 12:[20, 13, 5] Operation: 35/7=5 Exploring Operation: 35-13=22, Resulting Numbers: [20, 7, 22] Generated Node #0,1: 12:[20, 7, 22] Operation: 35-13=22 Exploring Operation: 35-20=15, Resulting Numbers: [7, 13, 15] Generated Node #0,2: 12:[7, 13, 15] Operation: 35-20=15 Exploring Operation: 35-7=28, Resulting Numbers: [20, 13, 28] Generated Node #0,3: 12:[20, 13, 28] Operation: 35-7=28 Moving to Node #0,2 Current State: 12:[7, 13, 15], Operations: ['35-20=15'] Exploring Operation: 13-7=6, Resulting Numbers: [15, 6] Generated Node #0,2,0: 12:[15, 6] Operation: 13-7=6 Exploring Operation: 7+13=20, Resulting Numbers: [15, 20] Generated Node #0,2,1: 12:[15, 20] Operation: 7+13=20 Exploring Operation: 15-13=2, Resulting Numbers: [7, 2] Generated Node #0,2,2: 12:[7, 2] Operation: 15-13=2 Exploring Operation: 15-7=8, Resulting Numbers: [13, 8] Generated Node #0,2,3: 12:[13, 8] Operation: 15-7=8 Moving to Node #0,0 Current State: 12:[20, 13, 5], Operations: ['35/7=5'] Exploring Operation: 20/5=4, Resulting Numbers: [13, 4] Generated Node #0,0,0: 12:[13, 4] Operation: 20/5=4 Exploring Operation: 20-13=7, Resulting Numbers: [5, 7] Generated Node #0,0,1: 12:[5, 7] Operation: 20-13=7 Exploring Operation: 13-5=8, Resulting Numbers: [20, 8] Generated Node #0,0,2: 12:[20, 8] Operation: 13-5=8 Exploring Operation: 20-5=15, Resulting Numbers: [13, 15] Generated Node #0,0,3: 12:[13, 15] Operation: 20-5=15 Moving to Node #0,1 Current State: 12:[20, 7, 22], Operations: ['35-13=22'] Exploring Operation: 20-7=13, Resulting Numbers: [22, 13] Generated Node #0,1,0: 12:[22, 13] Operation: 20-7=13 Exploring Operation: 22-20=2, Resulting Numbers: [7, 2] Generated Node #0,1,1: 12:[7, 2] Operation: 22-20=2 Exploring Operation: 20+7=27, Resulting Numbers: [22, 27] Generated Node #0,1,2: 12:[22, 27] Operation: 20+7=27 Exploring Operation: 22-7=15, Resulting Numbers: [20, 15] Generated Node #0,1,3: 12:[20, 15] Operation: 22-7=15 Moving to Node #0,3 Current State: 12:[20, 13, 28], Operations: ['35-7=28'] Exploring Operation: 20-13=7, Resulting Numbers: [28, 7] Generated Node #0,3,0: 12:[28, 7] Operation: 20-13=7 Exploring Operation: 28-13=15, Resulting Numbers: [20, 15] Generated Node #0,3,1: 12:[20, 15] Operation: 28-13=15 Exploring Operation: 20+13=33, Resulting Numbers: [28, 33] Generated Node #0,3,2: 12:[28, 33] Operation: 20+13=33 Exploring Operation: 28-20=8, Resulting Numbers: [13, 8] Generated Node #0,3,3: 12:[13, 8] Operation: 28-20=8 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 12:[13, 8], Operations: ['35-7=28', '28-20=8'] Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 12:[20, 15], Operations: ['35-7=28', '28-13=15'] Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,12 unequal: No Solution Exploring Operation: 20*15=300, Resulting Numbers: [300] 300,12 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 12:[28, 7], Operations: ['35-7=28', '20-13=7'] Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,12 unequal: No Solution Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,12 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 12:[28, 33], Operations: ['35-7=28', '20+13=33'] Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 28*33=924, Resulting Numbers: [924] 924,12 unequal: No Solution Exploring Operation: 28+33=61, Resulting Numbers: [61] 61,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 12:[7, 2], Operations: ['35-20=15', '15-13=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[13, 4], Operations: ['35/7=5', '20/5=4'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,12 unequal: No Solution Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[7, 2], Operations: ['35-13=22', '22-20=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[5, 7], Operations: ['35/7=5', '20-13=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[35, 20, 7, 13], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [20, 13, 5] Generated Node #0,0: 12:[20, 13, 5] Operation: 35/7=5 Moving to Node #0,0 Current State: 12:[20, 13, 5], Operations: ['35/7=5'] Exploring Operation: 20-13=7, Resulting Numbers: [5, 7] Generated Node #0,0,1: 12:[5, 7] Operation: 20-13=7 Moving to Node #0,0,1 Current State: 12:[5, 7], Operations: ['35/7=5', '20-13=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.958333
hs_4
mult_heuristic
[ 67, 45, 41, 49 ]
97
[ "49-45=4", "41*4=164", "164-67=97" ]
Current State: 97:[67, 45, 41, 49], Operations: [] Exploring Operation: 49-45=4, Resulting Numbers: [67, 41, 4] Generated Node #2: [67, 41, 4] from Operation: 49-45=4 Current State: 97:[67, 41, 4], Operations: ['49-45=4'] Exploring Operation: 41*4=164, Resulting Numbers: [67, 164] Generated Node #3: [67, 164] from Operation: 41*4=164 Current State: 97:[67, 164], Operations: ['49-45=4', '41*4=164'] Exploring Operation: 164-67=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[67, 45, 41, 49], Operations: [] Exploring Operation: 45+49=94, Resulting Numbers: [67, 41, 94] Generated Node #0,0: 97:[67, 41, 94] Operation: 45+49=94 Exploring Operation: 45+41=86, Resulting Numbers: [67, 49, 86] Generated Node #0,1: 97:[67, 49, 86] Operation: 45+41=86 Moving to Node #0,0 Current State: 97:[67, 41, 94], Operations: ['45+49=94'] Exploring Operation: 67+41=108, Resulting Numbers: [94, 108] Generated Node #0,0,0: 97:[94, 108] Operation: 67+41=108 Exploring Operation: 41+94=135, Resulting Numbers: [67, 135] Generated Node #0,0,1: 97:[67, 135] Operation: 41+94=135 Moving to Node #0,1 Current State: 97:[67, 49, 86], Operations: ['45+41=86'] Exploring Operation: 67+49=116, Resulting Numbers: [86, 116] Generated Node #0,1,0: 97:[86, 116] Operation: 67+49=116 Exploring Operation: 49+86=135, Resulting Numbers: [67, 135] Generated Node #0,1,1: 97:[67, 135] Operation: 49+86=135 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[86, 116], Operations: ['45+41=86', '67+49=116'] Exploring Operation: 116-86=30, Resulting Numbers: [30] 30,97 unequal: No Solution Exploring Operation: 86+116=202, Resulting Numbers: [202] 202,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[67, 135], Operations: ['45+41=86', '49+86=135'] Exploring Operation: 135-67=68, Resulting Numbers: [68] 68,97 unequal: No Solution Exploring Operation: 67+135=202, Resulting Numbers: [202] 202,97 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: 97:[94, 108], Operations: ['45+49=94', '67+41=108'] Exploring Operation: 108-94=14, Resulting Numbers: [14] 14,97 unequal: No Solution Exploring Operation: 94+108=202, Resulting Numbers: [202] 202,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[67, 135], Operations: ['45+49=94', '41+94=135'] Exploring Operation: 135-67=68, Resulting Numbers: [68] 68,97 unequal: No Solution Exploring Operation: 67+135=202, Resulting Numbers: [202] 202,97 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 17, 17, 4, 25 ]
36
[ "17+17=34", "34-25=9", "4*9=36" ]
Current State: 36:[17, 17, 4, 25], Operations: [] Exploring Operation: 17+17=34, Resulting Numbers: [4, 25, 34] Generated Node #2: [4, 25, 34] from Operation: 17+17=34 Current State: 36:[4, 25, 34], Operations: ['17+17=34'] Exploring Operation: 34-25=9, Resulting Numbers: [4, 9] Generated Node #3: [4, 9] from Operation: 34-25=9 Current State: 36:[4, 9], Operations: ['17+17=34', '34-25=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[17, 17, 4, 25], Operations: [] Exploring Operation: 17+25=42, Resulting Numbers: [17, 4, 42] Generated Node #0,0: 36:[17, 4, 42] Operation: 17+25=42 Exploring Operation: 25-17=8, Resulting Numbers: [17, 4, 8] Generated Node #0,1: 36:[17, 4, 8] Operation: 25-17=8 Exploring Operation: 25-4=21, Resulting Numbers: [17, 17, 21] Generated Node #0,2: 36:[17, 17, 21] Operation: 25-4=21 Exploring Operation: 25-17=8, Resulting Numbers: [17, 4, 8] Generated Node #0,3: 36:[17, 4, 8] Operation: 25-17=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[17, 4, 8], Operations: ['25-17=8'] Exploring Operation: 4+8=12, Resulting Numbers: [17, 12] Generated Node #0,1,0: 36:[17, 12] Operation: 4+8=12 Exploring Operation: 8-4=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 36:[17, 4] Operation: 8-4=4 Exploring Operation: 17-8=9, Resulting Numbers: [4, 9] Generated Node #0,1,2: 36:[4, 9] Operation: 17-8=9 Exploring Operation: 8/4=2, Resulting Numbers: [17, 2] Generated Node #0,1,3: 36:[17, 2] Operation: 8/4=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 36:[4, 9], Operations: ['25-17=8', '17-8=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[17, 17, 4, 25], Operations: [] Exploring Operation: 25-17=8, Resulting Numbers: [17, 4, 8] Generated Node #0,1: 36:[17, 4, 8] Operation: 25-17=8 Moving to Node #0,1 Current State: 36:[17, 4, 8], Operations: ['25-17=8'] Exploring Operation: 17-8=9, Resulting Numbers: [4, 9] Generated Node #0,1,2: 36:[4, 9] Operation: 17-8=9 Moving to Node #0,1,2 Current State: 36:[4, 9], Operations: ['25-17=8', '17-8=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 48, 7, 94, 20 ]
19
[ "48+7=55", "94-20=74", "74-55=19" ]
Current State: 19:[48, 7, 94, 20], Operations: [] Exploring Operation: 48+7=55, Resulting Numbers: [94, 20, 55] Generated Node #2: [94, 20, 55] from Operation: 48+7=55 Current State: 19:[94, 20, 55], Operations: ['48+7=55'] Exploring Operation: 94-20=74, Resulting Numbers: [55, 74] Generated Node #3: [55, 74] from Operation: 94-20=74 Current State: 19:[55, 74], Operations: ['48+7=55', '94-20=74'] Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[48, 7, 94, 20], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [7, 20, 46] Generated Node #0,0: 19:[7, 20, 46] Operation: 94-48=46 Moving to Node #0,0 Current State: 19:[7, 20, 46], Operations: ['94-48=46'] Exploring Operation: 46-20=26, Resulting Numbers: [7, 26] Generated Node #0,0,0: 19:[7, 26] Operation: 46-20=26 Moving to Node #0,0,0 Current State: 19:[7, 26], Operations: ['94-48=46', '46-20=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[48, 7, 94, 20], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [7, 20, 46] Generated Node #0,0: 19:[7, 20, 46] Operation: 94-48=46 Moving to Node #0,0 Current State: 19:[7, 20, 46], Operations: ['94-48=46'] Exploring Operation: 46-20=26, Resulting Numbers: [7, 26] Generated Node #0,0,0: 19:[7, 26] Operation: 46-20=26 Moving to Node #0,0,0 Current State: 19:[7, 26], Operations: ['94-48=46', '46-20=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 78, 39, 29, 45 ]
13
[ "78/39=2", "29*2=58", "58-45=13" ]
Current State: 13:[78, 39, 29, 45], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [29, 45, 2] Generated Node #2: [29, 45, 2] from Operation: 78/39=2 Current State: 13:[29, 45, 2], Operations: ['78/39=2'] Exploring Operation: 29*2=58, Resulting Numbers: [45, 58] Generated Node #3: [45, 58] from Operation: 29*2=58 Current State: 13:[45, 58], Operations: ['78/39=2', '29*2=58'] Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[78, 39, 29, 45], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [29, 45, 2] Generated Node #0,0: 13:[29, 45, 2] Operation: 78/39=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[29, 45, 2], Operations: ['78/39=2'] Exploring Operation: 45-29=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 13:[2, 16] Operation: 45-29=16 Moving to Node #0,0,0 Current State: 13:[2, 16], Operations: ['78/39=2', '45-29=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,13 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
[ 77, 26, 4, 84 ]
29
[ "77-26=51", "84-4=80", "80-51=29" ]
Current State: 29:[77, 26, 4, 84], Operations: [] Exploring Operation: 77-26=51, Resulting Numbers: [4, 84, 51] Generated Node #2: [4, 84, 51] from Operation: 77-26=51 Current State: 29:[4, 84, 51], Operations: ['77-26=51'] Exploring Operation: 84-4=80, Resulting Numbers: [51, 80] Generated Node #3: [51, 80] from Operation: 84-4=80 Current State: 29:[51, 80], Operations: ['77-26=51', '84-4=80'] Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[77, 26, 4, 84], Operations: [] Exploring Operation: 77-26=51, Resulting Numbers: [4, 84, 51] Generated Node #0,0: 29:[4, 84, 51] Operation: 77-26=51 Exploring Operation: 77-4=73, Resulting Numbers: [26, 84, 73] Generated Node #0,1: 29:[26, 84, 73] Operation: 77-4=73 Exploring Operation: 84/4=21, Resulting Numbers: [77, 26, 21] Generated Node #0,2: 29:[77, 26, 21] Operation: 84/4=21 Exploring Operation: 84-77=7, Resulting Numbers: [26, 4, 7] Generated Node #0,3: 29:[26, 4, 7] Operation: 84-77=7 Moving to Node #0,3 Current State: 29:[26, 4, 7], Operations: ['84-77=7'] Exploring Operation: 4*7=28, Resulting Numbers: [26, 28] Generated Node #0,3,0: 29:[26, 28] Operation: 4*7=28 Exploring Operation: 4+7=11, Resulting Numbers: [26, 11] Generated Node #0,3,1: 29:[26, 11] Operation: 4+7=11 Exploring Operation: 26-4=22, Resulting Numbers: [7, 22] Generated Node #0,3,2: 29:[7, 22] Operation: 26-4=22 Exploring Operation: 26+4=30, Resulting Numbers: [7, 30] Generated Node #0,3,3: 29:[7, 30] Operation: 26+4=30 Moving to Node #0,2 Current State: 29:[77, 26, 21], Operations: ['84/4=21'] Exploring Operation: 77-26=51, Resulting Numbers: [21, 51] Generated Node #0,2,0: 29:[21, 51] Operation: 77-26=51 Exploring Operation: 77+21=98, Resulting Numbers: [26, 98] Generated Node #0,2,1: 29:[26, 98] Operation: 77+21=98 Exploring Operation: 26+21=47, Resulting Numbers: [77, 47] Generated Node #0,2,2: 29:[77, 47] Operation: 26+21=47 Exploring Operation: 77-21=56, Resulting Numbers: [26, 56] Generated Node #0,2,3: 29:[26, 56] Operation: 77-21=56 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[21, 51], Operations: ['84/4=21', '77-26=51'] Exploring Operation: 21+51=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 21*51=1071, Resulting Numbers: [1071] 1071,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 29:[26, 56], Operations: ['84/4=21', '77-21=56'] Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 26+56=82, Resulting Numbers: [82] 82,29 unequal: No Solution Exploring Operation: 26*56=1456, Resulting Numbers: [1456] 1456,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[77, 47], Operations: ['84/4=21', '26+21=47'] Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 77*47=3619, Resulting Numbers: [3619] 3619,29 unequal: No Solution Exploring Operation: 77+47=124, Resulting Numbers: [124] 124,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[26, 98], Operations: ['84/4=21', '77+21=98'] Exploring Operation: 98-26=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 26*98=2548, Resulting Numbers: [2548] 2548,29 unequal: No Solution Exploring Operation: 26+98=124, Resulting Numbers: [124] 124,29 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: 29:[26, 84, 73], Operations: ['77-4=73'] Exploring Operation: 84-26=58, Resulting Numbers: [73, 58] Generated Node #0,1,0: 29:[73, 58] Operation: 84-26=58 Exploring Operation: 84-73=11, Resulting Numbers: [26, 11] Generated Node #0,1,1: 29:[26, 11] Operation: 84-73=11 Exploring Operation: 73-26=47, Resulting Numbers: [84, 47] Generated Node #0,1,2: 29:[84, 47] Operation: 73-26=47 Exploring Operation: 26+84=110, Resulting Numbers: [73, 110] Generated Node #0,1,3: 29:[73, 110] Operation: 26+84=110 Moving to Node #0,0 Current State: 29:[4, 84, 51], Operations: ['77-26=51'] Exploring Operation: 84-4=80, Resulting Numbers: [51, 80] Generated Node #0,0,0: 29:[51, 80] Operation: 84-4=80 Exploring Operation: 84/4=21, Resulting Numbers: [51, 21] Generated Node #0,0,1: 29:[51, 21] Operation: 84/4=21 Exploring Operation: 51-4=47, Resulting Numbers: [84, 47] Generated Node #0,0,2: 29:[84, 47] Operation: 51-4=47 Exploring Operation: 84-51=33, Resulting Numbers: [4, 33] Generated Node #0,0,3: 29:[4, 33] Operation: 84-51=33 Moving to Node #0,3,0 Current State: 29:[26, 28], Operations: ['84-77=7', '4*7=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,29 unequal: No Solution Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,29 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[26, 11], Operations: ['84-77=7', '4+7=11'] Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,29 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,29 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[26, 11], Operations: ['77-4=73', '84-73=11'] Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,29 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,29 unequal: No Solution Moving to Node #0,3,3 Current State: 29:[7, 30], Operations: ['84-77=7', '26+4=30'] Exploring Operation: 7+30=37, Resulting Numbers: [37] 37,29 unequal: No Solution Exploring Operation: 7*30=210, Resulting Numbers: [210] 210,29 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,29 unequal: No Solution Moving to Node #0,3,2 Current State: 29:[7, 22], Operations: ['84-77=7', '26-4=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,29 unequal: No Solution Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[77, 26, 4, 84], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [26, 4, 7] Generated Node #0,3: 29:[26, 4, 7] Operation: 84-77=7 Moving to Node #0,3 Current State: 29:[26, 4, 7], Operations: ['84-77=7'] Exploring Operation: 26-4=22, Resulting Numbers: [7, 22] Generated Node #0,3,2: 29:[7, 22] Operation: 26-4=22 Moving to Node #0,3,2 Current State: 29:[7, 22], Operations: ['84-77=7', '26-4=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 94, 2, 18, 64 ]
44
[ "94-18=76", "64/2=32", "76-32=44" ]
Current State: 44:[94, 2, 18, 64], Operations: [] Exploring Operation: 94-18=76, Resulting Numbers: [2, 64, 76] Generated Node #2: [2, 64, 76] from Operation: 94-18=76 Current State: 44:[2, 64, 76], Operations: ['94-18=76'] Exploring Operation: 64/2=32, Resulting Numbers: [76, 32] Generated Node #3: [76, 32] from Operation: 64/2=32 Current State: 44:[76, 32], Operations: ['94-18=76', '64/2=32'] Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[94, 2, 18, 64], Operations: [] Exploring Operation: 94-64=30, Resulting Numbers: [2, 18, 30] Generated Node #0,0: 44:[2, 18, 30] Operation: 94-64=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[2, 18, 30], Operations: ['94-64=30'] Exploring Operation: 30-18=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 44:[2, 12] Operation: 30-18=12 Moving to Node #0,0,0 Current State: 44:[2, 12], Operations: ['94-64=30', '30-18=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 34, 31, 84, 99 ]
80
[ "34+31=65", "99-84=15", "65+15=80" ]
Current State: 80:[34, 31, 84, 99], Operations: [] Exploring Operation: 34+31=65, Resulting Numbers: [84, 99, 65] Generated Node #2: [84, 99, 65] from Operation: 34+31=65 Current State: 80:[84, 99, 65], Operations: ['34+31=65'] Exploring Operation: 99-84=15, Resulting Numbers: [65, 15] Generated Node #3: [65, 15] from Operation: 99-84=15 Current State: 80:[65, 15], Operations: ['34+31=65', '99-84=15'] Exploring Operation: 65+15=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[34, 31, 84, 99], Operations: [] Exploring Operation: 99-31=68, Resulting Numbers: [34, 84, 68] Generated Node #0,0: 80:[34, 84, 68] Operation: 99-31=68 Exploring Operation: 99-84=15, Resulting Numbers: [34, 31, 15] Generated Node #0,1: 80:[34, 31, 15] Operation: 99-84=15 Exploring Operation: 34-31=3, Resulting Numbers: [84, 99, 3] Generated Node #0,2: 80:[84, 99, 3] Operation: 34-31=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[34, 31, 15], Operations: ['99-84=15'] Exploring Operation: 31-15=16, Resulting Numbers: [34, 16] Generated Node #0,1,0: 80:[34, 16] Operation: 31-15=16 Exploring Operation: 34-15=19, Resulting Numbers: [31, 19] Generated Node #0,1,1: 80:[31, 19] Operation: 34-15=19 Exploring Operation: 34-31=3, Resulting Numbers: [15, 3] Generated Node #0,1,2: 80:[15, 3] Operation: 34-31=3 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 80:[15, 3], Operations: ['99-84=15', '34-31=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[34, 16], Operations: ['99-84=15', '31-15=16'] Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,80 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,80 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[31, 19], Operations: ['99-84=15', '34-15=19'] Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 31+19=50, Resulting Numbers: [50] 50,80 unequal: No Solution Exploring Operation: 31*19=589, Resulting Numbers: [589] 589,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[34, 84, 68], Operations: ['99-31=68'] Exploring Operation: 68/34=2, Resulting Numbers: [84, 2] Generated Node #0,0,0: 80:[84, 2] Operation: 68/34=2 Exploring Operation: 84-68=16, Resulting Numbers: [34, 16] Generated Node #0,0,1: 80:[34, 16] Operation: 84-68=16 Exploring Operation: 68-34=34, Resulting Numbers: [84, 34] Generated Node #0,0,2: 80:[84, 34] Operation: 68-34=34 Moving to Node #0,0,0 Current State: 80:[84, 2], Operations: ['99-31=68', '68/34=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,80 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[34, 16], Operations: ['99-31=68', '84-68=16'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,80 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[84, 34], Operations: ['99-31=68', '68-34=34'] Exploring Operation: 84*34=2856, Resulting Numbers: [2856] 2856,80 unequal: No Solution Exploring Operation: 84+34=118, Resulting Numbers: [118] 118,80 unequal: No Solution Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,80 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 Current State: 80:[84, 99, 3], Operations: ['34-31=3'] Exploring Operation: 84-3=81, Resulting Numbers: [99, 81] Generated Node #0,2,0: 80:[99, 81] Operation: 84-3=81 Exploring Operation: 99-84=15, Resulting Numbers: [3, 15] Generated Node #0,2,1: 80:[3, 15] Operation: 99-84=15 Exploring Operation: 99/3=33, Resulting Numbers: [84, 33] Generated Node #0,2,2: 80:[84, 33] Operation: 99/3=33 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 80:[3, 15], Operations: ['34-31=3', '99-84=15'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 80:[84, 33], Operations: ['34-31=3', '99/3=33'] Exploring Operation: 84+33=117, Resulting Numbers: [117] 117,80 unequal: No Solution Exploring Operation: 84-33=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 84*33=2772, Resulting Numbers: [2772] 2772,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 80:[99, 81], Operations: ['34-31=3', '84-3=81'] Exploring Operation: 99+81=180, Resulting Numbers: [180] 180,80 unequal: No Solution Exploring Operation: 99*81=8019, Resulting Numbers: [8019] 8019,80 unequal: No Solution Exploring Operation: 99-81=18, Resulting Numbers: [18] 18,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 16, 9, 17, 1 ]
43
[ "16+9=25", "17+1=18", "25+18=43" ]
Current State: 43:[16, 9, 17, 1], Operations: [] Exploring Operation: 16+9=25, Resulting Numbers: [17, 1, 25] Generated Node #2: [17, 1, 25] from Operation: 16+9=25 Current State: 43:[17, 1, 25], Operations: ['16+9=25'] Exploring Operation: 17+1=18, Resulting Numbers: [25, 18] Generated Node #3: [25, 18] from Operation: 17+1=18 Current State: 43:[25, 18], Operations: ['16+9=25', '17+1=18'] Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[16, 9, 17, 1], Operations: [] Exploring Operation: 16+1=17, Resulting Numbers: [9, 17, 17] Generated Node #0,0: 43:[9, 17, 17] Operation: 16+1=17 Exploring Operation: 16+9=25, Resulting Numbers: [17, 1, 25] Generated Node #0,1: 43:[17, 1, 25] Operation: 16+9=25 Exploring Operation: 16+17=33, Resulting Numbers: [9, 1, 33] Generated Node #0,2: 43:[9, 1, 33] Operation: 16+17=33 Moving to Node #0,0 Current State: 43:[9, 17, 17], Operations: ['16+1=17'] Exploring Operation: 17+17=34, Resulting Numbers: [9, 34] Generated Node #0,0,0: 43:[9, 34] Operation: 17+17=34 Exploring Operation: 9+17=26, Resulting Numbers: [17, 26] Generated Node #0,0,1: 43:[17, 26] Operation: 9+17=26 Exploring Operation: 9+17=26, Resulting Numbers: [17, 26] Generated Node #0,0,2: 43:[17, 26] Operation: 9+17=26 Moving to Node #0,1 Current State: 43:[17, 1, 25], Operations: ['16+9=25'] Exploring Operation: 17+1=18, Resulting Numbers: [25, 18] Generated Node #0,1,0: 43:[25, 18] Operation: 17+1=18 Exploring Operation: 1+25=26, Resulting Numbers: [17, 26] Generated Node #0,1,1: 43:[17, 26] Operation: 1+25=26 Exploring Operation: 17+25=42, Resulting Numbers: [1, 42] Generated Node #0,1,2: 43:[1, 42] Operation: 17+25=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[25, 18], Operations: ['16+9=25', '17+1=18'] Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[16, 9, 17, 1], Operations: [] Exploring Operation: 16+9=25, Resulting Numbers: [17, 1, 25] Generated Node #0,1: 43:[17, 1, 25] Operation: 16+9=25 Moving to Node #0,1 Current State: 43:[17, 1, 25], Operations: ['16+9=25'] Exploring Operation: 17+1=18, Resulting Numbers: [25, 18] Generated Node #0,1,0: 43:[25, 18] Operation: 17+1=18 Moving to Node #0,1,0 Current State: 43:[25, 18], Operations: ['16+9=25', '17+1=18'] Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 7, 89, 90, 81 ]
91
[ "89-7=82", "90-81=9", "82+9=91" ]
Current State: 91:[7, 89, 90, 81], Operations: [] Exploring Operation: 89-7=82, Resulting Numbers: [90, 81, 82] Generated Node #2: [90, 81, 82] from Operation: 89-7=82 Current State: 91:[90, 81, 82], Operations: ['89-7=82'] Exploring Operation: 90-81=9, Resulting Numbers: [82, 9] Generated Node #3: [82, 9] from Operation: 90-81=9 Current State: 91:[82, 9], Operations: ['89-7=82', '90-81=9'] Exploring Operation: 82+9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[7, 89, 90, 81], Operations: [] Exploring Operation: 90-81=9, Resulting Numbers: [7, 89, 9] Generated Node #0,0: 91:[7, 89, 9] Operation: 90-81=9 Exploring Operation: 89-81=8, Resulting Numbers: [7, 90, 8] Generated Node #0,1: 91:[7, 90, 8] Operation: 89-81=8 Exploring Operation: 7+81=88, Resulting Numbers: [89, 90, 88] Generated Node #0,2: 91:[89, 90, 88] Operation: 7+81=88 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[7, 90, 8], Operations: ['89-81=8'] Exploring Operation: 7+8=15, Resulting Numbers: [90, 15] Generated Node #0,1,0: 91:[90, 15] Operation: 7+8=15 Exploring Operation: 7+90=97, Resulting Numbers: [8, 97] Generated Node #0,1,1: 91:[8, 97] Operation: 7+90=97 Exploring Operation: 8-7=1, Resulting Numbers: [90, 1] Generated Node #0,1,2: 91:[90, 1] Operation: 8-7=1 Moving to Node #0,1,0 Current State: 91:[90, 15], Operations: ['89-81=8', '7+8=15'] Exploring Operation: 90/15=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 90+15=105, Resulting Numbers: [105] 105,91 unequal: No Solution Exploring Operation: 90-15=75, Resulting Numbers: [75] 75,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[8, 97], Operations: ['89-81=8', '7+90=97'] Exploring Operation: 8*97=776, Resulting Numbers: [776] 776,91 unequal: No Solution Exploring Operation: 8+97=105, Resulting Numbers: [105] 105,91 unequal: No Solution Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[90, 1], Operations: ['89-81=8', '8-7=1'] Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[7, 89, 90, 81], Operations: [] Exploring Operation: 89-81=8, Resulting Numbers: [7, 90, 8] Generated Node #0,1: 91:[7, 90, 8] Operation: 89-81=8 Moving to Node #0,1 Current State: 91:[7, 90, 8], Operations: ['89-81=8'] Exploring Operation: 8-7=1, Resulting Numbers: [90, 1] Generated Node #0,1,2: 91:[90, 1] Operation: 8-7=1 Moving to Node #0,1,2 Current State: 91:[90, 1], Operations: ['89-81=8', '8-7=1'] Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 94, 5, 7, 58 ]
34
[ "94+5=99", "7+58=65", "99-65=34" ]
Current State: 34:[94, 5, 7, 58], Operations: [] Exploring Operation: 94+5=99, Resulting Numbers: [7, 58, 99] Generated Node #2: [7, 58, 99] from Operation: 94+5=99 Current State: 34:[7, 58, 99], Operations: ['94+5=99'] Exploring Operation: 7+58=65, Resulting Numbers: [99, 65] Generated Node #3: [99, 65] from Operation: 7+58=65 Current State: 34:[99, 65], Operations: ['94+5=99', '7+58=65'] Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[94, 5, 7, 58], Operations: [] Exploring Operation: 94-5=89, Resulting Numbers: [7, 58, 89] Generated Node #0,0: 34:[7, 58, 89] Operation: 94-5=89 Exploring Operation: 7-5=2, Resulting Numbers: [94, 58, 2] Generated Node #0,1: 34:[94, 58, 2] Operation: 7-5=2 Exploring Operation: 94-7=87, Resulting Numbers: [5, 58, 87] Generated Node #0,2: 34:[5, 58, 87] Operation: 94-7=87 Exploring Operation: 94-58=36, Resulting Numbers: [5, 7, 36] Generated Node #0,3: 34:[5, 7, 36] Operation: 94-58=36 Exploring Operation: 58-7=51, Resulting Numbers: [94, 5, 51] Generated Node #0,4: 34:[94, 5, 51] Operation: 58-7=51 Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[5, 7, 36], Operations: ['94-58=36'] Exploring Operation: 5*7=35, Resulting Numbers: [36, 35] Generated Node #0,3,0: 34:[36, 35] Operation: 5*7=35 Exploring Operation: 36-5=31, Resulting Numbers: [7, 31] Generated Node #0,3,1: 34:[7, 31] Operation: 36-5=31 Exploring Operation: 5+7=12, Resulting Numbers: [36, 12] Generated Node #0,3,2: 34:[36, 12] Operation: 5+7=12 Exploring Operation: 7-5=2, Resulting Numbers: [36, 2] Generated Node #0,3,3: 34:[36, 2] Operation: 7-5=2 Exploring Operation: 36-7=29, Resulting Numbers: [5, 29] Generated Node #0,3,4: 34:[5, 29] Operation: 36-7=29 Moving to Node #0,3,3 Current State: 34:[36, 2], Operations: ['94-58=36', '7-5=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[94, 5, 7, 58], Operations: [] Exploring Operation: 94-58=36, Resulting Numbers: [5, 7, 36] Generated Node #0,3: 34:[5, 7, 36] Operation: 94-58=36 Moving to Node #0,3 Current State: 34:[5, 7, 36], Operations: ['94-58=36'] Exploring Operation: 7-5=2, Resulting Numbers: [36, 2] Generated Node #0,3,3: 34:[36, 2] Operation: 7-5=2 Moving to Node #0,3,3 Current State: 34:[36, 2], Operations: ['94-58=36', '7-5=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 59, 73, 77, 88 ]
12
[ "59+73=132", "88-77=11", "132/11=12" ]
Current State: 12:[59, 73, 77, 88], Operations: [] Exploring Operation: 59+73=132, Resulting Numbers: [77, 88, 132] Generated Node #2: [77, 88, 132] from Operation: 59+73=132 Current State: 12:[77, 88, 132], Operations: ['59+73=132'] Exploring Operation: 88-77=11, Resulting Numbers: [132, 11] Generated Node #3: [132, 11] from Operation: 88-77=11 Current State: 12:[132, 11], Operations: ['59+73=132', '88-77=11'] Exploring Operation: 132/11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[59, 73, 77, 88], Operations: [] Exploring Operation: 73-59=14, Resulting Numbers: [77, 88, 14] Generated Node #0,0: 12:[77, 88, 14] Operation: 73-59=14 Exploring Operation: 77-73=4, Resulting Numbers: [59, 88, 4] Generated Node #0,1: 12:[59, 88, 4] Operation: 77-73=4 Exploring Operation: 88-73=15, Resulting Numbers: [59, 77, 15] Generated Node #0,2: 12:[59, 77, 15] Operation: 88-73=15 Exploring Operation: 77-59=18, Resulting Numbers: [73, 88, 18] Generated Node #0,3: 12:[73, 88, 18] Operation: 77-59=18 Exploring Operation: 88-77=11, Resulting Numbers: [59, 73, 11] Generated Node #0,4: 12:[59, 73, 11] Operation: 88-77=11 Start Sub Search at level 1: Moving to Node #0,4 Current State: 12:[59, 73, 11], Operations: ['88-77=11'] Exploring Operation: 73+11=84, Resulting Numbers: [59, 84] Generated Node #0,4,0: 12:[59, 84] Operation: 73+11=84 Exploring Operation: 73-59=14, Resulting Numbers: [11, 14] Generated Node #0,4,1: 12:[11, 14] Operation: 73-59=14 Exploring Operation: 73-11=62, Resulting Numbers: [59, 62] Generated Node #0,4,2: 12:[59, 62] Operation: 73-11=62 Exploring Operation: 59-11=48, Resulting Numbers: [73, 48] Generated Node #0,4,3: 12:[73, 48] Operation: 59-11=48 Exploring Operation: 59+11=70, Resulting Numbers: [73, 70] Generated Node #0,4,4: 12:[73, 70] Operation: 59+11=70 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 12:[11, 14], Operations: ['88-77=11', '73-59=14'] Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,12 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 12:[59, 62], Operations: ['88-77=11', '73-11=62'] Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,12 unequal: No Solution Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,12 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 12:[73, 48], Operations: ['88-77=11', '59-11=48'] Exploring Operation: 73-48=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 73+48=121, Resulting Numbers: [121] 121,12 unequal: No Solution Exploring Operation: 73*48=3504, Resulting Numbers: [3504] 3504,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 12:[59, 84], Operations: ['88-77=11', '73+11=84'] Exploring Operation: 59*84=4956, Resulting Numbers: [4956] 4956,12 unequal: No Solution Exploring Operation: 84-59=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 59+84=143, Resulting Numbers: [143] 143,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 12:[73, 70], Operations: ['88-77=11', '59+11=70'] Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 73+70=143, Resulting Numbers: [143] 143,12 unequal: No Solution Exploring Operation: 73*70=5110, Resulting Numbers: [5110] 5110,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[59, 77, 15], Operations: ['88-73=15'] Exploring Operation: 59+77=136, Resulting Numbers: [15, 136] Generated Node #0,2,0: 12:[15, 136] Operation: 59+77=136 Exploring Operation: 77-59=18, Resulting Numbers: [15, 18] Generated Node #0,2,1: 12:[15, 18] Operation: 77-59=18 Exploring Operation: 77-15=62, Resulting Numbers: [59, 62] Generated Node #0,2,2: 12:[59, 62] Operation: 77-15=62 Exploring Operation: 59-15=44, Resulting Numbers: [77, 44] Generated Node #0,2,3: 12:[77, 44] Operation: 59-15=44 Exploring Operation: 59+15=74, Resulting Numbers: [77, 74] Generated Node #0,2,4: 12:[77, 74] Operation: 59+15=74 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 12:[15, 18], Operations: ['88-73=15', '77-59=18'] Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,12 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 12:[59, 62], Operations: ['88-73=15', '77-15=62'] Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,12 unequal: No Solution Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 12:[77, 44], Operations: ['88-73=15', '59-15=44'] Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,12 unequal: No Solution Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 12:[15, 136], Operations: ['88-73=15', '59+77=136'] Exploring Operation: 15*136=2040, Resulting Numbers: [2040] 2040,12 unequal: No Solution Exploring Operation: 136-15=121, Resulting Numbers: [121] 121,12 unequal: No Solution Exploring Operation: 15+136=151, Resulting Numbers: [151] 151,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 12:[77, 74], Operations: ['88-73=15', '59+15=74'] Exploring Operation: 77+74=151, Resulting Numbers: [151] 151,12 unequal: No Solution Exploring Operation: 77*74=5698, Resulting Numbers: [5698] 5698,12 unequal: No Solution Exploring Operation: 77-74=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[59, 88, 4], Operations: ['77-73=4'] Exploring Operation: 88/4=22, Resulting Numbers: [59, 22] Generated Node #0,1,0: 12:[59, 22] Operation: 88/4=22 Exploring Operation: 88-4=84, Resulting Numbers: [59, 84] Generated Node #0,1,1: 12:[59, 84] Operation: 88-4=84 Exploring Operation: 59-4=55, Resulting Numbers: [88, 55] Generated Node #0,1,2: 12:[88, 55] Operation: 59-4=55 Exploring Operation: 59+4=63, Resulting Numbers: [88, 63] Generated Node #0,1,3: 12:[88, 63] Operation: 59+4=63 Exploring Operation: 88-59=29, Resulting Numbers: [4, 29] Generated Node #0,1,4: 12:[4, 29] Operation: 88-59=29 Moving to Node #0,1,4 Current State: 12:[4, 29], Operations: ['77-73=4', '88-59=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,12 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[59, 22], Operations: ['77-73=4', '88/4=22'] Exploring Operation: 59*22=1298, Resulting Numbers: [1298] 1298,12 unequal: No Solution Exploring Operation: 59+22=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[59, 84], Operations: ['77-73=4', '88-4=84'] Exploring Operation: 59*84=4956, Resulting Numbers: [4956] 4956,12 unequal: No Solution Exploring Operation: 84-59=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 59+84=143, Resulting Numbers: [143] 143,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[88, 55], Operations: ['77-73=4', '59-4=55'] Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,12 unequal: No Solution Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[88, 63], Operations: ['77-73=4', '59+4=63'] Exploring Operation: 88-63=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 88+63=151, Resulting Numbers: [151] 151,12 unequal: No Solution Exploring Operation: 88*63=5544, Resulting Numbers: [5544] 5544,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[77, 88, 14], Operations: ['73-59=14'] Exploring Operation: 77+14=91, Resulting Numbers: [88, 91] Generated Node #0,0,0: 12:[88, 91] Operation: 77+14=91 Exploring Operation: 88-77=11, Resulting Numbers: [14, 11] Generated Node #0,0,1: 12:[14, 11] Operation: 88-77=11 Exploring Operation: 88-14=74, Resulting Numbers: [77, 74] Generated Node #0,0,2: 12:[77, 74] Operation: 88-14=74 Exploring Operation: 77-14=63, Resulting Numbers: [88, 63] Generated Node #0,0,3: 12:[88, 63] Operation: 77-14=63 Exploring Operation: 77+88=165, Resulting Numbers: [14, 165] Generated Node #0,0,4: 12:[14, 165] Operation: 77+88=165 Moving to Node #0,0,1 Current State: 12:[14, 11], Operations: ['73-59=14', '88-77=11'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 14*11=154, Resulting Numbers: [154] 154,12 unequal: No Solution Moving to Node #0,0,3 Current State: 12:[88, 63], Operations: ['73-59=14', '77-14=63'] Exploring Operation: 88-63=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 88*63=5544, Resulting Numbers: [5544] 5544,12 unequal: No Solution Exploring Operation: 88+63=151, Resulting Numbers: [151] 151,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[77, 74], Operations: ['73-59=14', '88-14=74'] Exploring Operation: 77*74=5698, Resulting Numbers: [5698] 5698,12 unequal: No Solution Exploring Operation: 77+74=151, Resulting Numbers: [151] 151,12 unequal: No Solution Exploring Operation: 77-74=3, Resulting Numbers: [3] 3,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[88, 91], Operations: ['73-59=14', '77+14=91'] Exploring Operation: 88*91=8008, Resulting Numbers: [8008] 8008,12 unequal: No Solution Exploring Operation: 88+91=179, Resulting Numbers: [179] 179,12 unequal: No Solution Exploring Operation: 91-88=3, Resulting Numbers: [3] 3,12 unequal: No Solution Moving to Node #0,0,4 Current State: 12:[14, 165], Operations: ['73-59=14', '77+88=165'] Exploring Operation: 165-14=151, Resulting Numbers: [151] 151,12 unequal: No Solution Exploring Operation: 14*165=2310, Resulting Numbers: [2310] 2310,12 unequal: No Solution Exploring Operation: 14+165=179, Resulting Numbers: [179] 179,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[73, 88, 18], Operations: ['77-59=18'] Exploring Operation: 88-73=15, Resulting Numbers: [18, 15] Generated Node #0,3,0: 12:[18, 15] Operation: 88-73=15 Exploring Operation: 73+18=91, Resulting Numbers: [88, 91] Generated Node #0,3,1: 12:[88, 91] Operation: 73+18=91 Exploring Operation: 73+88=161, Resulting Numbers: [18, 161] Generated Node #0,3,2: 12:[18, 161] Operation: 73+88=161 Exploring Operation: 73-18=55, Resulting Numbers: [88, 55] Generated Node #0,3,3: 12:[88, 55] Operation: 73-18=55 Exploring Operation: 88-18=70, Resulting Numbers: [73, 70] Generated Node #0,3,4: 12:[73, 70] Operation: 88-18=70 Moving to Node #0,3,0 Current State: 12:[18, 15], Operations: ['77-59=18', '88-73=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,12 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,12 unequal: No Solution Moving to Node #0,3,4 Current State: 12:[73, 70], Operations: ['77-59=18', '88-18=70'] Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 73+70=143, Resulting Numbers: [143] 143,12 unequal: No Solution Exploring Operation: 73*70=5110, Resulting Numbers: [5110] 5110,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[88, 55], Operations: ['77-59=18', '73-18=55'] Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,12 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,12 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[88, 91], Operations: ['77-59=18', '73+18=91'] Exploring Operation: 91-88=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 88*91=8008, Resulting Numbers: [8008] 8008,12 unequal: No Solution Exploring Operation: 88+91=179, Resulting Numbers: [179] 179,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[18, 161], Operations: ['77-59=18', '73+88=161'] Exploring Operation: 18*161=2898, Resulting Numbers: [2898] 2898,12 unequal: No Solution Exploring Operation: 18+161=179, Resulting Numbers: [179] 179,12 unequal: No Solution Exploring Operation: 161-18=143, Resulting Numbers: [143] 143,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 69, 38, 35, 79 ]
63
[ "69+38=107", "79-35=44", "107-44=63" ]
Current State: 63:[69, 38, 35, 79], Operations: [] Exploring Operation: 69+38=107, Resulting Numbers: [35, 79, 107] Generated Node #2: [35, 79, 107] from Operation: 69+38=107 Current State: 63:[35, 79, 107], Operations: ['69+38=107'] Exploring Operation: 79-35=44, Resulting Numbers: [107, 44] Generated Node #3: [107, 44] from Operation: 79-35=44 Current State: 63:[107, 44], Operations: ['69+38=107', '79-35=44'] Exploring Operation: 107-44=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[69, 38, 35, 79], Operations: [] Exploring Operation: 38-35=3, Resulting Numbers: [69, 79, 3] Generated Node #0,0: 63:[69, 79, 3] Operation: 38-35=3 Exploring Operation: 69-38=31, Resulting Numbers: [35, 79, 31] Generated Node #0,1: 63:[35, 79, 31] Operation: 69-38=31 Exploring Operation: 79-69=10, Resulting Numbers: [38, 35, 10] Generated Node #0,2: 63:[38, 35, 10] Operation: 79-69=10 Exploring Operation: 38+35=73, Resulting Numbers: [69, 79, 73] Generated Node #0,3: 63:[69, 79, 73] Operation: 38+35=73 Moving to Node #0,0 Current State: 63:[69, 79, 3], Operations: ['38-35=3'] Exploring Operation: 69/3=23, Resulting Numbers: [79, 23] Generated Node #0,0,0: 63:[79, 23] Operation: 69/3=23 Exploring Operation: 79-3=76, Resulting Numbers: [69, 76] Generated Node #0,0,1: 63:[69, 76] Operation: 79-3=76 Exploring Operation: 79-69=10, Resulting Numbers: [3, 10] Generated Node #0,0,2: 63:[3, 10] Operation: 79-69=10 Exploring Operation: 69-3=66, Resulting Numbers: [79, 66] Generated Node #0,0,3: 63:[79, 66] Operation: 69-3=66 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[3, 10], Operations: ['38-35=3', '79-69=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,63 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[79, 23], Operations: ['38-35=3', '69/3=23'] Exploring Operation: 79*23=1817, Resulting Numbers: [1817] 1817,63 unequal: No Solution Exploring Operation: 79+23=102, Resulting Numbers: [102] 102,63 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[69, 76], Operations: ['38-35=3', '79-3=76'] Exploring Operation: 69*76=5244, Resulting Numbers: [5244] 5244,63 unequal: No Solution Exploring Operation: 76-69=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 69+76=145, Resulting Numbers: [145] 145,63 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:[79, 66], Operations: ['38-35=3', '69-3=66'] Exploring Operation: 79+66=145, Resulting Numbers: [145] 145,63 unequal: No Solution Exploring Operation: 79*66=5214, Resulting Numbers: [5214] 5214,63 unequal: No Solution Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,63 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:[69, 79, 73], Operations: ['38+35=73'] Exploring Operation: 69+79=148, Resulting Numbers: [73, 148] Generated Node #0,3,0: 63:[73, 148] Operation: 69+79=148 Exploring Operation: 73-69=4, Resulting Numbers: [79, 4] Generated Node #0,3,1: 63:[79, 4] Operation: 73-69=4 Exploring Operation: 79-73=6, Resulting Numbers: [69, 6] Generated Node #0,3,2: 63:[69, 6] Operation: 79-73=6 Exploring Operation: 79-69=10, Resulting Numbers: [73, 10] Generated Node #0,3,3: 63:[73, 10] Operation: 79-69=10 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 63:[69, 6], Operations: ['38+35=73', '79-73=6'] Exploring Operation: 69*6=414, Resulting Numbers: [414] 414,63 unequal: No Solution Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[69, 38, 35, 79], Operations: [] Exploring Operation: 38+35=73, Resulting Numbers: [69, 79, 73] Generated Node #0,3: 63:[69, 79, 73] Operation: 38+35=73 Moving to Node #0,3 Current State: 63:[69, 79, 73], Operations: ['38+35=73'] Exploring Operation: 79-73=6, Resulting Numbers: [69, 6] Generated Node #0,3,2: 63:[69, 6] Operation: 79-73=6 Moving to Node #0,3,2 Current State: 63:[69, 6], Operations: ['38+35=73', '79-73=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 64, 66, 60, 7 ]
55
[ "66-64=2", "60-7=53", "2+53=55" ]
Current State: 55:[64, 66, 60, 7], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [60, 7, 2] Generated Node #2: [60, 7, 2] from Operation: 66-64=2 Current State: 55:[60, 7, 2], Operations: ['66-64=2'] Exploring Operation: 60-7=53, Resulting Numbers: [2, 53] Generated Node #3: [2, 53] from Operation: 60-7=53 Current State: 55:[2, 53], Operations: ['66-64=2', '60-7=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[64, 66, 60, 7], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [60, 7, 2] Generated Node #0,0: 55:[60, 7, 2] Operation: 66-64=2 Moving to Node #0,0 Current State: 55:[60, 7, 2], Operations: ['66-64=2'] Exploring Operation: 60-7=53, Resulting Numbers: [2, 53] Generated Node #0,0,0: 55:[2, 53] Operation: 60-7=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[2, 53], Operations: ['66-64=2', '60-7=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[64, 66, 60, 7], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [60, 7, 2] Generated Node #0,0: 55:[60, 7, 2] Operation: 66-64=2 Moving to Node #0,0 Current State: 55:[60, 7, 2], Operations: ['66-64=2'] Exploring Operation: 60-7=53, Resulting Numbers: [2, 53] Generated Node #0,0,0: 55:[2, 53] Operation: 60-7=53 Moving to Node #0,0,0 Current State: 55:[2, 53], Operations: ['66-64=2', '60-7=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 70, 3, 50, 72 ]
51
[ "70+3=73", "72-50=22", "73-22=51" ]
Current State: 51:[70, 3, 50, 72], Operations: [] Exploring Operation: 70+3=73, Resulting Numbers: [50, 72, 73] Generated Node #2: [50, 72, 73] from Operation: 70+3=73 Current State: 51:[50, 72, 73], Operations: ['70+3=73'] Exploring Operation: 72-50=22, Resulting Numbers: [73, 22] Generated Node #3: [73, 22] from Operation: 72-50=22 Current State: 51:[73, 22], Operations: ['70+3=73', '72-50=22'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[70, 3, 50, 72], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [70, 3, 22] Generated Node #0,0: 51:[70, 3, 22] Operation: 72-50=22 Exploring Operation: 72/3=24, Resulting Numbers: [70, 50, 24] Generated Node #0,1: 51:[70, 50, 24] Operation: 72/3=24 Exploring Operation: 70-50=20, Resulting Numbers: [3, 72, 20] Generated Node #0,2: 51:[3, 72, 20] Operation: 70-50=20 Exploring Operation: 72-70=2, Resulting Numbers: [3, 50, 2] Generated Node #0,3: 51:[3, 50, 2] Operation: 72-70=2 Moving to Node #0,3 Current State: 51:[3, 50, 2], Operations: ['72-70=2'] Exploring Operation: 3+50=53, Resulting Numbers: [2, 53] Generated Node #0,3,0: 51:[2, 53] Operation: 3+50=53 Exploring Operation: 50+2=52, Resulting Numbers: [3, 52] Generated Node #0,3,1: 51:[3, 52] Operation: 50+2=52 Exploring Operation: 3-2=1, Resulting Numbers: [50, 1] Generated Node #0,3,2: 51:[50, 1] Operation: 3-2=1 Exploring Operation: 3+2=5, Resulting Numbers: [50, 5] Generated Node #0,3,3: 51:[50, 5] Operation: 3+2=5 Moving to Node #0,2 Current State: 51:[3, 72, 20], Operations: ['70-50=20'] Exploring Operation: 72-3=69, Resulting Numbers: [20, 69] Generated Node #0,2,0: 51:[20, 69] Operation: 72-3=69 Exploring Operation: 72/3=24, Resulting Numbers: [20, 24] Generated Node #0,2,1: 51:[20, 24] Operation: 72/3=24 Exploring Operation: 72-20=52, Resulting Numbers: [3, 52] Generated Node #0,2,2: 51:[3, 52] Operation: 72-20=52 Exploring Operation: 20-3=17, Resulting Numbers: [72, 17] Generated Node #0,2,3: 51:[72, 17] Operation: 20-3=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 51:[3, 52], Operations: ['70-50=20', '72-20=52'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,51 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[20, 24], Operations: ['70-50=20', '72/3=24'] Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,51 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 51:[20, 69], Operations: ['70-50=20', '72-3=69'] Exploring Operation: 20+69=89, Resulting Numbers: [89] 89,51 unequal: No Solution Exploring Operation: 69-20=49, Resulting Numbers: [49] 49,51 unequal: No Solution Exploring Operation: 20*69=1380, Resulting Numbers: [1380] 1380,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 51:[72, 17], Operations: ['70-50=20', '20-3=17'] Exploring Operation: 72-17=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 72+17=89, Resulting Numbers: [89] 89,51 unequal: No Solution Exploring Operation: 72*17=1224, Resulting Numbers: [1224] 1224,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 51:[70, 3, 22], Operations: ['72-50=22'] Exploring Operation: 70+3=73, Resulting Numbers: [22, 73] Generated Node #0,0,0: 51:[22, 73] Operation: 70+3=73 Exploring Operation: 70-3=67, Resulting Numbers: [22, 67] Generated Node #0,0,1: 51:[22, 67] Operation: 70-3=67 Exploring Operation: 22-3=19, Resulting Numbers: [70, 19] Generated Node #0,0,2: 51:[70, 19] Operation: 22-3=19 Exploring Operation: 70-22=48, Resulting Numbers: [3, 48] Generated Node #0,0,3: 51:[3, 48] Operation: 70-22=48 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 51:[3, 48], Operations: ['72-50=22', '70-22=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[70, 3, 50, 72], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [70, 3, 22] Generated Node #0,0: 51:[70, 3, 22] Operation: 72-50=22 Moving to Node #0,0 Current State: 51:[70, 3, 22], Operations: ['72-50=22'] Exploring Operation: 70-22=48, Resulting Numbers: [3, 48] Generated Node #0,0,3: 51:[3, 48] Operation: 70-22=48 Moving to Node #0,0,3 Current State: 51:[3, 48], Operations: ['72-50=22', '70-22=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 98, 65, 2, 47 ]
19
[ "98-65=33", "2*33=66", "66-47=19" ]
Current State: 19:[98, 65, 2, 47], Operations: [] Exploring Operation: 98-65=33, Resulting Numbers: [2, 47, 33] Generated Node #2: [2, 47, 33] from Operation: 98-65=33 Current State: 19:[2, 47, 33], Operations: ['98-65=33'] Exploring Operation: 2*33=66, Resulting Numbers: [47, 66] Generated Node #3: [47, 66] from Operation: 2*33=66 Current State: 19:[47, 66], Operations: ['98-65=33', '2*33=66'] Exploring Operation: 66-47=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[98, 65, 2, 47], Operations: [] Exploring Operation: 98-65=33, Resulting Numbers: [2, 47, 33] Generated Node #0,0: 19:[2, 47, 33] Operation: 98-65=33 Moving to Node #0,0 Current State: 19:[2, 47, 33], Operations: ['98-65=33'] Exploring Operation: 47-33=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 19:[2, 14] Operation: 47-33=14 Moving to Node #0,0,0 Current State: 19:[2, 14], Operations: ['98-65=33', '47-33=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,19 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 21, 6, 2, 88 ]
80
[ "6+2=8", "21*8=168", "168-88=80" ]
Current State: 80:[21, 6, 2, 88], Operations: [] Exploring Operation: 6+2=8, Resulting Numbers: [21, 88, 8] Generated Node #2: [21, 88, 8] from Operation: 6+2=8 Current State: 80:[21, 88, 8], Operations: ['6+2=8'] Exploring Operation: 21*8=168, Resulting Numbers: [88, 168] Generated Node #3: [88, 168] from Operation: 21*8=168 Current State: 80:[88, 168], Operations: ['6+2=8', '21*8=168'] Exploring Operation: 168-88=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[21, 6, 2, 88], Operations: [] Exploring Operation: 88-2=86, Resulting Numbers: [21, 6, 86] Generated Node #0,0: 80:[21, 6, 86] Operation: 88-2=86 Exploring Operation: 88-6=82, Resulting Numbers: [21, 2, 82] Generated Node #0,1: 80:[21, 2, 82] Operation: 88-6=82 Exploring Operation: 21-6=15, Resulting Numbers: [2, 88, 15] Generated Node #0,2: 80:[2, 88, 15] Operation: 21-6=15 Exploring Operation: 88/2=44, Resulting Numbers: [21, 6, 44] Generated Node #0,3: 80:[21, 6, 44] Operation: 88/2=44 Moving to Node #0,1 Current State: 80:[21, 2, 82], Operations: ['88-6=82'] Exploring Operation: 82/2=41, Resulting Numbers: [21, 41] Generated Node #0,1,0: 80:[21, 41] Operation: 82/2=41 Exploring Operation: 21*2=42, Resulting Numbers: [82, 42] Generated Node #0,1,1: 80:[82, 42] Operation: 21*2=42 Exploring Operation: 21-2=19, Resulting Numbers: [82, 19] Generated Node #0,1,2: 80:[82, 19] Operation: 21-2=19 Exploring Operation: 82-2=80, Resulting Numbers: [21, 80] Generated Node #0,1,3: 80:[21, 80] Operation: 82-2=80 Moving to Node #0,3 Current State: 80:[21, 6, 44], Operations: ['88/2=44'] Exploring Operation: 44-21=23, Resulting Numbers: [6, 23] Generated Node #0,3,0: 80:[6, 23] Operation: 44-21=23 Exploring Operation: 21-6=15, Resulting Numbers: [44, 15] Generated Node #0,3,1: 80:[44, 15] Operation: 21-6=15 Exploring Operation: 21+6=27, Resulting Numbers: [44, 27] Generated Node #0,3,2: 80:[44, 27] Operation: 21+6=27 Exploring Operation: 44-6=38, Resulting Numbers: [21, 38] Generated Node #0,3,3: 80:[21, 38] Operation: 44-6=38 Moving to Node #0,0 Current State: 80:[21, 6, 86], Operations: ['88-2=86'] Exploring Operation: 21-6=15, Resulting Numbers: [86, 15] Generated Node #0,0,0: 80:[86, 15] Operation: 21-6=15 Exploring Operation: 21+6=27, Resulting Numbers: [86, 27] Generated Node #0,0,1: 80:[86, 27] Operation: 21+6=27 Exploring Operation: 86-6=80, Resulting Numbers: [21, 80] Generated Node #0,0,2: 80:[21, 80] Operation: 86-6=80 Exploring Operation: 6+86=92, Resulting Numbers: [21, 92] Generated Node #0,0,3: 80:[21, 92] Operation: 6+86=92 Moving to Node #0,2 Current State: 80:[2, 88, 15], Operations: ['21-6=15'] Exploring Operation: 2+15=17, Resulting Numbers: [88, 17] Generated Node #0,2,0: 80:[88, 17] Operation: 2+15=17 Exploring Operation: 88-15=73, Resulting Numbers: [2, 73] Generated Node #0,2,1: 80:[2, 73] Operation: 88-15=73 Exploring Operation: 88-2=86, Resulting Numbers: [15, 86] Generated Node #0,2,2: 80:[15, 86] Operation: 88-2=86 Exploring Operation: 88/2=44, Resulting Numbers: [15, 44] Generated Node #0,2,3: 80:[15, 44] Operation: 88/2=44 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[15, 44], Operations: ['21-6=15', '88/2=44'] Exploring Operation: 15+44=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 15*44=660, Resulting Numbers: [660] 660,80 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:[2, 73], Operations: ['21-6=15', '88-15=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,80 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,80 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 #0,2,2 Current State: 80:[15, 86], Operations: ['21-6=15', '88-2=86'] Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 15+86=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 15*86=1290, Resulting Numbers: [1290] 1290,80 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:[88, 17], Operations: ['21-6=15', '2+15=17'] Exploring Operation: 88+17=105, Resulting Numbers: [105] 105,80 unequal: No Solution Exploring Operation: 88*17=1496, Resulting Numbers: [1496] 1496,80 unequal: No Solution Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,80 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: 80:[21, 80], Operations: ['88-6=82', '82-2=80'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 21+80=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 21*80=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[21, 80], Operations: ['88-2=86', '86-6=80'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 21*80=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Exploring Operation: 21+80=101, Resulting Numbers: [101] 101,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[21, 41], Operations: ['88-6=82', '82/2=41'] Exploring Operation: 21*41=861, Resulting Numbers: [861] 861,80 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 21+41=62, Resulting Numbers: [62] 62,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[82, 19], Operations: ['88-6=82', '21-2=19'] Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,80 unequal: No Solution Exploring Operation: 82*19=1558, Resulting Numbers: [1558] 1558,80 unequal: No Solution Exploring Operation: 82+19=101, Resulting Numbers: [101] 101,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[21, 38], Operations: ['88/2=44', '44-6=38'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 21*38=798, Resulting Numbers: [798] 798,80 unequal: No Solution Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[6, 23], Operations: ['88/2=44', '44-21=23'] Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,80 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[82, 42], Operations: ['88-6=82', '21*2=42'] Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 82*42=3444, Resulting Numbers: [3444] 3444,80 unequal: No Solution Exploring Operation: 82+42=124, Resulting Numbers: [124] 124,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[44, 15], Operations: ['88/2=44', '21-6=15'] Exploring Operation: 44+15=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 44*15=660, Resulting Numbers: [660] 660,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[86, 15], Operations: ['88-2=86', '21-6=15'] Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,80 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[44, 27], Operations: ['88/2=44', '21+6=27'] Exploring Operation: 44*27=1188, Resulting Numbers: [1188] 1188,80 unequal: No Solution Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[21, 92], Operations: ['88-2=86', '6+86=92'] Exploring Operation: 21*92=1932, Resulting Numbers: [1932] 1932,80 unequal: No Solution Exploring Operation: 92-21=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 21+92=113, Resulting Numbers: [113] 113,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[86, 27], Operations: ['88-2=86', '21+6=27'] Exploring Operation: 86*27=2322, Resulting Numbers: [2322] 2322,80 unequal: No Solution Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 86+27=113, Resulting Numbers: [113] 113,80 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 30, 85, 78, 50 ]
45
[ "78*50=3900", "3900/30=130", "130-85=45" ]
Current State: 45:[30, 85, 78, 50], Operations: [] Exploring Operation: 78*50=3900, Resulting Numbers: [30, 85, 3900] Generated Node #2: [30, 85, 3900] from Operation: 78*50=3900 Current State: 45:[30, 85, 3900], Operations: ['78*50=3900'] Exploring Operation: 3900/30=130, Resulting Numbers: [85, 130] Generated Node #3: [85, 130] from Operation: 3900/30=130 Current State: 45:[85, 130], Operations: ['78*50=3900', '3900/30=130'] Exploring Operation: 130-85=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[30, 85, 78, 50], Operations: [] Exploring Operation: 85-30=55, Resulting Numbers: [78, 50, 55] Generated Node #0,0: 45:[78, 50, 55] Operation: 85-30=55 Exploring Operation: 85-78=7, Resulting Numbers: [30, 50, 7] Generated Node #0,1: 45:[30, 50, 7] Operation: 85-78=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[30, 50, 7], Operations: ['85-78=7'] Exploring Operation: 50-30=20, Resulting Numbers: [7, 20] Generated Node #0,1,0: 45:[7, 20] Operation: 50-30=20 Exploring Operation: 30+7=37, Resulting Numbers: [50, 37] Generated Node #0,1,1: 45:[50, 37] Operation: 30+7=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[7, 20], Operations: ['85-78=7', '50-30=20'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[50, 37], Operations: ['85-78=7', '30+7=37'] Exploring Operation: 50+37=87, Resulting Numbers: [87] 87,45 unequal: No Solution Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[78, 50, 55], Operations: ['85-30=55'] Exploring Operation: 78-50=28, Resulting Numbers: [55, 28] Generated Node #0,0,0: 45:[55, 28] Operation: 78-50=28 Exploring Operation: 78-55=23, Resulting Numbers: [50, 23] Generated Node #0,0,1: 45:[50, 23] Operation: 78-55=23 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[50, 23], Operations: ['85-30=55', '78-55=23'] Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,45 unequal: No Solution Exploring Operation: 50+23=73, Resulting Numbers: [73] 73,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[55, 28], Operations: ['85-30=55', '78-50=28'] Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,45 unequal: No Solution Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 7, 79, 17, 88 ]
19
[ "7+79=86", "17+88=105", "105-86=19" ]
Current State: 19:[7, 79, 17, 88], Operations: [] Exploring Operation: 7+79=86, Resulting Numbers: [17, 88, 86] Generated Node #2: [17, 88, 86] from Operation: 7+79=86 Current State: 19:[17, 88, 86], Operations: ['7+79=86'] Exploring Operation: 17+88=105, Resulting Numbers: [86, 105] Generated Node #3: [86, 105] from Operation: 17+88=105 Current State: 19:[86, 105], Operations: ['7+79=86', '17+88=105'] Exploring Operation: 105-86=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[7, 79, 17, 88], Operations: [] Exploring Operation: 88-79=9, Resulting Numbers: [7, 17, 9] Generated Node #0,0: 19:[7, 17, 9] Operation: 88-79=9 Exploring Operation: 88-17=71, Resulting Numbers: [7, 79, 71] Generated Node #0,1: 19:[7, 79, 71] Operation: 88-17=71 Exploring Operation: 88-7=81, Resulting Numbers: [79, 17, 81] Generated Node #0,2: 19:[79, 17, 81] Operation: 88-7=81 Exploring Operation: 79-7=72, Resulting Numbers: [17, 88, 72] Generated Node #0,3: 19:[17, 88, 72] Operation: 79-7=72 Exploring Operation: 79-17=62, Resulting Numbers: [7, 88, 62] Generated Node #0,4: 19:[7, 88, 62] Operation: 79-17=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[7, 17, 9], Operations: ['88-79=9'] Exploring Operation: 7+9=16, Resulting Numbers: [17, 16] Generated Node #0,0,0: 19:[17, 16] Operation: 7+9=16 Exploring Operation: 9-7=2, Resulting Numbers: [17, 2] Generated Node #0,0,1: 19:[17, 2] Operation: 9-7=2 Exploring Operation: 7+17=24, Resulting Numbers: [9, 24] Generated Node #0,0,2: 19:[9, 24] Operation: 7+17=24 Exploring Operation: 17-7=10, Resulting Numbers: [9, 10] Generated Node #0,0,3: 19:[9, 10] Operation: 17-7=10 Exploring Operation: 17+9=26, Resulting Numbers: [7, 26] Generated Node #0,0,4: 19:[7, 26] Operation: 17+9=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[17, 16], Operations: ['88-79=9', '7+9=16'] Exploring Operation: 17+16=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 17*16=272, Resulting Numbers: [272] 272,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 19:[9, 24], Operations: ['88-79=9', '7+17=24'] Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 19:[17, 2], Operations: ['88-79=9', '9-7=2'] Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[7, 79, 17, 88], Operations: [] Exploring Operation: 88-79=9, Resulting Numbers: [7, 17, 9] Generated Node #0,0: 19:[7, 17, 9] Operation: 88-79=9 Moving to Node #0,0 Current State: 19:[7, 17, 9], Operations: ['88-79=9'] Exploring Operation: 9-7=2, Resulting Numbers: [17, 2] Generated Node #0,0,1: 19:[17, 2] Operation: 9-7=2 Moving to Node #0,0,1 Current State: 19:[17, 2], Operations: ['88-79=9', '9-7=2'] Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 21, 64, 13, 24 ]
25
[ "24-21=3", "13*3=39", "64-39=25" ]
Current State: 25:[21, 64, 13, 24], Operations: [] Exploring Operation: 24-21=3, Resulting Numbers: [64, 13, 3] Generated Node #2: [64, 13, 3] from Operation: 24-21=3 Current State: 25:[64, 13, 3], Operations: ['24-21=3'] Exploring Operation: 13*3=39, Resulting Numbers: [64, 39] Generated Node #3: [64, 39] from Operation: 13*3=39 Current State: 25:[64, 39], Operations: ['24-21=3', '13*3=39'] Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[21, 64, 13, 24], Operations: [] Exploring Operation: 64-24=40, Resulting Numbers: [21, 13, 40] Generated Node #0,0: 25:[21, 13, 40] Operation: 64-24=40 Exploring Operation: 64-13=51, Resulting Numbers: [21, 24, 51] Generated Node #0,1: 25:[21, 24, 51] Operation: 64-13=51 Exploring Operation: 64-21=43, Resulting Numbers: [13, 24, 43] Generated Node #0,2: 25:[13, 24, 43] Operation: 64-21=43 Moving to Node #0,0 Current State: 25:[21, 13, 40], Operations: ['64-24=40'] Exploring Operation: 40-21=19, Resulting Numbers: [13, 19] Generated Node #0,0,0: 25:[13, 19] Operation: 40-21=19 Exploring Operation: 40-13=27, Resulting Numbers: [21, 27] Generated Node #0,0,1: 25:[21, 27] Operation: 40-13=27 Exploring Operation: 21-13=8, Resulting Numbers: [40, 8] Generated Node #0,0,2: 25:[40, 8] Operation: 21-13=8 Moving to Node #0,2 Current State: 25:[13, 24, 43], Operations: ['64-21=43'] Exploring Operation: 43-13=30, Resulting Numbers: [24, 30] Generated Node #0,2,0: 25:[24, 30] Operation: 43-13=30 Exploring Operation: 43-24=19, Resulting Numbers: [13, 19] Generated Node #0,2,1: 25:[13, 19] Operation: 43-24=19 Exploring Operation: 24-13=11, Resulting Numbers: [43, 11] Generated Node #0,2,2: 25:[43, 11] Operation: 24-13=11 Moving to Node #0,1 Current State: 25:[21, 24, 51], Operations: ['64-13=51'] Exploring Operation: 51-21=30, Resulting Numbers: [24, 30] Generated Node #0,1,0: 25:[24, 30] Operation: 51-21=30 Exploring Operation: 24-21=3, Resulting Numbers: [51, 3] Generated Node #0,1,1: 25:[51, 3] Operation: 24-21=3 Exploring Operation: 51-24=27, Resulting Numbers: [21, 27] Generated Node #0,1,2: 25:[21, 27] Operation: 51-24=27 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 25:[24, 30], Operations: ['64-13=51', '51-21=30'] Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 25:[21, 27], Operations: ['64-13=51', '51-24=27'] Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,25 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[51, 3], Operations: ['64-13=51', '24-21=3'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,25 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,25 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: 25:[21, 27], Operations: ['64-24=40', '40-13=27'] Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,25 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[24, 30], Operations: ['64-21=43', '43-13=30'] Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,25 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,25 unequal: No Solution Moving to Node #0,2,1 Current State: 25:[13, 19], Operations: ['64-21=43', '43-24=19'] Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 13*19=247, Resulting Numbers: [247] 247,25 unequal: No Solution Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[13, 19], Operations: ['64-24=40', '40-21=19'] Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,25 unequal: No Solution Exploring Operation: 13*19=247, Resulting Numbers: [247] 247,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[40, 8], Operations: ['64-24=40', '21-13=8'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,25 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[43, 11], Operations: ['64-21=43', '24-13=11'] Exploring Operation: 43*11=473, Resulting Numbers: [473] 473,25 unequal: No Solution Exploring Operation: 43+11=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,25 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 10, 2, 85, 29 ]
52
[ "85-10=75", "29+75=104", "104/2=52" ]
Current State: 52:[10, 2, 85, 29], Operations: [] Exploring Operation: 85-10=75, Resulting Numbers: [2, 29, 75] Generated Node #2: [2, 29, 75] from Operation: 85-10=75 Current State: 52:[2, 29, 75], Operations: ['85-10=75'] Exploring Operation: 29+75=104, Resulting Numbers: [2, 104] Generated Node #3: [2, 104] from Operation: 29+75=104 Current State: 52:[2, 104], Operations: ['85-10=75', '29+75=104'] Exploring Operation: 104/2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[10, 2, 85, 29], Operations: [] Exploring Operation: 10+2=12, Resulting Numbers: [85, 29, 12] Generated Node #0,0: 52:[85, 29, 12] Operation: 10+2=12 Exploring Operation: 85-2=83, Resulting Numbers: [10, 29, 83] Generated Node #0,1: 52:[10, 29, 83] Operation: 85-2=83 Exploring Operation: 85-29=56, Resulting Numbers: [10, 2, 56] Generated Node #0,2: 52:[10, 2, 56] Operation: 85-29=56 Exploring Operation: 10/2=5, Resulting Numbers: [85, 29, 5] Generated Node #0,3: 52:[85, 29, 5] Operation: 10/2=5 Exploring Operation: 85-10=75, Resulting Numbers: [2, 29, 75] Generated Node #0,4: 52:[2, 29, 75] Operation: 85-10=75 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[10, 2, 56], Operations: ['85-29=56'] Exploring Operation: 56/2=28, Resulting Numbers: [10, 28] Generated Node #0,2,0: 52:[10, 28] Operation: 56/2=28 Exploring Operation: 10/2=5, Resulting Numbers: [56, 5] Generated Node #0,2,1: 52:[56, 5] Operation: 10/2=5 Exploring Operation: 56-2=54, Resulting Numbers: [10, 54] Generated Node #0,2,2: 52:[10, 54] Operation: 56-2=54 Exploring Operation: 10+2=12, Resulting Numbers: [56, 12] Generated Node #0,2,3: 52:[56, 12] Operation: 10+2=12 Exploring Operation: 56-10=46, Resulting Numbers: [2, 46] Generated Node #0,2,4: 52:[2, 46] Operation: 56-10=46 Moving to Node #0,2,0 Current State: 52:[10, 28], Operations: ['85-29=56', '56/2=28'] Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,52 unequal: No Solution Exploring Operation: 10*28=280, Resulting Numbers: [280] 280,52 unequal: No Solution Exploring Operation: 10+28=38, Resulting Numbers: [38] 38,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[10, 54], Operations: ['85-29=56', '56-2=54'] Exploring Operation: 54-10=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 10*54=540, Resulting Numbers: [540] 540,52 unequal: No Solution Exploring Operation: 10+54=64, Resulting Numbers: [64] 64,52 unequal: No Solution Moving to Node #0,2,1 Current State: 52:[56, 5], Operations: ['85-29=56', '10/2=5'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 56*5=280, Resulting Numbers: [280] 280,52 unequal: No Solution Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,2,3 Current State: 52:[56, 12], Operations: ['85-29=56', '10+2=12'] Exploring Operation: 56+12=68, Resulting Numbers: [68] 68,52 unequal: No Solution Exploring Operation: 56-12=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 56*12=672, Resulting Numbers: [672] 672,52 unequal: No Solution Moving to Node #0,2,4 Current State: 52:[2, 46], Operations: ['85-29=56', '56-10=46'] Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 52:[2, 29, 75], Operations: ['85-10=75'] Exploring Operation: 2+29=31, Resulting Numbers: [75, 31] Generated Node #0,4,0: 52:[75, 31] Operation: 2+29=31 Exploring Operation: 75-29=46, Resulting Numbers: [2, 46] Generated Node #0,4,1: 52:[2, 46] Operation: 75-29=46 Exploring Operation: 2+75=77, Resulting Numbers: [29, 77] Generated Node #0,4,2: 52:[29, 77] Operation: 2+75=77 Exploring Operation: 29-2=27, Resulting Numbers: [75, 27] Generated Node #0,4,3: 52:[75, 27] Operation: 29-2=27 Exploring Operation: 75-2=73, Resulting Numbers: [29, 73] Generated Node #0,4,4: 52:[29, 73] Operation: 75-2=73 Moving to Node #0,4,1 Current State: 52:[2, 46], Operations: ['85-10=75', '75-29=46'] Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,52 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,52 unequal: No Solution Moving to Node #0,4,4 Current State: 52:[29, 73], Operations: ['85-10=75', '75-2=73'] Exploring Operation: 73-29=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 29*73=2117, Resulting Numbers: [2117] 2117,52 unequal: No Solution Exploring Operation: 29+73=102, Resulting Numbers: [102] 102,52 unequal: No Solution Moving to Node #0,4,3 Current State: 52:[75, 27], Operations: ['85-10=75', '29-2=27'] Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 75+27=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 75*27=2025, Resulting Numbers: [2025] 2025,52 unequal: No Solution Moving to Node #0,4,0 Current State: 52:[75, 31], Operations: ['85-10=75', '2+29=31'] Exploring Operation: 75-31=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 75+31=106, Resulting Numbers: [106] 106,52 unequal: No Solution Exploring Operation: 75*31=2325, Resulting Numbers: [2325] 2325,52 unequal: No Solution Moving to Node #0,4,2 Current State: 52:[29, 77], Operations: ['85-10=75', '2+75=77'] Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 29+77=106, Resulting Numbers: [106] 106,52 unequal: No Solution Exploring Operation: 29*77=2233, Resulting Numbers: [2233] 2233,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[85, 29, 12], Operations: ['10+2=12'] Exploring Operation: 85-29=56, Resulting Numbers: [12, 56] Generated Node #0,0,0: 52:[12, 56] Operation: 85-29=56 Exploring Operation: 29+12=41, Resulting Numbers: [85, 41] Generated Node #0,0,1: 52:[85, 41] Operation: 29+12=41 Exploring Operation: 85-12=73, Resulting Numbers: [29, 73] Generated Node #0,0,2: 52:[29, 73] Operation: 85-12=73 Exploring Operation: 85+12=97, Resulting Numbers: [29, 97] Generated Node #0,0,3: 52:[29, 97] Operation: 85+12=97 Exploring Operation: 29-12=17, Resulting Numbers: [85, 17] Generated Node #0,0,4: 52:[85, 17] Operation: 29-12=17 Moving to Node #0,0,0 Current State: 52:[12, 56], Operations: ['10+2=12', '85-29=56'] Exploring Operation: 12*56=672, Resulting Numbers: [672] 672,52 unequal: No Solution Exploring Operation: 12+56=68, Resulting Numbers: [68] 68,52 unequal: No Solution Exploring Operation: 56-12=44, Resulting Numbers: [44] 44,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[29, 73], Operations: ['10+2=12', '85-12=73'] Exploring Operation: 29+73=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 29*73=2117, Resulting Numbers: [2117] 2117,52 unequal: No Solution Exploring Operation: 73-29=44, Resulting Numbers: [44] 44,52 unequal: No Solution Moving to Node #0,0,4 Current State: 52:[85, 17], Operations: ['10+2=12', '29-12=17'] Exploring Operation: 85-17=68, Resulting Numbers: [68] 68,52 unequal: No Solution Exploring Operation: 85+17=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 85*17=1445, Resulting Numbers: [1445] 1445,52 unequal: No Solution Exploring Operation: 85/17=5, Resulting Numbers: [5] 5,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[85, 41], Operations: ['10+2=12', '29+12=41'] Exploring Operation: 85+41=126, Resulting Numbers: [126] 126,52 unequal: No Solution Exploring Operation: 85-41=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 85*41=3485, Resulting Numbers: [3485] 3485,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[29, 97], Operations: ['10+2=12', '85+12=97'] Exploring Operation: 29*97=2813, Resulting Numbers: [2813] 2813,52 unequal: No Solution Exploring Operation: 29+97=126, Resulting Numbers: [126] 126,52 unequal: No Solution Exploring Operation: 97-29=68, Resulting Numbers: [68] 68,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[10, 29, 83], Operations: ['85-2=83'] Exploring Operation: 83-10=73, Resulting Numbers: [29, 73] Generated Node #0,1,0: 52:[29, 73] Operation: 83-10=73 Exploring Operation: 10+83=93, Resulting Numbers: [29, 93] Generated Node #0,1,1: 52:[29, 93] Operation: 10+83=93 Exploring Operation: 29-10=19, Resulting Numbers: [83, 19] Generated Node #0,1,2: 52:[83, 19] Operation: 29-10=19 Exploring Operation: 83-29=54, Resulting Numbers: [10, 54] Generated Node #0,1,3: 52:[10, 54] Operation: 83-29=54 Exploring Operation: 10+29=39, Resulting Numbers: [83, 39] Generated Node #0,1,4: 52:[83, 39] Operation: 10+29=39 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 52:[10, 54], Operations: ['85-2=83', '83-29=54'] Exploring Operation: 54-10=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 10+54=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 10*54=540, Resulting Numbers: [540] 540,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[29, 73], Operations: ['85-2=83', '83-10=73'] Exploring Operation: 29*73=2117, Resulting Numbers: [2117] 2117,52 unequal: No Solution Exploring Operation: 29+73=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 73-29=44, Resulting Numbers: [44] 44,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[83, 19], Operations: ['85-2=83', '29-10=19'] Exploring Operation: 83-19=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 83+19=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 83*19=1577, Resulting Numbers: [1577] 1577,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[29, 93], Operations: ['85-2=83', '10+83=93'] Exploring Operation: 29+93=122, Resulting Numbers: [122] 122,52 unequal: No Solution Exploring Operation: 93-29=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 29*93=2697, Resulting Numbers: [2697] 2697,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 52:[83, 39], Operations: ['85-2=83', '10+29=39'] Exploring Operation: 83+39=122, Resulting Numbers: [122] 122,52 unequal: No Solution Exploring Operation: 83*39=3237, Resulting Numbers: [3237] 3237,52 unequal: No Solution Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[85, 29, 5], Operations: ['10/2=5'] Exploring Operation: 85/5=17, Resulting Numbers: [29, 17] Generated Node #0,3,0: 52:[29, 17] Operation: 85/5=17 Exploring Operation: 29-5=24, Resulting Numbers: [85, 24] Generated Node #0,3,1: 52:[85, 24] Operation: 29-5=24 Exploring Operation: 85-29=56, Resulting Numbers: [5, 56] Generated Node #0,3,2: 52:[5, 56] Operation: 85-29=56 Exploring Operation: 85-5=80, Resulting Numbers: [29, 80] Generated Node #0,3,3: 52:[29, 80] Operation: 85-5=80 Exploring Operation: 85+5=90, Resulting Numbers: [29, 90] Generated Node #0,3,4: 52:[29, 90] Operation: 85+5=90 Moving to Node #0,3,2 Current State: 52:[5, 56], Operations: ['10/2=5', '85-29=56'] Exploring Operation: 5+56=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 5*56=280, Resulting Numbers: [280] 280,52 unequal: No Solution Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,52 unequal: No Solution Moving to Node #0,3,0 Current State: 52:[29, 17], Operations: ['10/2=5', '85/5=17'] Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,52 unequal: No Solution Exploring Operation: 29*17=493, Resulting Numbers: [493] 493,52 unequal: No Solution Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[29, 80], Operations: ['10/2=5', '85-5=80'] Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 29+80=109, Resulting Numbers: [109] 109,52 unequal: No Solution Exploring Operation: 29*80=2320, Resulting Numbers: [2320] 2320,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[85, 24], Operations: ['10/2=5', '29-5=24'] Exploring Operation: 85+24=109, Resulting Numbers: [109] 109,52 unequal: No Solution Exploring Operation: 85*24=2040, Resulting Numbers: [2040] 2040,52 unequal: No Solution Exploring Operation: 85-24=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,3,4 Current State: 52:[29, 90], Operations: ['10/2=5', '85+5=90'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 29+90=119, Resulting Numbers: [119] 119,52 unequal: No Solution Exploring Operation: 29*90=2610, Resulting Numbers: [2610] 2610,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 88, 32, 29, 88 ]
62
[ "88/88=1", "32+29=61", "1+61=62" ]
Current State: 62:[88, 32, 29, 88], Operations: [] Exploring Operation: 88/88=1, Resulting Numbers: [32, 29, 1] Generated Node #2: [32, 29, 1] from Operation: 88/88=1 Current State: 62:[32, 29, 1], Operations: ['88/88=1'] Exploring Operation: 32+29=61, Resulting Numbers: [1, 61] Generated Node #3: [1, 61] from Operation: 32+29=61 Current State: 62:[1, 61], Operations: ['88/88=1', '32+29=61'] Exploring Operation: 1+61=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[88, 32, 29, 88], Operations: [] Exploring Operation: 88/88=1, Resulting Numbers: [32, 29, 1] Generated Node #0,0: 62:[32, 29, 1] Operation: 88/88=1 Exploring Operation: 88-88=0, Resulting Numbers: [32, 29, 0] Generated Node #0,1: 62:[32, 29, 0] Operation: 88-88=0 Exploring Operation: 88-29=59, Resulting Numbers: [88, 32, 59] Generated Node #0,2: 62:[88, 32, 59] Operation: 88-29=59 Exploring Operation: 88-29=59, Resulting Numbers: [32, 88, 59] Generated Node #0,3: 62:[32, 88, 59] Operation: 88-29=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[32, 29, 1], Operations: ['88/88=1'] Exploring Operation: 32+29=61, Resulting Numbers: [1, 61] Generated Node #0,0,0: 62:[1, 61] Operation: 32+29=61 Exploring Operation: 32-1=31, Resulting Numbers: [29, 31] Generated Node #0,0,1: 62:[29, 31] Operation: 32-1=31 Exploring Operation: 32-29=3, Resulting Numbers: [1, 3] Generated Node #0,0,2: 62:[1, 3] Operation: 32-29=3 Exploring Operation: 29+1=30, Resulting Numbers: [32, 30] Generated Node #0,0,3: 62:[32, 30] Operation: 29+1=30 Moving to Node #0,0,0 Current State: 62:[1, 61], Operations: ['88/88=1', '32+29=61'] Exploring Operation: 1*61=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 1+61=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[88, 32, 29, 88], Operations: [] Exploring Operation: 88/88=1, Resulting Numbers: [32, 29, 1] Generated Node #0,0: 62:[32, 29, 1] Operation: 88/88=1 Moving to Node #0,0 Current State: 62:[32, 29, 1], Operations: ['88/88=1'] Exploring Operation: 32+29=61, Resulting Numbers: [1, 61] Generated Node #0,0,0: 62:[1, 61] Operation: 32+29=61 Moving to Node #0,0,0 Current State: 62:[1, 61], Operations: ['88/88=1', '32+29=61'] Exploring Operation: 1+61=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 75, 61, 60, 64 ]
85
[ "64-61=3", "75/3=25", "60+25=85" ]
Current State: 85:[75, 61, 60, 64], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [75, 60, 3] Generated Node #2: [75, 60, 3] from Operation: 64-61=3 Current State: 85:[75, 60, 3], Operations: ['64-61=3'] Exploring Operation: 75/3=25, Resulting Numbers: [60, 25] Generated Node #3: [60, 25] from Operation: 75/3=25 Current State: 85:[60, 25], Operations: ['64-61=3', '75/3=25'] Exploring Operation: 60+25=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[75, 61, 60, 64], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [75, 60, 3] Generated Node #0,0: 85:[75, 60, 3] Operation: 64-61=3 Exploring Operation: 64-60=4, Resulting Numbers: [75, 61, 4] Generated Node #0,1: 85:[75, 61, 4] Operation: 64-60=4 Exploring Operation: 75-60=15, Resulting Numbers: [61, 64, 15] Generated Node #0,2: 85:[61, 64, 15] Operation: 75-60=15 Exploring Operation: 75-61=14, Resulting Numbers: [60, 64, 14] Generated Node #0,3: 85:[60, 64, 14] Operation: 75-61=14 Exploring Operation: 61-60=1, Resulting Numbers: [75, 64, 1] Generated Node #0,4: 85:[75, 64, 1] Operation: 61-60=1 Moving to Node #0,1 Current State: 85:[75, 61, 4], Operations: ['64-60=4'] Exploring Operation: 61+4=65, Resulting Numbers: [75, 65] Generated Node #0,1,0: 85:[75, 65] Operation: 61+4=65 Exploring Operation: 61-4=57, Resulting Numbers: [75, 57] Generated Node #0,1,1: 85:[75, 57] Operation: 61-4=57 Exploring Operation: 75-61=14, Resulting Numbers: [4, 14] Generated Node #0,1,2: 85:[4, 14] Operation: 75-61=14 Exploring Operation: 75-4=71, Resulting Numbers: [61, 71] Generated Node #0,1,3: 85:[61, 71] Operation: 75-4=71 Exploring Operation: 75+4=79, Resulting Numbers: [61, 79] Generated Node #0,1,4: 85:[61, 79] Operation: 75+4=79 Moving to Node #0,4 Current State: 85:[75, 64, 1], Operations: ['61-60=1'] Exploring Operation: 75+1=76, Resulting Numbers: [64, 76] Generated Node #0,4,0: 85:[64, 76] Operation: 75+1=76 Exploring Operation: 75/1=75, Resulting Numbers: [64, 75] Generated Node #0,4,1: 85:[64, 75] Operation: 75/1=75 Exploring Operation: 75-64=11, Resulting Numbers: [1, 11] Generated Node #0,4,2: 85:[1, 11] Operation: 75-64=11 Exploring Operation: 64+1=65, Resulting Numbers: [75, 65] Generated Node #0,4,3: 85:[75, 65] Operation: 64+1=65 Exploring Operation: 75*1=75, Resulting Numbers: [64, 75] Generated Node #0,4,4: 85:[64, 75] Operation: 75*1=75 Moving to Node #0,0 Current State: 85:[75, 60, 3], Operations: ['64-61=3'] Exploring Operation: 75/3=25, Resulting Numbers: [60, 25] Generated Node #0,0,0: 85:[60, 25] Operation: 75/3=25 Exploring Operation: 60+3=63, Resulting Numbers: [75, 63] Generated Node #0,0,1: 85:[75, 63] Operation: 60+3=63 Exploring Operation: 75-60=15, Resulting Numbers: [3, 15] Generated Node #0,0,2: 85:[3, 15] Operation: 75-60=15 Exploring Operation: 60/3=20, Resulting Numbers: [75, 20] Generated Node #0,0,3: 85:[75, 20] Operation: 60/3=20 Exploring Operation: 75+3=78, Resulting Numbers: [60, 78] Generated Node #0,0,4: 85:[60, 78] Operation: 75+3=78 Moving to Node #0,2 Current State: 85:[61, 64, 15], Operations: ['75-60=15'] Exploring Operation: 61-15=46, Resulting Numbers: [64, 46] Generated Node #0,2,0: 85:[64, 46] Operation: 61-15=46 Exploring Operation: 61+15=76, Resulting Numbers: [64, 76] Generated Node #0,2,1: 85:[64, 76] Operation: 61+15=76 Exploring Operation: 64-61=3, Resulting Numbers: [15, 3] Generated Node #0,2,2: 85:[15, 3] Operation: 64-61=3 Exploring Operation: 61+64=125, Resulting Numbers: [15, 125] Generated Node #0,2,3: 85:[15, 125] Operation: 61+64=125 Exploring Operation: 64+15=79, Resulting Numbers: [61, 79] Generated Node #0,2,4: 85:[61, 79] Operation: 64+15=79 Moving to Node #0,3 Current State: 85:[60, 64, 14], Operations: ['75-61=14'] Exploring Operation: 60+64=124, Resulting Numbers: [14, 124] Generated Node #0,3,0: 85:[14, 124] Operation: 60+64=124 Exploring Operation: 64-60=4, Resulting Numbers: [14, 4] Generated Node #0,3,1: 85:[14, 4] Operation: 64-60=4 Exploring Operation: 60-14=46, Resulting Numbers: [64, 46] Generated Node #0,3,2: 85:[64, 46] Operation: 60-14=46 Exploring Operation: 60+14=74, Resulting Numbers: [64, 74] Generated Node #0,3,3: 85:[64, 74] Operation: 60+14=74 Exploring Operation: 64+14=78, Resulting Numbers: [60, 78] Generated Node #0,3,4: 85:[60, 78] Operation: 64+14=78 Moving to Node #0,1,2 Current State: 85:[4, 14], Operations: ['64-60=4', '75-61=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,85 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[3, 15], Operations: ['64-61=3', '75-60=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,85 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,85 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,85 unequal: No Solution Moving to Node #0,3,1 Current State: 85:[14, 4], Operations: ['75-61=14', '64-60=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,85 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[15, 3], Operations: ['75-60=15', '64-61=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,85 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[1, 11], Operations: ['61-60=1', '75-64=11'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[75, 20], Operations: ['64-61=3', '60/3=20'] Exploring Operation: 75+20=95, Resulting Numbers: [95] 95,85 unequal: No Solution Exploring Operation: 75*20=1500, Resulting Numbers: [1500] 1500,85 unequal: No Solution Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,85 unequal: No Solution Moving to Node #0,4,0 Current State: 85:[64, 76], Operations: ['61-60=1', '75+1=76'] Exploring Operation: 76-64=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 64*76=4864, Resulting Numbers: [4864] 4864,85 unequal: No Solution Exploring Operation: 64+76=140, Resulting Numbers: [140] 140,85 unequal: No Solution Moving to Node #0,1,4 Current State: 85:[61, 79], Operations: ['64-60=4', '75+4=79'] Exploring Operation: 79-61=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 61*79=4819, Resulting Numbers: [4819] 4819,85 unequal: No Solution Exploring Operation: 61+79=140, Resulting Numbers: [140] 140,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[75, 65], Operations: ['64-60=4', '61+4=65'] Exploring Operation: 75*65=4875, Resulting Numbers: [4875] 4875,85 unequal: No Solution Exploring Operation: 75+65=140, Resulting Numbers: [140] 140,85 unequal: No Solution Exploring Operation: 75-65=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[61, 79], Operations: ['75-60=15', '64+15=79'] Exploring Operation: 61*79=4819, Resulting Numbers: [4819] 4819,85 unequal: No Solution Exploring Operation: 61+79=140, Resulting Numbers: [140] 140,85 unequal: No Solution Exploring Operation: 79-61=18, Resulting Numbers: [18] 18,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[75, 65], Operations: ['61-60=1', '64+1=65'] Exploring Operation: 75*65=4875, Resulting Numbers: [4875] 4875,85 unequal: No Solution Exploring Operation: 75-65=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 75+65=140, Resulting Numbers: [140] 140,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[64, 76], Operations: ['75-60=15', '61+15=76'] Exploring Operation: 64*76=4864, Resulting Numbers: [4864] 4864,85 unequal: No Solution Exploring Operation: 64+76=140, Resulting Numbers: [140] 140,85 unequal: No Solution Exploring Operation: 76-64=12, Resulting Numbers: [12] 12,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[64, 75], Operations: ['61-60=1', '75*1=75'] Exploring Operation: 64*75=4800, Resulting Numbers: [4800] 4800,85 unequal: No Solution Exploring Operation: 64+75=139, Resulting Numbers: [139] 139,85 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[64, 75], Operations: ['61-60=1', '75/1=75'] Exploring Operation: 64+75=139, Resulting Numbers: [139] 139,85 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 64*75=4800, Resulting Numbers: [4800] 4800,85 unequal: No Solution Moving to Node #0,0,4 Current State: 85:[60, 78], Operations: ['64-61=3', '75+3=78'] Exploring Operation: 60+78=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 60*78=4680, Resulting Numbers: [4680] 4680,85 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[75, 63], Operations: ['64-61=3', '60+3=63'] Exploring Operation: 75*63=4725, Resulting Numbers: [4725] 4725,85 unequal: No Solution Exploring Operation: 75-63=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 75+63=138, Resulting Numbers: [138] 138,85 unequal: No Solution Moving to Node #0,3,4 Current State: 85:[60, 78], Operations: ['75-61=14', '64+14=78'] Exploring Operation: 60*78=4680, Resulting Numbers: [4680] 4680,85 unequal: No Solution Exploring Operation: 60+78=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[64, 74], Operations: ['75-61=14', '60+14=74'] Exploring Operation: 64*74=4736, Resulting Numbers: [4736] 4736,85 unequal: No Solution Exploring Operation: 64+74=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 74-64=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[60, 25], Operations: ['64-61=3', '75/3=25'] Exploring Operation: 60+25=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[75, 61, 60, 64], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [75, 60, 3] Generated Node #0,0: 85:[75, 60, 3] Operation: 64-61=3 Moving to Node #0,0 Current State: 85:[75, 60, 3], Operations: ['64-61=3'] Exploring Operation: 75/3=25, Resulting Numbers: [60, 25] Generated Node #0,0,0: 85:[60, 25] Operation: 75/3=25 Moving to Node #0,0,0 Current State: 85:[60, 25], Operations: ['64-61=3', '75/3=25'] Exploring Operation: 60+25=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.920139
hs_5
mult_heuristic
[ 94, 10, 5, 63 ]
26
[ "94-10=84", "63-5=58", "84-58=26" ]
Current State: 26:[94, 10, 5, 63], Operations: [] Exploring Operation: 94-10=84, Resulting Numbers: [5, 63, 84] Generated Node #2: [5, 63, 84] from Operation: 94-10=84 Current State: 26:[5, 63, 84], Operations: ['94-10=84'] Exploring Operation: 63-5=58, Resulting Numbers: [84, 58] Generated Node #3: [84, 58] from Operation: 63-5=58 Current State: 26:[84, 58], Operations: ['94-10=84', '63-5=58'] Exploring Operation: 84-58=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[94, 10, 5, 63], Operations: [] Exploring Operation: 94-5=89, Resulting Numbers: [10, 63, 89] Generated Node #0,0: 26:[10, 63, 89] Operation: 94-5=89 Exploring Operation: 94-10=84, Resulting Numbers: [5, 63, 84] Generated Node #0,1: 26:[5, 63, 84] Operation: 94-10=84 Exploring Operation: 94-63=31, Resulting Numbers: [10, 5, 31] Generated Node #0,2: 26:[10, 5, 31] Operation: 94-63=31 Exploring Operation: 63-5=58, Resulting Numbers: [94, 10, 58] Generated Node #0,3: 26:[94, 10, 58] Operation: 63-5=58 Exploring Operation: 63-10=53, Resulting Numbers: [94, 5, 53] Generated Node #0,4: 26:[94, 5, 53] Operation: 63-10=53 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[10, 5, 31], Operations: ['94-63=31'] Exploring Operation: 10+5=15, Resulting Numbers: [31, 15] Generated Node #0,2,0: 26:[31, 15] Operation: 10+5=15 Exploring Operation: 10/5=2, Resulting Numbers: [31, 2] Generated Node #0,2,1: 26:[31, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [31, 5] Generated Node #0,2,2: 26:[31, 5] Operation: 10-5=5 Exploring Operation: 31-10=21, Resulting Numbers: [5, 21] Generated Node #0,2,3: 26:[5, 21] Operation: 31-10=21 Exploring Operation: 31-5=26, Resulting Numbers: [10, 26] Generated Node #0,2,4: 26:[10, 26] Operation: 31-5=26 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 26:[10, 26], Operations: ['94-63=31', '31-5=26'] Exploring Operation: 10+26=36, Resulting Numbers: [36] 36,26 unequal: No Solution Exploring Operation: 10*26=260, Resulting Numbers: [260] 260,26 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 26:[31, 2], Operations: ['94-63=31', '10/5=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,26 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,26 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 26:[31, 15], Operations: ['94-63=31', '10+5=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,26 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,26 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 26:[31, 5], Operations: ['94-63=31', '10-5=5'] Exploring Operation: 31*5=155, Resulting Numbers: [155] 155,26 unequal: No Solution Exploring Operation: 31+5=36, Resulting Numbers: [36] 36,26 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[94, 10, 5, 63], Operations: [] Exploring Operation: 94-63=31, Resulting Numbers: [10, 5, 31] Generated Node #0,2: 26:[10, 5, 31] Operation: 94-63=31 Moving to Node #0,2 Current State: 26:[10, 5, 31], Operations: ['94-63=31'] Exploring Operation: 10-5=5, Resulting Numbers: [31, 5] Generated Node #0,2,2: 26:[31, 5] Operation: 10-5=5 Moving to Node #0,2,2 Current State: 26:[31, 5], Operations: ['94-63=31', '10-5=5'] Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.977431
hs_5
sum_heuristic
[ 52, 83, 96, 43 ]
22
[ "83-52=31", "96-43=53", "53-31=22" ]
Current State: 22:[52, 83, 96, 43], Operations: [] Exploring Operation: 83-52=31, Resulting Numbers: [96, 43, 31] Generated Node #2: [96, 43, 31] from Operation: 83-52=31 Current State: 22:[96, 43, 31], Operations: ['83-52=31'] Exploring Operation: 96-43=53, Resulting Numbers: [31, 53] Generated Node #3: [31, 53] from Operation: 96-43=53 Current State: 22:[31, 53], Operations: ['83-52=31', '96-43=53'] Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[52, 83, 96, 43], Operations: [] Exploring Operation: 96-83=13, Resulting Numbers: [52, 43, 13] Generated Node #0,0: 22:[52, 43, 13] Operation: 96-83=13 Exploring Operation: 83-52=31, Resulting Numbers: [96, 43, 31] Generated Node #0,1: 22:[96, 43, 31] Operation: 83-52=31 Exploring Operation: 96-52=44, Resulting Numbers: [83, 43, 44] Generated Node #0,2: 22:[83, 43, 44] Operation: 96-52=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[52, 43, 13], Operations: ['96-83=13'] Exploring Operation: 52/13=4, Resulting Numbers: [43, 4] Generated Node #0,0,0: 22:[43, 4] Operation: 52/13=4 Exploring Operation: 52-43=9, Resulting Numbers: [13, 9] Generated Node #0,0,1: 22:[13, 9] Operation: 52-43=9 Exploring Operation: 52-13=39, Resulting Numbers: [43, 39] Generated Node #0,0,2: 22:[43, 39] Operation: 52-13=39 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[13, 9], Operations: ['96-83=13', '52-43=9'] Exploring Operation: 13*9=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[52, 83, 96, 43], Operations: [] Exploring Operation: 96-83=13, Resulting Numbers: [52, 43, 13] Generated Node #0,0: 22:[52, 43, 13] Operation: 96-83=13 Moving to Node #0,0 Current State: 22:[52, 43, 13], Operations: ['96-83=13'] Exploring Operation: 52-43=9, Resulting Numbers: [13, 9] Generated Node #0,0,1: 22:[13, 9] Operation: 52-43=9 Moving to Node #0,0,1 Current State: 22:[13, 9], Operations: ['96-83=13', '52-43=9'] Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 78, 96, 25, 72 ]
41
[ "78-72=6", "96/6=16", "25+16=41" ]
Current State: 41:[78, 96, 25, 72], Operations: [] Exploring Operation: 78-72=6, Resulting Numbers: [96, 25, 6] Generated Node #2: [96, 25, 6] from Operation: 78-72=6 Current State: 41:[96, 25, 6], Operations: ['78-72=6'] Exploring Operation: 96/6=16, Resulting Numbers: [25, 16] Generated Node #3: [25, 16] from Operation: 96/6=16 Current State: 41:[25, 16], Operations: ['78-72=6', '96/6=16'] Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[78, 96, 25, 72], Operations: [] Exploring Operation: 78-25=53, Resulting Numbers: [96, 72, 53] Generated Node #0,0: 41:[96, 72, 53] Operation: 78-25=53 Exploring Operation: 96-72=24, Resulting Numbers: [78, 25, 24] Generated Node #0,1: 41:[78, 25, 24] Operation: 96-72=24 Exploring Operation: 96-25=71, Resulting Numbers: [78, 72, 71] Generated Node #0,2: 41:[78, 72, 71] Operation: 96-25=71 Exploring Operation: 96-78=18, Resulting Numbers: [25, 72, 18] Generated Node #0,3: 41:[25, 72, 18] Operation: 96-78=18 Moving to Node #0,1 Current State: 41:[78, 25, 24], Operations: ['96-72=24'] Exploring Operation: 78+24=102, Resulting Numbers: [25, 102] Generated Node #0,1,0: 41:[25, 102] Operation: 78+24=102 Exploring Operation: 78-24=54, Resulting Numbers: [25, 54] Generated Node #0,1,1: 41:[25, 54] Operation: 78-24=54 Exploring Operation: 25+24=49, Resulting Numbers: [78, 49] Generated Node #0,1,2: 41:[78, 49] Operation: 25+24=49 Exploring Operation: 78-25=53, Resulting Numbers: [24, 53] Generated Node #0,1,3: 41:[24, 53] Operation: 78-25=53 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[25, 54], Operations: ['96-72=24', '78-24=54'] Exploring Operation: 54-25=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 25+54=79, Resulting Numbers: [79] 79,41 unequal: No Solution Exploring Operation: 25*54=1350, Resulting Numbers: [1350] 1350,41 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 #0,1,3 Current State: 41:[24, 53], Operations: ['96-72=24', '78-25=53'] Exploring Operation: 24+53=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 24*53=1272, Resulting Numbers: [1272] 1272,41 unequal: No Solution Exploring Operation: 53-24=29, Resulting Numbers: [29] 29,41 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 #0,1,2 Current State: 41:[78, 49], Operations: ['96-72=24', '25+24=49'] Exploring Operation: 78+49=127, Resulting Numbers: [127] 127,41 unequal: No Solution Exploring Operation: 78*49=3822, Resulting Numbers: [3822] 3822,41 unequal: No Solution Exploring Operation: 78-49=29, Resulting Numbers: [29] 29,41 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 #0,1,0 Current State: 41:[25, 102], Operations: ['96-72=24', '78+24=102'] Exploring Operation: 102-25=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 25*102=2550, Resulting Numbers: [2550] 2550,41 unequal: No Solution Exploring Operation: 25+102=127, Resulting Numbers: [127] 127,41 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: 41:[25, 72, 18], Operations: ['96-78=18'] Exploring Operation: 72/18=4, Resulting Numbers: [25, 4] Generated Node #0,3,0: 41:[25, 4] Operation: 72/18=4 Exploring Operation: 72-25=47, Resulting Numbers: [18, 47] Generated Node #0,3,1: 41:[18, 47] Operation: 72-25=47 Exploring Operation: 25+18=43, Resulting Numbers: [72, 43] Generated Node #0,3,2: 41:[72, 43] Operation: 25+18=43 Exploring Operation: 72-18=54, Resulting Numbers: [25, 54] Generated Node #0,3,3: 41:[25, 54] Operation: 72-18=54 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 41:[18, 47], Operations: ['96-78=18', '72-25=47'] Exploring Operation: 18+47=65, Resulting Numbers: [65] 65,41 unequal: No Solution Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 18*47=846, Resulting Numbers: [846] 846,41 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:[25, 54], Operations: ['96-78=18', '72-18=54'] Exploring Operation: 25+54=79, Resulting Numbers: [79] 79,41 unequal: No Solution Exploring Operation: 54-25=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 25*54=1350, Resulting Numbers: [1350] 1350,41 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, 43], Operations: ['96-78=18', '25+18=43'] Exploring Operation: 72*43=3096, Resulting Numbers: [3096] 3096,41 unequal: No Solution Exploring Operation: 72-43=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 72+43=115, Resulting Numbers: [115] 115,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[25, 4], Operations: ['96-78=18', '72/18=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,41 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,41 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: 41:[78, 72, 71], Operations: ['96-25=71'] Exploring Operation: 72-71=1, Resulting Numbers: [78, 1] Generated Node #0,2,0: 41:[78, 1] Operation: 72-71=1 Exploring Operation: 78+72=150, Resulting Numbers: [71, 150] Generated Node #0,2,1: 41:[71, 150] Operation: 78+72=150 Exploring Operation: 78-71=7, Resulting Numbers: [72, 7] Generated Node #0,2,2: 41:[72, 7] Operation: 78-71=7 Exploring Operation: 78-72=6, Resulting Numbers: [71, 6] Generated Node #0,2,3: 41:[71, 6] Operation: 78-72=6 Moving to Node #0,0 Current State: 41:[96, 72, 53], Operations: ['78-25=53'] Exploring Operation: 96+72=168, Resulting Numbers: [53, 168] Generated Node #0,0,0: 41:[53, 168] Operation: 96+72=168 Exploring Operation: 72-53=19, Resulting Numbers: [96, 19] Generated Node #0,0,1: 41:[96, 19] Operation: 72-53=19 Exploring Operation: 96-72=24, Resulting Numbers: [53, 24] Generated Node #0,0,2: 41:[53, 24] Operation: 96-72=24 Exploring Operation: 96-53=43, Resulting Numbers: [72, 43] Generated Node #0,0,3: 41:[72, 43] Operation: 96-53=43 Moving to Node #0,0,2 Current State: 41:[53, 24], Operations: ['78-25=53', '96-72=24'] Exploring Operation: 53-24=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 53+24=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 53*24=1272, Resulting Numbers: [1272] 1272,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[72, 43], Operations: ['78-25=53', '96-53=43'] Exploring Operation: 72+43=115, Resulting Numbers: [115] 115,41 unequal: No Solution Exploring Operation: 72*43=3096, Resulting Numbers: [3096] 3096,41 unequal: No Solution Exploring Operation: 72-43=29, Resulting Numbers: [29] 29,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[72, 7], Operations: ['96-25=71', '78-71=7'] Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,41 unequal: No Solution Exploring Operation: 72*7=504, Resulting Numbers: [504] 504,41 unequal: No Solution Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[71, 6], Operations: ['96-25=71', '78-72=6'] Exploring Operation: 71+6=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 71*6=426, Resulting Numbers: [426] 426,41 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[96, 19], Operations: ['78-25=53', '72-53=19'] Exploring Operation: 96-19=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 96+19=115, Resulting Numbers: [115] 115,41 unequal: No Solution Exploring Operation: 96*19=1824, Resulting Numbers: [1824] 1824,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[78, 1], Operations: ['96-25=71', '72-71=1'] Exploring Operation: 78/1=78, Resulting Numbers: [78] 78,41 unequal: No Solution Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,41 unequal: No Solution Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 78+1=79, Resulting Numbers: [79] 79,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[71, 150], Operations: ['96-25=71', '78+72=150'] Exploring Operation: 71+150=221, Resulting Numbers: [221] 221,41 unequal: No Solution Exploring Operation: 71*150=10650, Resulting Numbers: [10650] 10650,41 unequal: No Solution Exploring Operation: 150-71=79, Resulting Numbers: [79] 79,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[53, 168], Operations: ['78-25=53', '96+72=168'] Exploring Operation: 168-53=115, Resulting Numbers: [115] 115,41 unequal: No Solution Exploring Operation: 53*168=8904, Resulting Numbers: [8904] 8904,41 unequal: No Solution Exploring Operation: 53+168=221, Resulting Numbers: [221] 221,41 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 71, 27, 21, 7 ]
13
[ "71+7=78", "27-21=6", "78/6=13" ]
Current State: 13:[71, 27, 21, 7], Operations: [] Exploring Operation: 71+7=78, Resulting Numbers: [27, 21, 78] Generated Node #2: [27, 21, 78] from Operation: 71+7=78 Current State: 13:[27, 21, 78], Operations: ['71+7=78'] Exploring Operation: 27-21=6, Resulting Numbers: [78, 6] Generated Node #3: [78, 6] from Operation: 27-21=6 Current State: 13:[78, 6], Operations: ['71+7=78', '27-21=6'] Exploring Operation: 78/6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[71, 27, 21, 7], Operations: [] Exploring Operation: 71-27=44, Resulting Numbers: [21, 7, 44] Generated Node #0,0: 13:[21, 7, 44] Operation: 71-27=44 Moving to Node #0,0 Current State: 13:[21, 7, 44], Operations: ['71-27=44'] Exploring Operation: 44-21=23, Resulting Numbers: [7, 23] Generated Node #0,0,0: 13:[7, 23] Operation: 44-21=23 Moving to Node #0,0,0 Current State: 13:[7, 23], Operations: ['71-27=44', '44-21=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,13 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 17, 27, 4, 43 ]
68
[ "43-27=16", "17*16=272", "272/4=68" ]
Current State: 68:[17, 27, 4, 43], Operations: [] Exploring Operation: 43-27=16, Resulting Numbers: [17, 4, 16] Generated Node #2: [17, 4, 16] from Operation: 43-27=16 Current State: 68:[17, 4, 16], Operations: ['43-27=16'] Exploring Operation: 17*16=272, Resulting Numbers: [4, 272] Generated Node #3: [4, 272] from Operation: 17*16=272 Current State: 68:[4, 272], Operations: ['43-27=16', '17*16=272'] Exploring Operation: 272/4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[17, 27, 4, 43], Operations: [] Exploring Operation: 27+43=70, Resulting Numbers: [17, 4, 70] Generated Node #0,0: 68:[17, 4, 70] Operation: 27+43=70 Exploring Operation: 43-4=39, Resulting Numbers: [17, 27, 39] Generated Node #0,1: 68:[17, 27, 39] Operation: 43-4=39 Exploring Operation: 27+4=31, Resulting Numbers: [17, 43, 31] Generated Node #0,2: 68:[17, 43, 31] Operation: 27+4=31 Exploring Operation: 43-27=16, Resulting Numbers: [17, 4, 16] Generated Node #0,3: 68:[17, 4, 16] Operation: 43-27=16 Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[17, 4, 16], Operations: ['43-27=16'] Exploring Operation: 17+16=33, Resulting Numbers: [4, 33] Generated Node #0,3,0: 68:[4, 33] Operation: 17+16=33 Exploring Operation: 17*4=68, Resulting Numbers: [16, 68] Generated Node #0,3,1: 68:[16, 68] Operation: 17*4=68 Exploring Operation: 17-16=1, Resulting Numbers: [4, 1] Generated Node #0,3,2: 68:[4, 1] Operation: 17-16=1 Exploring Operation: 16/4=4, Resulting Numbers: [17, 4] Generated Node #0,3,3: 68:[17, 4] Operation: 16/4=4 Moving to Node #0,3,3 Current State: 68:[17, 4], Operations: ['43-27=16', '16/4=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[17, 27, 4, 43], Operations: [] Exploring Operation: 43-27=16, Resulting Numbers: [17, 4, 16] Generated Node #0,3: 68:[17, 4, 16] Operation: 43-27=16 Moving to Node #0,3 Current State: 68:[17, 4, 16], Operations: ['43-27=16'] Exploring Operation: 16/4=4, Resulting Numbers: [17, 4] Generated Node #0,3,3: 68:[17, 4] Operation: 16/4=4 Moving to Node #0,3,3 Current State: 68:[17, 4], Operations: ['43-27=16', '16/4=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 20, 46, 79, 86 ]
81
[ "86-46=40", "40/20=2", "79+2=81" ]
Current State: 81:[20, 46, 79, 86], Operations: [] Exploring Operation: 86-46=40, Resulting Numbers: [20, 79, 40] Generated Node #2: [20, 79, 40] from Operation: 86-46=40 Current State: 81:[20, 79, 40], Operations: ['86-46=40'] Exploring Operation: 40/20=2, Resulting Numbers: [79, 2] Generated Node #3: [79, 2] from Operation: 40/20=2 Current State: 81:[79, 2], Operations: ['86-46=40', '40/20=2'] Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[20, 46, 79, 86], Operations: [] Exploring Operation: 46-20=26, Resulting Numbers: [79, 86, 26] Generated Node #0,0: 81:[79, 86, 26] Operation: 46-20=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[79, 86, 26], Operations: ['46-20=26'] Exploring Operation: 86-79=7, Resulting Numbers: [26, 7] Generated Node #0,0,0: 81:[26, 7] Operation: 86-79=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[26, 7], Operations: ['46-20=26', '86-79=7'] Exploring Operation: 26+7=33, Resulting Numbers: [33] 33,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 40, 79, 73, 66 ]
77
[ "73-40=33", "66/33=2", "79-2=77" ]
Current State: 77:[40, 79, 73, 66], Operations: [] Exploring Operation: 73-40=33, Resulting Numbers: [79, 66, 33] Generated Node #2: [79, 66, 33] from Operation: 73-40=33 Current State: 77:[79, 66, 33], Operations: ['73-40=33'] Exploring Operation: 66/33=2, Resulting Numbers: [79, 2] Generated Node #3: [79, 2] from Operation: 66/33=2 Current State: 77:[79, 2], Operations: ['73-40=33', '66/33=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[40, 79, 73, 66], Operations: [] Exploring Operation: 40+66=106, Resulting Numbers: [79, 73, 106] Generated Node #0,0: 77:[79, 73, 106] Operation: 40+66=106 Exploring Operation: 66-40=26, Resulting Numbers: [79, 73, 26] Generated Node #0,1: 77:[79, 73, 26] Operation: 66-40=26 Exploring Operation: 73-66=7, Resulting Numbers: [40, 79, 7] Generated Node #0,2: 77:[40, 79, 7] Operation: 73-66=7 Exploring Operation: 73-40=33, Resulting Numbers: [79, 66, 33] Generated Node #0,3: 77:[79, 66, 33] Operation: 73-40=33 Moving to Node #0,1 Current State: 77:[79, 73, 26], Operations: ['66-40=26'] Exploring Operation: 73+26=99, Resulting Numbers: [79, 99] Generated Node #0,1,0: 77:[79, 99] Operation: 73+26=99 Exploring Operation: 79+26=105, Resulting Numbers: [73, 105] Generated Node #0,1,1: 77:[73, 105] Operation: 79+26=105 Exploring Operation: 79-73=6, Resulting Numbers: [26, 6] Generated Node #0,1,2: 77:[26, 6] Operation: 79-73=6 Exploring Operation: 79-26=53, Resulting Numbers: [73, 53] Generated Node #0,1,3: 77:[73, 53] Operation: 79-26=53 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 77:[26, 6], Operations: ['66-40=26', '79-73=6'] Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,77 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,77 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 #0,1,0 Current State: 77:[79, 99], Operations: ['66-40=26', '73+26=99'] Exploring Operation: 79+99=178, Resulting Numbers: [178] 178,77 unequal: No Solution Exploring Operation: 99-79=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 79*99=7821, Resulting Numbers: [7821] 7821,77 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 #0,1,3 Current State: 77:[73, 53], Operations: ['66-40=26', '79-26=53'] Exploring Operation: 73+53=126, Resulting Numbers: [126] 126,77 unequal: No Solution Exploring Operation: 73*53=3869, Resulting Numbers: [3869] 3869,77 unequal: No Solution Exploring Operation: 73-53=20, Resulting Numbers: [20] 20,77 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 #0,1,1 Current State: 77:[73, 105], Operations: ['66-40=26', '79+26=105'] Exploring Operation: 73*105=7665, Resulting Numbers: [7665] 7665,77 unequal: No Solution Exploring Operation: 73+105=178, Resulting Numbers: [178] 178,77 unequal: No Solution Exploring Operation: 105-73=32, Resulting Numbers: [32] 32,77 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: 77:[40, 79, 7], Operations: ['73-66=7'] Exploring Operation: 79-7=72, Resulting Numbers: [40, 72] Generated Node #0,2,0: 77:[40, 72] Operation: 79-7=72 Exploring Operation: 79-40=39, Resulting Numbers: [7, 39] Generated Node #0,2,1: 77:[7, 39] Operation: 79-40=39 Exploring Operation: 40-7=33, Resulting Numbers: [79, 33] Generated Node #0,2,2: 77:[79, 33] Operation: 40-7=33 Exploring Operation: 40+7=47, Resulting Numbers: [79, 47] Generated Node #0,2,3: 77:[79, 47] Operation: 40+7=47 Moving to Node #0,3 Current State: 77:[79, 66, 33], Operations: ['73-40=33'] Exploring Operation: 79-66=13, Resulting Numbers: [33, 13] Generated Node #0,3,0: 77:[33, 13] Operation: 79-66=13 Exploring Operation: 66-33=33, Resulting Numbers: [79, 33] Generated Node #0,3,1: 77:[79, 33] Operation: 66-33=33 Exploring Operation: 66/33=2, Resulting Numbers: [79, 2] Generated Node #0,3,2: 77:[79, 2] Operation: 66/33=2 Exploring Operation: 66+33=99, Resulting Numbers: [79, 99] Generated Node #0,3,3: 77:[79, 99] Operation: 66+33=99 Moving to Node #0,0 Current State: 77:[79, 73, 106], Operations: ['40+66=106'] Exploring Operation: 106-79=27, Resulting Numbers: [73, 27] Generated Node #0,0,0: 77:[73, 27] Operation: 106-79=27 Exploring Operation: 106-73=33, Resulting Numbers: [79, 33] Generated Node #0,0,1: 77:[79, 33] Operation: 106-73=33 Exploring Operation: 79-73=6, Resulting Numbers: [106, 6] Generated Node #0,0,2: 77:[106, 6] Operation: 79-73=6 Exploring Operation: 79+73=152, Resulting Numbers: [106, 152] Generated Node #0,0,3: 77:[106, 152] Operation: 79+73=152 Moving to Node #0,3,2 Current State: 77:[79, 2], Operations: ['73-40=33', '66/33=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[40, 79, 73, 66], Operations: [] Exploring Operation: 73-40=33, Resulting Numbers: [79, 66, 33] Generated Node #0,3: 77:[79, 66, 33] Operation: 73-40=33 Moving to Node #0,3 Current State: 77:[79, 66, 33], Operations: ['73-40=33'] Exploring Operation: 66/33=2, Resulting Numbers: [79, 2] Generated Node #0,3,2: 77:[79, 2] Operation: 66/33=2 Moving to Node #0,3,2 Current State: 77:[79, 2], Operations: ['73-40=33', '66/33=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.967882
hs_4
mult_heuristic
[ 4, 2, 82, 34 ]
77
[ "4+82=86", "86/2=43", "34+43=77" ]
Current State: 77:[4, 2, 82, 34], Operations: [] Exploring Operation: 4+82=86, Resulting Numbers: [2, 34, 86] Generated Node #2: [2, 34, 86] from Operation: 4+82=86 Current State: 77:[2, 34, 86], Operations: ['4+82=86'] Exploring Operation: 86/2=43, Resulting Numbers: [34, 43] Generated Node #3: [34, 43] from Operation: 86/2=43 Current State: 77:[34, 43], Operations: ['4+82=86', '86/2=43'] Exploring Operation: 34+43=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[4, 2, 82, 34], Operations: [] Exploring Operation: 2*34=68, Resulting Numbers: [4, 82, 68] Generated Node #0,0: 77:[4, 82, 68] Operation: 2*34=68 Exploring Operation: 4*2=8, Resulting Numbers: [82, 34, 8] Generated Node #0,1: 77:[82, 34, 8] Operation: 4*2=8 Exploring Operation: 34/2=17, Resulting Numbers: [4, 82, 17] Generated Node #0,2: 77:[4, 82, 17] Operation: 34/2=17 Exploring Operation: 82-4=78, Resulting Numbers: [2, 34, 78] Generated Node #0,3: 77:[2, 34, 78] Operation: 82-4=78 Exploring Operation: 4+2=6, Resulting Numbers: [82, 34, 6] Generated Node #0,4: 77:[82, 34, 6] Operation: 4+2=6 Moving to Node #0,2 Current State: 77:[4, 82, 17], Operations: ['34/2=17'] Exploring Operation: 4+82=86, Resulting Numbers: [17, 86] Generated Node #0,2,0: 77:[17, 86] Operation: 4+82=86 Exploring Operation: 4*17=68, Resulting Numbers: [82, 68] Generated Node #0,2,1: 77:[82, 68] Operation: 4*17=68 Exploring Operation: 82-4=78, Resulting Numbers: [17, 78] Generated Node #0,2,2: 77:[17, 78] Operation: 82-4=78 Exploring Operation: 4+17=21, Resulting Numbers: [82, 21] Generated Node #0,2,3: 77:[82, 21] Operation: 4+17=21 Exploring Operation: 17-4=13, Resulting Numbers: [82, 13] Generated Node #0,2,4: 77:[82, 13] Operation: 17-4=13 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 77:[17, 78], Operations: ['34/2=17', '82-4=78'] Exploring Operation: 17*78=1326, Resulting Numbers: [1326] 1326,77 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,77 unequal: No Solution Exploring Operation: 17+78=95, Resulting Numbers: [95] 95,77 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 #0,2,4 Current State: 77:[82, 13], Operations: ['34/2=17', '17-4=13'] Exploring Operation: 82+13=95, Resulting Numbers: [95] 95,77 unequal: No Solution Exploring Operation: 82*13=1066, Resulting Numbers: [1066] 1066,77 unequal: No Solution Exploring Operation: 82-13=69, Resulting Numbers: [69] 69,77 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 #0,2,1 Current State: 77:[82, 68], Operations: ['34/2=17', '4*17=68'] Exploring Operation: 82+68=150, Resulting Numbers: [150] 150,77 unequal: No Solution Exploring Operation: 82-68=14, Resulting Numbers: [14] 14,77 unequal: No Solution Exploring Operation: 82*68=5576, Resulting Numbers: [5576] 5576,77 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 #0,2,0 Current State: 77:[17, 86], Operations: ['34/2=17', '4+82=86'] Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,77 unequal: No Solution Exploring Operation: 17+86=103, Resulting Numbers: [103] 103,77 unequal: No Solution Exploring Operation: 17*86=1462, Resulting Numbers: [1462] 1462,77 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 #0,2,3 Current State: 77:[82, 21], Operations: ['34/2=17', '4+17=21'] Exploring Operation: 82+21=103, Resulting Numbers: [103] 103,77 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,77 unequal: No Solution Exploring Operation: 82*21=1722, Resulting Numbers: [1722] 1722,77 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: 77:[4, 82, 68], Operations: ['2*34=68'] Exploring Operation: 82-68=14, Resulting Numbers: [4, 14] Generated Node #0,0,0: 77:[4, 14] Operation: 82-68=14 Exploring Operation: 4+82=86, Resulting Numbers: [68, 86] Generated Node #0,0,1: 77:[68, 86] Operation: 4+82=86 Exploring Operation: 4+68=72, Resulting Numbers: [82, 72] Generated Node #0,0,2: 77:[82, 72] Operation: 4+68=72 Exploring Operation: 68/4=17, Resulting Numbers: [82, 17] Generated Node #0,0,3: 77:[82, 17] Operation: 68/4=17 Exploring Operation: 82-4=78, Resulting Numbers: [68, 78] Generated Node #0,0,4: 77:[68, 78] Operation: 82-4=78 Moving to Node #0,1 Current State: 77:[82, 34, 8], Operations: ['4*2=8'] Exploring Operation: 34-8=26, Resulting Numbers: [82, 26] Generated Node #0,1,0: 77:[82, 26] Operation: 34-8=26 Exploring Operation: 34+8=42, Resulting Numbers: [82, 42] Generated Node #0,1,1: 77:[82, 42] Operation: 34+8=42 Exploring Operation: 82-34=48, Resulting Numbers: [8, 48] Generated Node #0,1,2: 77:[8, 48] Operation: 82-34=48 Exploring Operation: 82-8=74, Resulting Numbers: [34, 74] Generated Node #0,1,3: 77:[34, 74] Operation: 82-8=74 Exploring Operation: 82+8=90, Resulting Numbers: [34, 90] Generated Node #0,1,4: 77:[34, 90] Operation: 82+8=90 Moving to Node #0,3 Current State: 77:[2, 34, 78], Operations: ['82-4=78'] Exploring Operation: 34/2=17, Resulting Numbers: [78, 17] Generated Node #0,3,0: 77:[78, 17] Operation: 34/2=17 Exploring Operation: 78-2=76, Resulting Numbers: [34, 76] Generated Node #0,3,1: 77:[34, 76] Operation: 78-2=76 Exploring Operation: 34-2=32, Resulting Numbers: [78, 32] Generated Node #0,3,2: 77:[78, 32] Operation: 34-2=32 Exploring Operation: 2*34=68, Resulting Numbers: [78, 68] Generated Node #0,3,3: 77:[78, 68] Operation: 2*34=68 Exploring Operation: 2+34=36, Resulting Numbers: [78, 36] Generated Node #0,3,4: 77:[78, 36] Operation: 2+34=36 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 77:[78, 17], Operations: ['82-4=78', '34/2=17'] Exploring Operation: 78*17=1326, Resulting Numbers: [1326] 1326,77 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,77 unequal: No Solution Exploring Operation: 78+17=95, Resulting Numbers: [95] 95,77 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 #0,3,3 Current State: 77:[78, 68], Operations: ['82-4=78', '2*34=68'] Exploring Operation: 78+68=146, Resulting Numbers: [146] 146,77 unequal: No Solution Exploring Operation: 78-68=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 78*68=5304, Resulting Numbers: [5304] 5304,77 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 #0,3,2 Current State: 77:[78, 32], Operations: ['82-4=78', '34-2=32'] Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 78*32=2496, Resulting Numbers: [2496] 2496,77 unequal: No Solution Exploring Operation: 78+32=110, Resulting Numbers: [110] 110,77 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 #0,3,1 Current State: 77:[34, 76], Operations: ['82-4=78', '78-2=76'] Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,77 unequal: No Solution Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,77 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 #0,3,4 Current State: 77:[78, 36], Operations: ['82-4=78', '2+34=36'] Exploring Operation: 78+36=114, Resulting Numbers: [114] 114,77 unequal: No Solution Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 78*36=2808, Resulting Numbers: [2808] 2808,77 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: 77:[82, 34, 6], Operations: ['4+2=6'] Exploring Operation: 34-6=28, Resulting Numbers: [82, 28] Generated Node #0,4,0: 77:[82, 28] Operation: 34-6=28 Exploring Operation: 82+6=88, Resulting Numbers: [34, 88] Generated Node #0,4,1: 77:[34, 88] Operation: 82+6=88 Exploring Operation: 34+6=40, Resulting Numbers: [82, 40] Generated Node #0,4,2: 77:[82, 40] Operation: 34+6=40 Exploring Operation: 82-34=48, Resulting Numbers: [6, 48] Generated Node #0,4,3: 77:[6, 48] Operation: 82-34=48 Exploring Operation: 82-6=76, Resulting Numbers: [34, 76] Generated Node #0,4,4: 77:[34, 76] Operation: 82-6=76 Moving to Node #0,0,0 Current State: 77:[4, 14], Operations: ['2*34=68', '82-68=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,77 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,77 unequal: No Solution Moving to Node #0,0,4 Current State: 77:[68, 78], Operations: ['2*34=68', '82-4=78'] Exploring Operation: 68*78=5304, Resulting Numbers: [5304] 5304,77 unequal: No Solution Exploring Operation: 68+78=146, Resulting Numbers: [146] 146,77 unequal: No Solution Exploring Operation: 78-68=10, Resulting Numbers: [10] 10,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[82, 72], Operations: ['2*34=68', '4+68=72'] Exploring Operation: 82-72=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 82+72=154, Resulting Numbers: [154] 154,77 unequal: No Solution Exploring Operation: 82*72=5904, Resulting Numbers: [5904] 5904,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[82, 17], Operations: ['2*34=68', '68/4=17'] Exploring Operation: 82+17=99, Resulting Numbers: [99] 99,77 unequal: No Solution Exploring Operation: 82*17=1394, Resulting Numbers: [1394] 1394,77 unequal: No Solution Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[68, 86], Operations: ['2*34=68', '4+82=86'] Exploring Operation: 68*86=5848, Resulting Numbers: [5848] 5848,77 unequal: No Solution Exploring Operation: 86-68=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 68+86=154, Resulting Numbers: [154] 154,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[82, 26], Operations: ['4*2=8', '34-8=26'] Exploring Operation: 82*26=2132, Resulting Numbers: [2132] 2132,77 unequal: No Solution Exploring Operation: 82+26=108, Resulting Numbers: [108] 108,77 unequal: No Solution Exploring Operation: 82-26=56, Resulting Numbers: [56] 56,77 unequal: No Solution Moving to Node #0,4,0 Current State: 77:[82, 28], Operations: ['4+2=6', '34-6=28'] Exploring Operation: 82*28=2296, Resulting Numbers: [2296] 2296,77 unequal: No Solution Exploring Operation: 82+28=110, Resulting Numbers: [110] 110,77 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,77 unequal: No Solution Moving to Node #0,4,4 Current State: 77:[34, 76], Operations: ['4+2=6', '82-6=76'] Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,77 unequal: No Solution Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,77 unequal: No Solution Moving to Node #0,1,3 Current State: 77:[34, 74], Operations: ['4*2=8', '82-8=74'] Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,77 unequal: No Solution Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,77 unequal: No Solution Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,77 unequal: No Solution Moving to Node #0,4,3 Current State: 77:[6, 48], Operations: ['4+2=6', '82-34=48'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 6*48=288, Resulting Numbers: [288] 288,77 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[8, 48], Operations: ['4*2=8', '82-34=48'] Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,77 unequal: No Solution Exploring Operation: 8*48=384, Resulting Numbers: [384] 384,77 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 8+48=56, Resulting Numbers: [56] 56,77 unequal: No Solution Moving to Node #0,4,2 Current State: 77:[82, 40], Operations: ['4+2=6', '34+6=40'] Exploring Operation: 82+40=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 82-40=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 82*40=3280, Resulting Numbers: [3280] 3280,77 unequal: No Solution Moving to Node #0,4,1 Current State: 77:[34, 88], Operations: ['4+2=6', '82+6=88'] Exploring Operation: 88-34=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 34*88=2992, Resulting Numbers: [2992] 2992,77 unequal: No Solution Exploring Operation: 34+88=122, Resulting Numbers: [122] 122,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[82, 42], Operations: ['4*2=8', '34+8=42'] Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,77 unequal: No Solution Exploring Operation: 82*42=3444, Resulting Numbers: [3444] 3444,77 unequal: No Solution Exploring Operation: 82+42=124, Resulting Numbers: [124] 124,77 unequal: No Solution Moving to Node #0,1,4 Current State: 77:[34, 90], Operations: ['4*2=8', '82+8=90'] Exploring Operation: 34+90=124, Resulting Numbers: [124] 124,77 unequal: No Solution Exploring Operation: 90-34=56, Resulting Numbers: [56] 56,77 unequal: No Solution Exploring Operation: 34*90=3060, Resulting Numbers: [3060] 3060,77 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 90, 97, 81, 8 ]
82
[ "97-90=7", "81+8=89", "89-7=82" ]
Current State: 82:[90, 97, 81, 8], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [81, 8, 7] Generated Node #2: [81, 8, 7] from Operation: 97-90=7 Current State: 82:[81, 8, 7], Operations: ['97-90=7'] Exploring Operation: 81+8=89, Resulting Numbers: [7, 89] Generated Node #3: [7, 89] from Operation: 81+8=89 Current State: 82:[7, 89], Operations: ['97-90=7', '81+8=89'] Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[90, 97, 81, 8], Operations: [] Exploring Operation: 90-8=82, Resulting Numbers: [97, 81, 82] Generated Node #0,0: 82:[97, 81, 82] Operation: 90-8=82 Exploring Operation: 97-90=7, Resulting Numbers: [81, 8, 7] Generated Node #0,1: 82:[81, 8, 7] Operation: 97-90=7 Moving to Node #0,1 Current State: 82:[81, 8, 7], Operations: ['97-90=7'] Exploring Operation: 81+8=89, Resulting Numbers: [7, 89] Generated Node #0,1,0: 82:[7, 89] Operation: 81+8=89 Exploring Operation: 8-7=1, Resulting Numbers: [81, 1] Generated Node #0,1,1: 82:[81, 1] Operation: 8-7=1 Moving to Node #0,0 Current State: 82:[97, 81, 82], Operations: ['90-8=82'] Exploring Operation: 97-81=16, Resulting Numbers: [82, 16] Generated Node #0,0,0: 82:[82, 16] Operation: 97-81=16 Exploring Operation: 97-82=15, Resulting Numbers: [81, 15] Generated Node #0,0,1: 82:[81, 15] Operation: 97-82=15 Moving to Node #0,1,1 Current State: 82:[81, 1], Operations: ['97-90=7', '8-7=1'] Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[90, 97, 81, 8], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [81, 8, 7] Generated Node #0,1: 82:[81, 8, 7] Operation: 97-90=7 Moving to Node #0,1 Current State: 82:[81, 8, 7], Operations: ['97-90=7'] Exploring Operation: 8-7=1, Resulting Numbers: [81, 1] Generated Node #0,1,1: 82:[81, 1] Operation: 8-7=1 Moving to Node #0,1,1 Current State: 82:[81, 1], Operations: ['97-90=7', '8-7=1'] Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 41, 78, 62, 18 ]
82
[ "78-62=16", "18-16=2", "41*2=82" ]
Current State: 82:[41, 78, 62, 18], Operations: [] Exploring Operation: 78-62=16, Resulting Numbers: [41, 18, 16] Generated Node #2: [41, 18, 16] from Operation: 78-62=16 Current State: 82:[41, 18, 16], Operations: ['78-62=16'] Exploring Operation: 18-16=2, Resulting Numbers: [41, 2] Generated Node #3: [41, 2] from Operation: 18-16=2 Current State: 82:[41, 2], Operations: ['78-62=16', '18-16=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[41, 78, 62, 18], Operations: [] Exploring Operation: 62+18=80, Resulting Numbers: [41, 78, 80] Generated Node #0,0: 82:[41, 78, 80] Operation: 62+18=80 Moving to Node #0,0 Current State: 82:[41, 78, 80], Operations: ['62+18=80'] Exploring Operation: 80-78=2, Resulting Numbers: [41, 2] Generated Node #0,0,0: 82:[41, 2] Operation: 80-78=2 Moving to Node #0,0,0 Current State: 82:[41, 2], Operations: ['62+18=80', '80-78=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[41, 78, 62, 18], Operations: [] Exploring Operation: 62+18=80, Resulting Numbers: [41, 78, 80] Generated Node #0,0: 82:[41, 78, 80] Operation: 62+18=80 Moving to Node #0,0 Current State: 82:[41, 78, 80], Operations: ['62+18=80'] Exploring Operation: 80-78=2, Resulting Numbers: [41, 2] Generated Node #0,0,0: 82:[41, 2] Operation: 80-78=2 Moving to Node #0,0,0 Current State: 82:[41, 2], Operations: ['62+18=80', '80-78=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 49, 70, 40, 52 ]
33
[ "70-49=21", "52-40=12", "21+12=33" ]
Current State: 33:[49, 70, 40, 52], Operations: [] Exploring Operation: 70-49=21, Resulting Numbers: [40, 52, 21] Generated Node #2: [40, 52, 21] from Operation: 70-49=21 Current State: 33:[40, 52, 21], Operations: ['70-49=21'] Exploring Operation: 52-40=12, Resulting Numbers: [21, 12] Generated Node #3: [21, 12] from Operation: 52-40=12 Current State: 33:[21, 12], Operations: ['70-49=21', '52-40=12'] Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[49, 70, 40, 52], Operations: [] Exploring Operation: 70-52=18, Resulting Numbers: [49, 40, 18] Generated Node #0,0: 33:[49, 40, 18] Operation: 70-52=18 Moving to Node #0,0 Current State: 33:[49, 40, 18], Operations: ['70-52=18'] Exploring Operation: 49-40=9, Resulting Numbers: [18, 9] Generated Node #0,0,0: 33:[18, 9] Operation: 49-40=9 Moving to Node #0,0,0 Current State: 33:[18, 9], Operations: ['70-52=18', '49-40=9'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,33 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 45, 30, 10, 72 ]
77
[ "45-30=15", "72-10=62", "15+62=77" ]
Current State: 77:[45, 30, 10, 72], Operations: [] Exploring Operation: 45-30=15, Resulting Numbers: [10, 72, 15] Generated Node #2: [10, 72, 15] from Operation: 45-30=15 Current State: 77:[10, 72, 15], Operations: ['45-30=15'] Exploring Operation: 72-10=62, Resulting Numbers: [15, 62] Generated Node #3: [15, 62] from Operation: 72-10=62 Current State: 77:[15, 62], Operations: ['45-30=15', '72-10=62'] Exploring Operation: 15+62=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[45, 30, 10, 72], Operations: [] Exploring Operation: 45+30=75, Resulting Numbers: [10, 72, 75] Generated Node #0,0: 77:[10, 72, 75] Operation: 45+30=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[10, 72, 75], Operations: ['45+30=75'] Exploring Operation: 75-72=3, Resulting Numbers: [10, 3] Generated Node #0,0,0: 77:[10, 3] Operation: 75-72=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[10, 3], Operations: ['45+30=75', '75-72=3'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 8, 38, 78, 92 ]
87
[ "78-38=40", "40/8=5", "92-5=87" ]
Current State: 87:[8, 38, 78, 92], Operations: [] Exploring Operation: 78-38=40, Resulting Numbers: [8, 92, 40] Generated Node #2: [8, 92, 40] from Operation: 78-38=40 Current State: 87:[8, 92, 40], Operations: ['78-38=40'] Exploring Operation: 40/8=5, Resulting Numbers: [92, 5] Generated Node #3: [92, 5] from Operation: 40/8=5 Current State: 87:[92, 5], Operations: ['78-38=40', '40/8=5'] Exploring Operation: 92-5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[8, 38, 78, 92], Operations: [] Exploring Operation: 78-38=40, Resulting Numbers: [8, 92, 40] Generated Node #0,0: 87:[8, 92, 40] Operation: 78-38=40 Exploring Operation: 92-8=84, Resulting Numbers: [38, 78, 84] Generated Node #0,1: 87:[38, 78, 84] Operation: 92-8=84 Exploring Operation: 38-8=30, Resulting Numbers: [78, 92, 30] Generated Node #0,2: 87:[78, 92, 30] Operation: 38-8=30 Exploring Operation: 8+78=86, Resulting Numbers: [38, 92, 86] Generated Node #0,3: 87:[38, 92, 86] Operation: 8+78=86 Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[78, 92, 30], Operations: ['38-8=30'] Exploring Operation: 92-78=14, Resulting Numbers: [30, 14] Generated Node #0,2,0: 87:[30, 14] Operation: 92-78=14 Exploring Operation: 92-30=62, Resulting Numbers: [78, 62] Generated Node #0,2,1: 87:[78, 62] Operation: 92-30=62 Exploring Operation: 78+30=108, Resulting Numbers: [92, 108] Generated Node #0,2,2: 87:[92, 108] Operation: 78+30=108 Exploring Operation: 78-30=48, Resulting Numbers: [92, 48] Generated Node #0,2,3: 87:[92, 48] Operation: 78-30=48 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[30, 14], Operations: ['38-8=30', '92-78=14'] Exploring Operation: 30*14=420, Resulting Numbers: [420] 420,87 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,87 unequal: No Solution Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,87 unequal: No Solution No 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: 87:[92, 48], Operations: ['38-8=30', '78-30=48'] Exploring Operation: 92-48=44, Resulting Numbers: [44] 44,87 unequal: No Solution Exploring Operation: 92+48=140, Resulting Numbers: [140] 140,87 unequal: No Solution Exploring Operation: 92*48=4416, Resulting Numbers: [4416] 4416,87 unequal: No Solution No 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: 87:[92, 108], Operations: ['38-8=30', '78+30=108'] Exploring Operation: 92*108=9936, Resulting Numbers: [9936] 9936,87 unequal: No Solution Exploring Operation: 92+108=200, Resulting Numbers: [200] 200,87 unequal: No Solution Exploring Operation: 108-92=16, Resulting Numbers: [16] 16,87 unequal: No Solution No 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: 87:[78, 62], Operations: ['38-8=30', '92-30=62'] Exploring Operation: 78+62=140, Resulting Numbers: [140] 140,87 unequal: No Solution Exploring Operation: 78*62=4836, Resulting Numbers: [4836] 4836,87 unequal: No Solution Exploring Operation: 78-62=16, Resulting Numbers: [16] 16,87 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: 87:[38, 92, 86], Operations: ['8+78=86'] Exploring Operation: 92-86=6, Resulting Numbers: [38, 6] Generated Node #0,3,0: 87:[38, 6] Operation: 92-86=6 Exploring Operation: 86-38=48, Resulting Numbers: [92, 48] Generated Node #0,3,1: 87:[92, 48] Operation: 86-38=48 Exploring Operation: 92-38=54, Resulting Numbers: [86, 54] Generated Node #0,3,2: 87:[86, 54] Operation: 92-38=54 Exploring Operation: 38+86=124, Resulting Numbers: [92, 124] Generated Node #0,3,3: 87:[92, 124] Operation: 38+86=124 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 87:[38, 6], Operations: ['8+78=86', '92-86=6'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,87 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,87 unequal: No Solution No 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: 87:[92, 48], Operations: ['8+78=86', '86-38=48'] Exploring Operation: 92+48=140, Resulting Numbers: [140] 140,87 unequal: No Solution Exploring Operation: 92*48=4416, Resulting Numbers: [4416] 4416,87 unequal: No Solution Exploring Operation: 92-48=44, Resulting Numbers: [44] 44,87 unequal: No Solution No 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: 87:[86, 54], Operations: ['8+78=86', '92-38=54'] Exploring Operation: 86-54=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 86+54=140, Resulting Numbers: [140] 140,87 unequal: No Solution Exploring Operation: 86*54=4644, Resulting Numbers: [4644] 4644,87 unequal: No Solution No 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: 87:[92, 124], Operations: ['8+78=86', '38+86=124'] Exploring Operation: 92*124=11408, Resulting Numbers: [11408] 11408,87 unequal: No Solution Exploring Operation: 124-92=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 92+124=216, Resulting Numbers: [216] 216,87 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: 87:[8, 92, 40], Operations: ['78-38=40'] Exploring Operation: 8+92=100, Resulting Numbers: [40, 100] Generated Node #0,0,0: 87:[40, 100] Operation: 8+92=100 Exploring Operation: 40-8=32, Resulting Numbers: [92, 32] Generated Node #0,0,1: 87:[92, 32] Operation: 40-8=32 Exploring Operation: 92-8=84, Resulting Numbers: [40, 84] Generated Node #0,0,2: 87:[40, 84] Operation: 92-8=84 Exploring Operation: 40/8=5, Resulting Numbers: [92, 5] Generated Node #0,0,3: 87:[92, 5] Operation: 40/8=5 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[92, 5], Operations: ['78-38=40', '40/8=5'] Exploring Operation: 92+5=97, Resulting Numbers: [97] 97,87 unequal: No Solution Exploring Operation: 92-5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[8, 38, 78, 92], Operations: [] Exploring Operation: 78-38=40, Resulting Numbers: [8, 92, 40] Generated Node #0,0: 87:[8, 92, 40] Operation: 78-38=40 Moving to Node #0,0 Current State: 87:[8, 92, 40], Operations: ['78-38=40'] Exploring Operation: 40/8=5, Resulting Numbers: [92, 5] Generated Node #0,0,3: 87:[92, 5] Operation: 40/8=5 Moving to Node #0,0,3 Current State: 87:[92, 5], Operations: ['78-38=40', '40/8=5'] Exploring Operation: 92-5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_4
sum_heuristic
[ 50, 17, 18, 75 ]
79
[ "50+18=68", "68/17=4", "75+4=79" ]
Current State: 79:[50, 17, 18, 75], Operations: [] Exploring Operation: 50+18=68, Resulting Numbers: [17, 75, 68] Generated Node #2: [17, 75, 68] from Operation: 50+18=68 Current State: 79:[17, 75, 68], Operations: ['50+18=68'] Exploring Operation: 68/17=4, Resulting Numbers: [75, 4] Generated Node #3: [75, 4] from Operation: 68/17=4 Current State: 79:[75, 4], Operations: ['50+18=68', '68/17=4'] Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[50, 17, 18, 75], Operations: [] Exploring Operation: 50+18=68, Resulting Numbers: [17, 75, 68] Generated Node #0,0: 79:[17, 75, 68] Operation: 50+18=68 Exploring Operation: 50+17=67, Resulting Numbers: [18, 75, 67] Generated Node #0,1: 79:[18, 75, 67] Operation: 50+17=67 Moving to Node #0,0 Current State: 79:[17, 75, 68], Operations: ['50+18=68'] Exploring Operation: 17+68=85, Resulting Numbers: [75, 85] Generated Node #0,0,0: 79:[75, 85] Operation: 17+68=85 Exploring Operation: 17+75=92, Resulting Numbers: [68, 92] Generated Node #0,0,1: 79:[68, 92] Operation: 17+75=92 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[75, 85], Operations: ['50+18=68', '17+68=85'] Exploring Operation: 75+85=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 85-75=10, Resulting Numbers: [10] 10,79 unequal: No Solution No 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: 79:[68, 92], Operations: ['50+18=68', '17+75=92'] Exploring Operation: 68+92=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 92-68=24, Resulting Numbers: [24] 24,79 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: 79:[18, 75, 67], Operations: ['50+17=67'] Exploring Operation: 18+75=93, Resulting Numbers: [67, 93] Generated Node #0,1,0: 79:[67, 93] Operation: 18+75=93 Exploring Operation: 18+67=85, Resulting Numbers: [75, 85] Generated Node #0,1,1: 79:[75, 85] Operation: 18+67=85 Moving to Node #0,1,1 Current State: 79:[75, 85], Operations: ['50+17=67', '18+67=85'] Exploring Operation: 85-75=10, Resulting Numbers: [10] 10,79 unequal: No Solution Exploring Operation: 75+85=160, Resulting Numbers: [160] 160,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[67, 93], Operations: ['50+17=67', '18+75=93'] Exploring Operation: 67+93=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 93-67=26, Resulting Numbers: [26] 26,79 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 78, 41, 43, 65 ]
26
[ "78-65=13", "43-41=2", "13*2=26" ]
Current State: 26:[78, 41, 43, 65], Operations: [] Exploring Operation: 78-65=13, Resulting Numbers: [41, 43, 13] Generated Node #2: [41, 43, 13] from Operation: 78-65=13 Current State: 26:[41, 43, 13], Operations: ['78-65=13'] Exploring Operation: 43-41=2, Resulting Numbers: [13, 2] Generated Node #3: [13, 2] from Operation: 43-41=2 Current State: 26:[13, 2], Operations: ['78-65=13', '43-41=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[78, 41, 43, 65], Operations: [] Exploring Operation: 78-65=13, Resulting Numbers: [41, 43, 13] Generated Node #0,0: 26:[41, 43, 13] Operation: 78-65=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[41, 43, 13], Operations: ['78-65=13'] Exploring Operation: 43-41=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 26:[13, 2] Operation: 43-41=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 26:[13, 2], Operations: ['78-65=13', '43-41=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[78, 41, 43, 65], Operations: [] Exploring Operation: 78-65=13, Resulting Numbers: [41, 43, 13] Generated Node #0,0: 26:[41, 43, 13] Operation: 78-65=13 Moving to Node #0,0 Current State: 26:[41, 43, 13], Operations: ['78-65=13'] Exploring Operation: 43-41=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 26:[13, 2] Operation: 43-41=2 Moving to Node #0,0,0 Current State: 26:[13, 2], Operations: ['78-65=13', '43-41=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 11, 51, 99, 87 ]
27
[ "99/11=9", "87-51=36", "36-9=27" ]
Current State: 27:[11, 51, 99, 87], Operations: [] Exploring Operation: 99/11=9, Resulting Numbers: [51, 87, 9] Generated Node #2: [51, 87, 9] from Operation: 99/11=9 Current State: 27:[51, 87, 9], Operations: ['99/11=9'] Exploring Operation: 87-51=36, Resulting Numbers: [9, 36] Generated Node #3: [9, 36] from Operation: 87-51=36 Current State: 27:[9, 36], Operations: ['99/11=9', '87-51=36'] Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[11, 51, 99, 87], Operations: [] Exploring Operation: 87-51=36, Resulting Numbers: [11, 99, 36] Generated Node #0,0: 27:[11, 99, 36] Operation: 87-51=36 Exploring Operation: 99-51=48, Resulting Numbers: [11, 87, 48] Generated Node #0,1: 27:[11, 87, 48] Operation: 99-51=48 Exploring Operation: 99-87=12, Resulting Numbers: [11, 51, 12] Generated Node #0,2: 27:[11, 51, 12] Operation: 99-87=12 Exploring Operation: 99/11=9, Resulting Numbers: [51, 87, 9] Generated Node #0,3: 27:[51, 87, 9] Operation: 99/11=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[11, 51, 12], Operations: ['99-87=12'] Exploring Operation: 12-11=1, Resulting Numbers: [51, 1] Generated Node #0,2,0: 27:[51, 1] Operation: 12-11=1 Exploring Operation: 11+12=23, Resulting Numbers: [51, 23] Generated Node #0,2,1: 27:[51, 23] Operation: 11+12=23 Exploring Operation: 51-11=40, Resulting Numbers: [12, 40] Generated Node #0,2,2: 27:[12, 40] Operation: 51-11=40 Exploring Operation: 51-12=39, Resulting Numbers: [11, 39] Generated Node #0,2,3: 27:[11, 39] Operation: 51-12=39 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 27:[11, 39], Operations: ['99-87=12', '51-12=39'] Exploring Operation: 11*39=429, Resulting Numbers: [429] 429,27 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,27 unequal: No Solution No 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: 27:[12, 40], Operations: ['99-87=12', '51-11=40'] Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,27 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,27 unequal: No Solution No 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: 27:[51, 1], Operations: ['99-87=12', '12-11=1'] Exploring Operation: 51*1=51, Resulting Numbers: [51] 51,27 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,27 unequal: No Solution Exploring Operation: 51+1=52, Resulting Numbers: [52] 52,27 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,27 unequal: No Solution No 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: 27:[51, 23], Operations: ['99-87=12', '11+12=23'] Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 51*23=1173, Resulting Numbers: [1173] 1173,27 unequal: No Solution Exploring Operation: 51+23=74, Resulting Numbers: [74] 74,27 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: 27:[11, 99, 36], Operations: ['87-51=36'] Exploring Operation: 36-11=25, Resulting Numbers: [99, 25] Generated Node #0,0,0: 27:[99, 25] Operation: 36-11=25 Exploring Operation: 99-11=88, Resulting Numbers: [36, 88] Generated Node #0,0,1: 27:[36, 88] Operation: 99-11=88 Exploring Operation: 99-36=63, Resulting Numbers: [11, 63] Generated Node #0,0,2: 27:[11, 63] Operation: 99-36=63 Exploring Operation: 99/11=9, Resulting Numbers: [36, 9] Generated Node #0,0,3: 27:[36, 9] Operation: 99/11=9 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 27:[36, 9], Operations: ['87-51=36', '99/11=9'] Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[11, 51, 99, 87], Operations: [] Exploring Operation: 87-51=36, Resulting Numbers: [11, 99, 36] Generated Node #0,0: 27:[11, 99, 36] Operation: 87-51=36 Moving to Node #0,0 Current State: 27:[11, 99, 36], Operations: ['87-51=36'] Exploring Operation: 99/11=9, Resulting Numbers: [36, 9] Generated Node #0,0,3: 27:[36, 9] Operation: 99/11=9 Moving to Node #0,0,3 Current State: 27:[36, 9], Operations: ['87-51=36', '99/11=9'] Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 31, 45, 29, 33 ]
24
[ "31-29=2", "45-33=12", "2*12=24" ]
Current State: 24:[31, 45, 29, 33], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [45, 33, 2] Generated Node #2: [45, 33, 2] from Operation: 31-29=2 Current State: 24:[45, 33, 2], Operations: ['31-29=2'] Exploring Operation: 45-33=12, Resulting Numbers: [2, 12] Generated Node #3: [2, 12] from Operation: 45-33=12 Current State: 24:[2, 12], Operations: ['31-29=2', '45-33=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[31, 45, 29, 33], Operations: [] Exploring Operation: 45-29=16, Resulting Numbers: [31, 33, 16] Generated Node #0,0: 24:[31, 33, 16] Operation: 45-29=16 Exploring Operation: 45-33=12, Resulting Numbers: [31, 29, 12] Generated Node #0,1: 24:[31, 29, 12] Operation: 45-33=12 Exploring Operation: 45-31=14, Resulting Numbers: [29, 33, 14] Generated Node #0,2: 24:[29, 33, 14] Operation: 45-31=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[31, 29, 12], Operations: ['45-33=12'] Exploring Operation: 29-12=17, Resulting Numbers: [31, 17] Generated Node #0,1,0: 24:[31, 17] Operation: 29-12=17 Exploring Operation: 31-12=19, Resulting Numbers: [29, 19] Generated Node #0,1,1: 24:[29, 19] Operation: 31-12=19 Exploring Operation: 31-29=2, Resulting Numbers: [12, 2] Generated Node #0,1,2: 24:[12, 2] Operation: 31-29=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[12, 2], Operations: ['45-33=12', '31-29=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[31, 45, 29, 33], Operations: [] Exploring Operation: 45-33=12, Resulting Numbers: [31, 29, 12] Generated Node #0,1: 24:[31, 29, 12] Operation: 45-33=12 Moving to Node #0,1 Current State: 24:[31, 29, 12], Operations: ['45-33=12'] Exploring Operation: 31-29=2, Resulting Numbers: [12, 2] Generated Node #0,1,2: 24:[12, 2] Operation: 31-29=2 Moving to Node #0,1,2 Current State: 24:[12, 2], Operations: ['45-33=12', '31-29=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 2, 76, 70, 78 ]
30
[ "76/2=38", "78-70=8", "38-8=30" ]
Current State: 30:[2, 76, 70, 78], Operations: [] Exploring Operation: 76/2=38, Resulting Numbers: [70, 78, 38] Generated Node #2: [70, 78, 38] from Operation: 76/2=38 Current State: 30:[70, 78, 38], Operations: ['76/2=38'] Exploring Operation: 78-70=8, Resulting Numbers: [38, 8] Generated Node #3: [38, 8] from Operation: 78-70=8 Current State: 30:[38, 8], Operations: ['76/2=38', '78-70=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[2, 76, 70, 78], Operations: [] Exploring Operation: 78-70=8, Resulting Numbers: [2, 76, 8] Generated Node #0,0: 30:[2, 76, 8] Operation: 78-70=8 Exploring Operation: 78/2=39, Resulting Numbers: [76, 70, 39] Generated Node #0,1: 30:[76, 70, 39] Operation: 78/2=39 Exploring Operation: 76-70=6, Resulting Numbers: [2, 78, 6] Generated Node #0,2: 30:[2, 78, 6] Operation: 76-70=6 Exploring Operation: 78-76=2, Resulting Numbers: [2, 70, 2] Generated Node #0,3: 30:[2, 70, 2] Operation: 78-76=2 Exploring Operation: 76/2=38, Resulting Numbers: [70, 78, 38] Generated Node #0,4: 30:[70, 78, 38] Operation: 76/2=38 Moving to Node #0,3 Current State: 30:[2, 70, 2], Operations: ['78-76=2'] Exploring Operation: 70-2=68, Resulting Numbers: [2, 68] Generated Node #0,3,0: 30:[2, 68] Operation: 70-2=68 Exploring Operation: 2+2=4, Resulting Numbers: [70, 4] Generated Node #0,3,1: 30:[70, 4] Operation: 2+2=4 Exploring Operation: 70-2=68, Resulting Numbers: [2, 68] Generated Node #0,3,2: 30:[2, 68] Operation: 70-2=68 Exploring Operation: 70/2=35, Resulting Numbers: [2, 35] Generated Node #0,3,3: 30:[2, 35] Operation: 70/2=35 Exploring Operation: 70/2=35, Resulting Numbers: [2, 35] Generated Node #0,3,4: 30:[2, 35] Operation: 70/2=35 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 30:[2, 35], Operations: ['78-76=2', '70/2=35'] Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 30:[2, 35], Operations: ['78-76=2', '70/2=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,30 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 30:[2, 68], Operations: ['78-76=2', '70-2=68'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,30 unequal: No Solution Exploring Operation: 2+68=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 2*68=136, Resulting Numbers: [136] 136,30 unequal: No Solution Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 30:[2, 68], Operations: ['78-76=2', '70-2=68'] Exploring Operation: 2*68=136, Resulting Numbers: [136] 136,30 unequal: No Solution Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,30 unequal: No Solution Exploring Operation: 2+68=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 30:[70, 4], Operations: ['78-76=2', '2+2=4'] Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,30 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 30:[2, 78, 6], Operations: ['76-70=6'] Exploring Operation: 6/2=3, Resulting Numbers: [78, 3] Generated Node #0,2,0: 30:[78, 3] Operation: 6/2=3 Exploring Operation: 78-2=76, Resulting Numbers: [6, 76] Generated Node #0,2,1: 30:[6, 76] Operation: 78-2=76 Exploring Operation: 78/6=13, Resulting Numbers: [2, 13] Generated Node #0,2,2: 30:[2, 13] Operation: 78/6=13 Exploring Operation: 78/2=39, Resulting Numbers: [6, 39] Generated Node #0,2,3: 30:[6, 39] Operation: 78/2=39 Exploring Operation: 78-6=72, Resulting Numbers: [2, 72] Generated Node #0,2,4: 30:[2, 72] Operation: 78-6=72 Moving to Node #0,0 Current State: 30:[2, 76, 8], Operations: ['78-70=8'] Exploring Operation: 76-8=68, Resulting Numbers: [2, 68] Generated Node #0,0,0: 30:[2, 68] Operation: 76-8=68 Exploring Operation: 8-2=6, Resulting Numbers: [76, 6] Generated Node #0,0,1: 30:[76, 6] Operation: 8-2=6 Exploring Operation: 2+8=10, Resulting Numbers: [76, 10] Generated Node #0,0,2: 30:[76, 10] Operation: 2+8=10 Exploring Operation: 76-2=74, Resulting Numbers: [8, 74] Generated Node #0,0,3: 30:[8, 74] Operation: 76-2=74 Exploring Operation: 76/2=38, Resulting Numbers: [8, 38] Generated Node #0,0,4: 30:[8, 38] Operation: 76/2=38 Moving to Node #0,1 Current State: 30:[76, 70, 39], Operations: ['78/2=39'] Exploring Operation: 76+39=115, Resulting Numbers: [70, 115] Generated Node #0,1,0: 30:[70, 115] Operation: 76+39=115 Exploring Operation: 70-39=31, Resulting Numbers: [76, 31] Generated Node #0,1,1: 30:[76, 31] Operation: 70-39=31 Exploring Operation: 76-39=37, Resulting Numbers: [70, 37] Generated Node #0,1,2: 30:[70, 37] Operation: 76-39=37 Exploring Operation: 76+70=146, Resulting Numbers: [39, 146] Generated Node #0,1,3: 30:[39, 146] Operation: 76+70=146 Exploring Operation: 76-70=6, Resulting Numbers: [39, 6] Generated Node #0,1,4: 30:[39, 6] Operation: 76-70=6 Moving to Node #0,4 Current State: 30:[70, 78, 38], Operations: ['76/2=38'] Exploring Operation: 78-38=40, Resulting Numbers: [70, 40] Generated Node #0,4,0: 30:[70, 40] Operation: 78-38=40 Exploring Operation: 70-38=32, Resulting Numbers: [78, 32] Generated Node #0,4,1: 30:[78, 32] Operation: 70-38=32 Exploring Operation: 78-70=8, Resulting Numbers: [38, 8] Generated Node #0,4,2: 30:[38, 8] Operation: 78-70=8 Exploring Operation: 70+78=148, Resulting Numbers: [38, 148] Generated Node #0,4,3: 30:[38, 148] Operation: 70+78=148 Exploring Operation: 70+38=108, Resulting Numbers: [78, 108] Generated Node #0,4,4: 30:[78, 108] Operation: 70+38=108 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 30:[38, 8], Operations: ['76/2=38', '78-70=8'] Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[2, 76, 70, 78], Operations: [] Exploring Operation: 76/2=38, Resulting Numbers: [70, 78, 38] Generated Node #0,4: 30:[70, 78, 38] Operation: 76/2=38 Moving to Node #0,4 Current State: 30:[70, 78, 38], Operations: ['76/2=38'] Exploring Operation: 78-70=8, Resulting Numbers: [38, 8] Generated Node #0,4,2: 30:[38, 8] Operation: 78-70=8 Moving to Node #0,4,2 Current State: 30:[38, 8], Operations: ['76/2=38', '78-70=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_5
sum_heuristic
[ 18, 2, 90, 57 ]
49
[ "18-2=16", "90-57=33", "16+33=49" ]
Current State: 49:[18, 2, 90, 57], Operations: [] Exploring Operation: 18-2=16, Resulting Numbers: [90, 57, 16] Generated Node #2: [90, 57, 16] from Operation: 18-2=16 Current State: 49:[90, 57, 16], Operations: ['18-2=16'] Exploring Operation: 90-57=33, Resulting Numbers: [16, 33] Generated Node #3: [16, 33] from Operation: 90-57=33 Current State: 49:[16, 33], Operations: ['18-2=16', '90-57=33'] Exploring Operation: 16+33=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[18, 2, 90, 57], Operations: [] Exploring Operation: 90-18=72, Resulting Numbers: [2, 57, 72] Generated Node #0,0: 49:[2, 57, 72] Operation: 90-18=72 Exploring Operation: 90/18=5, Resulting Numbers: [2, 57, 5] Generated Node #0,1: 49:[2, 57, 5] Operation: 90/18=5 Exploring Operation: 90-57=33, Resulting Numbers: [18, 2, 33] Generated Node #0,2: 49:[18, 2, 33] Operation: 90-57=33 Exploring Operation: 18/2=9, Resulting Numbers: [90, 57, 9] Generated Node #0,3: 49:[90, 57, 9] Operation: 18/2=9 Exploring Operation: 90/2=45, Resulting Numbers: [18, 57, 45] Generated Node #0,4: 49:[18, 57, 45] Operation: 90/2=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[2, 57, 5], Operations: ['90/18=5'] Exploring Operation: 2*5=10, Resulting Numbers: [57, 10] Generated Node #0,1,0: 49:[57, 10] Operation: 2*5=10 Exploring Operation: 57-5=52, Resulting Numbers: [2, 52] Generated Node #0,1,1: 49:[2, 52] Operation: 57-5=52 Exploring Operation: 2+5=7, Resulting Numbers: [57, 7] Generated Node #0,1,2: 49:[57, 7] Operation: 2+5=7 Exploring Operation: 57-2=55, Resulting Numbers: [5, 55] Generated Node #0,1,3: 49:[5, 55] Operation: 57-2=55 Exploring Operation: 2+57=59, Resulting Numbers: [5, 59] Generated Node #0,1,4: 49:[5, 59] Operation: 2+57=59 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[2, 52], Operations: ['90/18=5', '57-5=52'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 2*52=104, Resulting Numbers: [104] 104,49 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,49 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:[57, 7], Operations: ['90/18=5', '2+5=7'] Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,49 unequal: No Solution Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,49 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,49 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:[5, 55], Operations: ['90/18=5', '57-2=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 5*55=275, Resulting Numbers: [275] 275,49 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[57, 10], Operations: ['90/18=5', '2*5=10'] Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,49 unequal: No Solution Exploring Operation: 57*10=570, Resulting Numbers: [570] 570,49 unequal: No Solution Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 49:[5, 59], Operations: ['90/18=5', '2+57=59'] Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,49 unequal: No Solution Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,49 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,49 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 #0,4 Current State: 49:[18, 57, 45], Operations: ['90/2=45'] Exploring Operation: 57-18=39, Resulting Numbers: [45, 39] Generated Node #0,4,0: 49:[45, 39] Operation: 57-18=39 Exploring Operation: 45-18=27, Resulting Numbers: [57, 27] Generated Node #0,4,1: 49:[57, 27] Operation: 45-18=27 Exploring Operation: 18+57=75, Resulting Numbers: [45, 75] Generated Node #0,4,2: 49:[45, 75] Operation: 18+57=75 Exploring Operation: 18+45=63, Resulting Numbers: [57, 63] Generated Node #0,4,3: 49:[57, 63] Operation: 18+45=63 Exploring Operation: 57-45=12, Resulting Numbers: [18, 12] Generated Node #0,4,4: 49:[18, 12] Operation: 57-45=12 Moving to Node #0,4,0 Current State: 49:[45, 39], Operations: ['90/2=45', '57-18=39'] Exploring Operation: 45*39=1755, Resulting Numbers: [1755] 1755,49 unequal: No Solution Exploring Operation: 45+39=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 45-39=6, Resulting Numbers: [6] 6,49 unequal: No Solution Moving to Node #0,4,4 Current State: 49:[18, 12], Operations: ['90/2=45', '57-45=12'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,49 unequal: No Solution Moving to Node #0,4,3 Current State: 49:[57, 63], Operations: ['90/2=45', '18+45=63'] Exploring Operation: 57+63=120, Resulting Numbers: [120] 120,49 unequal: No Solution Exploring Operation: 63-57=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 57*63=3591, Resulting Numbers: [3591] 3591,49 unequal: No Solution Moving to Node #0,4,1 Current State: 49:[57, 27], Operations: ['90/2=45', '45-18=27'] Exploring Operation: 57+27=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 57-27=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 57*27=1539, Resulting Numbers: [1539] 1539,49 unequal: No Solution Moving to Node #0,4,2 Current State: 49:[45, 75], Operations: ['90/2=45', '18+57=75'] Exploring Operation: 45+75=120, Resulting Numbers: [120] 120,49 unequal: No Solution Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 45*75=3375, Resulting Numbers: [3375] 3375,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[18, 2, 33], Operations: ['90-57=33'] Exploring Operation: 18+33=51, Resulting Numbers: [2, 51] Generated Node #0,2,0: 49:[2, 51] Operation: 18+33=51 Exploring Operation: 2+33=35, Resulting Numbers: [18, 35] Generated Node #0,2,1: 49:[18, 35] Operation: 2+33=35 Exploring Operation: 33-18=15, Resulting Numbers: [2, 15] Generated Node #0,2,2: 49:[2, 15] Operation: 33-18=15 Exploring Operation: 18-2=16, Resulting Numbers: [33, 16] Generated Node #0,2,3: 49:[33, 16] Operation: 18-2=16 Exploring Operation: 18/2=9, Resulting Numbers: [33, 9] Generated Node #0,2,4: 49:[33, 9] Operation: 18/2=9 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 49:[2, 51], Operations: ['90-57=33', '18+33=51'] Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[18, 2, 90, 57], Operations: [] Exploring Operation: 90-57=33, Resulting Numbers: [18, 2, 33] Generated Node #0,2: 49:[18, 2, 33] Operation: 90-57=33 Moving to Node #0,2 Current State: 49:[18, 2, 33], Operations: ['90-57=33'] Exploring Operation: 18+33=51, Resulting Numbers: [2, 51] Generated Node #0,2,0: 49:[2, 51] Operation: 18+33=51 Moving to Node #0,2,0 Current State: 49:[2, 51], Operations: ['90-57=33', '18+33=51'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 55, 72, 60, 2 ]
69
[ "55+72=127", "60-2=58", "127-58=69" ]
Current State: 69:[55, 72, 60, 2], Operations: [] Exploring Operation: 55+72=127, Resulting Numbers: [60, 2, 127] Generated Node #2: [60, 2, 127] from Operation: 55+72=127 Current State: 69:[60, 2, 127], Operations: ['55+72=127'] Exploring Operation: 60-2=58, Resulting Numbers: [127, 58] Generated Node #3: [127, 58] from Operation: 60-2=58 Current State: 69:[127, 58], Operations: ['55+72=127', '60-2=58'] Exploring Operation: 127-58=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[55, 72, 60, 2], Operations: [] Exploring Operation: 60-55=5, Resulting Numbers: [72, 2, 5] Generated Node #0,0: 69:[72, 2, 5] Operation: 60-55=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[72, 2, 5], Operations: ['60-55=5'] Exploring Operation: 72-2=70, Resulting Numbers: [5, 70] Generated Node #0,0,0: 69:[5, 70] Operation: 72-2=70 Moving to Node #0,0,0 Current State: 69:[5, 70], Operations: ['60-55=5', '72-2=70'] Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,69 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
[ 4, 76, 37, 24 ]
67
[ "4+76=80", "37-24=13", "80-13=67" ]
Current State: 67:[4, 76, 37, 24], Operations: [] Exploring Operation: 4+76=80, Resulting Numbers: [37, 24, 80] Generated Node #2: [37, 24, 80] from Operation: 4+76=80 Current State: 67:[37, 24, 80], Operations: ['4+76=80'] Exploring Operation: 37-24=13, Resulting Numbers: [80, 13] Generated Node #3: [80, 13] from Operation: 37-24=13 Current State: 67:[80, 13], Operations: ['4+76=80', '37-24=13'] Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[4, 76, 37, 24], Operations: [] Exploring Operation: 4+24=28, Resulting Numbers: [76, 37, 28] Generated Node #0,0: 67:[76, 37, 28] Operation: 4+24=28 Exploring Operation: 4*24=96, Resulting Numbers: [76, 37, 96] Generated Node #0,1: 67:[76, 37, 96] Operation: 4*24=96 Exploring Operation: 4+37=41, Resulting Numbers: [76, 24, 41] Generated Node #0,2: 67:[76, 24, 41] Operation: 4+37=41 Exploring Operation: 76-4=72, Resulting Numbers: [37, 24, 72] Generated Node #0,3: 67:[37, 24, 72] Operation: 76-4=72 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[76, 37, 96], Operations: ['4*24=96'] Exploring Operation: 96-37=59, Resulting Numbers: [76, 59] Generated Node #0,1,0: 67:[76, 59] Operation: 96-37=59 Exploring Operation: 76-37=39, Resulting Numbers: [96, 39] Generated Node #0,1,1: 67:[96, 39] Operation: 76-37=39 Exploring Operation: 76+37=113, Resulting Numbers: [96, 113] Generated Node #0,1,2: 67:[96, 113] Operation: 76+37=113 Exploring Operation: 37+96=133, Resulting Numbers: [76, 133] Generated Node #0,1,3: 67:[76, 133] Operation: 37+96=133 Moving to Node #0,1,0 Current State: 67:[76, 59], Operations: ['4*24=96', '96-37=59'] Exploring Operation: 76-59=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 76+59=135, Resulting Numbers: [135] 135,67 unequal: No Solution Exploring Operation: 76*59=4484, Resulting Numbers: [4484] 4484,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[96, 39], Operations: ['4*24=96', '76-37=39'] Exploring Operation: 96*39=3744, Resulting Numbers: [3744] 3744,67 unequal: No Solution Exploring Operation: 96+39=135, Resulting Numbers: [135] 135,67 unequal: No Solution Exploring Operation: 96-39=57, Resulting Numbers: [57] 57,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[76, 133], Operations: ['4*24=96', '37+96=133'] Exploring Operation: 76*133=10108, Resulting Numbers: [10108] 10108,67 unequal: No Solution Exploring Operation: 133-76=57, Resulting Numbers: [57] 57,67 unequal: No Solution Exploring Operation: 76+133=209, Resulting Numbers: [209] 209,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[96, 113], Operations: ['4*24=96', '76+37=113'] Exploring Operation: 96*113=10848, Resulting Numbers: [10848] 10848,67 unequal: No Solution Exploring Operation: 96+113=209, Resulting Numbers: [209] 209,67 unequal: No Solution Exploring Operation: 113-96=17, Resulting Numbers: [17] 17,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[76, 37, 28], Operations: ['4+24=28'] Exploring Operation: 76-28=48, Resulting Numbers: [37, 48] Generated Node #0,0,0: 67:[37, 48] Operation: 76-28=48 Exploring Operation: 76-37=39, Resulting Numbers: [28, 39] Generated Node #0,0,1: 67:[28, 39] Operation: 76-37=39 Exploring Operation: 37+28=65, Resulting Numbers: [76, 65] Generated Node #0,0,2: 67:[76, 65] Operation: 37+28=65 Exploring Operation: 76+28=104, Resulting Numbers: [37, 104] Generated Node #0,0,3: 67:[37, 104] Operation: 76+28=104 Moving to Node #0,0,2 Current State: 67:[76, 65], Operations: ['4+24=28', '37+28=65'] Exploring Operation: 76+65=141, Resulting Numbers: [141] 141,67 unequal: No Solution Exploring Operation: 76*65=4940, Resulting Numbers: [4940] 4940,67 unequal: No Solution Exploring Operation: 76-65=11, Resulting Numbers: [11] 11,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[37, 48], Operations: ['4+24=28', '76-28=48'] Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 37*48=1776, Resulting Numbers: [1776] 1776,67 unequal: No Solution Exploring Operation: 37+48=85, Resulting Numbers: [85] 85,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[37, 104], Operations: ['4+24=28', '76+28=104'] Exploring Operation: 37*104=3848, Resulting Numbers: [3848] 3848,67 unequal: No Solution Exploring Operation: 104-37=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[4, 76, 37, 24], Operations: [] Exploring Operation: 4+24=28, Resulting Numbers: [76, 37, 28] Generated Node #0,0: 67:[76, 37, 28] Operation: 4+24=28 Moving to Node #0,0 Current State: 67:[76, 37, 28], Operations: ['4+24=28'] Exploring Operation: 76+28=104, Resulting Numbers: [37, 104] Generated Node #0,0,3: 67:[37, 104] Operation: 76+28=104 Moving to Node #0,0,3 Current State: 67:[37, 104], Operations: ['4+24=28', '76+28=104'] Exploring Operation: 104-37=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 30, 40, 22, 87 ]
39
[ "30+40=70", "22+87=109", "109-70=39" ]
Current State: 39:[30, 40, 22, 87], Operations: [] Exploring Operation: 30+40=70, Resulting Numbers: [22, 87, 70] Generated Node #2: [22, 87, 70] from Operation: 30+40=70 Current State: 39:[22, 87, 70], Operations: ['30+40=70'] Exploring Operation: 22+87=109, Resulting Numbers: [70, 109] Generated Node #3: [70, 109] from Operation: 22+87=109 Current State: 39:[70, 109], Operations: ['30+40=70', '22+87=109'] Exploring Operation: 109-70=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[30, 40, 22, 87], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [30, 22, 47] Generated Node #0,0: 39:[30, 22, 47] Operation: 87-40=47 Exploring Operation: 87-22=65, Resulting Numbers: [30, 40, 65] Generated Node #0,1: 39:[30, 40, 65] Operation: 87-22=65 Exploring Operation: 87-30=57, Resulting Numbers: [40, 22, 57] Generated Node #0,2: 39:[40, 22, 57] Operation: 87-30=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[30, 22, 47], Operations: ['87-40=47'] Exploring Operation: 47-30=17, Resulting Numbers: [22, 17] Generated Node #0,0,0: 39:[22, 17] Operation: 47-30=17 Exploring Operation: 30-22=8, Resulting Numbers: [47, 8] Generated Node #0,0,1: 39:[47, 8] Operation: 30-22=8 Exploring Operation: 30+22=52, Resulting Numbers: [47, 52] Generated Node #0,0,2: 39:[47, 52] Operation: 30+22=52 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[22, 17], Operations: ['87-40=47', '47-30=17'] Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[30, 40, 22, 87], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [30, 22, 47] Generated Node #0,0: 39:[30, 22, 47] Operation: 87-40=47 Moving to Node #0,0 Current State: 39:[30, 22, 47], Operations: ['87-40=47'] Exploring Operation: 47-30=17, Resulting Numbers: [22, 17] Generated Node #0,0,0: 39:[22, 17] Operation: 47-30=17 Moving to Node #0,0,0 Current State: 39:[22, 17], Operations: ['87-40=47', '47-30=17'] Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 67, 84, 29, 21 ]
67
[ "84-67=17", "29+21=50", "17+50=67" ]
Current State: 67:[67, 84, 29, 21], Operations: [] Exploring Operation: 84-67=17, Resulting Numbers: [29, 21, 17] Generated Node #2: [29, 21, 17] from Operation: 84-67=17 Current State: 67:[29, 21, 17], Operations: ['84-67=17'] Exploring Operation: 29+21=50, Resulting Numbers: [17, 50] Generated Node #3: [17, 50] from Operation: 29+21=50 Current State: 67:[17, 50], Operations: ['84-67=17', '29+21=50'] Exploring Operation: 17+50=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[67, 84, 29, 21], Operations: [] Exploring Operation: 84-29=55, Resulting Numbers: [67, 21, 55] Generated Node #0,0: 67:[67, 21, 55] Operation: 84-29=55 Exploring Operation: 84-21=63, Resulting Numbers: [67, 29, 63] Generated Node #0,1: 67:[67, 29, 63] Operation: 84-21=63 Exploring Operation: 67+21=88, Resulting Numbers: [84, 29, 88] Generated Node #0,2: 67:[84, 29, 88] Operation: 67+21=88 Exploring Operation: 29+21=50, Resulting Numbers: [67, 84, 50] Generated Node #0,3: 67:[67, 84, 50] Operation: 29+21=50 Moving to Node #0,3 Current State: 67:[67, 84, 50], Operations: ['29+21=50'] Exploring Operation: 67+50=117, Resulting Numbers: [84, 117] Generated Node #0,3,0: 67:[84, 117] Operation: 67+50=117 Exploring Operation: 84-50=34, Resulting Numbers: [67, 34] Generated Node #0,3,1: 67:[67, 34] Operation: 84-50=34 Exploring Operation: 84-67=17, Resulting Numbers: [50, 17] Generated Node #0,3,2: 67:[50, 17] Operation: 84-67=17 Exploring Operation: 67-50=17, Resulting Numbers: [84, 17] Generated Node #0,3,3: 67:[84, 17] Operation: 67-50=17 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 67:[67, 34], Operations: ['29+21=50', '84-50=34'] Exploring Operation: 67+34=101, Resulting Numbers: [101] 101,67 unequal: No Solution Exploring Operation: 67*34=2278, Resulting Numbers: [2278] 2278,67 unequal: No Solution Exploring Operation: 67-34=33, Resulting Numbers: [33] 33,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 67:[84, 117], Operations: ['29+21=50', '67+50=117'] Exploring Operation: 84*117=9828, Resulting Numbers: [9828] 9828,67 unequal: No Solution Exploring Operation: 84+117=201, Resulting Numbers: [201] 201,67 unequal: No Solution Exploring Operation: 117-84=33, Resulting Numbers: [33] 33,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 67:[50, 17], Operations: ['29+21=50', '84-67=17'] Exploring Operation: 50*17=850, Resulting Numbers: [850] 850,67 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[67, 84, 29, 21], Operations: [] Exploring Operation: 29+21=50, Resulting Numbers: [67, 84, 50] Generated Node #0,3: 67:[67, 84, 50] Operation: 29+21=50 Moving to Node #0,3 Current State: 67:[67, 84, 50], Operations: ['29+21=50'] Exploring Operation: 84-67=17, Resulting Numbers: [50, 17] Generated Node #0,3,2: 67:[50, 17] Operation: 84-67=17 Moving to Node #0,3,2 Current State: 67:[50, 17], Operations: ['29+21=50', '84-67=17'] Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 98, 96, 12, 32 ]
89
[ "98-12=86", "96/32=3", "86+3=89" ]
Current State: 89:[98, 96, 12, 32], Operations: [] Exploring Operation: 98-12=86, Resulting Numbers: [96, 32, 86] Generated Node #2: [96, 32, 86] from Operation: 98-12=86 Current State: 89:[96, 32, 86], Operations: ['98-12=86'] Exploring Operation: 96/32=3, Resulting Numbers: [86, 3] Generated Node #3: [86, 3] from Operation: 96/32=3 Current State: 89:[86, 3], Operations: ['98-12=86', '96/32=3'] Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[98, 96, 12, 32], Operations: [] Exploring Operation: 12+32=44, Resulting Numbers: [98, 96, 44] Generated Node #0,0: 89:[98, 96, 44] Operation: 12+32=44 Moving to Node #0,0 Current State: 89:[98, 96, 44], Operations: ['12+32=44'] Exploring Operation: 98-44=54, Resulting Numbers: [96, 54] Generated Node #0,0,0: 89:[96, 54] Operation: 98-44=54 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[96, 54], Operations: ['12+32=44', '98-44=54'] Exploring Operation: 96-54=42, Resulting Numbers: [42] 42,89 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
[ 45, 26, 73, 54 ]
11
[ "54-45=9", "26+73=99", "99/9=11" ]
Current State: 11:[45, 26, 73, 54], Operations: [] Exploring Operation: 54-45=9, Resulting Numbers: [26, 73, 9] Generated Node #2: [26, 73, 9] from Operation: 54-45=9 Current State: 11:[26, 73, 9], Operations: ['54-45=9'] Exploring Operation: 26+73=99, Resulting Numbers: [9, 99] Generated Node #3: [9, 99] from Operation: 26+73=99 Current State: 11:[9, 99], Operations: ['54-45=9', '26+73=99'] Exploring Operation: 99/9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[45, 26, 73, 54], Operations: [] Exploring Operation: 73-45=28, Resulting Numbers: [26, 54, 28] Generated Node #0,0: 11:[26, 54, 28] Operation: 73-45=28 Exploring Operation: 73-54=19, Resulting Numbers: [45, 26, 19] Generated Node #0,1: 11:[45, 26, 19] Operation: 73-54=19 Moving to Node #0,1 Current State: 11:[45, 26, 19], Operations: ['73-54=19'] Exploring Operation: 45-19=26, Resulting Numbers: [26, 26] Generated Node #0,1,0: 11:[26, 26] Operation: 45-19=26 Exploring Operation: 45-26=19, Resulting Numbers: [19, 19] Generated Node #0,1,1: 11:[19, 19] Operation: 45-26=19 Moving to Node #0,0 Current State: 11:[26, 54, 28], Operations: ['73-45=28'] Exploring Operation: 54-28=26, Resulting Numbers: [26, 26] Generated Node #0,0,0: 11:[26, 26] Operation: 54-28=26 Exploring Operation: 54-26=28, Resulting Numbers: [28, 28] Generated Node #0,0,1: 11:[28, 28] Operation: 54-26=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[26, 26], Operations: ['73-45=28', '54-28=26'] Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 26-26=0, Resulting Numbers: [0] 0,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[28, 28], Operations: ['73-45=28', '54-26=28'] Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 11:[19, 19], Operations: ['73-54=19', '45-26=19'] Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,11 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[26, 26], Operations: ['73-54=19', '45-19=26'] Exploring Operation: 26-26=0, Resulting Numbers: [0] 0,11 unequal: No Solution Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,11 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 41, 37, 58, 72 ]
76
[ "41-37=4", "72/4=18", "58+18=76" ]
Current State: 76:[41, 37, 58, 72], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [58, 72, 4] Generated Node #2: [58, 72, 4] from Operation: 41-37=4 Current State: 76:[58, 72, 4], Operations: ['41-37=4'] Exploring Operation: 72/4=18, Resulting Numbers: [58, 18] Generated Node #3: [58, 18] from Operation: 72/4=18 Current State: 76:[58, 18], Operations: ['41-37=4', '72/4=18'] Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[41, 37, 58, 72], Operations: [] Exploring Operation: 58-41=17, Resulting Numbers: [37, 72, 17] Generated Node #0,0: 76:[37, 72, 17] Operation: 58-41=17 Exploring Operation: 41-37=4, Resulting Numbers: [58, 72, 4] Generated Node #0,1: 76:[58, 72, 4] Operation: 41-37=4 Exploring Operation: 58-37=21, Resulting Numbers: [41, 72, 21] Generated Node #0,2: 76:[41, 72, 21] Operation: 58-37=21 Exploring Operation: 72-58=14, Resulting Numbers: [41, 37, 14] Generated Node #0,3: 76:[41, 37, 14] Operation: 72-58=14 Exploring Operation: 41+37=78, Resulting Numbers: [58, 72, 78] Generated Node #0,4: 76:[58, 72, 78] Operation: 41+37=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[37, 72, 17], Operations: ['58-41=17'] Exploring Operation: 37-17=20, Resulting Numbers: [72, 20] Generated Node #0,0,0: 76:[72, 20] Operation: 37-17=20 Exploring Operation: 37+17=54, Resulting Numbers: [72, 54] Generated Node #0,0,1: 76:[72, 54] Operation: 37+17=54 Exploring Operation: 72-17=55, Resulting Numbers: [37, 55] Generated Node #0,0,2: 76:[37, 55] Operation: 72-17=55 Exploring Operation: 72-37=35, Resulting Numbers: [17, 35] Generated Node #0,0,3: 76:[17, 35] Operation: 72-37=35 Exploring Operation: 72+17=89, Resulting Numbers: [37, 89] Generated Node #0,0,4: 76:[37, 89] Operation: 72+17=89 Moving to Node #0,0,0 Current State: 76:[72, 20], Operations: ['58-41=17', '37-17=20'] Exploring Operation: 72+20=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 72-20=52, Resulting Numbers: [52] 52,76 unequal: No Solution Exploring Operation: 72*20=1440, Resulting Numbers: [1440] 1440,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[17, 35], Operations: ['58-41=17', '72-37=35'] Exploring Operation: 17*35=595, Resulting Numbers: [595] 595,76 unequal: No Solution Exploring Operation: 17+35=52, Resulting Numbers: [52] 52,76 unequal: No Solution Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,76 unequal: No Solution Moving to Node #0,0,4 Current State: 76:[37, 89], Operations: ['58-41=17', '72+17=89'] Exploring Operation: 37+89=126, Resulting Numbers: [126] 126,76 unequal: No Solution Exploring Operation: 37*89=3293, Resulting Numbers: [3293] 3293,76 unequal: No Solution Exploring Operation: 89-37=52, Resulting Numbers: [52] 52,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[37, 55], Operations: ['58-41=17', '72-17=55'] Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 37+55=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 37*55=2035, Resulting Numbers: [2035] 2035,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[72, 54], Operations: ['58-41=17', '37+17=54'] Exploring Operation: 72+54=126, Resulting Numbers: [126] 126,76 unequal: No Solution Exploring Operation: 72*54=3888, Resulting Numbers: [3888] 3888,76 unequal: No Solution Exploring Operation: 72-54=18, Resulting Numbers: [18] 18,76 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 #0,2 Current State: 76:[41, 72, 21], Operations: ['58-37=21'] Exploring Operation: 72-41=31, Resulting Numbers: [21, 31] Generated Node #0,2,0: 76:[21, 31] Operation: 72-41=31 Exploring Operation: 41-21=20, Resulting Numbers: [72, 20] Generated Node #0,2,1: 76:[72, 20] Operation: 41-21=20 Exploring Operation: 72+21=93, Resulting Numbers: [41, 93] Generated Node #0,2,2: 76:[41, 93] Operation: 72+21=93 Exploring Operation: 72-21=51, Resulting Numbers: [41, 51] Generated Node #0,2,3: 76:[41, 51] Operation: 72-21=51 Exploring Operation: 41+21=62, Resulting Numbers: [72, 62] Generated Node #0,2,4: 76:[72, 62] Operation: 41+21=62 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[72, 20], Operations: ['58-37=21', '41-21=20'] Exploring Operation: 72*20=1440, Resulting Numbers: [1440] 1440,76 unequal: No Solution Exploring Operation: 72-20=52, Resulting Numbers: [52] 52,76 unequal: No Solution Exploring Operation: 72+20=92, Resulting Numbers: [92] 92,76 unequal: No Solution No 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: 76:[21, 31], Operations: ['58-37=21', '72-41=31'] Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,76 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,76 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,76 unequal: No Solution No 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: 76:[41, 51], Operations: ['58-37=21', '72-21=51'] Exploring Operation: 51-41=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 41+51=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 41*51=2091, Resulting Numbers: [2091] 2091,76 unequal: No Solution No 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: 76:[72, 62], Operations: ['58-37=21', '41+21=62'] Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 72+62=134, Resulting Numbers: [134] 134,76 unequal: No Solution Exploring Operation: 72*62=4464, Resulting Numbers: [4464] 4464,76 unequal: No Solution No 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: 76:[41, 93], Operations: ['58-37=21', '72+21=93'] Exploring Operation: 41*93=3813, Resulting Numbers: [3813] 3813,76 unequal: No Solution Exploring Operation: 41+93=134, Resulting Numbers: [134] 134,76 unequal: No Solution Exploring Operation: 93-41=52, Resulting Numbers: [52] 52,76 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: 76:[41, 37, 14], Operations: ['72-58=14'] Exploring Operation: 41-37=4, Resulting Numbers: [14, 4] Generated Node #0,3,0: 76:[14, 4] Operation: 41-37=4 Exploring Operation: 37+14=51, Resulting Numbers: [41, 51] Generated Node #0,3,1: 76:[41, 51] Operation: 37+14=51 Exploring Operation: 41-14=27, Resulting Numbers: [37, 27] Generated Node #0,3,2: 76:[37, 27] Operation: 41-14=27 Exploring Operation: 41+37=78, Resulting Numbers: [14, 78] Generated Node #0,3,3: 76:[14, 78] Operation: 41+37=78 Exploring Operation: 37-14=23, Resulting Numbers: [41, 23] Generated Node #0,3,4: 76:[41, 23] Operation: 37-14=23 Moving to Node #0,3,0 Current State: 76:[14, 4], Operations: ['72-58=14', '41-37=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,76 unequal: No Solution Moving to Node #0,3,4 Current State: 76:[41, 23], Operations: ['72-58=14', '37-14=23'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[14, 78], Operations: ['72-58=14', '41+37=78'] Exploring Operation: 14+78=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 14*78=1092, Resulting Numbers: [1092] 1092,76 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[37, 27], Operations: ['72-58=14', '41-14=27'] Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[41, 51], Operations: ['72-58=14', '37+14=51'] Exploring Operation: 51-41=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 41+51=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 41*51=2091, Resulting Numbers: [2091] 2091,76 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 Current State: 76:[58, 72, 4], Operations: ['41-37=4'] Exploring Operation: 58+4=62, Resulting Numbers: [72, 62] Generated Node #0,1,0: 76:[72, 62] Operation: 58+4=62 Exploring Operation: 72/4=18, Resulting Numbers: [58, 18] Generated Node #0,1,1: 76:[58, 18] Operation: 72/4=18 Exploring Operation: 72+4=76, Resulting Numbers: [58, 76] Generated Node #0,1,2: 76:[58, 76] Operation: 72+4=76 Exploring Operation: 72-58=14, Resulting Numbers: [4, 14] Generated Node #0,1,3: 76:[4, 14] Operation: 72-58=14 Exploring Operation: 58-4=54, Resulting Numbers: [72, 54] Generated Node #0,1,4: 76:[72, 54] Operation: 58-4=54 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 76:[4, 14], Operations: ['41-37=4', '72-58=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,76 unequal: No Solution No 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: 76:[72, 62], Operations: ['41-37=4', '58+4=62'] Exploring Operation: 72*62=4464, Resulting Numbers: [4464] 4464,76 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 72+62=134, Resulting Numbers: [134] 134,76 unequal: No Solution No 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: 76:[58, 76], Operations: ['41-37=4', '72+4=76'] Exploring Operation: 58*76=4408, Resulting Numbers: [4408] 4408,76 unequal: No Solution Exploring Operation: 76-58=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 58+76=134, Resulting Numbers: [134] 134,76 unequal: No Solution No 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: 76:[58, 18], Operations: ['41-37=4', '72/4=18'] Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[41, 37, 58, 72], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [58, 72, 4] Generated Node #0,1: 76:[58, 72, 4] Operation: 41-37=4 Moving to Node #0,1 Current State: 76:[58, 72, 4], Operations: ['41-37=4'] Exploring Operation: 72/4=18, Resulting Numbers: [58, 18] Generated Node #0,1,1: 76:[58, 18] Operation: 72/4=18 Moving to Node #0,1,1 Current State: 76:[58, 18], Operations: ['41-37=4', '72/4=18'] Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.927083
hs_5
sum_heuristic
[ 14, 47, 3, 1 ]
86
[ "14-1=13", "3*13=39", "47+39=86" ]
Current State: 86:[14, 47, 3, 1], Operations: [] Exploring Operation: 14-1=13, Resulting Numbers: [47, 3, 13] Generated Node #2: [47, 3, 13] from Operation: 14-1=13 Current State: 86:[47, 3, 13], Operations: ['14-1=13'] Exploring Operation: 3*13=39, Resulting Numbers: [47, 39] Generated Node #3: [47, 39] from Operation: 3*13=39 Current State: 86:[47, 39], Operations: ['14-1=13', '3*13=39'] Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[14, 47, 3, 1], Operations: [] Exploring Operation: 47-3=44, Resulting Numbers: [14, 1, 44] Generated Node #0,0: 86:[14, 1, 44] Operation: 47-3=44 Exploring Operation: 14*3=42, Resulting Numbers: [47, 1, 42] Generated Node #0,1: 86:[47, 1, 42] Operation: 14*3=42 Exploring Operation: 47-14=33, Resulting Numbers: [3, 1, 33] Generated Node #0,2: 86:[3, 1, 33] Operation: 47-14=33 Exploring Operation: 14-3=11, Resulting Numbers: [47, 1, 11] Generated Node #0,3: 86:[47, 1, 11] Operation: 14-3=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[47, 1, 42], Operations: ['14*3=42'] Exploring Operation: 1+42=43, Resulting Numbers: [47, 43] Generated Node #0,1,0: 86:[47, 43] Operation: 1+42=43 Exploring Operation: 47-1=46, Resulting Numbers: [42, 46] Generated Node #0,1,1: 86:[42, 46] Operation: 47-1=46 Exploring Operation: 47-42=5, Resulting Numbers: [1, 5] Generated Node #0,1,2: 86:[1, 5] Operation: 47-42=5 Exploring Operation: 47+42=89, Resulting Numbers: [1, 89] Generated Node #0,1,3: 86:[1, 89] Operation: 47+42=89 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 86:[47, 43], Operations: ['14*3=42', '1+42=43'] Exploring Operation: 47-43=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,86 unequal: No Solution Exploring Operation: 47*43=2021, Resulting Numbers: [2021] 2021,86 unequal: No Solution No 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: 86:[42, 46], Operations: ['14*3=42', '47-1=46'] Exploring Operation: 42*46=1932, Resulting Numbers: [1932] 1932,86 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,86 unequal: No Solution No 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: 86:[1, 5], Operations: ['14*3=42', '47-42=5'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,86 unequal: No Solution No 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: 86:[1, 89], Operations: ['14*3=42', '47+42=89'] Exploring Operation: 1+89=90, Resulting Numbers: [90] 90,86 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 1*89=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,86 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: 86:[3, 1, 33], Operations: ['47-14=33'] Exploring Operation: 3-1=2, Resulting Numbers: [33, 2] Generated Node #0,2,0: 86:[33, 2] Operation: 3-1=2 Exploring Operation: 3+33=36, Resulting Numbers: [1, 36] Generated Node #0,2,1: 86:[1, 36] Operation: 3+33=36 Exploring Operation: 1+33=34, Resulting Numbers: [3, 34] Generated Node #0,2,2: 86:[3, 34] Operation: 1+33=34 Exploring Operation: 33/3=11, Resulting Numbers: [1, 11] Generated Node #0,2,3: 86:[1, 11] Operation: 33/3=11 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[1, 36], Operations: ['47-14=33', '3+33=36'] Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 1*36=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,86 unequal: No Solution No 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: 86:[33, 2], Operations: ['47-14=33', '3-1=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,86 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,86 unequal: No Solution No 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: 86:[3, 34], Operations: ['47-14=33', '1+33=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,86 unequal: No Solution No 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: 86:[1, 11], Operations: ['47-14=33', '33/3=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,86 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: 86:[14, 1, 44], Operations: ['47-3=44'] Exploring Operation: 44-1=43, Resulting Numbers: [14, 43] Generated Node #0,0,0: 86:[14, 43] Operation: 44-1=43 Exploring Operation: 14*1=14, Resulting Numbers: [44, 14] Generated Node #0,0,1: 86:[44, 14] Operation: 14*1=14 Exploring Operation: 14-1=13, Resulting Numbers: [44, 13] Generated Node #0,0,2: 86:[44, 13] Operation: 14-1=13 Exploring Operation: 14/1=14, Resulting Numbers: [44, 14] Generated Node #0,0,3: 86:[44, 14] Operation: 14/1=14 Moving to Node #0,0,0 Current State: 86:[14, 43], Operations: ['47-3=44', '44-1=43'] Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,86 unequal: No Solution Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[44, 13], Operations: ['47-3=44', '14-1=13'] Exploring Operation: 44*13=572, Resulting Numbers: [572] 572,86 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 44+13=57, Resulting Numbers: [57] 57,86 unequal: No Solution Moving to Node #0,0,3 Current State: 86:[44, 14], Operations: ['47-3=44', '14/1=14'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,86 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[44, 14], Operations: ['47-3=44', '14*1=14'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,86 unequal: No Solution Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[47, 1, 11], Operations: ['14-3=11'] Exploring Operation: 11-1=10, Resulting Numbers: [47, 10] Generated Node #0,3,0: 86:[47, 10] Operation: 11-1=10 Exploring Operation: 47-1=46, Resulting Numbers: [11, 46] Generated Node #0,3,1: 86:[11, 46] Operation: 47-1=46 Exploring Operation: 47-11=36, Resulting Numbers: [1, 36] Generated Node #0,3,2: 86:[1, 36] Operation: 47-11=36 Exploring Operation: 47*1=47, Resulting Numbers: [11, 47] Generated Node #0,3,3: 86:[11, 47] Operation: 47*1=47 Moving to Node #0,3,2 Current State: 86:[1, 36], Operations: ['14-3=11', '47-11=36'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 1*36=36, Resulting Numbers: [36] 36,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[11, 46], Operations: ['14-3=11', '47-1=46'] Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,86 unequal: No Solution Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[47, 10], Operations: ['14-3=11', '11-1=10'] Exploring Operation: 47*10=470, Resulting Numbers: [470] 470,86 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[11, 47], Operations: ['14-3=11', '47*1=47'] Exploring Operation: 11*47=517, Resulting Numbers: [517] 517,86 unequal: No Solution Exploring Operation: 11+47=58, Resulting Numbers: [58] 58,86 unequal: No Solution Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,86 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
[ 8, 15, 68, 26 ]
71
[ "8+15=23", "68+26=94", "94-23=71" ]
Current State: 71:[8, 15, 68, 26], Operations: [] Exploring Operation: 8+15=23, Resulting Numbers: [68, 26, 23] Generated Node #2: [68, 26, 23] from Operation: 8+15=23 Current State: 71:[68, 26, 23], Operations: ['8+15=23'] Exploring Operation: 68+26=94, Resulting Numbers: [23, 94] Generated Node #3: [23, 94] from Operation: 68+26=94 Current State: 71:[23, 94], Operations: ['8+15=23', '68+26=94'] Exploring Operation: 94-23=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[8, 15, 68, 26], Operations: [] Exploring Operation: 8*15=120, Resulting Numbers: [68, 26, 120] Generated Node #0,0: 71:[68, 26, 120] Operation: 8*15=120 Exploring Operation: 8+26=34, Resulting Numbers: [15, 68, 34] Generated Node #0,1: 71:[15, 68, 34] Operation: 8+26=34 Exploring Operation: 15+26=41, Resulting Numbers: [8, 68, 41] Generated Node #0,2: 71:[8, 68, 41] Operation: 15+26=41 Exploring Operation: 8+15=23, Resulting Numbers: [68, 26, 23] Generated Node #0,3: 71:[68, 26, 23] Operation: 8+15=23 Exploring Operation: 8+68=76, Resulting Numbers: [15, 26, 76] Generated Node #0,4: 71:[15, 26, 76] Operation: 8+68=76 Moving to Node #0,1 Current State: 71:[15, 68, 34], Operations: ['8+26=34'] Exploring Operation: 15+34=49, Resulting Numbers: [68, 49] Generated Node #0,1,0: 71:[68, 49] Operation: 15+34=49 Exploring Operation: 15+68=83, Resulting Numbers: [34, 83] Generated Node #0,1,1: 71:[34, 83] Operation: 15+68=83 Exploring Operation: 68+34=102, Resulting Numbers: [15, 102] Generated Node #0,1,2: 71:[15, 102] Operation: 68+34=102 Exploring Operation: 68-15=53, Resulting Numbers: [34, 53] Generated Node #0,1,3: 71:[34, 53] Operation: 68-15=53 Exploring Operation: 34-15=19, Resulting Numbers: [68, 19] Generated Node #0,1,4: 71:[68, 19] Operation: 34-15=19 Moving to Node #0,3 Current State: 71:[68, 26, 23], Operations: ['8+15=23'] Exploring Operation: 68-23=45, Resulting Numbers: [26, 45] Generated Node #0,3,0: 71:[26, 45] Operation: 68-23=45 Exploring Operation: 26+23=49, Resulting Numbers: [68, 49] Generated Node #0,3,1: 71:[68, 49] Operation: 26+23=49 Exploring Operation: 68+26=94, Resulting Numbers: [23, 94] Generated Node #0,3,2: 71:[23, 94] Operation: 68+26=94 Exploring Operation: 26-23=3, Resulting Numbers: [68, 3] Generated Node #0,3,3: 71:[68, 3] Operation: 26-23=3 Exploring Operation: 68+23=91, Resulting Numbers: [26, 91] Generated Node #0,3,4: 71:[26, 91] Operation: 68+23=91 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 71:[68, 49], Operations: ['8+15=23', '26+23=49'] Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 68*49=3332, Resulting Numbers: [3332] 3332,71 unequal: No Solution Exploring Operation: 68+49=117, Resulting Numbers: [117] 117,71 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 #0,3,4 Current State: 71:[26, 91], Operations: ['8+15=23', '68+23=91'] Exploring Operation: 91-26=65, Resulting Numbers: [65] 65,71 unequal: No Solution Exploring Operation: 26+91=117, Resulting Numbers: [117] 117,71 unequal: No Solution Exploring Operation: 26*91=2366, Resulting Numbers: [2366] 2366,71 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 #0,3,0 Current State: 71:[26, 45], Operations: ['8+15=23', '68-23=45'] Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,71 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[8, 15, 68, 26], Operations: [] Exploring Operation: 8+15=23, Resulting Numbers: [68, 26, 23] Generated Node #0,3: 71:[68, 26, 23] Operation: 8+15=23 Moving to Node #0,3 Current State: 71:[68, 26, 23], Operations: ['8+15=23'] Exploring Operation: 68-23=45, Resulting Numbers: [26, 45] Generated Node #0,3,0: 71:[26, 45] Operation: 68-23=45 Moving to Node #0,3,0 Current State: 71:[26, 45], Operations: ['8+15=23', '68-23=45'] Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 51, 37, 49, 94 ]
20
[ "51-49=2", "37*2=74", "94-74=20" ]
Current State: 20:[51, 37, 49, 94], Operations: [] Exploring Operation: 51-49=2, Resulting Numbers: [37, 94, 2] Generated Node #2: [37, 94, 2] from Operation: 51-49=2 Current State: 20:[37, 94, 2], Operations: ['51-49=2'] Exploring Operation: 37*2=74, Resulting Numbers: [94, 74] Generated Node #3: [94, 74] from Operation: 37*2=74 Current State: 20:[94, 74], Operations: ['51-49=2', '37*2=74'] Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[51, 37, 49, 94], Operations: [] Exploring Operation: 51-49=2, Resulting Numbers: [37, 94, 2] Generated Node #0,0: 20:[37, 94, 2] Operation: 51-49=2 Exploring Operation: 51-37=14, Resulting Numbers: [49, 94, 14] Generated Node #0,1: 20:[49, 94, 14] Operation: 51-37=14 Exploring Operation: 94-51=43, Resulting Numbers: [37, 49, 43] Generated Node #0,2: 20:[37, 49, 43] Operation: 94-51=43 Exploring Operation: 94-49=45, Resulting Numbers: [51, 37, 45] Generated Node #0,3: 20:[51, 37, 45] Operation: 94-49=45 Exploring Operation: 94-37=57, Resulting Numbers: [51, 49, 57] Generated Node #0,4: 20:[51, 49, 57] Operation: 94-37=57 Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[37, 49, 43], Operations: ['94-51=43'] Exploring Operation: 49-43=6, Resulting Numbers: [37, 6] Generated Node #0,2,0: 20:[37, 6] Operation: 49-43=6 Exploring Operation: 37+49=86, Resulting Numbers: [43, 86] Generated Node #0,2,1: 20:[43, 86] Operation: 37+49=86 Exploring Operation: 49-37=12, Resulting Numbers: [43, 12] Generated Node #0,2,2: 20:[43, 12] Operation: 49-37=12 Exploring Operation: 37+43=80, Resulting Numbers: [49, 80] Generated Node #0,2,3: 20:[49, 80] Operation: 37+43=80 Exploring Operation: 43-37=6, Resulting Numbers: [49, 6] Generated Node #0,2,4: 20:[49, 6] Operation: 43-37=6 Moving to Node #0,2,0 Current State: 20:[37, 6], Operations: ['94-51=43', '49-43=6'] Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,20 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[43, 12], Operations: ['94-51=43', '49-37=12'] Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,20 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,20 unequal: No Solution Moving to Node #0,2,4 Current State: 20:[49, 6], Operations: ['94-51=43', '43-37=6'] Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 49*6=294, Resulting Numbers: [294] 294,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[43, 86], Operations: ['94-51=43', '37+49=86'] Exploring Operation: 86-43=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 43*86=3698, Resulting Numbers: [3698] 3698,20 unequal: No Solution Exploring Operation: 43+86=129, Resulting Numbers: [129] 129,20 unequal: No Solution Exploring Operation: 86/43=2, Resulting Numbers: [2] 2,20 unequal: No Solution Moving to Node #0,2,3 Current State: 20:[49, 80], Operations: ['94-51=43', '37+43=80'] Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,20 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 20:[51, 37, 45], Operations: ['94-49=45'] Exploring Operation: 51-37=14, Resulting Numbers: [45, 14] Generated Node #0,3,0: 20:[45, 14] Operation: 51-37=14 Exploring Operation: 51+37=88, Resulting Numbers: [45, 88] Generated Node #0,3,1: 20:[45, 88] Operation: 51+37=88 Exploring Operation: 51+45=96, Resulting Numbers: [37, 96] Generated Node #0,3,2: 20:[37, 96] Operation: 51+45=96 Exploring Operation: 51-45=6, Resulting Numbers: [37, 6] Generated Node #0,3,3: 20:[37, 6] Operation: 51-45=6 Exploring Operation: 45-37=8, Resulting Numbers: [51, 8] Generated Node #0,3,4: 20:[51, 8] Operation: 45-37=8 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 20:[37, 6], Operations: ['94-49=45', '51-45=6'] Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,20 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,20 unequal: No Solution No 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: 20:[45, 14], Operations: ['94-49=45', '51-37=14'] Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 45*14=630, Resulting Numbers: [630] 630,20 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,20 unequal: No Solution No 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: 20:[51, 8], Operations: ['94-49=45', '45-37=8'] Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,20 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,20 unequal: No Solution No 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: 20:[45, 88], Operations: ['94-49=45', '51+37=88'] Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 45*88=3960, Resulting Numbers: [3960] 3960,20 unequal: No Solution Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,20 unequal: No Solution No 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: 20:[37, 96], Operations: ['94-49=45', '51+45=96'] Exploring Operation: 37+96=133, Resulting Numbers: [133] 133,20 unequal: No Solution Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 37*96=3552, Resulting Numbers: [3552] 3552,20 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: 20:[37, 94, 2], Operations: ['51-49=2'] Exploring Operation: 94-2=92, Resulting Numbers: [37, 92] Generated Node #0,0,0: 20:[37, 92] Operation: 94-2=92 Exploring Operation: 37+2=39, Resulting Numbers: [94, 39] Generated Node #0,0,1: 20:[94, 39] Operation: 37+2=39 Exploring Operation: 94-37=57, Resulting Numbers: [2, 57] Generated Node #0,0,2: 20:[2, 57] Operation: 94-37=57 Exploring Operation: 37-2=35, Resulting Numbers: [94, 35] Generated Node #0,0,3: 20:[94, 35] Operation: 37-2=35 Exploring Operation: 94/2=47, Resulting Numbers: [37, 47] Generated Node #0,0,4: 20:[37, 47] Operation: 94/2=47 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 20:[2, 57], Operations: ['51-49=2', '94-37=57'] Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,20 unequal: No Solution No 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: 20:[37, 47], Operations: ['51-49=2', '94/2=47'] Exploring Operation: 37*47=1739, Resulting Numbers: [1739] 1739,20 unequal: No Solution Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,20 unequal: No Solution No 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: 20:[37, 92], Operations: ['51-49=2', '94-2=92'] Exploring Operation: 37*92=3404, Resulting Numbers: [3404] 3404,20 unequal: No Solution Exploring Operation: 92-37=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 37+92=129, Resulting Numbers: [129] 129,20 unequal: No Solution No 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: 20:[94, 35], Operations: ['51-49=2', '37-2=35'] Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 94*35=3290, Resulting Numbers: [3290] 3290,20 unequal: No Solution Exploring Operation: 94+35=129, Resulting Numbers: [129] 129,20 unequal: No Solution No 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: 20:[94, 39], Operations: ['51-49=2', '37+2=39'] Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,20 unequal: No Solution Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,20 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: 20:[51, 49, 57], Operations: ['94-37=57'] Exploring Operation: 51+49=100, Resulting Numbers: [57, 100] Generated Node #0,4,0: 20:[57, 100] Operation: 51+49=100 Exploring Operation: 51+57=108, Resulting Numbers: [49, 108] Generated Node #0,4,1: 20:[49, 108] Operation: 51+57=108 Exploring Operation: 57-51=6, Resulting Numbers: [49, 6] Generated Node #0,4,2: 20:[49, 6] Operation: 57-51=6 Exploring Operation: 51-49=2, Resulting Numbers: [57, 2] Generated Node #0,4,3: 20:[57, 2] Operation: 51-49=2 Exploring Operation: 57-49=8, Resulting Numbers: [51, 8] Generated Node #0,4,4: 20:[51, 8] Operation: 57-49=8 Moving to Node #0,4,2 Current State: 20:[49, 6], Operations: ['94-37=57', '57-51=6'] Exploring Operation: 49*6=294, Resulting Numbers: [294] 294,20 unequal: No Solution Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,20 unequal: No Solution Moving to Node #0,4,4 Current State: 20:[51, 8], Operations: ['94-37=57', '57-49=8'] Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,20 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,20 unequal: No Solution Moving to Node #0,4,3 Current State: 20:[57, 2], Operations: ['94-37=57', '51-49=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,20 unequal: No Solution Moving to Node #0,4,0 Current State: 20:[57, 100], Operations: ['94-37=57', '51+49=100'] Exploring Operation: 100-57=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 57+100=157, Resulting Numbers: [157] 157,20 unequal: No Solution Exploring Operation: 57*100=5700, Resulting Numbers: [5700] 5700,20 unequal: No Solution Moving to Node #0,4,1 Current State: 20:[49, 108], Operations: ['94-37=57', '51+57=108'] Exploring Operation: 49+108=157, Resulting Numbers: [157] 157,20 unequal: No Solution Exploring Operation: 49*108=5292, Resulting Numbers: [5292] 5292,20 unequal: No Solution Exploring Operation: 108-49=59, Resulting Numbers: [59] 59,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[49, 94, 14], Operations: ['51-37=14'] Exploring Operation: 49-14=35, Resulting Numbers: [94, 35] Generated Node #0,1,0: 20:[94, 35] Operation: 49-14=35 Exploring Operation: 49+14=63, Resulting Numbers: [94, 63] Generated Node #0,1,1: 20:[94, 63] Operation: 49+14=63 Exploring Operation: 94+14=108, Resulting Numbers: [49, 108] Generated Node #0,1,2: 20:[49, 108] Operation: 94+14=108 Exploring Operation: 94-14=80, Resulting Numbers: [49, 80] Generated Node #0,1,3: 20:[49, 80] Operation: 94-14=80 Exploring Operation: 94-49=45, Resulting Numbers: [14, 45] Generated Node #0,1,4: 20:[14, 45] Operation: 94-49=45 Moving to Node #0,1,4 Current State: 20:[14, 45], Operations: ['51-37=14', '94-49=45'] Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,20 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,20 unequal: No Solution Moving to Node #0,1,3 Current State: 20:[49, 80], Operations: ['51-37=14', '94-14=80'] Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,20 unequal: No Solution Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,20 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[94, 35], Operations: ['51-37=14', '49-14=35'] Exploring Operation: 94+35=129, Resulting Numbers: [129] 129,20 unequal: No Solution Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 94*35=3290, Resulting Numbers: [3290] 3290,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[94, 63], Operations: ['51-37=14', '49+14=63'] Exploring Operation: 94-63=31, Resulting Numbers: [31] 31,20 unequal: No Solution Exploring Operation: 94+63=157, Resulting Numbers: [157] 157,20 unequal: No Solution Exploring Operation: 94*63=5922, Resulting Numbers: [5922] 5922,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[49, 108], Operations: ['51-37=14', '94+14=108'] Exploring Operation: 49+108=157, Resulting Numbers: [157] 157,20 unequal: No Solution Exploring Operation: 49*108=5292, Resulting Numbers: [5292] 5292,20 unequal: No Solution Exploring Operation: 108-49=59, Resulting Numbers: [59] 59,20 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
[ 20, 39, 74, 95 ]
79
[ "39-20=19", "95/19=5", "74+5=79" ]
Current State: 79:[20, 39, 74, 95], Operations: [] Exploring Operation: 39-20=19, Resulting Numbers: [74, 95, 19] Generated Node #2: [74, 95, 19] from Operation: 39-20=19 Current State: 79:[74, 95, 19], Operations: ['39-20=19'] Exploring Operation: 95/19=5, Resulting Numbers: [74, 5] Generated Node #3: [74, 5] from Operation: 95/19=5 Current State: 79:[74, 5], Operations: ['39-20=19', '95/19=5'] Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[20, 39, 74, 95], Operations: [] Exploring Operation: 20+39=59, Resulting Numbers: [74, 95, 59] Generated Node #0,0: 79:[74, 95, 59] Operation: 20+39=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[74, 95, 59], Operations: ['20+39=59'] Exploring Operation: 95-59=36, Resulting Numbers: [74, 36] Generated Node #0,0,0: 79:[74, 36] Operation: 95-59=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[74, 36], Operations: ['20+39=59', '95-59=36'] Exploring Operation: 74+36=110, Resulting Numbers: [110] 110,79 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
[ 35, 98, 7, 23 ]
79
[ "98-35=63", "23-7=16", "63+16=79" ]
Current State: 79:[35, 98, 7, 23], Operations: [] Exploring Operation: 98-35=63, Resulting Numbers: [7, 23, 63] Generated Node #2: [7, 23, 63] from Operation: 98-35=63 Current State: 79:[7, 23, 63], Operations: ['98-35=63'] Exploring Operation: 23-7=16, Resulting Numbers: [63, 16] Generated Node #3: [63, 16] from Operation: 23-7=16 Current State: 79:[63, 16], Operations: ['98-35=63', '23-7=16'] Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[35, 98, 7, 23], Operations: [] Exploring Operation: 35+23=58, Resulting Numbers: [98, 7, 58] Generated Node #0,0: 79:[98, 7, 58] Operation: 35+23=58 Exploring Operation: 35+7=42, Resulting Numbers: [98, 23, 42] Generated Node #0,1: 79:[98, 23, 42] Operation: 35+7=42 Exploring Operation: 98-7=91, Resulting Numbers: [35, 23, 91] Generated Node #0,2: 79:[35, 23, 91] Operation: 98-7=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[98, 7, 58], Operations: ['35+23=58'] Exploring Operation: 98+7=105, Resulting Numbers: [58, 105] Generated Node #0,0,0: 79:[58, 105] Operation: 98+7=105 Exploring Operation: 7+58=65, Resulting Numbers: [98, 65] Generated Node #0,0,1: 79:[98, 65] Operation: 7+58=65 Exploring Operation: 98-7=91, Resulting Numbers: [58, 91] Generated Node #0,0,2: 79:[58, 91] Operation: 98-7=91 Moving to Node #0,0,1 Current State: 79:[98, 65], Operations: ['35+23=58', '7+58=65'] Exploring Operation: 98*65=6370, Resulting Numbers: [6370] 6370,79 unequal: No Solution Exploring Operation: 98-65=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 98+65=163, Resulting Numbers: [163] 163,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[58, 91], Operations: ['35+23=58', '98-7=91'] Exploring Operation: 91-58=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 58*91=5278, Resulting Numbers: [5278] 5278,79 unequal: No Solution Exploring Operation: 58+91=149, Resulting Numbers: [149] 149,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[58, 105], Operations: ['35+23=58', '98+7=105'] Exploring Operation: 58*105=6090, Resulting Numbers: [6090] 6090,79 unequal: No Solution Exploring Operation: 58+105=163, Resulting Numbers: [163] 163,79 unequal: No Solution Exploring Operation: 105-58=47, Resulting Numbers: [47] 47,79 unequal: No Solution No 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: 79:[98, 23, 42], Operations: ['35+7=42'] Exploring Operation: 23+42=65, Resulting Numbers: [98, 65] Generated Node #0,1,0: 79:[98, 65] Operation: 23+42=65 Exploring Operation: 98-23=75, Resulting Numbers: [42, 75] Generated Node #0,1,1: 79:[42, 75] Operation: 98-23=75 Exploring Operation: 98+23=121, Resulting Numbers: [42, 121] Generated Node #0,1,2: 79:[42, 121] Operation: 98+23=121 Moving to Node #0,1,0 Current State: 79:[98, 65], Operations: ['35+7=42', '23+42=65'] Exploring Operation: 98+65=163, Resulting Numbers: [163] 163,79 unequal: No Solution Exploring Operation: 98*65=6370, Resulting Numbers: [6370] 6370,79 unequal: No Solution Exploring Operation: 98-65=33, Resulting Numbers: [33] 33,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[42, 75], Operations: ['35+7=42', '98-23=75'] Exploring Operation: 42+75=117, Resulting Numbers: [117] 117,79 unequal: No Solution Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 42*75=3150, Resulting Numbers: [3150] 3150,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[42, 121], Operations: ['35+7=42', '98+23=121'] Exploring Operation: 42*121=5082, Resulting Numbers: [5082] 5082,79 unequal: No Solution Exploring Operation: 42+121=163, Resulting Numbers: [163] 163,79 unequal: No Solution Exploring Operation: 121-42=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[35, 98, 7, 23], Operations: [] Exploring Operation: 35+7=42, Resulting Numbers: [98, 23, 42] Generated Node #0,1: 79:[98, 23, 42] Operation: 35+7=42 Moving to Node #0,1 Current State: 79:[98, 23, 42], Operations: ['35+7=42'] Exploring Operation: 98+23=121, Resulting Numbers: [42, 121] Generated Node #0,1,2: 79:[42, 121] Operation: 98+23=121 Moving to Node #0,1,2 Current State: 79:[42, 121], Operations: ['35+7=42', '98+23=121'] Exploring Operation: 121-42=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
mult_heuristic
[ 21, 91, 3, 5 ]
13
[ "21+5=26", "3*26=78", "91-78=13" ]
Current State: 13:[21, 91, 3, 5], Operations: [] Exploring Operation: 21+5=26, Resulting Numbers: [91, 3, 26] Generated Node #2: [91, 3, 26] from Operation: 21+5=26 Current State: 13:[91, 3, 26], Operations: ['21+5=26'] Exploring Operation: 3*26=78, Resulting Numbers: [91, 78] Generated Node #3: [91, 78] from Operation: 3*26=78 Current State: 13:[91, 78], Operations: ['21+5=26', '3*26=78'] Exploring Operation: 91-78=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[21, 91, 3, 5], Operations: [] Exploring Operation: 3*5=15, Resulting Numbers: [21, 91, 15] Generated Node #0,0: 13:[21, 91, 15] Operation: 3*5=15 Exploring Operation: 91-21=70, Resulting Numbers: [3, 5, 70] Generated Node #0,1: 13:[3, 5, 70] Operation: 91-21=70 Moving to Node #0,1 Current State: 13:[3, 5, 70], Operations: ['91-21=70'] Exploring Operation: 70/5=14, Resulting Numbers: [3, 14] Generated Node #0,1,0: 13:[3, 14] Operation: 70/5=14 Exploring Operation: 3*5=15, Resulting Numbers: [70, 15] Generated Node #0,1,1: 13:[70, 15] Operation: 3*5=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[3, 14], Operations: ['91-21=70', '70/5=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,13 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,13 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 #0,1,1 Current State: 13:[70, 15], Operations: ['91-21=70', '3*5=15'] Exploring Operation: 70+15=85, Resulting Numbers: [85] 85,13 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 13:[21, 91, 15], Operations: ['3*5=15'] Exploring Operation: 91-15=76, Resulting Numbers: [21, 76] Generated Node #0,0,0: 13:[21, 76] Operation: 91-15=76 Exploring Operation: 91-21=70, Resulting Numbers: [15, 70] Generated Node #0,0,1: 13:[15, 70] Operation: 91-21=70 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 13:[15, 70], Operations: ['3*5=15', '91-21=70'] Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,13 unequal: No Solution Exploring Operation: 15+70=85, Resulting Numbers: [85] 85,13 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 #0,0,0 Current State: 13:[21, 76], Operations: ['3*5=15', '91-15=76'] Exploring Operation: 76-21=55, Resulting Numbers: [55] 55,13 unequal: No Solution Exploring Operation: 21+76=97, Resulting Numbers: [97] 97,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 10, 39, 68, 1 ]
96
[ "39-10=29", "68-1=67", "29+67=96" ]
Current State: 96:[10, 39, 68, 1], Operations: [] Exploring Operation: 39-10=29, Resulting Numbers: [68, 1, 29] Generated Node #2: [68, 1, 29] from Operation: 39-10=29 Current State: 96:[68, 1, 29], Operations: ['39-10=29'] Exploring Operation: 68-1=67, Resulting Numbers: [29, 67] Generated Node #3: [29, 67] from Operation: 68-1=67 Current State: 96:[29, 67], Operations: ['39-10=29', '68-1=67'] Exploring Operation: 29+67=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[10, 39, 68, 1], Operations: [] Exploring Operation: 39+68=107, Resulting Numbers: [10, 1, 107] Generated Node #0,0: 96:[10, 1, 107] Operation: 39+68=107 Exploring Operation: 68-39=29, Resulting Numbers: [10, 1, 29] Generated Node #0,1: 96:[10, 1, 29] Operation: 68-39=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[10, 1, 29], Operations: ['68-39=29'] Exploring Operation: 10-1=9, Resulting Numbers: [29, 9] Generated Node #0,1,0: 96:[29, 9] Operation: 10-1=9 Exploring Operation: 10+1=11, Resulting Numbers: [29, 11] Generated Node #0,1,1: 96:[29, 11] Operation: 10+1=11 Moving to Node #0,1,0 Current State: 96:[29, 9], Operations: ['68-39=29', '10-1=9'] Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[29, 11], Operations: ['68-39=29', '10+1=11'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 29+11=40, Resulting Numbers: [40] 40,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[10, 1, 107], Operations: ['39+68=107'] Exploring Operation: 107-10=97, Resulting Numbers: [1, 97] Generated Node #0,0,0: 96:[1, 97] Operation: 107-10=97 Exploring Operation: 10+1=11, Resulting Numbers: [107, 11] Generated Node #0,0,1: 96:[107, 11] Operation: 10+1=11 Moving to Node #0,0,0 Current State: 96:[1, 97], Operations: ['39+68=107', '107-10=97'] Exploring Operation: 1*97=97, Resulting Numbers: [97] 97,96 unequal: No Solution Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[10, 39, 68, 1], Operations: [] Exploring Operation: 39+68=107, Resulting Numbers: [10, 1, 107] Generated Node #0,0: 96:[10, 1, 107] Operation: 39+68=107 Moving to Node #0,0 Current State: 96:[10, 1, 107], Operations: ['39+68=107'] Exploring Operation: 107-10=97, Resulting Numbers: [1, 97] Generated Node #0,0,0: 96:[1, 97] Operation: 107-10=97 Moving to Node #0,0,0 Current State: 96:[1, 97], Operations: ['39+68=107', '107-10=97'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 79, 23, 75, 82 ]
95
[ "79+23=102", "82-75=7", "102-7=95" ]
Current State: 95:[79, 23, 75, 82], Operations: [] Exploring Operation: 79+23=102, Resulting Numbers: [75, 82, 102] Generated Node #2: [75, 82, 102] from Operation: 79+23=102 Current State: 95:[75, 82, 102], Operations: ['79+23=102'] Exploring Operation: 82-75=7, Resulting Numbers: [102, 7] Generated Node #3: [102, 7] from Operation: 82-75=7 Current State: 95:[102, 7], Operations: ['79+23=102', '82-75=7'] Exploring Operation: 102-7=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[79, 23, 75, 82], Operations: [] Exploring Operation: 82-75=7, Resulting Numbers: [79, 23, 7] Generated Node #0,0: 95:[79, 23, 7] Operation: 82-75=7 Exploring Operation: 79-75=4, Resulting Numbers: [23, 82, 4] Generated Node #0,1: 95:[23, 82, 4] Operation: 79-75=4 Exploring Operation: 23+75=98, Resulting Numbers: [79, 82, 98] Generated Node #0,2: 95:[79, 82, 98] Operation: 23+75=98 Exploring Operation: 82-79=3, Resulting Numbers: [23, 75, 3] Generated Node #0,3: 95:[23, 75, 3] Operation: 82-79=3 Moving to Node #0,1 Current State: 95:[23, 82, 4], Operations: ['79-75=4'] Exploring Operation: 23+82=105, Resulting Numbers: [4, 105] Generated Node #0,1,0: 95:[4, 105] Operation: 23+82=105 Exploring Operation: 23-4=19, Resulting Numbers: [82, 19] Generated Node #0,1,1: 95:[82, 19] Operation: 23-4=19 Exploring Operation: 23*4=92, Resulting Numbers: [82, 92] Generated Node #0,1,2: 95:[82, 92] Operation: 23*4=92 Exploring Operation: 82+4=86, Resulting Numbers: [23, 86] Generated Node #0,1,3: 95:[23, 86] Operation: 82+4=86 Moving to Node #0,0 Current State: 95:[79, 23, 7], Operations: ['82-75=7'] Exploring Operation: 79+7=86, Resulting Numbers: [23, 86] Generated Node #0,0,0: 95:[23, 86] Operation: 79+7=86 Exploring Operation: 79-7=72, Resulting Numbers: [23, 72] Generated Node #0,0,1: 95:[23, 72] Operation: 79-7=72 Exploring Operation: 79+23=102, Resulting Numbers: [7, 102] Generated Node #0,0,2: 95:[7, 102] Operation: 79+23=102 Exploring Operation: 23-7=16, Resulting Numbers: [79, 16] Generated Node #0,0,3: 95:[79, 16] Operation: 23-7=16 Moving to Node #0,3 Current State: 95:[23, 75, 3], Operations: ['82-79=3'] Exploring Operation: 75+3=78, Resulting Numbers: [23, 78] Generated Node #0,3,0: 95:[23, 78] Operation: 75+3=78 Exploring Operation: 23+75=98, Resulting Numbers: [3, 98] Generated Node #0,3,1: 95:[3, 98] Operation: 23+75=98 Exploring Operation: 75/3=25, Resulting Numbers: [23, 25] Generated Node #0,3,2: 95:[23, 25] Operation: 75/3=25 Exploring Operation: 23-3=20, Resulting Numbers: [75, 20] Generated Node #0,3,3: 95:[75, 20] Operation: 23-3=20 Moving to Node #0,2 Current State: 95:[79, 82, 98], Operations: ['23+75=98'] Exploring Operation: 79+82=161, Resulting Numbers: [98, 161] Generated Node #0,2,0: 95:[98, 161] Operation: 79+82=161 Exploring Operation: 82-79=3, Resulting Numbers: [98, 3] Generated Node #0,2,1: 95:[98, 3] Operation: 82-79=3 Exploring Operation: 98-79=19, Resulting Numbers: [82, 19] Generated Node #0,2,2: 95:[82, 19] Operation: 98-79=19 Exploring Operation: 98-82=16, Resulting Numbers: [79, 16] Generated Node #0,2,3: 95:[79, 16] Operation: 98-82=16 Moving to Node #0,3,1 Current State: 95:[3, 98], Operations: ['82-79=3', '23+75=98'] Exploring Operation: 3+98=101, Resulting Numbers: [101] 101,95 unequal: No Solution Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[79, 23, 75, 82], Operations: [] Exploring Operation: 82-79=3, Resulting Numbers: [23, 75, 3] Generated Node #0,3: 95:[23, 75, 3] Operation: 82-79=3 Moving to Node #0,3 Current State: 95:[23, 75, 3], Operations: ['82-79=3'] Exploring Operation: 23+75=98, Resulting Numbers: [3, 98] Generated Node #0,3,1: 95:[3, 98] Operation: 23+75=98 Moving to Node #0,3,1 Current State: 95:[3, 98], Operations: ['82-79=3', '23+75=98'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.977431
hs_4
mult_heuristic
[ 81, 64, 3, 76 ]
31
[ "81-64=17", "76+17=93", "93/3=31" ]
Current State: 31:[81, 64, 3, 76], Operations: [] Exploring Operation: 81-64=17, Resulting Numbers: [3, 76, 17] Generated Node #2: [3, 76, 17] from Operation: 81-64=17 Current State: 31:[3, 76, 17], Operations: ['81-64=17'] Exploring Operation: 76+17=93, Resulting Numbers: [3, 93] Generated Node #3: [3, 93] from Operation: 76+17=93 Current State: 31:[3, 93], Operations: ['81-64=17', '76+17=93'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[81, 64, 3, 76], Operations: [] Exploring Operation: 81-76=5, Resulting Numbers: [64, 3, 5] Generated Node #0,0: 31:[64, 3, 5] Operation: 81-76=5 Exploring Operation: 81-3=78, Resulting Numbers: [64, 76, 78] Generated Node #0,1: 31:[64, 76, 78] Operation: 81-3=78 Exploring Operation: 76-64=12, Resulting Numbers: [81, 3, 12] Generated Node #0,2: 31:[81, 3, 12] Operation: 76-64=12 Exploring Operation: 81-64=17, Resulting Numbers: [3, 76, 17] Generated Node #0,3: 31:[3, 76, 17] Operation: 81-64=17 Exploring Operation: 81/3=27, Resulting Numbers: [64, 76, 27] Generated Node #0,4: 31:[64, 76, 27] Operation: 81/3=27 Start Sub Search at level 1: Moving to Node #0,4 Current State: 31:[64, 76, 27], Operations: ['81/3=27'] Exploring Operation: 64+27=91, Resulting Numbers: [76, 91] Generated Node #0,4,0: 31:[76, 91] Operation: 64+27=91 Exploring Operation: 76-27=49, Resulting Numbers: [64, 49] Generated Node #0,4,1: 31:[64, 49] Operation: 76-27=49 Exploring Operation: 76-64=12, Resulting Numbers: [27, 12] Generated Node #0,4,2: 31:[27, 12] Operation: 76-64=12 Exploring Operation: 64-27=37, Resulting Numbers: [76, 37] Generated Node #0,4,3: 31:[76, 37] Operation: 64-27=37 Exploring Operation: 76+27=103, Resulting Numbers: [64, 103] Generated Node #0,4,4: 31:[64, 103] Operation: 76+27=103 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 31:[27, 12], Operations: ['81/3=27', '76-64=12'] Exploring Operation: 27*12=324, Resulting Numbers: [324] 324,31 unequal: No Solution Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 31:[64, 49], Operations: ['81/3=27', '76-27=49'] Exploring Operation: 64*49=3136, Resulting Numbers: [3136] 3136,31 unequal: No Solution Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 64+49=113, Resulting Numbers: [113] 113,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 31:[76, 37], Operations: ['81/3=27', '64-27=37'] Exploring Operation: 76+37=113, Resulting Numbers: [113] 113,31 unequal: No Solution Exploring Operation: 76*37=2812, Resulting Numbers: [2812] 2812,31 unequal: No Solution Exploring Operation: 76-37=39, Resulting Numbers: [39] 39,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 31:[76, 91], Operations: ['81/3=27', '64+27=91'] Exploring Operation: 91-76=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 76+91=167, Resulting Numbers: [167] 167,31 unequal: No Solution Exploring Operation: 76*91=6916, Resulting Numbers: [6916] 6916,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 31:[64, 103], Operations: ['81/3=27', '76+27=103'] Exploring Operation: 64*103=6592, Resulting Numbers: [6592] 6592,31 unequal: No Solution Exploring Operation: 103-64=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 64+103=167, Resulting Numbers: [167] 167,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[64, 3, 5], Operations: ['81-76=5'] Exploring Operation: 64-5=59, Resulting Numbers: [3, 59] Generated Node #0,0,0: 31:[3, 59] Operation: 64-5=59 Exploring Operation: 3+5=8, Resulting Numbers: [64, 8] Generated Node #0,0,1: 31:[64, 8] Operation: 3+5=8 Exploring Operation: 3*5=15, Resulting Numbers: [64, 15] Generated Node #0,0,2: 31:[64, 15] Operation: 3*5=15 Exploring Operation: 64-3=61, Resulting Numbers: [5, 61] Generated Node #0,0,3: 31:[5, 61] Operation: 64-3=61 Exploring Operation: 64+3=67, Resulting Numbers: [5, 67] Generated Node #0,0,4: 31:[5, 67] Operation: 64+3=67 Moving to Node #0,0,2 Current State: 31:[64, 15], Operations: ['81-76=5', '3*5=15'] Exploring Operation: 64*15=960, Resulting Numbers: [960] 960,31 unequal: No Solution Exploring Operation: 64-15=49, Resulting Numbers: [49] 49,31 unequal: No Solution Exploring Operation: 64+15=79, Resulting Numbers: [79] 79,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[64, 8], Operations: ['81-76=5', '3+5=8'] Exploring Operation: 64+8=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 64/8=8, Resulting Numbers: [8] 8,31 unequal: No Solution Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 64*8=512, Resulting Numbers: [512] 512,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[3, 59], Operations: ['81-76=5', '64-5=59'] Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,31 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[5, 61], Operations: ['81-76=5', '64-3=61'] Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 5*61=305, Resulting Numbers: [305] 305,31 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,31 unequal: No Solution Moving to Node #0,0,4 Current State: 31:[5, 67], Operations: ['81-76=5', '64+3=67'] Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,31 unequal: No Solution Exploring Operation: 5+67=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 5*67=335, Resulting Numbers: [335] 335,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 31:[3, 76, 17], Operations: ['81-64=17'] Exploring Operation: 17-3=14, Resulting Numbers: [76, 14] Generated Node #0,3,0: 31:[76, 14] Operation: 17-3=14 Exploring Operation: 3+17=20, Resulting Numbers: [76, 20] Generated Node #0,3,1: 31:[76, 20] Operation: 3+17=20 Exploring Operation: 76-17=59, Resulting Numbers: [3, 59] Generated Node #0,3,2: 31:[3, 59] Operation: 76-17=59 Exploring Operation: 3+76=79, Resulting Numbers: [17, 79] Generated Node #0,3,3: 31:[17, 79] Operation: 3+76=79 Exploring Operation: 76-3=73, Resulting Numbers: [17, 73] Generated Node #0,3,4: 31:[17, 73] Operation: 76-3=73 Moving to Node #0,3,1 Current State: 31:[76, 20], Operations: ['81-64=17', '3+17=20'] Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 76*20=1520, Resulting Numbers: [1520] 1520,31 unequal: No Solution Exploring Operation: 76+20=96, Resulting Numbers: [96] 96,31 unequal: No Solution Moving to Node #0,3,4 Current State: 31:[17, 73], Operations: ['81-64=17', '76-3=73'] Exploring Operation: 17+73=90, Resulting Numbers: [90] 90,31 unequal: No Solution Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 17*73=1241, Resulting Numbers: [1241] 1241,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[3, 59], Operations: ['81-64=17', '76-17=59'] Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,31 unequal: No Solution Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,31 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,31 unequal: No Solution Moving to Node #0,3,0 Current State: 31:[76, 14], Operations: ['81-64=17', '17-3=14'] Exploring Operation: 76+14=90, Resulting Numbers: [90] 90,31 unequal: No Solution Exploring Operation: 76*14=1064, Resulting Numbers: [1064] 1064,31 unequal: No Solution Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[17, 79], Operations: ['81-64=17', '3+76=79'] Exploring Operation: 79-17=62, Resulting Numbers: [62] 62,31 unequal: No Solution Exploring Operation: 17+79=96, Resulting Numbers: [96] 96,31 unequal: No Solution Exploring Operation: 17*79=1343, Resulting Numbers: [1343] 1343,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[81, 3, 12], Operations: ['76-64=12'] Exploring Operation: 81-12=69, Resulting Numbers: [3, 69] Generated Node #0,2,0: 31:[3, 69] Operation: 81-12=69 Exploring Operation: 3*12=36, Resulting Numbers: [81, 36] Generated Node #0,2,1: 31:[81, 36] Operation: 3*12=36 Exploring Operation: 81-3=78, Resulting Numbers: [12, 78] Generated Node #0,2,2: 31:[12, 78] Operation: 81-3=78 Exploring Operation: 81/3=27, Resulting Numbers: [12, 27] Generated Node #0,2,3: 31:[12, 27] Operation: 81/3=27 Exploring Operation: 3+12=15, Resulting Numbers: [81, 15] Generated Node #0,2,4: 31:[81, 15] Operation: 3+12=15 Moving to Node #0,2,3 Current State: 31:[12, 27], Operations: ['76-64=12', '81/3=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,31 unequal: No Solution Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[81, 36], Operations: ['76-64=12', '3*12=36'] Exploring Operation: 81+36=117, Resulting Numbers: [117] 117,31 unequal: No Solution Exploring Operation: 81*36=2916, Resulting Numbers: [2916] 2916,31 unequal: No Solution Exploring Operation: 81-36=45, Resulting Numbers: [45] 45,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[3, 69], Operations: ['76-64=12', '81-12=69'] Exploring Operation: 3*69=207, Resulting Numbers: [207] 207,31 unequal: No Solution Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[12, 78], Operations: ['76-64=12', '81-3=78'] Exploring Operation: 12*78=936, Resulting Numbers: [936] 936,31 unequal: No Solution Exploring Operation: 12+78=90, Resulting Numbers: [90] 90,31 unequal: No Solution Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,31 unequal: No Solution Moving to Node #0,2,4 Current State: 31:[81, 15], Operations: ['76-64=12', '3+12=15'] Exploring Operation: 81-15=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 81+15=96, Resulting Numbers: [96] 96,31 unequal: No Solution Exploring Operation: 81*15=1215, Resulting Numbers: [1215] 1215,31 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:[64, 76, 78], Operations: ['81-3=78'] Exploring Operation: 78-64=14, Resulting Numbers: [76, 14] Generated Node #0,1,0: 31:[76, 14] Operation: 78-64=14 Exploring Operation: 76-64=12, Resulting Numbers: [78, 12] Generated Node #0,1,1: 31:[78, 12] Operation: 76-64=12 Exploring Operation: 64+78=142, Resulting Numbers: [76, 142] Generated Node #0,1,2: 31:[76, 142] Operation: 64+78=142 Exploring Operation: 78-76=2, Resulting Numbers: [64, 2] Generated Node #0,1,3: 31:[64, 2] Operation: 78-76=2 Exploring Operation: 64+76=140, Resulting Numbers: [78, 140] Generated Node #0,1,4: 31:[78, 140] Operation: 64+76=140 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[76, 14], Operations: ['81-3=78', '78-64=14'] Exploring Operation: 76*14=1064, Resulting Numbers: [1064] 1064,31 unequal: No Solution Exploring Operation: 76+14=90, Resulting Numbers: [90] 90,31 unequal: No Solution Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 31:[64, 2], Operations: ['81-3=78', '78-76=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,31 unequal: No Solution Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,31 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 31:[78, 12], Operations: ['81-3=78', '76-64=12'] Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 78+12=90, Resulting Numbers: [90] 90,31 unequal: No Solution Exploring Operation: 78*12=936, Resulting Numbers: [936] 936,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 31:[76, 142], Operations: ['81-3=78', '64+78=142'] Exploring Operation: 76+142=218, Resulting Numbers: [218] 218,31 unequal: No Solution Exploring Operation: 142-76=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 76*142=10792, Resulting Numbers: [10792] 10792,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 31:[78, 140], Operations: ['81-3=78', '64+76=140'] Exploring Operation: 78*140=10920, Resulting Numbers: [10920] 10920,31 unequal: No Solution Exploring Operation: 78+140=218, Resulting Numbers: [218] 218,31 unequal: No Solution Exploring Operation: 140-78=62, Resulting Numbers: [62] 62,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 1, 92, 34, 51 ]
62
[ "1+92=93", "34*93=3162", "3162/51=62" ]
Current State: 62:[1, 92, 34, 51], Operations: [] Exploring Operation: 1+92=93, Resulting Numbers: [34, 51, 93] Generated Node #2: [34, 51, 93] from Operation: 1+92=93 Current State: 62:[34, 51, 93], Operations: ['1+92=93'] Exploring Operation: 34*93=3162, Resulting Numbers: [51, 3162] Generated Node #3: [51, 3162] from Operation: 34*93=3162 Current State: 62:[51, 3162], Operations: ['1+92=93', '34*93=3162'] Exploring Operation: 3162/51=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[1, 92, 34, 51], Operations: [] Exploring Operation: 92-51=41, Resulting Numbers: [1, 34, 41] Generated Node #0,0: 62:[1, 34, 41] Operation: 92-51=41 Moving to Node #0,0 Current State: 62:[1, 34, 41], Operations: ['92-51=41'] Exploring Operation: 41-34=7, Resulting Numbers: [1, 7] Generated Node #0,0,0: 62:[1, 7] Operation: 41-34=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[1, 7], Operations: ['92-51=41', '41-34=7'] Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,62 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
[ 39, 78, 81, 66 ]
96
[ "78/39=2", "81*2=162", "162-66=96" ]
Current State: 96:[39, 78, 81, 66], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [81, 66, 2] Generated Node #2: [81, 66, 2] from Operation: 78/39=2 Current State: 96:[81, 66, 2], Operations: ['78/39=2'] Exploring Operation: 81*2=162, Resulting Numbers: [66, 162] Generated Node #3: [66, 162] from Operation: 81*2=162 Current State: 96:[66, 162], Operations: ['78/39=2', '81*2=162'] Exploring Operation: 162-66=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[39, 78, 81, 66], Operations: [] Exploring Operation: 78-66=12, Resulting Numbers: [39, 81, 12] Generated Node #0,0: 96:[39, 81, 12] Operation: 78-66=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[39, 81, 12], Operations: ['78-66=12'] Exploring Operation: 81-39=42, Resulting Numbers: [12, 42] Generated Node #0,0,0: 96:[12, 42] Operation: 81-39=42 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[12, 42], Operations: ['78-66=12', '81-39=42'] Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 40, 42, 31, 42 ]
40
[ "42-42=0", "31*0=0", "40+0=40" ]
Current State: 40:[40, 42, 31, 42], Operations: [] Exploring Operation: 42-42=0, Resulting Numbers: [40, 31, 0] Generated Node #2: [40, 31, 0] from Operation: 42-42=0 Current State: 40:[40, 31, 0], Operations: ['42-42=0'] Exploring Operation: 31*0=0, Resulting Numbers: [40, 0] Generated Node #3: [40, 0] from Operation: 31*0=0 Current State: 40:[40, 0], Operations: ['42-42=0', '31*0=0'] Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[40, 42, 31, 42], Operations: [] Exploring Operation: 42-31=11, Resulting Numbers: [40, 42, 11] Generated Node #0,0: 40:[40, 42, 11] Operation: 42-31=11 Exploring Operation: 42-31=11, Resulting Numbers: [40, 42, 11] Generated Node #0,1: 40:[40, 42, 11] Operation: 42-31=11 Moving to Node #0,0 Current State: 40:[40, 42, 11], Operations: ['42-31=11'] Exploring Operation: 42-40=2, Resulting Numbers: [11, 2] Generated Node #0,0,0: 40:[11, 2] Operation: 42-40=2 Exploring Operation: 42-11=31, Resulting Numbers: [40, 31] Generated Node #0,0,1: 40:[40, 31] Operation: 42-11=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[11, 2], Operations: ['42-31=11', '42-40=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,40 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[40, 31], Operations: ['42-31=11', '42-11=31'] Exploring Operation: 40+31=71, Resulting Numbers: [71] 71,40 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 40:[40, 42, 11], Operations: ['42-31=11'] Exploring Operation: 42-11=31, Resulting Numbers: [40, 31] Generated Node #0,1,0: 40:[40, 31] Operation: 42-11=31 Exploring Operation: 42-40=2, Resulting Numbers: [11, 2] Generated Node #0,1,1: 40:[11, 2] Operation: 42-40=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[11, 2], Operations: ['42-31=11', '42-40=2'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,40 unequal: No Solution Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[40, 31], Operations: ['42-31=11', '42-11=31'] Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,40 unequal: No Solution Exploring Operation: 40+31=71, Resulting Numbers: [71] 71,40 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
[ 43, 16, 15, 38 ]
48
[ "43-38=5", "16*15=240", "240/5=48" ]
Current State: 48:[43, 16, 15, 38], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [16, 15, 5] Generated Node #2: [16, 15, 5] from Operation: 43-38=5 Current State: 48:[16, 15, 5], Operations: ['43-38=5'] Exploring Operation: 16*15=240, Resulting Numbers: [5, 240] Generated Node #3: [5, 240] from Operation: 16*15=240 Current State: 48:[5, 240], Operations: ['43-38=5', '16*15=240'] Exploring Operation: 240/5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[43, 16, 15, 38], Operations: [] Exploring Operation: 38-15=23, Resulting Numbers: [43, 16, 23] Generated Node #0,0: 48:[43, 16, 23] Operation: 38-15=23 Exploring Operation: 43-38=5, Resulting Numbers: [16, 15, 5] Generated Node #0,1: 48:[16, 15, 5] Operation: 43-38=5 Exploring Operation: 38-16=22, Resulting Numbers: [43, 15, 22] Generated Node #0,2: 48:[43, 15, 22] Operation: 38-16=22 Moving to Node #0,1 Current State: 48:[16, 15, 5], Operations: ['43-38=5'] Exploring Operation: 16-15=1, Resulting Numbers: [5, 1] Generated Node #0,1,0: 48:[5, 1] Operation: 16-15=1 Exploring Operation: 15/5=3, Resulting Numbers: [16, 3] Generated Node #0,1,1: 48:[16, 3] Operation: 15/5=3 Exploring Operation: 16-5=11, Resulting Numbers: [15, 11] Generated Node #0,1,2: 48:[15, 11] Operation: 16-5=11 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 48:[16, 3], Operations: ['43-38=5', '15/5=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,48 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[43, 16, 15, 38], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [16, 15, 5] Generated Node #0,1: 48:[16, 15, 5] Operation: 43-38=5 Moving to Node #0,1 Current State: 48:[16, 15, 5], Operations: ['43-38=5'] Exploring Operation: 15/5=3, Resulting Numbers: [16, 3] Generated Node #0,1,1: 48:[16, 3] Operation: 15/5=3 Moving to Node #0,1,1 Current State: 48:[16, 3], Operations: ['43-38=5', '15/5=3'] Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 3, 21, 60, 33 ]
70
[ "33/3=11", "21+60=81", "81-11=70" ]
Current State: 70:[3, 21, 60, 33], Operations: [] Exploring Operation: 33/3=11, Resulting Numbers: [21, 60, 11] Generated Node #2: [21, 60, 11] from Operation: 33/3=11 Current State: 70:[21, 60, 11], Operations: ['33/3=11'] Exploring Operation: 21+60=81, Resulting Numbers: [11, 81] Generated Node #3: [11, 81] from Operation: 21+60=81 Current State: 70:[11, 81], Operations: ['33/3=11', '21+60=81'] Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[3, 21, 60, 33], Operations: [] Exploring Operation: 60-21=39, Resulting Numbers: [3, 33, 39] Generated Node #0,0: 70:[3, 33, 39] Operation: 60-21=39 Moving to Node #0,0 Current State: 70:[3, 33, 39], Operations: ['60-21=39'] Exploring Operation: 39-33=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 70:[3, 6] Operation: 39-33=6 Moving to Node #0,0,0 Current State: 70:[3, 6], Operations: ['60-21=39', '39-33=6'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,70 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 45, 74, 26, 16 ]
77
[ "45+74=119", "26+16=42", "119-42=77" ]
Current State: 77:[45, 74, 26, 16], Operations: [] Exploring Operation: 45+74=119, Resulting Numbers: [26, 16, 119] Generated Node #2: [26, 16, 119] from Operation: 45+74=119 Current State: 77:[26, 16, 119], Operations: ['45+74=119'] Exploring Operation: 26+16=42, Resulting Numbers: [119, 42] Generated Node #3: [119, 42] from Operation: 26+16=42 Current State: 77:[119, 42], Operations: ['45+74=119', '26+16=42'] Exploring Operation: 119-42=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[45, 74, 26, 16], Operations: [] Exploring Operation: 45-16=29, Resulting Numbers: [74, 26, 29] Generated Node #0,0: 77:[74, 26, 29] Operation: 45-16=29 Exploring Operation: 45+16=61, Resulting Numbers: [74, 26, 61] Generated Node #0,1: 77:[74, 26, 61] Operation: 45+16=61 Exploring Operation: 45+26=71, Resulting Numbers: [74, 16, 71] Generated Node #0,2: 77:[74, 16, 71] Operation: 45+26=71 Exploring Operation: 45-26=19, Resulting Numbers: [74, 16, 19] Generated Node #0,3: 77:[74, 16, 19] Operation: 45-26=19 Exploring Operation: 26-16=10, Resulting Numbers: [45, 74, 10] Generated Node #0,4: 77:[45, 74, 10] Operation: 26-16=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[74, 16, 71], Operations: ['45+26=71'] Exploring Operation: 74-71=3, Resulting Numbers: [16, 3] Generated Node #0,2,0: 77:[16, 3] Operation: 74-71=3 Exploring Operation: 74+16=90, Resulting Numbers: [71, 90] Generated Node #0,2,1: 77:[71, 90] Operation: 74+16=90 Exploring Operation: 16+71=87, Resulting Numbers: [74, 87] Generated Node #0,2,2: 77:[74, 87] Operation: 16+71=87 Exploring Operation: 74-16=58, Resulting Numbers: [71, 58] Generated Node #0,2,3: 77:[71, 58] Operation: 74-16=58 Exploring Operation: 71-16=55, Resulting Numbers: [74, 55] Generated Node #0,2,4: 77:[74, 55] Operation: 71-16=55 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 77:[16, 3], Operations: ['45+26=71', '74-71=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,77 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 #0,2,2 Current State: 77:[74, 87], Operations: ['45+26=71', '16+71=87'] Exploring Operation: 87-74=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 74*87=6438, Resulting Numbers: [6438] 6438,77 unequal: No Solution Exploring Operation: 74+87=161, Resulting Numbers: [161] 161,77 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 #0,2,1 Current State: 77:[71, 90], Operations: ['45+26=71', '74+16=90'] Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 71*90=6390, Resulting Numbers: [6390] 6390,77 unequal: No Solution Exploring Operation: 71+90=161, Resulting Numbers: [161] 161,77 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 #0,2,3 Current State: 77:[71, 58], Operations: ['45+26=71', '74-16=58'] Exploring Operation: 71+58=129, Resulting Numbers: [129] 129,77 unequal: No Solution Exploring Operation: 71-58=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 71*58=4118, Resulting Numbers: [4118] 4118,77 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 #0,2,4 Current State: 77:[74, 55], Operations: ['45+26=71', '71-16=55'] Exploring Operation: 74+55=129, Resulting Numbers: [129] 129,77 unequal: No Solution Exploring Operation: 74*55=4070, Resulting Numbers: [4070] 4070,77 unequal: No Solution Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,77 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: 77:[74, 16, 19], Operations: ['45-26=19'] Exploring Operation: 74+19=93, Resulting Numbers: [16, 93] Generated Node #0,3,0: 77:[16, 93] Operation: 74+19=93 Exploring Operation: 74+16=90, Resulting Numbers: [19, 90] Generated Node #0,3,1: 77:[19, 90] Operation: 74+16=90 Exploring Operation: 74-16=58, Resulting Numbers: [19, 58] Generated Node #0,3,2: 77:[19, 58] Operation: 74-16=58 Exploring Operation: 74-19=55, Resulting Numbers: [16, 55] Generated Node #0,3,3: 77:[16, 55] Operation: 74-19=55 Exploring Operation: 19-16=3, Resulting Numbers: [74, 3] Generated Node #0,3,4: 77:[74, 3] Operation: 19-16=3 Moving to Node #0,3,4 Current State: 77:[74, 3], Operations: ['45-26=19', '19-16=3'] Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[45, 74, 26, 16], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [74, 16, 19] Generated Node #0,3: 77:[74, 16, 19] Operation: 45-26=19 Moving to Node #0,3 Current State: 77:[74, 16, 19], Operations: ['45-26=19'] Exploring Operation: 19-16=3, Resulting Numbers: [74, 3] Generated Node #0,3,4: 77:[74, 3] Operation: 19-16=3 Moving to Node #0,3,4 Current State: 77:[74, 3], Operations: ['45-26=19', '19-16=3'] Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
sum_heuristic
[ 10, 88, 2, 22 ]
16
[ "10+2=12", "88/22=4", "12+4=16" ]
Current State: 16:[10, 88, 2, 22], Operations: [] Exploring Operation: 10+2=12, Resulting Numbers: [88, 22, 12] Generated Node #2: [88, 22, 12] from Operation: 10+2=12 Current State: 16:[88, 22, 12], Operations: ['10+2=12'] Exploring Operation: 88/22=4, Resulting Numbers: [12, 4] Generated Node #3: [12, 4] from Operation: 88/22=4 Current State: 16:[12, 4], Operations: ['10+2=12', '88/22=4'] Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[10, 88, 2, 22], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [10, 22, 44] Generated Node #0,0: 16:[10, 22, 44] Operation: 88/2=44 Exploring Operation: 88/22=4, Resulting Numbers: [10, 2, 4] Generated Node #0,1: 16:[10, 2, 4] Operation: 88/22=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[10, 2, 4], Operations: ['88/22=4'] Exploring Operation: 10/2=5, Resulting Numbers: [4, 5] Generated Node #0,1,0: 16:[4, 5] Operation: 10/2=5 Exploring Operation: 10-2=8, Resulting Numbers: [4, 8] Generated Node #0,1,1: 16:[4, 8] Operation: 10-2=8 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[4, 8], Operations: ['88/22=4', '10-2=8'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,16 unequal: No Solution No 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: 16:[4, 5], Operations: ['88/22=4', '10/2=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,16 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: 16:[10, 22, 44], Operations: ['88/2=44'] Exploring Operation: 44-22=22, Resulting Numbers: [10, 22] Generated Node #0,0,0: 16:[10, 22] Operation: 44-22=22 Exploring Operation: 44/22=2, Resulting Numbers: [10, 2] Generated Node #0,0,1: 16:[10, 2] Operation: 44/22=2 Moving to Node #0,0,1 Current State: 16:[10, 2], Operations: ['88/2=44', '44/22=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[10, 22], Operations: ['88/2=44', '44-22=22'] Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,16 unequal: No Solution Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 51, 11, 28, 48 ]
60
[ "51-11=40", "48-28=20", "40+20=60" ]
Current State: 60:[51, 11, 28, 48], Operations: [] Exploring Operation: 51-11=40, Resulting Numbers: [28, 48, 40] Generated Node #2: [28, 48, 40] from Operation: 51-11=40 Current State: 60:[28, 48, 40], Operations: ['51-11=40'] Exploring Operation: 48-28=20, Resulting Numbers: [40, 20] Generated Node #3: [40, 20] from Operation: 48-28=20 Current State: 60:[40, 20], Operations: ['51-11=40', '48-28=20'] Exploring Operation: 40+20=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[51, 11, 28, 48], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [11, 28, 3] Generated Node #0,0: 60:[11, 28, 3] Operation: 51-48=3 Moving to Node #0,0 Current State: 60:[11, 28, 3], Operations: ['51-48=3'] Exploring Operation: 28-11=17, Resulting Numbers: [3, 17] Generated Node #0,0,0: 60:[3, 17] Operation: 28-11=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[3, 17], Operations: ['51-48=3', '28-11=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,60 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
[ 42, 59, 97, 25 ]
53
[ "42*59=2478", "97*25=2425", "2478-2425=53" ]
Current State: 53:[42, 59, 97, 25], Operations: [] Exploring Operation: 42*59=2478, Resulting Numbers: [97, 25, 2478] Generated Node #2: [97, 25, 2478] from Operation: 42*59=2478 Current State: 53:[97, 25, 2478], Operations: ['42*59=2478'] Exploring Operation: 97*25=2425, Resulting Numbers: [2478, 2425] Generated Node #3: [2478, 2425] from Operation: 97*25=2425 Current State: 53:[2478, 2425], Operations: ['42*59=2478', '97*25=2425'] Exploring Operation: 2478-2425=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[42, 59, 97, 25], Operations: [] Exploring Operation: 97-42=55, Resulting Numbers: [59, 25, 55] Generated Node #0,0: 53:[59, 25, 55] Operation: 97-42=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[59, 25, 55], Operations: ['97-42=55'] Exploring Operation: 59-25=34, Resulting Numbers: [55, 34] Generated Node #0,0,0: 53:[55, 34] Operation: 59-25=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[55, 34], Operations: ['97-42=55', '59-25=34'] Exploring Operation: 55-34=21, Resulting Numbers: [21] 21,53 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_1
sum_heuristic
[ 2, 71, 61, 53 ]
33
[ "71-61=10", "2*10=20", "53-20=33" ]
Current State: 33:[2, 71, 61, 53], Operations: [] Exploring Operation: 71-61=10, Resulting Numbers: [2, 53, 10] Generated Node #2: [2, 53, 10] from Operation: 71-61=10 Current State: 33:[2, 53, 10], Operations: ['71-61=10'] Exploring Operation: 2*10=20, Resulting Numbers: [53, 20] Generated Node #3: [53, 20] from Operation: 2*10=20 Current State: 33:[53, 20], Operations: ['71-61=10', '2*10=20'] Exploring Operation: 53-20=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[2, 71, 61, 53], Operations: [] Exploring Operation: 71-61=10, Resulting Numbers: [2, 53, 10] Generated Node #0,0: 33:[2, 53, 10] Operation: 71-61=10 Exploring Operation: 61-53=8, Resulting Numbers: [2, 71, 8] Generated Node #0,1: 33:[2, 71, 8] Operation: 61-53=8 Exploring Operation: 71-53=18, Resulting Numbers: [2, 61, 18] Generated Node #0,2: 33:[2, 61, 18] Operation: 71-53=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[2, 53, 10], Operations: ['71-61=10'] Exploring Operation: 53-2=51, Resulting Numbers: [10, 51] Generated Node #0,0,0: 33:[10, 51] Operation: 53-2=51 Exploring Operation: 2+10=12, Resulting Numbers: [53, 12] Generated Node #0,0,1: 33:[53, 12] Operation: 2+10=12 Exploring Operation: 53-10=43, Resulting Numbers: [2, 43] Generated Node #0,0,2: 33:[2, 43] Operation: 53-10=43 Moving to Node #0,0,2 Current State: 33:[2, 43], Operations: ['71-61=10', '53-10=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,33 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,33 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[10, 51], Operations: ['71-61=10', '53-2=51'] Exploring Operation: 10*51=510, Resulting Numbers: [510] 510,33 unequal: No Solution Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,33 unequal: No Solution Exploring Operation: 10+51=61, Resulting Numbers: [61] 61,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[53, 12], Operations: ['71-61=10', '2+10=12'] Exploring Operation: 53*12=636, Resulting Numbers: [636] 636,33 unequal: No Solution Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,33 unequal: No Solution Exploring Operation: 53+12=65, Resulting Numbers: [65] 65,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[2, 61, 18], Operations: ['71-53=18'] Exploring Operation: 61-18=43, Resulting Numbers: [2, 43] Generated Node #0,2,0: 33:[2, 43] Operation: 61-18=43 Exploring Operation: 18/2=9, Resulting Numbers: [61, 9] Generated Node #0,2,1: 33:[61, 9] Operation: 18/2=9 Exploring Operation: 2*18=36, Resulting Numbers: [61, 36] Generated Node #0,2,2: 33:[61, 36] Operation: 2*18=36 Moving to Node #0,2,0 Current State: 33:[2, 43], Operations: ['71-53=18', '61-18=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,33 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[61, 9], Operations: ['71-53=18', '18/2=9'] Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,33 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,33 unequal: No Solution Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,33 unequal: No Solution Moving to Node #0,2,2 Current State: 33:[61, 36], Operations: ['71-53=18', '2*18=36'] Exploring Operation: 61+36=97, Resulting Numbers: [97] 97,33 unequal: No Solution Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,33 unequal: No Solution Exploring Operation: 61*36=2196, Resulting Numbers: [2196] 2196,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[2, 71, 8], Operations: ['61-53=8'] Exploring Operation: 2+8=10, Resulting Numbers: [71, 10] Generated Node #0,1,0: 33:[71, 10] Operation: 2+8=10 Exploring Operation: 71-8=63, Resulting Numbers: [2, 63] Generated Node #0,1,1: 33:[2, 63] Operation: 71-8=63 Exploring Operation: 71-2=69, Resulting Numbers: [8, 69] Generated Node #0,1,2: 33:[8, 69] Operation: 71-2=69 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 33:[2, 63], Operations: ['61-53=8', '71-8=63'] Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,33 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,33 unequal: No Solution Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,33 unequal: No Solution No 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: 33:[71, 10], Operations: ['61-53=8', '2+8=10'] Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,33 unequal: No Solution Exploring Operation: 71+10=81, Resulting Numbers: [81] 81,33 unequal: No Solution Exploring Operation: 71*10=710, Resulting Numbers: [710] 710,33 unequal: No Solution No 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: 33:[8, 69], Operations: ['61-53=8', '71-2=69'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,33 unequal: No Solution Exploring Operation: 8*69=552, Resulting Numbers: [552] 552,33 unequal: No Solution Exploring Operation: 8+69=77, Resulting Numbers: [77] 77,33 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
[ 41, 9, 85, 89 ]
46
[ "41+9=50", "89-85=4", "50-4=46" ]
Current State: 46:[41, 9, 85, 89], Operations: [] Exploring Operation: 41+9=50, Resulting Numbers: [85, 89, 50] Generated Node #2: [85, 89, 50] from Operation: 41+9=50 Current State: 46:[85, 89, 50], Operations: ['41+9=50'] Exploring Operation: 89-85=4, Resulting Numbers: [50, 4] Generated Node #3: [50, 4] from Operation: 89-85=4 Current State: 46:[50, 4], Operations: ['41+9=50', '89-85=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[41, 9, 85, 89], Operations: [] Exploring Operation: 85-9=76, Resulting Numbers: [41, 89, 76] Generated Node #0,0: 46:[41, 89, 76] Operation: 85-9=76 Exploring Operation: 85-41=44, Resulting Numbers: [9, 89, 44] Generated Node #0,1: 46:[9, 89, 44] Operation: 85-41=44 Exploring Operation: 89-41=48, Resulting Numbers: [9, 85, 48] Generated Node #0,2: 46:[9, 85, 48] Operation: 89-41=48 Exploring Operation: 89-85=4, Resulting Numbers: [41, 9, 4] Generated Node #0,3: 46:[41, 9, 4] Operation: 89-85=4 Moving to Node #0,3 Current State: 46:[41, 9, 4], Operations: ['89-85=4'] Exploring Operation: 41+4=45, Resulting Numbers: [9, 45] Generated Node #0,3,0: 46:[9, 45] Operation: 41+4=45 Exploring Operation: 41-9=32, Resulting Numbers: [4, 32] Generated Node #0,3,1: 46:[4, 32] Operation: 41-9=32 Exploring Operation: 9-4=5, Resulting Numbers: [41, 5] Generated Node #0,3,2: 46:[41, 5] Operation: 9-4=5 Exploring Operation: 41+9=50, Resulting Numbers: [4, 50] Generated Node #0,3,3: 46:[4, 50] Operation: 41+9=50 Moving to Node #0,2 Current State: 46:[9, 85, 48], Operations: ['89-41=48'] Exploring Operation: 9+85=94, Resulting Numbers: [48, 94] Generated Node #0,2,0: 46:[48, 94] Operation: 9+85=94 Exploring Operation: 85-48=37, Resulting Numbers: [9, 37] Generated Node #0,2,1: 46:[9, 37] Operation: 85-48=37 Exploring Operation: 85-9=76, Resulting Numbers: [48, 76] Generated Node #0,2,2: 46:[48, 76] Operation: 85-9=76 Exploring Operation: 48-9=39, Resulting Numbers: [85, 39] Generated Node #0,2,3: 46:[85, 39] Operation: 48-9=39 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 46:[9, 37], Operations: ['89-41=48', '85-48=37'] Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,46 unequal: No Solution Exploring Operation: 9*37=333, Resulting Numbers: [333] 333,46 unequal: No Solution Exploring Operation: 9+37=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[41, 9, 85, 89], Operations: [] Exploring Operation: 89-41=48, Resulting Numbers: [9, 85, 48] Generated Node #0,2: 46:[9, 85, 48] Operation: 89-41=48 Moving to Node #0,2 Current State: 46:[9, 85, 48], Operations: ['89-41=48'] Exploring Operation: 85-48=37, Resulting Numbers: [9, 37] Generated Node #0,2,1: 46:[9, 37] Operation: 85-48=37 Moving to Node #0,2,1 Current State: 46:[9, 37], Operations: ['89-41=48', '85-48=37'] Exploring Operation: 9+37=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 45, 53, 78, 5 ]
14
[ "53-45=8", "78-8=70", "70/5=14" ]
Current State: 14:[45, 53, 78, 5], Operations: [] Exploring Operation: 53-45=8, Resulting Numbers: [78, 5, 8] Generated Node #2: [78, 5, 8] from Operation: 53-45=8 Current State: 14:[78, 5, 8], Operations: ['53-45=8'] Exploring Operation: 78-8=70, Resulting Numbers: [5, 70] Generated Node #3: [5, 70] from Operation: 78-8=70 Current State: 14:[5, 70], Operations: ['53-45=8', '78-8=70'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[45, 53, 78, 5], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [45, 5, 25] Generated Node #0,0: 14:[45, 5, 25] Operation: 78-53=25 Exploring Operation: 78-45=33, Resulting Numbers: [53, 5, 33] Generated Node #0,1: 14:[53, 5, 33] Operation: 78-45=33 Exploring Operation: 53-45=8, Resulting Numbers: [78, 5, 8] Generated Node #0,2: 14:[78, 5, 8] Operation: 53-45=8 Moving to Node #0,0 Current State: 14:[45, 5, 25], Operations: ['78-53=25'] Exploring Operation: 45/5=9, Resulting Numbers: [25, 9] Generated Node #0,0,0: 14:[25, 9] Operation: 45/5=9 Exploring Operation: 25/5=5, Resulting Numbers: [45, 5] Generated Node #0,0,1: 14:[45, 5] Operation: 25/5=5 Exploring Operation: 45-25=20, Resulting Numbers: [5, 20] Generated Node #0,0,2: 14:[5, 20] Operation: 45-25=20 Moving to Node #0,1 Current State: 14:[53, 5, 33], Operations: ['78-45=33'] Exploring Operation: 33-5=28, Resulting Numbers: [53, 28] Generated Node #0,1,0: 14:[53, 28] Operation: 33-5=28 Exploring Operation: 53-5=48, Resulting Numbers: [33, 48] Generated Node #0,1,1: 14:[33, 48] Operation: 53-5=48 Exploring Operation: 53-33=20, Resulting Numbers: [5, 20] Generated Node #0,1,2: 14:[5, 20] Operation: 53-33=20 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 14:[5, 20], Operations: ['78-45=33', '53-33=20'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[53, 28], Operations: ['78-45=33', '33-5=28'] Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,14 unequal: No Solution Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 14:[33, 48], Operations: ['78-45=33', '53-5=48'] Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,14 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,14 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 14:[78, 5, 8], Operations: ['53-45=8'] Exploring Operation: 5+8=13, Resulting Numbers: [78, 13] Generated Node #0,2,0: 14:[78, 13] Operation: 5+8=13 Exploring Operation: 78-8=70, Resulting Numbers: [5, 70] Generated Node #0,2,1: 14:[5, 70] Operation: 78-8=70 Exploring Operation: 78-5=73, Resulting Numbers: [8, 73] Generated Node #0,2,2: 14:[8, 73] Operation: 78-5=73 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[5, 70], Operations: ['53-45=8', '78-8=70'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[45, 53, 78, 5], Operations: [] Exploring Operation: 53-45=8, Resulting Numbers: [78, 5, 8] Generated Node #0,2: 14:[78, 5, 8] Operation: 53-45=8 Moving to Node #0,2 Current State: 14:[78, 5, 8], Operations: ['53-45=8'] Exploring Operation: 78-8=70, Resulting Numbers: [5, 70] Generated Node #0,2,1: 14:[5, 70] Operation: 78-8=70 Moving to Node #0,2,1 Current State: 14:[5, 70], Operations: ['53-45=8', '78-8=70'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
mult_heuristic
[ 95, 11, 97, 35 ]
23
[ "97-95=2", "11+35=46", "46/2=23" ]
Current State: 23:[95, 11, 97, 35], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [11, 35, 2] Generated Node #2: [11, 35, 2] from Operation: 97-95=2 Current State: 23:[11, 35, 2], Operations: ['97-95=2'] Exploring Operation: 11+35=46, Resulting Numbers: [2, 46] Generated Node #3: [2, 46] from Operation: 11+35=46 Current State: 23:[2, 46], Operations: ['97-95=2', '11+35=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[95, 11, 97, 35], Operations: [] Exploring Operation: 97-35=62, Resulting Numbers: [95, 11, 62] Generated Node #0,0: 23:[95, 11, 62] Operation: 97-35=62 Exploring Operation: 95-11=84, Resulting Numbers: [97, 35, 84] Generated Node #0,1: 23:[97, 35, 84] Operation: 95-11=84 Exploring Operation: 97-95=2, Resulting Numbers: [11, 35, 2] Generated Node #0,2: 23:[11, 35, 2] Operation: 97-95=2 Exploring Operation: 95-35=60, Resulting Numbers: [11, 97, 60] Generated Node #0,3: 23:[11, 97, 60] Operation: 95-35=60 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[11, 35, 2], Operations: ['97-95=2'] Exploring Operation: 35-11=24, Resulting Numbers: [2, 24] Generated Node #0,2,0: 23:[2, 24] Operation: 35-11=24 Exploring Operation: 11*2=22, Resulting Numbers: [35, 22] Generated Node #0,2,1: 23:[35, 22] Operation: 11*2=22 Exploring Operation: 35-2=33, Resulting Numbers: [11, 33] Generated Node #0,2,2: 23:[11, 33] Operation: 35-2=33 Exploring Operation: 11+2=13, Resulting Numbers: [35, 13] Generated Node #0,2,3: 23:[35, 13] Operation: 11+2=13 Moving to Node #0,2,1 Current State: 23:[35, 22], Operations: ['97-95=2', '11*2=22'] Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[11, 33], Operations: ['97-95=2', '35-2=33'] Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 11+33=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 11*33=363, Resulting Numbers: [363] 363,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[2, 24], Operations: ['97-95=2', '35-11=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[35, 13], Operations: ['97-95=2', '11+2=13'] Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[95, 11, 62], Operations: ['97-35=62'] Exploring Operation: 95+11=106, Resulting Numbers: [62, 106] Generated Node #0,0,0: 23:[62, 106] Operation: 95+11=106 Exploring Operation: 62-11=51, Resulting Numbers: [95, 51] Generated Node #0,0,1: 23:[95, 51] Operation: 62-11=51 Exploring Operation: 95-62=33, Resulting Numbers: [11, 33] Generated Node #0,0,2: 23:[11, 33] Operation: 95-62=33 Exploring Operation: 95-11=84, Resulting Numbers: [62, 84] Generated Node #0,0,3: 23:[62, 84] Operation: 95-11=84 Moving to Node #0,0,2 Current State: 23:[11, 33], Operations: ['97-35=62', '95-62=33'] Exploring Operation: 11+33=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 11*33=363, Resulting Numbers: [363] 363,23 unequal: No Solution Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[62, 84], Operations: ['97-35=62', '95-11=84'] Exploring Operation: 62+84=146, Resulting Numbers: [146] 146,23 unequal: No Solution Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 62*84=5208, Resulting Numbers: [5208] 5208,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[95, 51], Operations: ['97-35=62', '62-11=51'] Exploring Operation: 95*51=4845, Resulting Numbers: [4845] 4845,23 unequal: No Solution Exploring Operation: 95+51=146, Resulting Numbers: [146] 146,23 unequal: No Solution Exploring Operation: 95-51=44, Resulting Numbers: [44] 44,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[62, 106], Operations: ['97-35=62', '95+11=106'] Exploring Operation: 62+106=168, Resulting Numbers: [168] 168,23 unequal: No Solution Exploring Operation: 106-62=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 62*106=6572, Resulting Numbers: [6572] 6572,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[11, 97, 60], Operations: ['95-35=60'] Exploring Operation: 97-11=86, Resulting Numbers: [60, 86] Generated Node #0,3,0: 23:[60, 86] Operation: 97-11=86 Exploring Operation: 60-11=49, Resulting Numbers: [97, 49] Generated Node #0,3,1: 23:[97, 49] Operation: 60-11=49 Exploring Operation: 97-60=37, Resulting Numbers: [11, 37] Generated Node #0,3,2: 23:[11, 37] Operation: 97-60=37 Exploring Operation: 11+97=108, Resulting Numbers: [60, 108] Generated Node #0,3,3: 23:[60, 108] Operation: 11+97=108 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 23:[11, 37], Operations: ['95-35=60', '97-60=37'] Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 11*37=407, Resulting Numbers: [407] 407,23 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,23 unequal: No Solution No 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: 23:[60, 86], Operations: ['95-35=60', '97-11=86'] Exploring Operation: 60+86=146, Resulting Numbers: [146] 146,23 unequal: No Solution Exploring Operation: 86-60=26, Resulting Numbers: [26] 26,23 unequal: No Solution Exploring Operation: 60*86=5160, Resulting Numbers: [5160] 5160,23 unequal: No Solution No 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: 23:[97, 49], Operations: ['95-35=60', '60-11=49'] Exploring Operation: 97*49=4753, Resulting Numbers: [4753] 4753,23 unequal: No Solution Exploring Operation: 97-49=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 97+49=146, Resulting Numbers: [146] 146,23 unequal: No Solution No 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: 23:[60, 108], Operations: ['95-35=60', '11+97=108'] Exploring Operation: 60+108=168, Resulting Numbers: [168] 168,23 unequal: No Solution Exploring Operation: 60*108=6480, Resulting Numbers: [6480] 6480,23 unequal: No Solution Exploring Operation: 108-60=48, Resulting Numbers: [48] 48,23 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: 23:[97, 35, 84], Operations: ['95-11=84'] Exploring Operation: 97+35=132, Resulting Numbers: [84, 132] Generated Node #0,1,0: 23:[84, 132] Operation: 97+35=132 Exploring Operation: 84-35=49, Resulting Numbers: [97, 49] Generated Node #0,1,1: 23:[97, 49] Operation: 84-35=49 Exploring Operation: 97-84=13, Resulting Numbers: [35, 13] Generated Node #0,1,2: 23:[35, 13] Operation: 97-84=13 Exploring Operation: 97-35=62, Resulting Numbers: [84, 62] Generated Node #0,1,3: 23:[84, 62] Operation: 97-35=62 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 23:[35, 13], Operations: ['95-11=84', '97-84=13'] Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,23 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,23 unequal: No Solution No 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: 23:[97, 49], Operations: ['95-11=84', '84-35=49'] Exploring Operation: 97+49=146, Resulting Numbers: [146] 146,23 unequal: No Solution Exploring Operation: 97*49=4753, Resulting Numbers: [4753] 4753,23 unequal: No Solution Exploring Operation: 97-49=48, Resulting Numbers: [48] 48,23 unequal: No Solution No 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: 23:[84, 62], Operations: ['95-11=84', '97-35=62'] Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 84+62=146, Resulting Numbers: [146] 146,23 unequal: No Solution Exploring Operation: 84*62=5208, Resulting Numbers: [5208] 5208,23 unequal: No Solution No 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: 23:[84, 132], Operations: ['95-11=84', '97+35=132'] Exploring Operation: 84+132=216, Resulting Numbers: [216] 216,23 unequal: No Solution Exploring Operation: 84*132=11088, Resulting Numbers: [11088] 11088,23 unequal: No Solution Exploring Operation: 132-84=48, Resulting Numbers: [48] 48,23 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
[ 93, 53, 52, 86 ]
15
[ "93-86=7", "53+52=105", "105/7=15" ]
Current State: 15:[93, 53, 52, 86], Operations: [] Exploring Operation: 93-86=7, Resulting Numbers: [53, 52, 7] Generated Node #2: [53, 52, 7] from Operation: 93-86=7 Current State: 15:[53, 52, 7], Operations: ['93-86=7'] Exploring Operation: 53+52=105, Resulting Numbers: [7, 105] Generated Node #3: [7, 105] from Operation: 53+52=105 Current State: 15:[7, 105], Operations: ['93-86=7', '53+52=105'] Exploring Operation: 105/7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[93, 53, 52, 86], Operations: [] Exploring Operation: 93-53=40, Resulting Numbers: [52, 86, 40] Generated Node #0,0: 15:[52, 86, 40] Operation: 93-53=40 Exploring Operation: 93-86=7, Resulting Numbers: [53, 52, 7] Generated Node #0,1: 15:[53, 52, 7] Operation: 93-86=7 Exploring Operation: 86-52=34, Resulting Numbers: [93, 53, 34] Generated Node #0,2: 15:[93, 53, 34] Operation: 86-52=34 Exploring Operation: 93-52=41, Resulting Numbers: [53, 86, 41] Generated Node #0,3: 15:[53, 86, 41] Operation: 93-52=41 Exploring Operation: 86-53=33, Resulting Numbers: [93, 52, 33] Generated Node #0,4: 15:[93, 52, 33] Operation: 86-53=33 Moving to Node #0,1 Current State: 15:[53, 52, 7], Operations: ['93-86=7'] Exploring Operation: 53-7=46, Resulting Numbers: [52, 46] Generated Node #0,1,0: 15:[52, 46] Operation: 53-7=46 Exploring Operation: 53-52=1, Resulting Numbers: [7, 1] Generated Node #0,1,1: 15:[7, 1] Operation: 53-52=1 Exploring Operation: 53+7=60, Resulting Numbers: [52, 60] Generated Node #0,1,2: 15:[52, 60] Operation: 53+7=60 Exploring Operation: 52+7=59, Resulting Numbers: [53, 59] Generated Node #0,1,3: 15:[53, 59] Operation: 52+7=59 Exploring Operation: 52-7=45, Resulting Numbers: [53, 45] Generated Node #0,1,4: 15:[53, 45] Operation: 52-7=45 Moving to Node #0,4 Current State: 15:[93, 52, 33], Operations: ['86-53=33'] Exploring Operation: 93-33=60, Resulting Numbers: [52, 60] Generated Node #0,4,0: 15:[52, 60] Operation: 93-33=60 Exploring Operation: 93+52=145, Resulting Numbers: [33, 145] Generated Node #0,4,1: 15:[33, 145] Operation: 93+52=145 Exploring Operation: 93+33=126, Resulting Numbers: [52, 126] Generated Node #0,4,2: 15:[52, 126] Operation: 93+33=126 Exploring Operation: 52-33=19, Resulting Numbers: [93, 19] Generated Node #0,4,3: 15:[93, 19] Operation: 52-33=19 Exploring Operation: 93-52=41, Resulting Numbers: [33, 41] Generated Node #0,4,4: 15:[33, 41] Operation: 93-52=41 Moving to Node #0,0 Current State: 15:[52, 86, 40], Operations: ['93-53=40'] Exploring Operation: 86-40=46, Resulting Numbers: [52, 46] Generated Node #0,0,0: 15:[52, 46] Operation: 86-40=46 Exploring Operation: 52-40=12, Resulting Numbers: [86, 12] Generated Node #0,0,1: 15:[86, 12] Operation: 52-40=12 Exploring Operation: 52+40=92, Resulting Numbers: [86, 92] Generated Node #0,0,2: 15:[86, 92] Operation: 52+40=92 Exploring Operation: 52+86=138, Resulting Numbers: [40, 138] Generated Node #0,0,3: 15:[40, 138] Operation: 52+86=138 Exploring Operation: 86-52=34, Resulting Numbers: [40, 34] Generated Node #0,0,4: 15:[40, 34] Operation: 86-52=34 Moving to Node #0,2 Current State: 15:[93, 53, 34], Operations: ['86-52=34'] Exploring Operation: 93-34=59, Resulting Numbers: [53, 59] Generated Node #0,2,0: 15:[53, 59] Operation: 93-34=59 Exploring Operation: 93+53=146, Resulting Numbers: [34, 146] Generated Node #0,2,1: 15:[34, 146] Operation: 93+53=146 Exploring Operation: 93+34=127, Resulting Numbers: [53, 127] Generated Node #0,2,2: 15:[53, 127] Operation: 93+34=127 Exploring Operation: 53-34=19, Resulting Numbers: [93, 19] Generated Node #0,2,3: 15:[93, 19] Operation: 53-34=19 Exploring Operation: 93-53=40, Resulting Numbers: [34, 40] Generated Node #0,2,4: 15:[34, 40] Operation: 93-53=40 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 15:[34, 40], Operations: ['86-52=34', '93-53=40'] Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,15 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[53, 59], Operations: ['86-52=34', '93-34=59'] Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,15 unequal: No Solution Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,15 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 15:[93, 19], Operations: ['86-52=34', '53-34=19'] Exploring Operation: 93-19=74, Resulting Numbers: [74] 74,15 unequal: No Solution Exploring Operation: 93+19=112, Resulting Numbers: [112] 112,15 unequal: No Solution Exploring Operation: 93*19=1767, Resulting Numbers: [1767] 1767,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[34, 146], Operations: ['86-52=34', '93+53=146'] Exploring Operation: 34*146=4964, Resulting Numbers: [4964] 4964,15 unequal: No Solution Exploring Operation: 34+146=180, Resulting Numbers: [180] 180,15 unequal: No Solution Exploring Operation: 146-34=112, Resulting Numbers: [112] 112,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[53, 127], Operations: ['86-52=34', '93+34=127'] Exploring Operation: 53*127=6731, Resulting Numbers: [6731] 6731,15 unequal: No Solution Exploring Operation: 53+127=180, Resulting Numbers: [180] 180,15 unequal: No Solution Exploring Operation: 127-53=74, Resulting Numbers: [74] 74,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 15:[53, 86, 41], Operations: ['93-52=41'] Exploring Operation: 86-41=45, Resulting Numbers: [53, 45] Generated Node #0,3,0: 15:[53, 45] Operation: 86-41=45 Exploring Operation: 53-41=12, Resulting Numbers: [86, 12] Generated Node #0,3,1: 15:[86, 12] Operation: 53-41=12 Exploring Operation: 53+86=139, Resulting Numbers: [41, 139] Generated Node #0,3,2: 15:[41, 139] Operation: 53+86=139 Exploring Operation: 53+41=94, Resulting Numbers: [86, 94] Generated Node #0,3,3: 15:[86, 94] Operation: 53+41=94 Exploring Operation: 86-53=33, Resulting Numbers: [41, 33] Generated Node #0,3,4: 15:[41, 33] Operation: 86-53=33 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 15:[41, 33], Operations: ['93-52=41', '86-53=33'] Exploring Operation: 41+33=74, Resulting Numbers: [74] 74,15 unequal: No Solution Exploring Operation: 41*33=1353, Resulting Numbers: [1353] 1353,15 unequal: No Solution Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 15:[53, 45], Operations: ['93-52=41', '86-41=45'] Exploring Operation: 53*45=2385, Resulting Numbers: [2385] 2385,15 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 15:[86, 12], Operations: ['93-52=41', '53-41=12'] Exploring Operation: 86-12=74, Resulting Numbers: [74] 74,15 unequal: No Solution Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 86*12=1032, Resulting Numbers: [1032] 1032,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 15:[41, 139], Operations: ['93-52=41', '53+86=139'] Exploring Operation: 41*139=5699, Resulting Numbers: [5699] 5699,15 unequal: No Solution Exploring Operation: 41+139=180, Resulting Numbers: [180] 180,15 unequal: No Solution Exploring Operation: 139-41=98, Resulting Numbers: [98] 98,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 15:[86, 94], Operations: ['93-52=41', '53+41=94'] Exploring Operation: 86*94=8084, Resulting Numbers: [8084] 8084,15 unequal: No Solution Exploring Operation: 86+94=180, Resulting Numbers: [180] 180,15 unequal: No Solution Exploring Operation: 94-86=8, Resulting Numbers: [8] 8,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 15:[7, 1], Operations: ['93-86=7', '53-52=1'] Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,15 unequal: No Solution Moving to Node #0,4,4 Current State: 15:[33, 41], Operations: ['86-53=33', '93-52=41'] Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 33*41=1353, Resulting Numbers: [1353] 1353,15 unequal: No Solution Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,15 unequal: No Solution Moving to Node #0,0,4 Current State: 15:[40, 34], Operations: ['93-53=40', '86-52=34'] Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,15 unequal: No Solution Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,15 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,15 unequal: No Solution Moving to Node #0,1,4 Current State: 15:[53, 45], Operations: ['93-86=7', '52-7=45'] Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 53*45=2385, Resulting Numbers: [2385] 2385,15 unequal: No Solution Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,15 unequal: No Solution Moving to Node #0,0,0 Current State: 15:[52, 46], Operations: ['93-53=40', '86-40=46'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 52+46=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 52*46=2392, Resulting Numbers: [2392] 2392,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[52, 46], Operations: ['93-86=7', '53-7=46'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 52+46=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 52*46=2392, Resulting Numbers: [2392] 2392,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[86, 12], Operations: ['93-53=40', '52-40=12'] Exploring Operation: 86-12=74, Resulting Numbers: [74] 74,15 unequal: No Solution Exploring Operation: 86*12=1032, Resulting Numbers: [1032] 1032,15 unequal: No Solution Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,15 unequal: No Solution Moving to Node #0,4,0 Current State: 15:[52, 60], Operations: ['86-53=33', '93-33=60'] Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,15 unequal: No Solution Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[53, 59], Operations: ['93-86=7', '52+7=59'] Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,15 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[52, 60], Operations: ['93-86=7', '53+7=60'] Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,15 unequal: No Solution Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,15 unequal: No Solution Moving to Node #0,4,3 Current State: 15:[93, 19], Operations: ['86-53=33', '52-33=19'] Exploring Operation: 93*19=1767, Resulting Numbers: [1767] 1767,15 unequal: No Solution Exploring Operation: 93+19=112, Resulting Numbers: [112] 112,15 unequal: No Solution Exploring Operation: 93-19=74, Resulting Numbers: [74] 74,15 unequal: No Solution Moving to Node #0,0,2 Current State: 15:[86, 92], Operations: ['93-53=40', '52+40=92'] Exploring Operation: 92-86=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 86+92=178, Resulting Numbers: [178] 178,15 unequal: No Solution Exploring Operation: 86*92=7912, Resulting Numbers: [7912] 7912,15 unequal: No Solution Moving to Node #0,0,3 Current State: 15:[40, 138], Operations: ['93-53=40', '52+86=138'] Exploring Operation: 138-40=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 40*138=5520, Resulting Numbers: [5520] 5520,15 unequal: No Solution Exploring Operation: 40+138=178, Resulting Numbers: [178] 178,15 unequal: No Solution Moving to Node #0,4,2 Current State: 15:[52, 126], Operations: ['86-53=33', '93+33=126'] Exploring Operation: 52*126=6552, Resulting Numbers: [6552] 6552,15 unequal: No Solution Exploring Operation: 52+126=178, Resulting Numbers: [178] 178,15 unequal: No Solution Exploring Operation: 126-52=74, Resulting Numbers: [74] 74,15 unequal: No Solution Moving to Node #0,4,1 Current State: 15:[33, 145], Operations: ['86-53=33', '93+52=145'] Exploring Operation: 33+145=178, Resulting Numbers: [178] 178,15 unequal: No Solution Exploring Operation: 145-33=112, Resulting Numbers: [112] 112,15 unequal: No Solution Exploring Operation: 33*145=4785, Resulting Numbers: [4785] 4785,15 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 19, 83, 80, 25 ]
47
[ "19+83=102", "80-25=55", "102-55=47" ]
Current State: 47:[19, 83, 80, 25], Operations: [] Exploring Operation: 19+83=102, Resulting Numbers: [80, 25, 102] Generated Node #2: [80, 25, 102] from Operation: 19+83=102 Current State: 47:[80, 25, 102], Operations: ['19+83=102'] Exploring Operation: 80-25=55, Resulting Numbers: [102, 55] Generated Node #3: [102, 55] from Operation: 80-25=55 Current State: 47:[102, 55], Operations: ['19+83=102', '80-25=55'] Exploring Operation: 102-55=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[19, 83, 80, 25], Operations: [] Exploring Operation: 80-25=55, Resulting Numbers: [19, 83, 55] Generated Node #0,0: 47:[19, 83, 55] Operation: 80-25=55 Exploring Operation: 80-19=61, Resulting Numbers: [83, 25, 61] Generated Node #0,1: 47:[83, 25, 61] Operation: 80-19=61 Exploring Operation: 83-19=64, Resulting Numbers: [80, 25, 64] Generated Node #0,2: 47:[80, 25, 64] Operation: 83-19=64 Exploring Operation: 19+25=44, Resulting Numbers: [83, 80, 44] Generated Node #0,3: 47:[83, 80, 44] Operation: 19+25=44 Exploring Operation: 83-25=58, Resulting Numbers: [19, 80, 58] Generated Node #0,4: 47:[19, 80, 58] Operation: 83-25=58 Moving to Node #0,0 Current State: 47:[19, 83, 55], Operations: ['80-25=55'] Exploring Operation: 83-19=64, Resulting Numbers: [55, 64] Generated Node #0,0,0: 47:[55, 64] Operation: 83-19=64 Exploring Operation: 19+55=74, Resulting Numbers: [83, 74] Generated Node #0,0,1: 47:[83, 74] Operation: 19+55=74 Exploring Operation: 19+83=102, Resulting Numbers: [55, 102] Generated Node #0,0,2: 47:[55, 102] Operation: 19+83=102 Exploring Operation: 55-19=36, Resulting Numbers: [83, 36] Generated Node #0,0,3: 47:[83, 36] Operation: 55-19=36 Exploring Operation: 83-55=28, Resulting Numbers: [19, 28] Generated Node #0,0,4: 47:[19, 28] Operation: 83-55=28 Moving to Node #0,2 Current State: 47:[80, 25, 64], Operations: ['83-19=64'] Exploring Operation: 64-25=39, Resulting Numbers: [80, 39] Generated Node #0,2,0: 47:[80, 39] Operation: 64-25=39 Exploring Operation: 80-25=55, Resulting Numbers: [64, 55] Generated Node #0,2,1: 47:[64, 55] Operation: 80-25=55 Exploring Operation: 80+25=105, Resulting Numbers: [64, 105] Generated Node #0,2,2: 47:[64, 105] Operation: 80+25=105 Exploring Operation: 25+64=89, Resulting Numbers: [80, 89] Generated Node #0,2,3: 47:[80, 89] Operation: 25+64=89 Exploring Operation: 80-64=16, Resulting Numbers: [25, 16] Generated Node #0,2,4: 47:[25, 16] Operation: 80-64=16 Moving to Node #0,4 Current State: 47:[19, 80, 58], Operations: ['83-25=58'] Exploring Operation: 80-58=22, Resulting Numbers: [19, 22] Generated Node #0,4,0: 47:[19, 22] Operation: 80-58=22 Exploring Operation: 80-19=61, Resulting Numbers: [58, 61] Generated Node #0,4,1: 47:[58, 61] Operation: 80-19=61 Exploring Operation: 19+80=99, Resulting Numbers: [58, 99] Generated Node #0,4,2: 47:[58, 99] Operation: 19+80=99 Exploring Operation: 58-19=39, Resulting Numbers: [80, 39] Generated Node #0,4,3: 47:[80, 39] Operation: 58-19=39 Exploring Operation: 19+58=77, Resulting Numbers: [80, 77] Generated Node #0,4,4: 47:[80, 77] Operation: 19+58=77 Moving to Node #0,1 Current State: 47:[83, 25, 61], Operations: ['80-19=61'] Exploring Operation: 83+25=108, Resulting Numbers: [61, 108] Generated Node #0,1,0: 47:[61, 108] Operation: 83+25=108 Exploring Operation: 61-25=36, Resulting Numbers: [83, 36] Generated Node #0,1,1: 47:[83, 36] Operation: 61-25=36 Exploring Operation: 83-25=58, Resulting Numbers: [61, 58] Generated Node #0,1,2: 47:[61, 58] Operation: 83-25=58 Exploring Operation: 25+61=86, Resulting Numbers: [83, 86] Generated Node #0,1,3: 47:[83, 86] Operation: 25+61=86 Exploring Operation: 83-61=22, Resulting Numbers: [25, 22] Generated Node #0,1,4: 47:[25, 22] Operation: 83-61=22 Moving to Node #0,3 Current State: 47:[83, 80, 44], Operations: ['19+25=44'] Exploring Operation: 83-80=3, Resulting Numbers: [44, 3] Generated Node #0,3,0: 47:[44, 3] Operation: 83-80=3 Exploring Operation: 80+44=124, Resulting Numbers: [83, 124] Generated Node #0,3,1: 47:[83, 124] Operation: 80+44=124 Exploring Operation: 80-44=36, Resulting Numbers: [83, 36] Generated Node #0,3,2: 47:[83, 36] Operation: 80-44=36 Exploring Operation: 83+44=127, Resulting Numbers: [80, 127] Generated Node #0,3,3: 47:[80, 127] Operation: 83+44=127 Exploring Operation: 83-44=39, Resulting Numbers: [80, 39] Generated Node #0,3,4: 47:[80, 39] Operation: 83-44=39 Moving to Node #0,0,0 Current State: 47:[55, 64], Operations: ['80-25=55', '83-19=64'] Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[64, 55], Operations: ['83-19=64', '80-25=55'] Exploring Operation: 64*55=3520, Resulting Numbers: [3520] 3520,47 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 64+55=119, Resulting Numbers: [119] 119,47 unequal: No Solution Moving to Node #0,4,1 Current State: 47:[58, 61], Operations: ['83-25=58', '80-19=61'] Exploring Operation: 58+61=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 58*61=3538, Resulting Numbers: [3538] 3538,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[61, 58], Operations: ['80-19=61', '83-25=58'] Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 61*58=3538, Resulting Numbers: [3538] 3538,47 unequal: No Solution Exploring Operation: 61+58=119, Resulting Numbers: [119] 119,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[80, 39], Operations: ['83-19=64', '64-25=39'] Exploring Operation: 80*39=3120, Resulting Numbers: [3120] 3120,47 unequal: No Solution Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,47 unequal: No Solution Moving to Node #0,4,3 Current State: 47:[80, 39], Operations: ['83-25=58', '58-19=39'] Exploring Operation: 80*39=3120, Resulting Numbers: [3120] 3120,47 unequal: No Solution Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,47 unequal: No Solution Moving to Node #0,3,4 Current State: 47:[80, 39], Operations: ['19+25=44', '83-44=39'] Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 80*39=3120, Resulting Numbers: [3120] 3120,47 unequal: No Solution Moving to Node #0,0,4 Current State: 47:[19, 28], Operations: ['80-25=55', '83-55=28'] Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 19*28=532, Resulting Numbers: [532] 532,47 unequal: No Solution Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[19, 83, 80, 25], Operations: [] Exploring Operation: 80-25=55, Resulting Numbers: [19, 83, 55] Generated Node #0,0: 47:[19, 83, 55] Operation: 80-25=55 Moving to Node #0,0 Current State: 47:[19, 83, 55], Operations: ['80-25=55'] Exploring Operation: 83-55=28, Resulting Numbers: [19, 28] Generated Node #0,0,4: 47:[19, 28] Operation: 83-55=28 Moving to Node #0,0,4 Current State: 47:[19, 28], Operations: ['80-25=55', '83-55=28'] Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
0.949653
hs_5
mult_heuristic
[ 63, 60, 24, 21 ]
43
[ "24-21=3", "60/3=20", "63-20=43" ]
Current State: 43:[63, 60, 24, 21], Operations: [] Exploring Operation: 24-21=3, Resulting Numbers: [63, 60, 3] Generated Node #2: [63, 60, 3] from Operation: 24-21=3 Current State: 43:[63, 60, 3], Operations: ['24-21=3'] Exploring Operation: 60/3=20, Resulting Numbers: [63, 20] Generated Node #3: [63, 20] from Operation: 60/3=20 Current State: 43:[63, 20], Operations: ['24-21=3', '60/3=20'] Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[63, 60, 24, 21], Operations: [] Exploring Operation: 63-24=39, Resulting Numbers: [60, 21, 39] Generated Node #0,0: 43:[60, 21, 39] Operation: 63-24=39 Exploring Operation: 24+21=45, Resulting Numbers: [63, 60, 45] Generated Node #0,1: 43:[63, 60, 45] Operation: 24+21=45 Exploring Operation: 63-21=42, Resulting Numbers: [60, 24, 42] Generated Node #0,2: 43:[60, 24, 42] Operation: 63-21=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[60, 24, 42], Operations: ['63-21=42'] Exploring Operation: 60+24=84, Resulting Numbers: [42, 84] Generated Node #0,2,0: 43:[42, 84] Operation: 60+24=84 Exploring Operation: 24+42=66, Resulting Numbers: [60, 66] Generated Node #0,2,1: 43:[60, 66] Operation: 24+42=66 Exploring Operation: 60-24=36, Resulting Numbers: [42, 36] Generated Node #0,2,2: 43:[42, 36] Operation: 60-24=36 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 43:[42, 36], Operations: ['63-21=42', '60-24=36'] Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,43 unequal: No Solution Exploring Operation: 42*36=1512, Resulting Numbers: [1512] 1512,43 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:[60, 66], Operations: ['63-21=42', '24+42=66'] Exploring Operation: 66-60=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 60*66=3960, Resulting Numbers: [3960] 3960,43 unequal: No Solution Exploring Operation: 60+66=126, Resulting Numbers: [126] 126,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 43:[42, 84], Operations: ['63-21=42', '60+24=84'] Exploring Operation: 84/42=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 42+84=126, Resulting Numbers: [126] 126,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[63, 60, 45], Operations: ['24+21=45'] Exploring Operation: 63-45=18, Resulting Numbers: [60, 18] Generated Node #0,1,0: 43:[60, 18] Operation: 63-45=18 Exploring Operation: 63-60=3, Resulting Numbers: [45, 3] Generated Node #0,1,1: 43:[45, 3] Operation: 63-60=3 Exploring Operation: 60-45=15, Resulting Numbers: [63, 15] Generated Node #0,1,2: 43:[63, 15] Operation: 60-45=15 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[60, 18], Operations: ['24+21=45', '63-45=18'] Exploring Operation: 60+18=78, Resulting Numbers: [78] 78,43 unequal: No Solution Exploring Operation: 60*18=1080, Resulting Numbers: [1080] 1080,43 unequal: No Solution Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,43 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:[45, 3], Operations: ['24+21=45', '63-60=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,43 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,43 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:[63, 15], Operations: ['24+21=45', '60-45=15'] Exploring Operation: 63*15=945, Resulting Numbers: [945] 945,43 unequal: No Solution Exploring Operation: 63+15=78, Resulting Numbers: [78] 78,43 unequal: No Solution Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[60, 21, 39], Operations: ['63-24=39'] Exploring Operation: 60-21=39, Resulting Numbers: [39, 39] Generated Node #0,0,0: 43:[39, 39] Operation: 60-21=39 Exploring Operation: 60+21=81, Resulting Numbers: [39, 81] Generated Node #0,0,1: 43:[39, 81] Operation: 60+21=81 Exploring Operation: 21+39=60, Resulting Numbers: [60, 60] Generated Node #0,0,2: 43:[60, 60] Operation: 21+39=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[39, 39], Operations: ['63-24=39', '60-21=39'] Exploring Operation: 39/39=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 39-39=0, Resulting Numbers: [0] 0,43 unequal: No Solution Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 43:[60, 60], Operations: ['63-24=39', '21+39=60'] Exploring Operation: 60+60=120, Resulting Numbers: [120] 120,43 unequal: No Solution Exploring Operation: 60-60=0, Resulting Numbers: [0] 0,43 unequal: No Solution Exploring Operation: 60/60=1, Resulting Numbers: [1] 1,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[39, 81], Operations: ['63-24=39', '60+21=81'] Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 39+81=120, Resulting Numbers: [120] 120,43 unequal: No Solution Exploring Operation: 39*81=3159, Resulting Numbers: [3159] 3159,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 83, 55, 71, 2 ]
31
[ "83-71=12", "2*12=24", "55-24=31" ]
Current State: 31:[83, 55, 71, 2], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [55, 2, 12] Generated Node #2: [55, 2, 12] from Operation: 83-71=12 Current State: 31:[55, 2, 12], Operations: ['83-71=12'] Exploring Operation: 2*12=24, Resulting Numbers: [55, 24] Generated Node #3: [55, 24] from Operation: 2*12=24 Current State: 31:[55, 24], Operations: ['83-71=12', '2*12=24'] Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[83, 55, 71, 2], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [55, 2, 12] Generated Node #0,0: 31:[55, 2, 12] Operation: 83-71=12 Exploring Operation: 83-55=28, Resulting Numbers: [71, 2, 28] Generated Node #0,1: 31:[71, 2, 28] Operation: 83-55=28 Moving to Node #0,0 Current State: 31:[55, 2, 12], Operations: ['83-71=12'] Exploring Operation: 2*12=24, Resulting Numbers: [55, 24] Generated Node #0,0,0: 31:[55, 24] Operation: 2*12=24 Exploring Operation: 55-2=53, Resulting Numbers: [12, 53] Generated Node #0,0,1: 31:[12, 53] Operation: 55-2=53 Moving to Node #0,1 Current State: 31:[71, 2, 28], Operations: ['83-55=28'] Exploring Operation: 71-2=69, Resulting Numbers: [28, 69] Generated Node #0,1,0: 31:[28, 69] Operation: 71-2=69 Exploring Operation: 71-28=43, Resulting Numbers: [2, 43] Generated Node #0,1,1: 31:[2, 43] Operation: 71-28=43 Moving to Node #0,0,0 Current State: 31:[55, 24], Operations: ['83-71=12', '2*12=24'] Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[83, 55, 71, 2], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [55, 2, 12] Generated Node #0,0: 31:[55, 2, 12] Operation: 83-71=12 Moving to Node #0,0 Current State: 31:[55, 2, 12], Operations: ['83-71=12'] Exploring Operation: 2*12=24, Resulting Numbers: [55, 24] Generated Node #0,0,0: 31:[55, 24] Operation: 2*12=24 Moving to Node #0,0,0 Current State: 31:[55, 24], Operations: ['83-71=12', '2*12=24'] Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 56, 10, 74, 21 ]
99
[ "56-10=46", "74-21=53", "46+53=99" ]
Current State: 99:[56, 10, 74, 21], Operations: [] Exploring Operation: 56-10=46, Resulting Numbers: [74, 21, 46] Generated Node #2: [74, 21, 46] from Operation: 56-10=46 Current State: 99:[74, 21, 46], Operations: ['56-10=46'] Exploring Operation: 74-21=53, Resulting Numbers: [46, 53] Generated Node #3: [46, 53] from Operation: 74-21=53 Current State: 99:[46, 53], Operations: ['56-10=46', '74-21=53'] Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[56, 10, 74, 21], Operations: [] Exploring Operation: 56-21=35, Resulting Numbers: [10, 74, 35] Generated Node #0,0: 99:[10, 74, 35] Operation: 56-21=35 Exploring Operation: 74-56=18, Resulting Numbers: [10, 21, 18] Generated Node #0,1: 99:[10, 21, 18] Operation: 74-56=18 Exploring Operation: 74+21=95, Resulting Numbers: [56, 10, 95] Generated Node #0,2: 99:[56, 10, 95] Operation: 74+21=95 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[10, 21, 18], Operations: ['74-56=18'] Exploring Operation: 21-10=11, Resulting Numbers: [18, 11] Generated Node #0,1,0: 99:[18, 11] Operation: 21-10=11 Exploring Operation: 21-18=3, Resulting Numbers: [10, 3] Generated Node #0,1,1: 99:[10, 3] Operation: 21-18=3 Exploring Operation: 21+18=39, Resulting Numbers: [10, 39] Generated Node #0,1,2: 99:[10, 39] Operation: 21+18=39 Moving to Node #0,1,1 Current State: 99:[10, 3], Operations: ['74-56=18', '21-18=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,99 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[18, 11], Operations: ['74-56=18', '21-10=11'] Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,99 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,99 unequal: No Solution Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[10, 39], Operations: ['74-56=18', '21+18=39'] Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,99 unequal: No Solution Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,99 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[10, 74, 35], Operations: ['56-21=35'] Exploring Operation: 74+35=109, Resulting Numbers: [10, 109] Generated Node #0,0,0: 99:[10, 109] Operation: 74+35=109 Exploring Operation: 74-35=39, Resulting Numbers: [10, 39] Generated Node #0,0,1: 99:[10, 39] Operation: 74-35=39 Exploring Operation: 10+74=84, Resulting Numbers: [35, 84] Generated Node #0,0,2: 99:[35, 84] Operation: 10+74=84 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 99:[10, 39], Operations: ['56-21=35', '74-35=39'] Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,99 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[10, 109], Operations: ['56-21=35', '74+35=109'] Exploring Operation: 109-10=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[56, 10, 74, 21], Operations: [] Exploring Operation: 56-21=35, Resulting Numbers: [10, 74, 35] Generated Node #0,0: 99:[10, 74, 35] Operation: 56-21=35 Moving to Node #0,0 Current State: 99:[10, 74, 35], Operations: ['56-21=35'] Exploring Operation: 74+35=109, Resulting Numbers: [10, 109] Generated Node #0,0,0: 99:[10, 109] Operation: 74+35=109 Moving to Node #0,0,0 Current State: 99:[10, 109], Operations: ['56-21=35', '74+35=109'] Exploring Operation: 109-10=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.977431
hs_3
sum_heuristic
[ 81, 3, 31, 56 ]
60
[ "81/3=27", "31+56=87", "87-27=60" ]
Current State: 60:[81, 3, 31, 56], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [31, 56, 27] Generated Node #2: [31, 56, 27] from Operation: 81/3=27 Current State: 60:[31, 56, 27], Operations: ['81/3=27'] Exploring Operation: 31+56=87, Resulting Numbers: [27, 87] Generated Node #3: [27, 87] from Operation: 31+56=87 Current State: 60:[27, 87], Operations: ['81/3=27', '31+56=87'] Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[81, 3, 31, 56], Operations: [] Exploring Operation: 3+56=59, Resulting Numbers: [81, 31, 59] Generated Node #0,0: 60:[81, 31, 59] Operation: 3+56=59 Exploring Operation: 81-31=50, Resulting Numbers: [3, 56, 50] Generated Node #0,1: 60:[3, 56, 50] Operation: 81-31=50 Exploring Operation: 81-56=25, Resulting Numbers: [3, 31, 25] Generated Node #0,2: 60:[3, 31, 25] Operation: 81-56=25 Exploring Operation: 81/3=27, Resulting Numbers: [31, 56, 27] Generated Node #0,3: 60:[31, 56, 27] Operation: 81/3=27 Exploring Operation: 81-3=78, Resulting Numbers: [31, 56, 78] Generated Node #0,4: 60:[31, 56, 78] Operation: 81-3=78 Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[3, 31, 25], Operations: ['81-56=25'] Exploring Operation: 3+25=28, Resulting Numbers: [31, 28] Generated Node #0,2,0: 60:[31, 28] Operation: 3+25=28 Exploring Operation: 31-3=28, Resulting Numbers: [25, 28] Generated Node #0,2,1: 60:[25, 28] Operation: 31-3=28 Exploring Operation: 25-3=22, Resulting Numbers: [31, 22] Generated Node #0,2,2: 60:[31, 22] Operation: 25-3=22 Exploring Operation: 31-25=6, Resulting Numbers: [3, 6] Generated Node #0,2,3: 60:[3, 6] Operation: 31-25=6 Exploring Operation: 31+25=56, Resulting Numbers: [3, 56] Generated Node #0,2,4: 60:[3, 56] Operation: 31+25=56 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 60:[3, 6], Operations: ['81-56=25', '31-25=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,60 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 60:[31, 28], Operations: ['81-56=25', '3+25=28'] Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 60:[31, 22], Operations: ['81-56=25', '25-3=22'] Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,60 unequal: No Solution Exploring Operation: 31*22=682, Resulting Numbers: [682] 682,60 unequal: No Solution Exploring Operation: 31+22=53, Resulting Numbers: [53] 53,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 60:[3, 56], Operations: ['81-56=25', '31+25=56'] Exploring Operation: 3*56=168, Resulting Numbers: [168] 168,60 unequal: No Solution Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 60:[25, 28], Operations: ['81-56=25', '31-3=28'] Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,60 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 60:[31, 56, 27], Operations: ['81/3=27'] Exploring Operation: 56-27=29, Resulting Numbers: [31, 29] Generated Node #0,3,0: 60:[31, 29] Operation: 56-27=29 Exploring Operation: 56-31=25, Resulting Numbers: [27, 25] Generated Node #0,3,1: 60:[27, 25] Operation: 56-31=25 Exploring Operation: 31+27=58, Resulting Numbers: [56, 58] Generated Node #0,3,2: 60:[56, 58] Operation: 31+27=58 Exploring Operation: 31-27=4, Resulting Numbers: [56, 4] Generated Node #0,3,3: 60:[56, 4] Operation: 31-27=4 Exploring Operation: 56+27=83, Resulting Numbers: [31, 83] Generated Node #0,3,4: 60:[31, 83] Operation: 56+27=83 Moving to Node #0,3,0 Current State: 60:[31, 29], Operations: ['81/3=27', '56-27=29'] Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[81, 3, 31, 56], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [31, 56, 27] Generated Node #0,3: 60:[31, 56, 27] Operation: 81/3=27 Moving to Node #0,3 Current State: 60:[31, 56, 27], Operations: ['81/3=27'] Exploring Operation: 56-27=29, Resulting Numbers: [31, 29] Generated Node #0,3,0: 60:[31, 29] Operation: 56-27=29 Moving to Node #0,3,0 Current State: 60:[31, 29], Operations: ['81/3=27', '56-27=29'] Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 74, 93, 41, 24 ]
36
[ "93-74=19", "41-24=17", "19+17=36" ]
Current State: 36:[74, 93, 41, 24], Operations: [] Exploring Operation: 93-74=19, Resulting Numbers: [41, 24, 19] Generated Node #2: [41, 24, 19] from Operation: 93-74=19 Current State: 36:[41, 24, 19], Operations: ['93-74=19'] Exploring Operation: 41-24=17, Resulting Numbers: [19, 17] Generated Node #3: [19, 17] from Operation: 41-24=17 Current State: 36:[19, 17], Operations: ['93-74=19', '41-24=17'] Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[74, 93, 41, 24], Operations: [] Exploring Operation: 74-41=33, Resulting Numbers: [93, 24, 33] Generated Node #0,0: 36:[93, 24, 33] Operation: 74-41=33 Exploring Operation: 74-24=50, Resulting Numbers: [93, 41, 50] Generated Node #0,1: 36:[93, 41, 50] Operation: 74-24=50 Exploring Operation: 93-74=19, Resulting Numbers: [41, 24, 19] Generated Node #0,2: 36:[41, 24, 19] Operation: 93-74=19 Exploring Operation: 93-41=52, Resulting Numbers: [74, 24, 52] Generated Node #0,3: 36:[74, 24, 52] Operation: 93-41=52 Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[41, 24, 19], Operations: ['93-74=19'] Exploring Operation: 24+19=43, Resulting Numbers: [41, 43] Generated Node #0,2,0: 36:[41, 43] Operation: 24+19=43 Exploring Operation: 41-19=22, Resulting Numbers: [24, 22] Generated Node #0,2,1: 36:[24, 22] Operation: 41-19=22 Exploring Operation: 41-24=17, Resulting Numbers: [19, 17] Generated Node #0,2,2: 36:[19, 17] Operation: 41-24=17 Exploring Operation: 24-19=5, Resulting Numbers: [41, 5] Generated Node #0,2,3: 36:[41, 5] Operation: 24-19=5 Moving to Node #0,2,2 Current State: 36:[19, 17], Operations: ['93-74=19', '41-24=17'] Exploring Operation: 19*17=323, Resulting Numbers: [323] 323,36 unequal: No Solution Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[74, 93, 41, 24], Operations: [] Exploring Operation: 93-74=19, Resulting Numbers: [41, 24, 19] Generated Node #0,2: 36:[41, 24, 19] Operation: 93-74=19 Moving to Node #0,2 Current State: 36:[41, 24, 19], Operations: ['93-74=19'] Exploring Operation: 41-24=17, Resulting Numbers: [19, 17] Generated Node #0,2,2: 36:[19, 17] Operation: 41-24=17 Moving to Node #0,2,2 Current State: 36:[19, 17], Operations: ['93-74=19', '41-24=17'] Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 68, 81, 92, 3 ]
31
[ "68*3=204", "81+92=173", "204-173=31" ]
Current State: 31:[68, 81, 92, 3], Operations: [] Exploring Operation: 68*3=204, Resulting Numbers: [81, 92, 204] Generated Node #2: [81, 92, 204] from Operation: 68*3=204 Current State: 31:[81, 92, 204], Operations: ['68*3=204'] Exploring Operation: 81+92=173, Resulting Numbers: [204, 173] Generated Node #3: [204, 173] from Operation: 81+92=173 Current State: 31:[204, 173], Operations: ['68*3=204', '81+92=173'] Exploring Operation: 204-173=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[68, 81, 92, 3], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [68, 92, 27] Generated Node #0,0: 31:[68, 92, 27] Operation: 81/3=27 Exploring Operation: 68-3=65, Resulting Numbers: [81, 92, 65] Generated Node #0,1: 31:[81, 92, 65] Operation: 68-3=65 Exploring Operation: 81-68=13, Resulting Numbers: [92, 3, 13] Generated Node #0,2: 31:[92, 3, 13] Operation: 81-68=13 Exploring Operation: 92-81=11, Resulting Numbers: [68, 3, 11] Generated Node #0,3: 31:[68, 3, 11] Operation: 92-81=11 Exploring Operation: 92-68=24, Resulting Numbers: [81, 3, 24] Generated Node #0,4: 31:[81, 3, 24] Operation: 92-68=24 Moving to Node #0,3 Current State: 31:[68, 3, 11], Operations: ['92-81=11'] Exploring Operation: 68+3=71, Resulting Numbers: [11, 71] Generated Node #0,3,0: 31:[11, 71] Operation: 68+3=71 Exploring Operation: 3*11=33, Resulting Numbers: [68, 33] Generated Node #0,3,1: 31:[68, 33] Operation: 3*11=33 Exploring Operation: 68-11=57, Resulting Numbers: [3, 57] Generated Node #0,3,2: 31:[3, 57] Operation: 68-11=57 Exploring Operation: 3+11=14, Resulting Numbers: [68, 14] Generated Node #0,3,3: 31:[68, 14] Operation: 3+11=14 Exploring Operation: 68-3=65, Resulting Numbers: [11, 65] Generated Node #0,3,4: 31:[11, 65] Operation: 68-3=65 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 31:[68, 33], Operations: ['92-81=11', '3*11=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 68+33=101, Resulting Numbers: [101] 101,31 unequal: No Solution Exploring Operation: 68*33=2244, Resulting Numbers: [2244] 2244,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[3, 57], Operations: ['92-81=11', '68-11=57'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,31 unequal: No Solution Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 3*57=171, Resulting Numbers: [171] 171,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 31:[68, 14], Operations: ['92-81=11', '3+11=14'] Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,31 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 31:[11, 65], Operations: ['92-81=11', '68-3=65'] Exploring Operation: 11*65=715, Resulting Numbers: [715] 715,31 unequal: No Solution Exploring Operation: 11+65=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[11, 71], Operations: ['92-81=11', '68+3=71'] Exploring Operation: 11*71=781, Resulting Numbers: [781] 781,31 unequal: No Solution Exploring Operation: 11+71=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,31 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: 31:[81, 3, 24], Operations: ['92-68=24'] Exploring Operation: 81/3=27, Resulting Numbers: [24, 27] Generated Node #0,4,0: 31:[24, 27] Operation: 81/3=27 Exploring Operation: 81-24=57, Resulting Numbers: [3, 57] Generated Node #0,4,1: 31:[3, 57] Operation: 81-24=57 Exploring Operation: 3+24=27, Resulting Numbers: [81, 27] Generated Node #0,4,2: 31:[81, 27] Operation: 3+24=27 Exploring Operation: 81-3=78, Resulting Numbers: [24, 78] Generated Node #0,4,3: 31:[24, 78] Operation: 81-3=78 Exploring Operation: 81+3=84, Resulting Numbers: [24, 84] Generated Node #0,4,4: 31:[24, 84] Operation: 81+3=84 Moving to Node #0,0 Current State: 31:[68, 92, 27], Operations: ['81/3=27'] Exploring Operation: 68-27=41, Resulting Numbers: [92, 41] Generated Node #0,0,0: 31:[92, 41] Operation: 68-27=41 Exploring Operation: 68+27=95, Resulting Numbers: [92, 95] Generated Node #0,0,1: 31:[92, 95] Operation: 68+27=95 Exploring Operation: 92-68=24, Resulting Numbers: [27, 24] Generated Node #0,0,2: 31:[27, 24] Operation: 92-68=24 Exploring Operation: 92+27=119, Resulting Numbers: [68, 119] Generated Node #0,0,3: 31:[68, 119] Operation: 92+27=119 Exploring Operation: 92-27=65, Resulting Numbers: [68, 65] Generated Node #0,0,4: 31:[68, 65] Operation: 92-27=65 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[27, 24], Operations: ['81/3=27', '92-68=24'] Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 27*24=648, Resulting Numbers: [648] 648,31 unequal: No Solution Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,31 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:[92, 41], Operations: ['81/3=27', '68-27=41'] Exploring Operation: 92*41=3772, Resulting Numbers: [3772] 3772,31 unequal: No Solution Exploring Operation: 92+41=133, Resulting Numbers: [133] 133,31 unequal: No Solution Exploring Operation: 92-41=51, Resulting Numbers: [51] 51,31 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 #0,0,4 Current State: 31:[68, 65], Operations: ['81/3=27', '92-27=65'] Exploring Operation: 68-65=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 68+65=133, Resulting Numbers: [133] 133,31 unequal: No Solution Exploring Operation: 68*65=4420, Resulting Numbers: [4420] 4420,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[92, 95], Operations: ['81/3=27', '68+27=95'] Exploring Operation: 92+95=187, Resulting Numbers: [187] 187,31 unequal: No Solution Exploring Operation: 95-92=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 92*95=8740, Resulting Numbers: [8740] 8740,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 31:[68, 119], Operations: ['81/3=27', '92+27=119'] Exploring Operation: 119-68=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 68+119=187, Resulting Numbers: [187] 187,31 unequal: No Solution Exploring Operation: 68*119=8092, Resulting Numbers: [8092] 8092,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 31:[92, 3, 13], Operations: ['81-68=13'] Exploring Operation: 92-13=79, Resulting Numbers: [3, 79] Generated Node #0,2,0: 31:[3, 79] Operation: 92-13=79 Exploring Operation: 3+13=16, Resulting Numbers: [92, 16] Generated Node #0,2,1: 31:[92, 16] Operation: 3+13=16 Exploring Operation: 92-3=89, Resulting Numbers: [13, 89] Generated Node #0,2,2: 31:[13, 89] Operation: 92-3=89 Exploring Operation: 92+3=95, Resulting Numbers: [13, 95] Generated Node #0,2,3: 31:[13, 95] Operation: 92+3=95 Exploring Operation: 3*13=39, Resulting Numbers: [92, 39] Generated Node #0,2,4: 31:[92, 39] Operation: 3*13=39 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 31:[92, 39], Operations: ['81-68=13', '3*13=39'] Exploring Operation: 92*39=3588, Resulting Numbers: [3588] 3588,31 unequal: No Solution Exploring Operation: 92+39=131, Resulting Numbers: [131] 131,31 unequal: No Solution Exploring Operation: 92-39=53, Resulting Numbers: [53] 53,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[3, 79], Operations: ['81-68=13', '92-13=79'] Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,31 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[92, 16], Operations: ['81-68=13', '3+13=16'] Exploring Operation: 92-16=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 92*16=1472, Resulting Numbers: [1472] 1472,31 unequal: No Solution Exploring Operation: 92+16=108, Resulting Numbers: [108] 108,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[13, 89], Operations: ['81-68=13', '92-3=89'] Exploring Operation: 13*89=1157, Resulting Numbers: [1157] 1157,31 unequal: No Solution Exploring Operation: 89-13=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 13+89=102, Resulting Numbers: [102] 102,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[13, 95], Operations: ['81-68=13', '92+3=95'] Exploring Operation: 13*95=1235, Resulting Numbers: [1235] 1235,31 unequal: No Solution Exploring Operation: 13+95=108, Resulting Numbers: [108] 108,31 unequal: No Solution Exploring Operation: 95-13=82, Resulting Numbers: [82] 82,31 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:[81, 92, 65], Operations: ['68-3=65'] Exploring Operation: 81-65=16, Resulting Numbers: [92, 16] Generated Node #0,1,0: 31:[92, 16] Operation: 81-65=16 Exploring Operation: 81+92=173, Resulting Numbers: [65, 173] Generated Node #0,1,1: 31:[65, 173] Operation: 81+92=173 Exploring Operation: 92-65=27, Resulting Numbers: [81, 27] Generated Node #0,1,2: 31:[81, 27] Operation: 92-65=27 Exploring Operation: 92-81=11, Resulting Numbers: [65, 11] Generated Node #0,1,3: 31:[65, 11] Operation: 92-81=11 Exploring Operation: 81+65=146, Resulting Numbers: [92, 146] Generated Node #0,1,4: 31:[92, 146] Operation: 81+65=146 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[81, 27], Operations: ['68-3=65', '92-65=27'] Exploring Operation: 81+27=108, Resulting Numbers: [108] 108,31 unequal: No Solution Exploring Operation: 81-27=54, Resulting Numbers: [54] 54,31 unequal: No Solution Exploring Operation: 81*27=2187, Resulting Numbers: [2187] 2187,31 unequal: No Solution Exploring Operation: 81/27=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 #0,1,3 Current State: 31:[65, 11], Operations: ['68-3=65', '92-81=11'] Exploring Operation: 65*11=715, Resulting Numbers: [715] 715,31 unequal: No Solution Exploring Operation: 65+11=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[92, 16], Operations: ['68-3=65', '81-65=16'] Exploring Operation: 92-16=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 92+16=108, Resulting Numbers: [108] 108,31 unequal: No Solution Exploring Operation: 92*16=1472, Resulting Numbers: [1472] 1472,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[65, 173], Operations: ['68-3=65', '81+92=173'] Exploring Operation: 65*173=11245, Resulting Numbers: [11245] 11245,31 unequal: No Solution Exploring Operation: 173-65=108, Resulting Numbers: [108] 108,31 unequal: No Solution Exploring Operation: 65+173=238, Resulting Numbers: [238] 238,31 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 #0,1,4 Current State: 31:[92, 146], Operations: ['68-3=65', '81+65=146'] Exploring Operation: 92+146=238, Resulting Numbers: [238] 238,31 unequal: No Solution Exploring Operation: 92*146=13432, Resulting Numbers: [13432] 13432,31 unequal: No Solution Exploring Operation: 146-92=54, Resulting Numbers: [54] 54,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 31:[24, 27], Operations: ['92-68=24', '81/3=27'] Exploring Operation: 24*27=648, Resulting Numbers: [648] 648,31 unequal: No Solution Exploring Operation: 24+27=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,31 unequal: No Solution Moving to Node #0,4,2 Current State: 31:[81, 27], Operations: ['92-68=24', '3+24=27'] Exploring Operation: 81+27=108, Resulting Numbers: [108] 108,31 unequal: No Solution Exploring Operation: 81-27=54, Resulting Numbers: [54] 54,31 unequal: No Solution Exploring Operation: 81/27=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 81*27=2187, Resulting Numbers: [2187] 2187,31 unequal: No Solution Moving to Node #0,4,1 Current State: 31:[3, 57], Operations: ['92-68=24', '81-24=57'] Exploring Operation: 3*57=171, Resulting Numbers: [171] 171,31 unequal: No Solution Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,31 unequal: No Solution Moving to Node #0,4,3 Current State: 31:[24, 78], Operations: ['92-68=24', '81-3=78'] Exploring Operation: 24+78=102, Resulting Numbers: [102] 102,31 unequal: No Solution Exploring Operation: 24*78=1872, Resulting Numbers: [1872] 1872,31 unequal: No Solution Exploring Operation: 78-24=54, Resulting Numbers: [54] 54,31 unequal: No Solution Moving to Node #0,4,4 Current State: 31:[24, 84], Operations: ['92-68=24', '81+3=84'] Exploring Operation: 24+84=108, Resulting Numbers: [108] 108,31 unequal: No Solution Exploring Operation: 84-24=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 24*84=2016, Resulting Numbers: [2016] 2016,31 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 48, 6, 29, 27 ]
31
[ "48+6=54", "54/27=2", "29+2=31" ]
Current State: 31:[48, 6, 29, 27], Operations: [] Exploring Operation: 48+6=54, Resulting Numbers: [29, 27, 54] Generated Node #2: [29, 27, 54] from Operation: 48+6=54 Current State: 31:[29, 27, 54], Operations: ['48+6=54'] Exploring Operation: 54/27=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 54/27=2 Current State: 31:[29, 2], Operations: ['48+6=54', '54/27=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[48, 6, 29, 27], Operations: [] Exploring Operation: 48-6=42, Resulting Numbers: [29, 27, 42] Generated Node #0,0: 31:[29, 27, 42] Operation: 48-6=42 Exploring Operation: 6+27=33, Resulting Numbers: [48, 29, 33] Generated Node #0,1: 31:[48, 29, 33] Operation: 6+27=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[29, 27, 42], Operations: ['48-6=42'] Exploring Operation: 42-29=13, Resulting Numbers: [27, 13] Generated Node #0,0,0: 31:[27, 13] Operation: 42-29=13 Exploring Operation: 42-27=15, Resulting Numbers: [29, 15] Generated Node #0,0,1: 31:[29, 15] Operation: 42-27=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 31:[29, 15], Operations: ['48-6=42', '42-27=15'] Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 29+15=44, Resulting Numbers: [44] 44,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[27, 13], Operations: ['48-6=42', '42-29=13'] Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[48, 29, 33], Operations: ['6+27=33'] Exploring Operation: 48-33=15, Resulting Numbers: [29, 15] Generated Node #0,1,0: 31:[29, 15] Operation: 48-33=15 Exploring Operation: 48-29=19, Resulting Numbers: [33, 19] Generated Node #0,1,1: 31:[33, 19] Operation: 48-29=19 Moving to Node #0,1,1 Current State: 31:[33, 19], Operations: ['6+27=33', '48-29=19'] Exploring Operation: 33+19=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[29, 15], Operations: ['6+27=33', '48-33=15'] Exploring Operation: 29+15=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 97, 74, 38, 92 ]
41
[ "97+74=171", "38+92=130", "171-130=41" ]
Current State: 41:[97, 74, 38, 92], Operations: [] Exploring Operation: 97+74=171, Resulting Numbers: [38, 92, 171] Generated Node #2: [38, 92, 171] from Operation: 97+74=171 Current State: 41:[38, 92, 171], Operations: ['97+74=171'] Exploring Operation: 38+92=130, Resulting Numbers: [171, 130] Generated Node #3: [171, 130] from Operation: 38+92=130 Current State: 41:[171, 130], Operations: ['97+74=171', '38+92=130'] Exploring Operation: 171-130=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[97, 74, 38, 92], Operations: [] Exploring Operation: 97-74=23, Resulting Numbers: [38, 92, 23] Generated Node #0,0: 41:[38, 92, 23] Operation: 97-74=23 Exploring Operation: 97-92=5, Resulting Numbers: [74, 38, 5] Generated Node #0,1: 41:[74, 38, 5] Operation: 97-92=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[38, 92, 23], Operations: ['97-74=23'] Exploring Operation: 92-38=54, Resulting Numbers: [23, 54] Generated Node #0,0,0: 41:[23, 54] Operation: 92-38=54 Exploring Operation: 92-23=69, Resulting Numbers: [38, 69] Generated Node #0,0,1: 41:[38, 69] Operation: 92-23=69 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[23, 54], Operations: ['97-74=23', '92-38=54'] Exploring Operation: 23+54=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[38, 69], Operations: ['97-74=23', '92-23=69'] Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 38+69=107, Resulting Numbers: [107] 107,41 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: 41:[74, 38, 5], Operations: ['97-92=5'] Exploring Operation: 74-5=69, Resulting Numbers: [38, 69] Generated Node #0,1,0: 41:[38, 69] Operation: 74-5=69 Exploring Operation: 38+5=43, Resulting Numbers: [74, 43] Generated Node #0,1,1: 41:[74, 43] Operation: 38+5=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[38, 69], Operations: ['97-92=5', '74-5=69'] Exploring Operation: 38+69=107, Resulting Numbers: [107] 107,41 unequal: No Solution Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[74, 43], Operations: ['97-92=5', '38+5=43'] Exploring Operation: 74+43=117, Resulting Numbers: [117] 117,41 unequal: No Solution Exploring Operation: 74-43=31, Resulting Numbers: [31] 31,41 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
[ 52, 19, 11, 48 ]
51
[ "52-19=33", "33/11=3", "48+3=51" ]
Current State: 51:[52, 19, 11, 48], Operations: [] Exploring Operation: 52-19=33, Resulting Numbers: [11, 48, 33] Generated Node #2: [11, 48, 33] from Operation: 52-19=33 Current State: 51:[11, 48, 33], Operations: ['52-19=33'] Exploring Operation: 33/11=3, Resulting Numbers: [48, 3] Generated Node #3: [48, 3] from Operation: 33/11=3 Current State: 51:[48, 3], Operations: ['52-19=33', '33/11=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[52, 19, 11, 48], Operations: [] Exploring Operation: 52-11=41, Resulting Numbers: [19, 48, 41] Generated Node #0,0: 51:[19, 48, 41] Operation: 52-11=41 Exploring Operation: 11+48=59, Resulting Numbers: [52, 19, 59] Generated Node #0,1: 51:[52, 19, 59] Operation: 11+48=59 Exploring Operation: 19-11=8, Resulting Numbers: [52, 48, 8] Generated Node #0,2: 51:[52, 48, 8] Operation: 19-11=8 Exploring Operation: 52-48=4, Resulting Numbers: [19, 11, 4] Generated Node #0,3: 51:[19, 11, 4] Operation: 52-48=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[52, 48, 8], Operations: ['19-11=8'] Exploring Operation: 52-8=44, Resulting Numbers: [48, 44] Generated Node #0,2,0: 51:[48, 44] Operation: 52-8=44 Exploring Operation: 48+8=56, Resulting Numbers: [52, 56] Generated Node #0,2,1: 51:[52, 56] Operation: 48+8=56 Exploring Operation: 48/8=6, Resulting Numbers: [52, 6] Generated Node #0,2,2: 51:[52, 6] Operation: 48/8=6 Exploring Operation: 52-48=4, Resulting Numbers: [8, 4] Generated Node #0,2,3: 51:[8, 4] Operation: 52-48=4 Moving to Node #0,2,2 Current State: 51:[52, 6], Operations: ['19-11=8', '48/8=6'] Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,51 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[8, 4], Operations: ['19-11=8', '52-48=4'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,51 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[52, 56], Operations: ['19-11=8', '48+8=56'] Exploring Operation: 52*56=2912, Resulting Numbers: [2912] 2912,51 unequal: No Solution Exploring Operation: 56-52=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 52+56=108, Resulting Numbers: [108] 108,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[48, 44], Operations: ['19-11=8', '52-8=44'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,51 unequal: No Solution Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,51 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 Current State: 51:[19, 11, 4], Operations: ['52-48=4'] Exploring Operation: 19-11=8, Resulting Numbers: [4, 8] Generated Node #0,3,0: 51:[4, 8] Operation: 19-11=8 Exploring Operation: 19-4=15, Resulting Numbers: [11, 15] Generated Node #0,3,1: 51:[11, 15] Operation: 19-4=15 Exploring Operation: 11+4=15, Resulting Numbers: [19, 15] Generated Node #0,3,2: 51:[19, 15] Operation: 11+4=15 Exploring Operation: 11-4=7, Resulting Numbers: [19, 7] Generated Node #0,3,3: 51:[19, 7] Operation: 11-4=7 Moving to Node #0,3,2 Current State: 51:[19, 15], Operations: ['52-48=4', '11+4=15'] Exploring Operation: 19+15=34, Resulting Numbers: [34] 34,51 unequal: No Solution Exploring Operation: 19*15=285, Resulting Numbers: [285] 285,51 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,51 unequal: No Solution Moving to Node #0,3,3 Current State: 51:[19, 7], Operations: ['52-48=4', '11-4=7'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,51 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,51 unequal: No Solution Moving to Node #0,3,0 Current State: 51:[4, 8], Operations: ['52-48=4', '19-11=8'] Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,51 unequal: No Solution Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,51 unequal: No Solution Moving to Node #0,3,1 Current State: 51:[11, 15], Operations: ['52-48=4', '19-4=15'] Exploring Operation: 11*15=165, Resulting Numbers: [165] 165,51 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[52, 19, 59], Operations: ['11+48=59'] Exploring Operation: 59-19=40, Resulting Numbers: [52, 40] Generated Node #0,1,0: 51:[52, 40] Operation: 59-19=40 Exploring Operation: 52+19=71, Resulting Numbers: [59, 71] Generated Node #0,1,1: 51:[59, 71] Operation: 52+19=71 Exploring Operation: 52-19=33, Resulting Numbers: [59, 33] Generated Node #0,1,2: 51:[59, 33] Operation: 52-19=33 Exploring Operation: 59-52=7, Resulting Numbers: [19, 7] Generated Node #0,1,3: 51:[19, 7] Operation: 59-52=7 Moving to Node #0,1,3 Current State: 51:[19, 7], Operations: ['11+48=59', '59-52=7'] Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,51 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[52, 40], Operations: ['11+48=59', '59-19=40'] Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,51 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,51 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[59, 33], Operations: ['11+48=59', '52-19=33'] Exploring Operation: 59*33=1947, Resulting Numbers: [1947] 1947,51 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 59+33=92, Resulting Numbers: [92] 92,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[59, 71], Operations: ['11+48=59', '52+19=71'] Exploring Operation: 71-59=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 59+71=130, Resulting Numbers: [130] 130,51 unequal: No Solution Exploring Operation: 59*71=4189, Resulting Numbers: [4189] 4189,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[19, 48, 41], Operations: ['52-11=41'] Exploring Operation: 48-19=29, Resulting Numbers: [41, 29] Generated Node #0,0,0: 51:[41, 29] Operation: 48-19=29 Exploring Operation: 19+41=60, Resulting Numbers: [48, 60] Generated Node #0,0,1: 51:[48, 60] Operation: 19+41=60 Exploring Operation: 48-41=7, Resulting Numbers: [19, 7] Generated Node #0,0,2: 51:[19, 7] Operation: 48-41=7 Exploring Operation: 41-19=22, Resulting Numbers: [48, 22] Generated Node #0,0,3: 51:[48, 22] Operation: 41-19=22 Moving to Node #0,0,2 Current State: 51:[19, 7], Operations: ['52-11=41', '48-41=7'] Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,51 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[48, 22], Operations: ['52-11=41', '41-19=22'] Exploring Operation: 48*22=1056, Resulting Numbers: [1056] 1056,51 unequal: No Solution Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[48, 60], Operations: ['52-11=41', '19+41=60'] Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,51 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[41, 29], Operations: ['52-11=41', '48-19=29'] Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,51 unequal: No Solution Exploring Operation: 41*29=1189, Resulting Numbers: [1189] 1189,51 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,51 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
[ 88, 67, 76, 41 ]
14
[ "88-67=21", "76-41=35", "35-21=14" ]
Current State: 14:[88, 67, 76, 41], Operations: [] Exploring Operation: 88-67=21, Resulting Numbers: [76, 41, 21] Generated Node #2: [76, 41, 21] from Operation: 88-67=21 Current State: 14:[76, 41, 21], Operations: ['88-67=21'] Exploring Operation: 76-41=35, Resulting Numbers: [21, 35] Generated Node #3: [21, 35] from Operation: 76-41=35 Current State: 14:[21, 35], Operations: ['88-67=21', '76-41=35'] Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[88, 67, 76, 41], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [67, 41, 12] Generated Node #0,0: 14:[67, 41, 12] Operation: 88-76=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[67, 41, 12], Operations: ['88-76=12'] Exploring Operation: 67-41=26, Resulting Numbers: [12, 26] Generated Node #0,0,0: 14:[12, 26] Operation: 67-41=26 Moving to Node #0,0,0 Current State: 14:[12, 26], Operations: ['88-76=12', '67-41=26'] Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[88, 67, 76, 41], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [67, 41, 12] Generated Node #0,0: 14:[67, 41, 12] Operation: 88-76=12 Moving to Node #0,0 Current State: 14:[67, 41, 12], Operations: ['88-76=12'] Exploring Operation: 67-41=26, Resulting Numbers: [12, 26] Generated Node #0,0,0: 14:[12, 26] Operation: 67-41=26 Moving to Node #0,0,0 Current State: 14:[12, 26], Operations: ['88-76=12', '67-41=26'] Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 87, 95, 9, 91 ]
26
[ "91-87=4", "95+9=104", "104/4=26" ]
Current State: 26:[87, 95, 9, 91], Operations: [] Exploring Operation: 91-87=4, Resulting Numbers: [95, 9, 4] Generated Node #2: [95, 9, 4] from Operation: 91-87=4 Current State: 26:[95, 9, 4], Operations: ['91-87=4'] Exploring Operation: 95+9=104, Resulting Numbers: [4, 104] Generated Node #3: [4, 104] from Operation: 95+9=104 Current State: 26:[4, 104], Operations: ['91-87=4', '95+9=104'] Exploring Operation: 104/4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[87, 95, 9, 91], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [87, 9, 4] Generated Node #0,0: 26:[87, 9, 4] Operation: 95-91=4 Exploring Operation: 91-87=4, Resulting Numbers: [95, 9, 4] Generated Node #0,1: 26:[95, 9, 4] Operation: 91-87=4 Exploring Operation: 95-87=8, Resulting Numbers: [9, 91, 8] Generated Node #0,2: 26:[9, 91, 8] Operation: 95-87=8 Moving to Node #0,0 Current State: 26:[87, 9, 4], Operations: ['95-91=4'] Exploring Operation: 87-9=78, Resulting Numbers: [4, 78] Generated Node #0,0,0: 26:[4, 78] Operation: 87-9=78 Exploring Operation: 87-4=83, Resulting Numbers: [9, 83] Generated Node #0,0,1: 26:[9, 83] Operation: 87-4=83 Exploring Operation: 9+4=13, Resulting Numbers: [87, 13] Generated Node #0,0,2: 26:[87, 13] Operation: 9+4=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[4, 78], Operations: ['95-91=4', '87-9=78'] Exploring Operation: 4+78=82, Resulting Numbers: [82] 82,26 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,26 unequal: No Solution Exploring Operation: 4*78=312, Resulting Numbers: [312] 312,26 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:[9, 83], Operations: ['95-91=4', '87-4=83'] Exploring Operation: 9*83=747, Resulting Numbers: [747] 747,26 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,26 unequal: No Solution Exploring Operation: 9+83=92, Resulting Numbers: [92] 92,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[87, 13], Operations: ['95-91=4', '9+4=13'] Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,26 unequal: No Solution Exploring Operation: 87+13=100, Resulting Numbers: [100] 100,26 unequal: No Solution Exploring Operation: 87*13=1131, Resulting Numbers: [1131] 1131,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 26:[9, 91, 8], Operations: ['95-87=8'] Exploring Operation: 91-8=83, Resulting Numbers: [9, 83] Generated Node #0,2,0: 26:[9, 83] Operation: 91-8=83 Exploring Operation: 91-9=82, Resulting Numbers: [8, 82] Generated Node #0,2,1: 26:[8, 82] Operation: 91-9=82 Exploring Operation: 9-8=1, Resulting Numbers: [91, 1] Generated Node #0,2,2: 26:[91, 1] Operation: 9-8=1 Moving to Node #0,1 Current State: 26:[95, 9, 4], Operations: ['91-87=4'] Exploring Operation: 95-4=91, Resulting Numbers: [9, 91] Generated Node #0,1,0: 26:[9, 91] Operation: 95-4=91 Exploring Operation: 95-9=86, Resulting Numbers: [4, 86] Generated Node #0,1,1: 26:[4, 86] Operation: 95-9=86 Exploring Operation: 9+4=13, Resulting Numbers: [95, 13] Generated Node #0,1,2: 26:[95, 13] Operation: 9+4=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[4, 86], Operations: ['91-87=4', '95-9=86'] Exploring Operation: 4*86=344, Resulting Numbers: [344] 344,26 unequal: No Solution Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,26 unequal: No Solution Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[9, 91], Operations: ['91-87=4', '95-4=91'] Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,26 unequal: No Solution Exploring Operation: 9*91=819, Resulting Numbers: [819] 819,26 unequal: No Solution Exploring Operation: 9+91=100, Resulting Numbers: [100] 100,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[95, 13], Operations: ['91-87=4', '9+4=13'] Exploring Operation: 95*13=1235, Resulting Numbers: [1235] 1235,26 unequal: No Solution Exploring Operation: 95+13=108, Resulting Numbers: [108] 108,26 unequal: No Solution Exploring Operation: 95-13=82, Resulting Numbers: [82] 82,26 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: 26:[9, 83], Operations: ['95-87=8', '91-8=83'] Exploring Operation: 9*83=747, Resulting Numbers: [747] 747,26 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,26 unequal: No Solution Exploring Operation: 9+83=92, Resulting Numbers: [92] 92,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[8, 82], Operations: ['95-87=8', '91-9=82'] Exploring Operation: 8+82=90, Resulting Numbers: [90] 90,26 unequal: No Solution Exploring Operation: 8*82=656, Resulting Numbers: [656] 656,26 unequal: No Solution Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[91, 1], Operations: ['95-87=8', '9-8=1'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,26 unequal: No Solution Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,26 unequal: No Solution Exploring Operation: 91*1=91, Resulting Numbers: [91] 91,26 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 59, 27, 15, 65 ]
18
[ "59-27=32", "65-15=50", "50-32=18" ]
Current State: 18:[59, 27, 15, 65], Operations: [] Exploring Operation: 59-27=32, Resulting Numbers: [15, 65, 32] Generated Node #2: [15, 65, 32] from Operation: 59-27=32 Current State: 18:[15, 65, 32], Operations: ['59-27=32'] Exploring Operation: 65-15=50, Resulting Numbers: [32, 50] Generated Node #3: [32, 50] from Operation: 65-15=50 Current State: 18:[32, 50], Operations: ['59-27=32', '65-15=50'] Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[59, 27, 15, 65], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [27, 15, 6] Generated Node #0,0: 18:[27, 15, 6] Operation: 65-59=6 Moving to Node #0,0 Current State: 18:[27, 15, 6], Operations: ['65-59=6'] Exploring Operation: 27-15=12, Resulting Numbers: [6, 12] Generated Node #0,0,0: 18:[6, 12] Operation: 27-15=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[6, 12], Operations: ['65-59=6', '27-15=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[59, 27, 15, 65], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [27, 15, 6] Generated Node #0,0: 18:[27, 15, 6] Operation: 65-59=6 Moving to Node #0,0 Current State: 18:[27, 15, 6], Operations: ['65-59=6'] Exploring Operation: 27-15=12, Resulting Numbers: [6, 12] Generated Node #0,0,0: 18:[6, 12] Operation: 27-15=12 Moving to Node #0,0,0 Current State: 18:[6, 12], Operations: ['65-59=6', '27-15=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 22, 54, 84, 40 ]
81
[ "40-22=18", "54/18=3", "84-3=81" ]
Current State: 81:[22, 54, 84, 40], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [54, 84, 18] Generated Node #2: [54, 84, 18] from Operation: 40-22=18 Current State: 81:[54, 84, 18], Operations: ['40-22=18'] Exploring Operation: 54/18=3, Resulting Numbers: [84, 3] Generated Node #3: [84, 3] from Operation: 54/18=3 Current State: 81:[84, 3], Operations: ['40-22=18', '54/18=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[22, 54, 84, 40], Operations: [] Exploring Operation: 54-40=14, Resulting Numbers: [22, 84, 14] Generated Node #0,0: 81:[22, 84, 14] Operation: 54-40=14 Exploring Operation: 22+54=76, Resulting Numbers: [84, 40, 76] Generated Node #0,1: 81:[84, 40, 76] Operation: 22+54=76 Moving to Node #0,0 Current State: 81:[22, 84, 14], Operations: ['54-40=14'] Exploring Operation: 84/14=6, Resulting Numbers: [22, 6] Generated Node #0,0,0: 81:[22, 6] Operation: 84/14=6 Exploring Operation: 22-14=8, Resulting Numbers: [84, 8] Generated Node #0,0,1: 81:[84, 8] Operation: 22-14=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[84, 8], Operations: ['54-40=14', '22-14=8'] Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,81 unequal: No Solution Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[22, 6], Operations: ['54-40=14', '84/14=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,81 unequal: No Solution Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 81:[84, 40, 76], Operations: ['22+54=76'] Exploring Operation: 84-76=8, Resulting Numbers: [40, 8] Generated Node #0,1,0: 81:[40, 8] Operation: 84-76=8 Exploring Operation: 76-40=36, Resulting Numbers: [84, 36] Generated Node #0,1,1: 81:[84, 36] Operation: 76-40=36 Moving to Node #0,1,1 Current State: 81:[84, 36], Operations: ['22+54=76', '76-40=36'] Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,81 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[40, 8], Operations: ['22+54=76', '84-76=8'] Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,81 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 79, 67, 2, 20 ]
75
[ "79-20=59", "67*2=134", "134-59=75" ]
Current State: 75:[79, 67, 2, 20], Operations: [] Exploring Operation: 79-20=59, Resulting Numbers: [67, 2, 59] Generated Node #2: [67, 2, 59] from Operation: 79-20=59 Current State: 75:[67, 2, 59], Operations: ['79-20=59'] Exploring Operation: 67*2=134, Resulting Numbers: [59, 134] Generated Node #3: [59, 134] from Operation: 67*2=134 Current State: 75:[59, 134], Operations: ['79-20=59', '67*2=134'] Exploring Operation: 134-59=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[79, 67, 2, 20], Operations: [] Exploring Operation: 67+2=69, Resulting Numbers: [79, 20, 69] Generated Node #0,0: 75:[79, 20, 69] Operation: 67+2=69 Exploring Operation: 2+20=22, Resulting Numbers: [79, 67, 22] Generated Node #0,1: 75:[79, 67, 22] Operation: 2+20=22 Exploring Operation: 79-67=12, Resulting Numbers: [2, 20, 12] Generated Node #0,2: 75:[2, 20, 12] Operation: 79-67=12 Exploring Operation: 79-2=77, Resulting Numbers: [67, 20, 77] Generated Node #0,3: 75:[67, 20, 77] Operation: 79-2=77 Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[2, 20, 12], Operations: ['79-67=12'] Exploring Operation: 2+20=22, Resulting Numbers: [12, 22] Generated Node #0,2,0: 75:[12, 22] Operation: 2+20=22 Exploring Operation: 2+12=14, Resulting Numbers: [20, 14] Generated Node #0,2,1: 75:[20, 14] Operation: 2+12=14 Exploring Operation: 20-12=8, Resulting Numbers: [2, 8] Generated Node #0,2,2: 75:[2, 8] Operation: 20-12=8 Exploring Operation: 20-2=18, Resulting Numbers: [12, 18] Generated Node #0,2,3: 75:[12, 18] Operation: 20-2=18 Moving to Node #0,2,2 Current State: 75:[2, 8], Operations: ['79-67=12', '20-12=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[20, 14], Operations: ['79-67=12', '2+12=14'] Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,75 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[12, 22], Operations: ['79-67=12', '2+20=22'] Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,75 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,75 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,75 unequal: No Solution Moving to Node #0,2,3 Current State: 75:[12, 18], Operations: ['79-67=12', '20-2=18'] Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,75 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[79, 20, 69], Operations: ['67+2=69'] Exploring Operation: 79-69=10, Resulting Numbers: [20, 10] Generated Node #0,0,0: 75:[20, 10] Operation: 79-69=10 Exploring Operation: 79-20=59, Resulting Numbers: [69, 59] Generated Node #0,0,1: 75:[69, 59] Operation: 79-20=59 Exploring Operation: 69-20=49, Resulting Numbers: [79, 49] Generated Node #0,0,2: 75:[79, 49] Operation: 69-20=49 Exploring Operation: 20+69=89, Resulting Numbers: [79, 89] Generated Node #0,0,3: 75:[79, 89] Operation: 20+69=89 Moving to Node #0,0,0 Current State: 75:[20, 10], Operations: ['67+2=69', '79-69=10'] Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,75 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,75 unequal: No Solution Moving to Node #0,0,3 Current State: 75:[79, 89], Operations: ['67+2=69', '20+69=89'] Exploring Operation: 79*89=7031, Resulting Numbers: [7031] 7031,75 unequal: No Solution Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 79+89=168, Resulting Numbers: [168] 168,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[69, 59], Operations: ['67+2=69', '79-20=59'] Exploring Operation: 69*59=4071, Resulting Numbers: [4071] 4071,75 unequal: No Solution Exploring Operation: 69-59=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 69+59=128, Resulting Numbers: [128] 128,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[79, 49], Operations: ['67+2=69', '69-20=49'] Exploring Operation: 79*49=3871, Resulting Numbers: [3871] 3871,75 unequal: No Solution Exploring Operation: 79-49=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 79+49=128, Resulting Numbers: [128] 128,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[79, 67, 22], Operations: ['2+20=22'] Exploring Operation: 67-22=45, Resulting Numbers: [79, 45] Generated Node #0,1,0: 75:[79, 45] Operation: 67-22=45 Exploring Operation: 79-67=12, Resulting Numbers: [22, 12] Generated Node #0,1,1: 75:[22, 12] Operation: 79-67=12 Exploring Operation: 79-22=57, Resulting Numbers: [67, 57] Generated Node #0,1,2: 75:[67, 57] Operation: 79-22=57 Exploring Operation: 67+22=89, Resulting Numbers: [79, 89] Generated Node #0,1,3: 75:[79, 89] Operation: 67+22=89 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[22, 12], Operations: ['2+20=22', '79-67=12'] Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,75 unequal: No Solution Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,75 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 75:[79, 89], Operations: ['2+20=22', '67+22=89'] Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 79+89=168, Resulting Numbers: [168] 168,75 unequal: No Solution Exploring Operation: 79*89=7031, Resulting Numbers: [7031] 7031,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 75:[79, 45], Operations: ['2+20=22', '67-22=45'] Exploring Operation: 79*45=3555, Resulting Numbers: [3555] 3555,75 unequal: No Solution Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,75 unequal: No Solution Exploring Operation: 79+45=124, Resulting Numbers: [124] 124,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 75:[67, 57], Operations: ['2+20=22', '79-22=57'] Exploring Operation: 67-57=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 67*57=3819, Resulting Numbers: [3819] 3819,75 unequal: No Solution Exploring Operation: 67+57=124, Resulting Numbers: [124] 124,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[67, 20, 77], Operations: ['79-2=77'] Exploring Operation: 67-20=47, Resulting Numbers: [77, 47] Generated Node #0,3,0: 75:[77, 47] Operation: 67-20=47 Exploring Operation: 67+20=87, Resulting Numbers: [77, 87] Generated Node #0,3,1: 75:[77, 87] Operation: 67+20=87 Exploring Operation: 77-67=10, Resulting Numbers: [20, 10] Generated Node #0,3,2: 75:[20, 10] Operation: 77-67=10 Exploring Operation: 77-20=57, Resulting Numbers: [67, 57] Generated Node #0,3,3: 75:[67, 57] Operation: 77-20=57 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 75:[20, 10], Operations: ['79-2=77', '77-67=10'] Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,75 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 75:[77, 87], Operations: ['79-2=77', '67+20=87'] Exploring Operation: 87-77=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 77+87=164, Resulting Numbers: [164] 164,75 unequal: No Solution Exploring Operation: 77*87=6699, Resulting Numbers: [6699] 6699,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 75:[77, 47], Operations: ['79-2=77', '67-20=47'] Exploring Operation: 77*47=3619, Resulting Numbers: [3619] 3619,75 unequal: No Solution Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 77+47=124, Resulting Numbers: [124] 124,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 75:[67, 57], Operations: ['79-2=77', '77-20=57'] Exploring Operation: 67*57=3819, Resulting Numbers: [3819] 3819,75 unequal: No Solution Exploring Operation: 67+57=124, Resulting Numbers: [124] 124,75 unequal: No Solution Exploring Operation: 67-57=10, Resulting Numbers: [10] 10,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 49, 55, 77, 58 ]
13
[ "55-49=6", "77-58=19", "19-6=13" ]
Current State: 13:[49, 55, 77, 58], Operations: [] Exploring Operation: 55-49=6, Resulting Numbers: [77, 58, 6] Generated Node #2: [77, 58, 6] from Operation: 55-49=6 Current State: 13:[77, 58, 6], Operations: ['55-49=6'] Exploring Operation: 77-58=19, Resulting Numbers: [6, 19] Generated Node #3: [6, 19] from Operation: 77-58=19 Current State: 13:[6, 19], Operations: ['55-49=6', '77-58=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[49, 55, 77, 58], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [49, 55, 19] Generated Node #0,0: 13:[49, 55, 19] Operation: 77-58=19 Exploring Operation: 58-49=9, Resulting Numbers: [55, 77, 9] Generated Node #0,1: 13:[55, 77, 9] Operation: 58-49=9 Exploring Operation: 77-49=28, Resulting Numbers: [55, 58, 28] Generated Node #0,2: 13:[55, 58, 28] Operation: 77-49=28 Exploring Operation: 77-55=22, Resulting Numbers: [49, 58, 22] Generated Node #0,3: 13:[49, 58, 22] Operation: 77-55=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[49, 55, 19], Operations: ['77-58=19'] Exploring Operation: 49+55=104, Resulting Numbers: [19, 104] Generated Node #0,0,0: 13:[19, 104] Operation: 49+55=104 Exploring Operation: 55-49=6, Resulting Numbers: [19, 6] Generated Node #0,0,1: 13:[19, 6] Operation: 55-49=6 Exploring Operation: 49-19=30, Resulting Numbers: [55, 30] Generated Node #0,0,2: 13:[55, 30] Operation: 49-19=30 Exploring Operation: 55-19=36, Resulting Numbers: [49, 36] Generated Node #0,0,3: 13:[49, 36] Operation: 55-19=36 Moving to Node #0,0,1 Current State: 13:[19, 6], Operations: ['77-58=19', '55-49=6'] Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,13 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[49, 55, 77, 58], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [49, 55, 19] Generated Node #0,0: 13:[49, 55, 19] Operation: 77-58=19 Moving to Node #0,0 Current State: 13:[49, 55, 19], Operations: ['77-58=19'] Exploring Operation: 55-49=6, Resulting Numbers: [19, 6] Generated Node #0,0,1: 13:[19, 6] Operation: 55-49=6 Moving to Node #0,0,1 Current State: 13:[19, 6], Operations: ['77-58=19', '55-49=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 41, 10, 70, 20 ]
48
[ "20-10=10", "70/10=7", "41+7=48" ]
Current State: 48:[41, 10, 70, 20], Operations: [] Exploring Operation: 20-10=10, Resulting Numbers: [41, 70, 10] Generated Node #2: [41, 70, 10] from Operation: 20-10=10 Current State: 48:[41, 70, 10], Operations: ['20-10=10'] Exploring Operation: 70/10=7, Resulting Numbers: [41, 7] Generated Node #3: [41, 7] from Operation: 70/10=7 Current State: 48:[41, 7], Operations: ['20-10=10', '70/10=7'] Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[41, 10, 70, 20], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [41, 20, 7] Generated Node #0,0: 48:[41, 20, 7] Operation: 70/10=7 Exploring Operation: 70-20=50, Resulting Numbers: [41, 10, 50] Generated Node #0,1: 48:[41, 10, 50] Operation: 70-20=50 Exploring Operation: 70-41=29, Resulting Numbers: [10, 20, 29] Generated Node #0,2: 48:[10, 20, 29] Operation: 70-41=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[41, 10, 50], Operations: ['70-20=50'] Exploring Operation: 41+10=51, Resulting Numbers: [50, 51] Generated Node #0,1,0: 48:[50, 51] Operation: 41+10=51 Exploring Operation: 50/10=5, Resulting Numbers: [41, 5] Generated Node #0,1,1: 48:[41, 5] Operation: 50/10=5 Exploring Operation: 50-41=9, Resulting Numbers: [10, 9] Generated Node #0,1,2: 48:[10, 9] Operation: 50-41=9 Moving to Node #0,1,2 Current State: 48:[10, 9], Operations: ['70-20=50', '50-41=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,48 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[50, 51], Operations: ['70-20=50', '41+10=51'] Exploring Operation: 50+51=101, Resulting Numbers: [101] 101,48 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 50*51=2550, Resulting Numbers: [2550] 2550,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[41, 5], Operations: ['70-20=50', '50/10=5'] Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,48 unequal: No Solution Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,48 unequal: No Solution No 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: 48:[10, 20, 29], Operations: ['70-41=29'] Exploring Operation: 20+29=49, Resulting Numbers: [10, 49] Generated Node #0,2,0: 48:[10, 49] Operation: 20+29=49 Exploring Operation: 29-20=9, Resulting Numbers: [10, 9] Generated Node #0,2,1: 48:[10, 9] Operation: 29-20=9 Exploring Operation: 20/10=2, Resulting Numbers: [29, 2] Generated Node #0,2,2: 48:[29, 2] Operation: 20/10=2 Moving to Node #0,2,0 Current State: 48:[10, 49], Operations: ['70-41=29', '20+29=49'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,48 unequal: No Solution Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[10, 9], Operations: ['70-41=29', '29-20=9'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[29, 2], Operations: ['70-41=29', '20/10=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,48 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,48 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,48 unequal: No Solution No 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: 48:[41, 20, 7], Operations: ['70/10=7'] Exploring Operation: 41-20=21, Resulting Numbers: [7, 21] Generated Node #0,0,0: 48:[7, 21] Operation: 41-20=21 Exploring Operation: 20-7=13, Resulting Numbers: [41, 13] Generated Node #0,0,1: 48:[41, 13] Operation: 20-7=13 Exploring Operation: 41+7=48, Resulting Numbers: [20, 48] Generated Node #0,0,2: 48:[20, 48] Operation: 41+7=48 Moving to Node #0,0,0 Current State: 48:[7, 21], Operations: ['70/10=7', '41-20=21'] Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[20, 48], Operations: ['70/10=7', '41+7=48'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 20*48=960, Resulting Numbers: [960] 960,48 unequal: No Solution Exploring Operation: 20+48=68, Resulting Numbers: [68] 68,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[41, 13], Operations: ['70/10=7', '20-7=13'] Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,48 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic